{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#
Notebook S11. Coagulation Theory and PartMC Simulations \n",
"\n",
" Notebook Version 2: This notebook has been updated to reflect changes made to the package DifferentialMobilityAnalyzers.jl to work with the Julia v1 series (tested with Julia 1.1.0). To read the original supplement published with the paper please switch to v1.0.0 of the package DifferentialMobilityAnalyzers.jl and/or download the virtual machine on zenodo.org which contains a complete installation that works with Julia 0.6.4 \n",
"\n",
"\n",
"This notebook presents an overview over coagulation theory. It is shown how to predict the coagulated distribution using Size Distribution Arithmetic (Notebook S3). The approach is compared to model predictions with the Particle-resolved Monte Carlo code for atmospheric aerosol simulation [(PartMC)](http://lagrange.mechse.illinois.edu/partmc/). The notebook is a supplement to the manuscript \n",
"\n",
"Petters, M. D. (2018) A language to simplify computation of differential mobility analyzer response functions , Aerosol Science & Technology. \n",
"\n",
"__ Note that exectuting this Notebook requires that PartMC is installed. The Julia/PartMC interface has only been tested on a linux install. __\n",
"\n",
"### Problem description\n",
"Two aerosol populations with identities \"1\" and \"2\" are introduced into in a chamber. Each population has unique and defined chemical composition, charge state (0, Β±1, or Β±2) and size distribution (πβ and πβ). Chemical composition and charge state are identical for particles within a population. There are no wall losses in the chamber. What is the size distribution of dimers comprising one \"1\" and one \"2\" particle (denoted πββ) after elapsed time $t$ due to coagulation?\n",
"\n",
" \n",
" Figure 1. Schematic of problem setup. The two populations, each generated by a differential mobility analyzer, enter a chamber where they are allowed to coagulate. After time $t$ (1,2) coagulated particles emerge. This sheet demonstrates how to model that distribution. \n",
"\n",
"\n",
"### Coagulation Theory\n",
"\n",
"For monodisperse particles the rate of coagulation is \n",
"\n",
" $\\frac{dN}{dt} = \\beta_{i,j}N_iN_j$ \n",
"\n",
"where $N_i$ and $N_j$ are number concentrations and $\\beta_{i,j}$ is the coagulation kernel. For submicron particles, Brownian motion dominates the collision rate between particles of size $i$ and $j$ and is given by (Jacobson, 2005, Eq. 15.33)\n",
"\n",
" $\\beta_{i,j}^B = \\frac{4\\pi\\left(r_i + r_j\\right)\\left(D_{i} + D_{j}\\right)}{\\frac{r_i + r_j}{r_i + r_j + \\sqrt{\\delta_i^2 + \\delta_j^2}} + \\frac{4\\left(D_{i} + D_{j}\\right)}{\\sqrt{v_{p,i}^2 + v_{p,j}^2}\\left(r_i + r_j\\right) } }$ \n",
"\n",
"where, $\\beta_{i,j}^B$ denotes the Brownian coagulation kernel, $r_i$ and $r_j$ are the radii, $D_i$ and $D_j$ are the diffusion coefficient, and $v_i$ and $v_j$ are thermal velocities of particles $i$ and $j$ in air. The parameters $\\delta_i$ and $\\delta_j$ are the mean distances from the center of a sphere reached by particles leaving the sphereβs surface and traveling a distance of particle mean free path. Using the following relationships, the coagulation rate can be readily computed.\n",
" $\\delta_i = \\frac{\\left(2r_i + \\lambda_{p,i} \\right)^3 - \\left(4r_i^2 + \\lambda_{p,i}^2\\right)^{3/2}}{6r_i\\lambda_{p,i}} - 2r_i$ \n",
"$\\lambda_{p,i} = \\frac{8D_i}{\\pi v_i}$ \n",
"$v_i = \\sqrt{\\frac{8k_bT}{\\pi M_i}}$ \n",
"$M_i = \\frac{4}{3}\\pi r_i^3 \\rho_i$ \n",
"$D_i$ is defined in Notebook S1, and $\\rho_i$ is the density and particle sphericity is assumed. The Brownian coagulation rate depends thus on the diameters $D_i$, $D_j$, densities $\\rho_i$, $\\rho_j$ as well as pressure and temperature for the free molecular regime corrections. \n",
"\n",
"Coagulation rates are enhanced or suppressed if particles carry the charges of the same or opposite polarity, respectively. The effect is described by Zebel (1958)\n",
"\n",
" $\\beta_{i,j}^{z(k_i,k_j)} = \\beta_{i,j}^B \\frac{\\frac{a}{r_i + r_j}}{exp\\left(\\frac{a}{r_i + r_j}\\right)-1 + G_0 \\frac{a}{rij} \\exp{\\frac{a}{r_i + r_j}}}$ \n",
" $a = k_i k_j\\frac{e^2}{k_bT}$ \n",
" $G_0 = 4\\frac{D_i + D_j}{r_i + r_j} \\sqrt{\\frac{M_i M_j}{(M_i + M_j) 3k_b T}}$ \n",
"where, $k_i$, $k_j$ are the charges and $\\beta_b$ is Boltzmann's constant, and $e$ is the elementary charge ($e = \\sqrt{1.43996\\; MeV\\; fm}$). The Zebel-corrected Brownian coagulation rate ($\\beta_{i,j}^{z(k_i,k_j)}$) depends on the diameters $D_i$, $D_j$, densities $\\rho_i$, $\\rho_j$, charges $k_i$, $k_j$, as well as pressure and temperature for the free molecular regime corrections. Note that for either $k_i = 0$ or $k_j = 0$ the regular Brownian coagulation rate is retained, i.e. $\\beta_{i,j}^{z(k_i,k_j)} = \\beta_{i,j}^B$ \n",
"\n",
"The above functions are implemented in file coagulationrates.jl. The rate is obtained through the function call\n",
"\n",
"```julia\n",
" Ξ²12 = Ξ²12(Dp_i, Dp_j, k_i, k_j;Οi = 1000.0, Οj = 1000.0, p = 1e5, T = 293.0)\n",
"```\n",
"The truncated call \n",
"```julia\n",
" Ξ²12 = Ξ²12(Dp_i, Dp_j, k_i, k_j)\n",
"```\n",
"assumes that Οi = 1000 kg mβ»Β³, Οj = 1000 kg mβ»Β³, p = 1e5 Pa, T = 293 K. Coagulation rates between particles of the same diameter (i.e. Dp_i = Dp_j) and enhancement factors based on charge state as a function of diameter are shown in Figure 2 below. "
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" \n"
],
"text/plain": [
"HTML{String}(\" \\n\")"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
],
"text/plain": [
"HTML{String}(\"\")"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
],
"text/plain": [
"HTML{String}(\"\")"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
" \n"
],
"text/plain": [
"HTML{String}(\" \\n\")"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"using Plots, Plots.PlotMeasures, DifferentialMobilityAnalyzers, Printf, Random, LinearAlgebra\n",
"plotlyjs();"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.plotly.v1+json": {
"data": [
{
"colorbar": {
"title": ""
},
"hoverinfo": "text",
"legendgroup": "kβ=0, kβ=0",
"line": {
"color": "rgba(0, 0, 0, 1.000)",
"dash": "solid",
"shape": "linear",
"width": 2
},
"mode": "lines",
"name": "kβ=0, kβ=0",
"showlegend": true,
"text": [
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null
],
"type": "scatter",
"x": [
10,
10.47615752789664,
10.974987654930569,
11.497569953977356,
12.04503540258781,
12.61856883066021,
13.219411484660288,
13.848863713938718,
14.508287784959402,
15.19911082952933,
15.92282793341094,
16.68100537200059,
17.47528400007683,
18.307382802953697,
19.179102616724887,
20.09233002565046,
21.04904144512022,
22.051307399030453,
23.10129700083158,
24.201282647943835,
25.353644939701113,
26.56087782946684,
27.82559402207126,
29.150530628251758,
30.53855508833412,
31.992671377973846,
33.51602650938841,
35.111917342151344,
36.78379771828634,
38.53528593710527,
40.37017258596558,
42.29242874389499,
44.30621457583878,
46.41588833612782,
48.62601580065353,
50.94138014816375,
53.366992312063125,
55.90810182512222,
58.57020818056662,
61.359072734131765,
64.28073117284319,
67.34150657750816,
70.54802310718645,
73.90722033525775,
77.42636826811277,
81.11308307896873,
84.97534359086438,
89.02150854450392,
93.260334688322,
97.70099572992247,
102.35310218990269,
107.22672220103232,
112.33240329780266,
117.68119524349991,
123.28467394420659,
129.15496650148827,
135.30477745798075,
141.7474162926805,
148.49682622544665,
155.56761439304722,
162.97508346206436,
170.7352647470692,
178.8649529057435,
187.3817422860383,
196.30406500402725,
205.65123083486515,
215.44346900318823,
225.70197196339217,
236.44894126454074,
247.70763559917086,
259.50242113997376,
271.858824273294,
284.8035868435799,
298.3647240283341,
312.5715849688235,
327.4549162877732,
343.04692863149194,
359.38136638046257,
376.49358067924715,
394.4206059437656,
413.20124001153346,
432.87612810830615,
453.4878508128582,
475.08101621027936,
497.7023564332114,
521.4008287999684,
546.2277217684338,
572.236765935022,
599.4842503189409,
628.0291441834247,
657.9332246575682,
689.2612104349695,
722.0809018385471,
756.463327554629,
792.4828983539169,
830.2175681319752,
869.7490026177835,
911.1627561154886,
954.5484566618346,
1000
],
"xaxis": "x1",
"y": [
1.9121396626604057,
1.9491878449186737,
1.985948160115937,
2.022270454595213,
2.0579898675783013,
2.0929272365285603,
2.1268899746765397,
2.159673486179367,
2.191063168698472,
2.2208370294240294,
2.2487689088702925,
2.2746322683043045,
2.2982044538673243,
2.3192713069154465,
2.3376319503810317,
2.353103549973142,
2.3655258313905843,
2.37476513386043,
2.380717797806253,
2.38331271953335,
2.382512955361635,
2.3783163165488563,
2.3707549583654344,
2.3598940253767897,
2.3458294647479683,
2.328685156185836,
2.3086095289546535,
2.285771843238918,
2.2603583066792874,
2.2325681800326853,
2.2026100020197066,
2.1706980359315873,
2.1370490124626516,
2.1018792168252456,
2.0654019450449645,
2.0278253352552844,
1.9893505650449368,
1.9501703952508453,
1.910468033548143,
1.870416287141245,
1.8301769721495176,
1.7899005472918061,
1.7497259406734762,
1.7097805404352204,
1.6701803224038427,
1.6310300904511301,
1.5924238078536512,
1.5544450004492358,
1.5171672147437183,
1.4806545163043647,
1.4449620157737237,
1.4101364116514876,
1.3762165406306714,
1.3432339277498284,
1.3112133299468924,
1.2801732677848052,
1.250126541174819,
1.2210807258601797,
1.1930386482492887,
1.1659988369114862,
1.139955949677209,
1.1149011758244327,
1.0908226132914076,
1.0677056212376166,
1.0455331485868227,
1.024286039433701,
1.003943316384211,
0.9844824430349371,
0.965879566883489,
0.9481097440048155,
0.9311471468327727,
0.9149652563557934,
0.8995370399754499,
0.8848351161908509,
0.8708319071648357,
0.857499780103913,
0.8448111782478547,
0.8327387421208448,
0.8212554215495499,
0.8103345788088442,
0.7999500831186117,
0.7900763965900017,
0.7806886516116048,
0.7717627195799894,
0.7632752708189563,
0.7552038255011989,
0.7475267953868819,
0.7402235162274796,
0.7332742707494432,
0.7266603022288447,
0.720363818791236,
0.7143679887156669,
0.7086569271797091,
0.703215675046749,
0.6980301704565579,
0.6930872141271408,
0.6883744293993342,
0.6838802181480271,
0.6795937137377636,
0.6755047322117365
],
"yaxis": "y1",
"zmax": 0.1,
"zmin": -0.1
},
{
"colorbar": {
"title": ""
},
"hoverinfo": "text",
"legendgroup": "kβ=+1, kβ=-1",
"line": {
"color": "rgba(204, 0, 0, 1.000)",
"dash": "solid",
"shape": "linear",
"width": 1
},
"mode": "lines",
"name": "kβ=+1, kβ=-1",
"showlegend": true,
"text": [
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null
],
"type": "scatter",
"x": [
10,
10.47615752789664,
10.974987654930569,
11.497569953977356,
12.04503540258781,
12.61856883066021,
13.219411484660288,
13.848863713938718,
14.508287784959402,
15.19911082952933,
15.92282793341094,
16.68100537200059,
17.47528400007683,
18.307382802953697,
19.179102616724887,
20.09233002565046,
21.04904144512022,
22.051307399030453,
23.10129700083158,
24.201282647943835,
25.353644939701113,
26.56087782946684,
27.82559402207126,
29.150530628251758,
30.53855508833412,
31.992671377973846,
33.51602650938841,
35.111917342151344,
36.78379771828634,
38.53528593710527,
40.37017258596558,
42.29242874389499,
44.30621457583878,
46.41588833612782,
48.62601580065353,
50.94138014816375,
53.366992312063125,
55.90810182512222,
58.57020818056662,
61.359072734131765,
64.28073117284319,
67.34150657750816,
70.54802310718645,
73.90722033525775,
77.42636826811277,
81.11308307896873,
84.97534359086438,
89.02150854450392,
93.260334688322,
97.70099572992247,
102.35310218990269,
107.22672220103232,
112.33240329780266,
117.68119524349991,
123.28467394420659,
129.15496650148827,
135.30477745798075,
141.7474162926805,
148.49682622544665,
155.56761439304722,
162.97508346206436,
170.7352647470692,
178.8649529057435,
187.3817422860383,
196.30406500402725,
205.65123083486515,
215.44346900318823,
225.70197196339217,
236.44894126454074,
247.70763559917086,
259.50242113997376,
271.858824273294,
284.8035868435799,
298.3647240283341,
312.5715849688235,
327.4549162877732,
343.04692863149194,
359.38136638046257,
376.49358067924715,
394.4206059437656,
413.20124001153346,
432.87612810830615,
453.4878508128582,
475.08101621027936,
497.7023564332114,
521.4008287999684,
546.2277217684338,
572.236765935022,
599.4842503189409,
628.0291441834247,
657.9332246575682,
689.2612104349695,
722.0809018385471,
756.463327554629,
792.4828983539169,
830.2175681319752,
869.7490026177835,
911.1627561154886,
954.5484566618346,
1000
],
"xaxis": "x1",
"y": [
9.767449717370534,
9.356549638633334,
8.954352436191535,
8.563070020938447,
8.184617524523679,
7.820550397268465,
7.4720337677698145,
7.139840671019205,
6.824373501915959,
6.525702102512579,
6.24361200224459,
5.9776571512912335,
5.727212670701753,
5.491524410181466,
5.269753269652519,
5.061013205849931,
4.8644025795323795,
4.67902901468873,
4.504028272674501,
4.338577832578956,
4.181905953062452,
4.033297002643271,
3.892093809668002,
3.757697717979272,
3.6295669524009755,
3.5072138086862092,
3.390201092072557,
3.278138141849235,
3.170676699800606,
3.0675068103566923,
2.96835288104419,
2.87296998377405,
2.781140440244903,
2.6926707073212865,
2.607388559314278,
2.5251405521124077,
2.4457897475239254,
2.3692136735446288,
2.295302496295236,
2.2239573810454476,
2.1550890222646575,
2.088616325440239,
2.024465226105201,
1.962567633894355,
1.9028604913974116,
1.8452849390768535,
1.7897855786007408,
1.7363098276697784,
1.6848073598705473,
1.6352296233417523,
1.5875294321692246,
1.5416606244892361,
1.4975777813263904,
1.455236000257329,
1.4145907180973691,
1.375597576967159,
1.3382123283145686,
1.3023907697414752,
1.2680887098090279,
1.2352619563591158,
1.203866324282554,
1.1738576590746055,
1.1451918729344612,
1.1178249905763948,
1.091713202317598,
1.0668129223832463,
1.0430808507167093,
1.0204740368973906,
0.9989499450472759,
0.9784665188472939,
0.9589822459862961,
0.9404562215279131,
0.9228482098060299,
0.9061187045495541,
0.89022898699473,
0.875141181771559,
0.860818310354489,
0.8472243418503687,
0.8343242408643157,
0.8220840121413888,
0.8104707416346842,
0.7994526336042482,
0.7889990433114864,
0.7790805048460097,
0.7696687536109235,
0.760736743002592,
0.7522586548548651,
0.7442099032779304,
0.7365671316085919,
0.729308202300808,
0.7224121797196921,
0.7158593059549875,
0.7096309699337481,
0.7037096702806764,
0.6980789725380079,
0.6927234615075271,
0.6876286896050171,
0.6827811222152179,
0.6781680810958624,
0.6737776868986636
],
"yaxis": "y1",
"zmax": 0.1,
"zmin": -0.1
},
{
"colorbar": {
"title": ""
},
"hoverinfo": "text",
"legendgroup": "kβ=+2, kβ=-2",
"line": {
"color": "rgba(255, 140, 0, 1.000)",
"dash": "solid",
"shape": "linear",
"width": 1
},
"mode": "lines",
"name": "kβ=+2, kβ=-2",
"showlegend": true,
"text": [
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null
],
"type": "scatter",
"x": [
10,
10.47615752789664,
10.974987654930569,
11.497569953977356,
12.04503540258781,
12.61856883066021,
13.219411484660288,
13.848863713938718,
14.508287784959402,
15.19911082952933,
15.92282793341094,
16.68100537200059,
17.47528400007683,
18.307382802953697,
19.179102616724887,
20.09233002565046,
21.04904144512022,
22.051307399030453,
23.10129700083158,
24.201282647943835,
25.353644939701113,
26.56087782946684,
27.82559402207126,
29.150530628251758,
30.53855508833412,
31.992671377973846,
33.51602650938841,
35.111917342151344,
36.78379771828634,
38.53528593710527,
40.37017258596558,
42.29242874389499,
44.30621457583878,
46.41588833612782,
48.62601580065353,
50.94138014816375,
53.366992312063125,
55.90810182512222,
58.57020818056662,
61.359072734131765,
64.28073117284319,
67.34150657750816,
70.54802310718645,
73.90722033525775,
77.42636826811277,
81.11308307896873,
84.97534359086438,
89.02150854450392,
93.260334688322,
97.70099572992247,
102.35310218990269,
107.22672220103232,
112.33240329780266,
117.68119524349991,
123.28467394420659,
129.15496650148827,
135.30477745798075,
141.7474162926805,
148.49682622544665,
155.56761439304722,
162.97508346206436,
170.7352647470692,
178.8649529057435,
187.3817422860383,
196.30406500402725,
205.65123083486515,
215.44346900318823,
225.70197196339217,
236.44894126454074,
247.70763559917086,
259.50242113997376,
271.858824273294,
284.8035868435799,
298.3647240283341,
312.5715849688235,
327.4549162877732,
343.04692863149194,
359.38136638046257,
376.49358067924715,
394.4206059437656,
413.20124001153346,
432.87612810830615,
453.4878508128582,
475.08101621027936,
497.7023564332114,
521.4008287999684,
546.2277217684338,
572.236765935022,
599.4842503189409,
628.0291441834247,
657.9332246575682,
689.2612104349695,
722.0809018385471,
756.463327554629,
792.4828983539169,
830.2175681319752,
869.7490026177835,
911.1627561154886,
954.5484566618346,
1000
],
"xaxis": "x1",
"y": [
43.62062669914001,
42.44474741906402,
41.279660774217994,
40.12410599377127,
38.976893085060205,
37.83692537398197,
36.70322376974133,
35.5749519826285,
34.451441709534976,
33.33221663687234,
32.217014025457566,
31.105802660548292,
29.998796082489804,
28.896460250864447,
27.7995151097263,
26.708929869955355,
25.62591215591884,
24.551891429723437,
23.488497274032632,
22.437533173208344,
21.400946398150733,
20.380794511643526,
19.37920892138947,
18.39835587117676,
17.440395317108937,
16.50743830050717,
15.601503685570984,
14.724475432273872,
13.878061857415117,
13.063758528447465,
12.282816476661168,
11.536217275406813,
10.824656205881352,
10.148534261634468,
9.507959183050446,
8.902755136993456,
8.332480135210526,
7.796449874506271,
7.293766416762419,
6.823350017937435,
6.383972450920104,
5.97429032040069,
5.592877103093533,
5.238252926370413,
4.9089113890247935,
4.603343002880297,
4.320055075032353,
4.05758804753868,
3.814528461075687,
3.5895188133092875,
3.381264646672799,
3.188539230835685,
3.0101862098341305,
2.845120569727652,
2.6923282559965287,
2.550864735860466,
2.419852763290111,
2.2984795666455766,
2.185993642634677,
2.0817013069143036,
1.9849631218581687,
1.895190296057197,
1.8118411279835185,
1.7344175477227963,
1.6624617954386993,
1.5955532628987068,
1.5333055145687648,
1.4753634970946208,
1.4214009400766598,
1.3711179465949102,
1.3242387686757644,
1.2805097605723867,
1.2396975011579845,
1.2015870757381912,
1.1659805070400329,
1.132695324920394,
1.1015632643697084,
1.0724290815974193,
1.0451494783225337,
1.0195921248144428,
0.9956347727068752,
0.9731644491197985,
0.952076724155245,
0.9322750443735098,
0.9136701253995856,
0.8961793973521603,
0.8797264973263801,
0.8642408036956706,
0.8496570075252942,
0.8359147169089255,
0.8229580905463586,
0.8107354973722932,
0.7991991995164534,
0.7883050563202372,
0.7780122475459439,
0.7682830142865638,
0.7590824164092126,
0.7503781056391637,
0.7421401136094703,
0.7343406543619849
],
"yaxis": "y1",
"zmax": 0.1,
"zmin": -0.1
},
{
"colorbar": {
"title": ""
},
"hoverinfo": "text",
"legendgroup": "kβ=+1, kβ=+1",
"line": {
"color": "rgba(204, 0, 0, 1.000)",
"dash": "dashdot",
"shape": "linear",
"width": 1
},
"mode": "lines",
"name": "kβ=+1, kβ=+1",
"showlegend": true,
"text": [
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null
],
"type": "scatter",
"x": [
10,
10.47615752789664,
10.974987654930569,
11.497569953977356,
12.04503540258781,
12.61856883066021,
13.219411484660288,
13.848863713938718,
14.508287784959402,
15.19911082952933,
15.92282793341094,
16.68100537200059,
17.47528400007683,
18.307382802953697,
19.179102616724887,
20.09233002565046,
21.04904144512022,
22.051307399030453,
23.10129700083158,
24.201282647943835,
25.353644939701113,
26.56087782946684,
27.82559402207126,
29.150530628251758,
30.53855508833412,
31.992671377973846,
33.51602650938841,
35.111917342151344,
36.78379771828634,
38.53528593710527,
40.37017258596558,
42.29242874389499,
44.30621457583878,
46.41588833612782,
48.62601580065353,
50.94138014816375,
53.366992312063125,
55.90810182512222,
58.57020818056662,
61.359072734131765,
64.28073117284319,
67.34150657750816,
70.54802310718645,
73.90722033525775,
77.42636826811277,
81.11308307896873,
84.97534359086438,
89.02150854450392,
93.260334688322,
97.70099572992247,
102.35310218990269,
107.22672220103232,
112.33240329780266,
117.68119524349991,
123.28467394420659,
129.15496650148827,
135.30477745798075,
141.7474162926805,
148.49682622544665,
155.56761439304722,
162.97508346206436,
170.7352647470692,
178.8649529057435,
187.3817422860383,
196.30406500402725,
205.65123083486515,
215.44346900318823,
225.70197196339217,
236.44894126454074,
247.70763559917086,
259.50242113997376,
271.858824273294,
284.8035868435799,
298.3647240283341,
312.5715849688235,
327.4549162877732,
343.04692863149194,
359.38136638046257,
376.49358067924715,
394.4206059437656,
413.20124001153346,
432.87612810830615,
453.4878508128582,
475.08101621027936,
497.7023564332114,
521.4008287999684,
546.2277217684338,
572.236765935022,
599.4842503189409,
628.0291441834247,
657.9332246575682,
689.2612104349695,
722.0809018385471,
756.463327554629,
792.4828983539169,
830.2175681319752,
869.7490026177835,
911.1627561154886,
954.5484566618346,
1000
],
"xaxis": "x1",
"y": [
0.0009853034808527648,
0.0013892197098174504,
0.0019339527126573772,
0.0026594173986609123,
0.0036138599717754714,
0.004854740059336672,
0.006449470711738081,
0.008475938240960103,
0.011022716378125701,
0.014188886114843967,
0.018083375424226538,
0.02282374325025418,
0.028534350722446252,
0.035343889848054436,
0.04338227541043947,
0.05277694786087526,
0.06364868095482938,
0.07610703413950937,
0.09024563201124604,
0.10613748712663947,
0.12383060403593994,
0.14334410847333223,
0.16466513438303612,
0.187746672689061,
0.21250654092361201,
0.2388275750687135,
0.26655907854822714,
0.2955194933637651,
0.32550019033621286,
0.35627021450930035,
0.3875817724884991,
0.41917621419649037,
0.4507902441861562,
0.4821620976907815,
0.5130374329445134,
0.5431747216156922,
0.5723499601341812,
0.6003605723690117,
0.6270284244942753,
0.6522019221966717,
0.6757572054313665,
0.6975984943157093,
0.7176576699400052,
0.7358931952207918,
0.7522884935483771,
0.7668499076261243,
0.7796043587337864,
0.7905968190833872,
0.7998876984619515,
0.8075502323998159,
0.8136679439398389,
0.8183322357718242,
0.8216401548595121,
0.8236923583100496,
0.8245912974871537,
0.8244396274345884,
0.8233388405941328,
0.8213881175005865,
0.8186833824686024,
0.8153165490600817,
0.8113749381225338,
0.806940850200809,
0.8020912739395292,
0.7968977125212788,
0.7914261110595824,
0.7857368690436294,
0.7798849232960217,
0.773919888361246,
0.7678862427181466,
0.7618235506488946,
0.7557667109612917,
0.7497462250235251,
0.7437884777153325,
0.7379160259189491,
0.7321478900661301,
0.7264998450272169,
0.7209847072822543,
0.7156126158616848,
0.710391304996965,
0.7053263667915998,
0.7004215025236792,
0.6956787614349919,
0.6910987660617296,
0.686680923329888,
0.6824236207857279,
0.6783244074680834,
0.6743801590629649,
0.6705872271187758,
0.6669415722469435,
0.6634388813902533,
0.6600746694098708,
0.6568443654204149,
0.6537433844852688,
0.6507671854672575,
0.6479113160038702,
0.6451714457347888,
0.6425433890430027,
0.6400231186723601,
0.6376067716469882,
0.6352906489372996
],
"yaxis": "y1",
"zmax": 0.1,
"zmin": -0.1
},
{
"colorbar": {
"title": ""
},
"hoverinfo": "text",
"legendgroup": "kβ=+2, kβ=+2",
"line": {
"color": "rgba(255, 140, 0, 1.000)",
"dash": "dashdot",
"shape": "linear",
"width": 1
},
"mode": "lines",
"name": "kβ=+2, kβ=+2",
"showlegend": true,
"text": [
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null
],
"type": "scatter",
"x": [
10,
10.47615752789664,
10.974987654930569,
11.497569953977356,
12.04503540258781,
12.61856883066021,
13.219411484660288,
13.848863713938718,
14.508287784959402,
15.19911082952933,
15.92282793341094,
16.68100537200059,
17.47528400007683,
18.307382802953697,
19.179102616724887,
20.09233002565046,
21.04904144512022,
22.051307399030453,
23.10129700083158,
24.201282647943835,
25.353644939701113,
26.56087782946684,
27.82559402207126,
29.150530628251758,
30.53855508833412,
31.992671377973846,
33.51602650938841,
35.111917342151344,
36.78379771828634,
38.53528593710527,
40.37017258596558,
42.29242874389499,
44.30621457583878,
46.41588833612782,
48.62601580065353,
50.94138014816375,
53.366992312063125,
55.90810182512222,
58.57020818056662,
61.359072734131765,
64.28073117284319,
67.34150657750816,
70.54802310718645,
73.90722033525775,
77.42636826811277,
81.11308307896873,
84.97534359086438,
89.02150854450392,
93.260334688322,
97.70099572992247,
102.35310218990269,
107.22672220103232,
112.33240329780266,
117.68119524349991,
123.28467394420659,
129.15496650148827,
135.30477745798075,
141.7474162926805,
148.49682622544665,
155.56761439304722,
162.97508346206436,
170.7352647470692,
178.8649529057435,
187.3817422860383,
196.30406500402725,
205.65123083486515,
215.44346900318823,
225.70197196339217,
236.44894126454074,
247.70763559917086,
259.50242113997376,
271.858824273294,
284.8035868435799,
298.3647240283341,
312.5715849688235,
327.4549162877732,
343.04692863149194,
359.38136638046257,
376.49358067924715,
394.4206059437656,
413.20124001153346,
432.87612810830615,
453.4878508128582,
475.08101621027936,
497.7023564332114,
521.4008287999684,
546.2277217684338,
572.236765935022,
599.4842503189409,
628.0291441834247,
657.9332246575682,
689.2612104349695,
722.0809018385471,
756.463327554629,
792.4828983539169,
830.2175681319752,
869.7490026177835,
911.1627561154886,
954.5484566618346,
1000
],
"xaxis": "x1",
"y": [
3.7320430516170877e-11,
1.1479479567424754e-10,
3.3661875713724136e-10,
9.42965217768398e-10,
2.528428051060051e-09,
6.501551551229604e-09,
1.6060844027658085e-08,
3.818031982082131e-08,
8.748403680761172e-08,
1.9350825200101364e-07,
4.1379184284417227e-07,
8.565943555100091e-07,
1.718893292913131e-06,
3.34768667175676e-06,
6.3354637773740895e-06,
1.1663814890277394e-05,
2.091216837794628e-05,
3.655102026482616e-05,
6.234002797193617e-05,
0.0001038501208234396,
0.00016912445177897143,
0.00026948480761211874,
0.0004204775227041014,
0.0006429359828960112,
0.0009641160629733554,
0.0014188376527407788,
0.0020505418997692694,
0.0029121527382164327,
0.004066615996549829,
0.005586983383403834,
0.007555915185632419,
0.010064497029774064,
0.013210303644548336,
0.01709469540797455,
0.021819398489954164,
0.027482491173128495,
0.03417398995980733,
0.041971290558483,
0.050934761871402445,
0.061103808077856134,
0.07249370001493302,
0.08509343143036292,
0.0988647819374035,
0.11374267446497625,
0.12963681159133775,
0.14643447465036197,
0.1640042835107608,
0.18220065253733903,
0.20086864473291813,
0.21984892241774048,
0.23898251605120305,
0.2581151769722583,
0.2771011373121281,
0.2958061632207313,
0.3141098488176916,
0.3319071525252987,
0.3491092212138139,
0.36564357934991704,
0.38145378015345877,
0.3964986248670027,
0.4107510565546185,
0.42419682858038876,
0.43683303724579275,
0.448666594912399,
0.45971270586599705,
0.46999339336006396,
0.47953611350607167,
0.48837248043021125,
0.49653711761026087,
0.5040666425736592,
0.5109987860832303,
0.517371642387484,
0.5232230438576972,
0.5285900511530844,
0.5335085487361494,
0.538012934909991,
0.5421358954011245,
0.545908249725294,
0.5493588600369848,
0.5525145927871808,
0.5554003242313355,
0.5580389815915843,
0.5604516124497645,
0.5626574757085958,
0.5646741481940158,
0.5665176416756026,
0.5682025257516725,
0.5697420526819305,
0.57114828085507,
0.5724321941534837,
0.5736038150235332,
0.5746723095782617,
0.5756460835474968,
0.5765328683463821,
0.5773397969515324,
0.5780734696500398,
0.5787400100534545,
0.5793451120416212,
0.5798940785145446,
0.5803918529815373
],
"yaxis": "y1",
"zmax": 0.1,
"zmin": -0.1
}
],
"layout": {
"annotations": [],
"height": 288,
"legend": {
"bgcolor": "rgba(255, 255, 255, 1.000)",
"bordercolor": "rgba(0, 0, 0, 1.000)",
"font": {
"color": "rgba(0, 0, 0, 1.000)",
"family": "Nimbus Sans L",
"size": 14
},
"tracegroupgap": 0,
"x": 1,
"y": 1
},
"margin": {
"b": 20,
"l": 0,
"r": 0,
"t": 20
},
"paper_bgcolor": "rgba(255, 255, 255, 1.000)",
"plot_bgcolor": "rgba(255, 255, 255, 1.000)",
"showlegend": true,
"width": 432,
"xaxis": {
"anchor": "y1",
"domain": [
0.2623456790123456,
0.9908865558471858
],
"gridcolor": "rgba(0, 0, 0, 0.100)",
"gridwidth": 0.5,
"linecolor": "rgba(0, 0, 0, 1.000)",
"mirror": false,
"range": [
0.94,
3.06
],
"showgrid": true,
"showline": true,
"showticklabels": true,
"tickangle": 0,
"tickcolor": "rgb(0, 0, 0)",
"tickfont": {
"color": "rgba(0, 0, 0, 1.000)",
"family": "Nimbus Sans L",
"size": 17
},
"tickmode": "array",
"ticks": "inside",
"ticktext": [
"10^1.0",
"10^1.5",
"10^2.0",
"10^2.5",
"10^3.0"
],
"tickvals": [
10,
31.622776601683793,
100,
316.22776601683796,
1000
],
"title": "Diameter (nm)",
"titlefont": {
"color": "rgba(0, 0, 0, 1.000)",
"family": "Nimbus Sans L",
"size": 17
},
"type": "log",
"visible": true,
"zeroline": false,
"zerolinecolor": "rgba(0, 0, 0, 1.000)"
},
"yaxis": {
"anchor": "x1",
"domain": [
0.1294109069699621,
0.9863298337707787
],
"gridcolor": "rgba(0, 0, 0, 0.100)",
"gridwidth": 0.5,
"linecolor": "rgba(0, 0, 0, 1.000)",
"mirror": false,
"range": [
-3,
2
],
"showgrid": true,
"showline": true,
"showticklabels": true,
"tickangle": 0,
"tickcolor": "rgb(0, 0, 0)",
"tickfont": {
"color": "rgba(0, 0, 0, 1.000)",
"family": "Nimbus Sans L",
"size": 17
},
"tickmode": "array",
"ticks": "inside",
"ticktext": [
"10^-3",
"10^-2",
"10^-1",
"10^0",
"10^1",
"10^2"
],
"tickvals": [
0.001,
0.01,
0.1,
1,
10,
100
],
"title": "Rate Γ 10β»ΒΉβ΅ (mβ»Β³ sβ»ΒΉ)",
"titlefont": {
"color": "rgba(0, 0, 0, 1.000)",
"family": "Nimbus Sans L",
"size": 17
},
"type": "log",
"visible": true,
"zeroline": false,
"zerolinecolor": "rgba(0, 0, 0, 1.000)"
}
}
},
"image/svg+xml": [
"10 2 5 100 2 5 1000 0.001 0.01 0.1 1 10 100 kβ=0, kβ=0 kβ=+1, kβ=-1 kβ=+2, kβ=-2 kβ=+1, kβ=+1 kβ=+2, kβ=+2 Diameter (nm) Rate Γ 10β»ΒΉβ΅ (mβ»Β³ sβ»ΒΉ) "
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"figure(\"Nimbus Sans L\", 2, 3, 2, 8)\n",
"Dp = exp10.(range(log10(10e-9), stop=log10(1000e-9), length=100))\n",
"Ξ²α΅’β±Ό = map(Dp->Ξ²12(Dp, Dp, 0, 0), Dp) # no charge\n",
"Ξ²α΅’β±ΌαΆ»β½ΒΉβ»ΒΉβΎ = map(Dp->Ξ²12(Dp, Dp, 1, -1), Dp) # +1 -1 charge\n",
"Ξ²α΅’β±ΌαΆ»β½Β²β»Β²βΎ = map(Dp->Ξ²12(Dp, Dp, 2, -2), Dp) # +2 -2 charge\n",
"Ξ²α΅’β±ΌαΆ»β½ΒΉβΊΒΉβΎ = map(Dp->Ξ²12(Dp, Dp, 1, 1), Dp) # +1 +1 charge\n",
"Ξ²α΅’β±ΌαΆ»β½Β²βΊΒ²βΎ = map(Dp->Ξ²12(Dp, Dp, 2, 2), Dp) # +2 +2 charge\n",
"plot(Dp*1e9, Ξ²α΅’β±Ό*1e15, xaxis = :log10, xlabel = \"Diameter (nm)\", yaxis = :log10, ylim = (1e-3, 100),\n",
" ylabel = \"Rate Γ 10β»ΒΉβ΅ (mβ»Β³ sβ»ΒΉ)\", label = \"kβ=0, kβ=0\", left_margin = 30px, color = :black, lw = 2)\n",
"plot!(Dp*1e9, Ξ²α΅’β±ΌαΆ»β½ΒΉβ»ΒΉβΎ*1e15, label = \"kβ=+1, kβ=-1\", color = RGBA(0.8,0,0,1))\n",
"plot!(Dp*1e9, Ξ²α΅’β±ΌαΆ»β½Β²β»Β²βΎ*1e15, label = \"kβ=+2, kβ=-2\", color = :darkorange)\n",
"plot!(Dp*1e9, Ξ²α΅’β±ΌαΆ»β½ΒΉβΊΒΉβΎ*1e15, label = \"kβ=+1, kβ=+1\", color = RGBA(0.8,0,0,1), ls = :dashdot)\n",
"plot!(Dp*1e9, Ξ²α΅’β±ΌαΆ»β½Β²βΊΒ²βΎ*1e15, label = \"kβ=+2, kβ=+2\", color = :darkorange, ls = :dashdot, fmt = :svg)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Figure 2. Zebel-corrected Brownian coagulatation rates between particles of the same diameter. Coagulation between oppositely charged particle is enhanced while coagulation between particles of equal polarity is suppressed. The effect of particle charge is strongest in the free molecular regime. Suppression of coagulation due to repelling charges is stronger than enhancement due to attraction. This is because the enhancement is proportional to $k_i k_j\\frac{e^2}{k_bT(r_i + r_j)}$ while the supressenion is proportional to $\\exp\\left(k_i k_j\\frac{e^2}{k_bT(r_i + r_j)}\\right)$ (Zebel, 1957).\n",
"\n",
"### Application to Distributions\n",
"\n",
"Recall the original problem definition: two aerosol populations with identities \"1\" and \"2\" are introduced into in a chamber. Each population has unique and defined chemical composition, charge state (0, Β±1, or Β±2) and size distribution (πβ and πβ). Chemical composition and charge state are identical for particles within a population. There are no wall losses in the chamber. What is the size distribution of dimers comprising one \"1\" and one \"2\" particle (denoted πββ) after elapsed time $t$ due to coagulation? And further recall\n",
"\n",
" $\\frac{dN}{dt} = \\beta_{i,j}N_iN_j$ \n",
"\n",
"The general solution to this problem requires a coagulation model. However, assuming that the rate of dimer formation is small enough that number concentrations $N_1$ and $N_2$ are constant, assuming that $\\beta_{i,j}$ is constant over the spread the size distribution, one might intuit the following solution to the stated problem in terms of the size distribution arithmetic formalism developed in Notebook S3\n",
"\n",
"```julia\n",
"πββ = fβ
((Ξ²ββαΆ»*t)*(πβ*πβ))\n",
"```\n",
"where $t$ is time elapsed, Ξ²ββαΆ» is the Zebel-corrected Brownian coagulatation rate $f = \\frac{\\sqrt[3]{D_m^3 + D_m^3}}{D_m} = \\sqrt[3]{2}$, $D_m$ is the mode diameter of the distribution, $β
$ is the operator that shifts the distribution along the diameter axis, $*$ is the operator that scales the concentration of a distribution, $.*$ is the square of two size distributions. The factor $f$ accounts for the increase in sphere equivalent volume of the formed dimers.\n",
"\n",
"Although intuitive, it is neither immediately obvious that the above is correct, nor how the above could be formally proved. To do so, the Particle-resolved Monte Carlo code for atmospheric aerosol simulation (PartMC) is used (Riemer et al., 2009). The model is run in a similar manner than the chamber simulations described by Tian (2017).\n",
"\n",
"### PartMC Model\n",
"The PartMC model conceptualizes the population as a discrete number of individual particles. The model assumes that coagulation evens are stochastic following a Poisson distribution. The assumed coagulation rate is also calculated using Eq. (15.33) in Jacobson (2005). \n",
"\n",
"PartMC is free software available under the GNU General Public License v2 (http://lagrange.mechse.illinois.edu/partmc/). Version 2.4.0 was used. In a first test, the model is initialzed with two lognormal size distributions that have equal mode diameter and geometric standard deviation, but different number concentrations. The composition of the two distributions is assumed to be of different composition, although density and molecular weight of the two types are identical. The model is initialized with 10βΆ particles and the simulation proceeds for 60s. The model tracks the number of original particles from each source that formed each aerosol particle (n_orig_part), the constituent masses of each aerosol particle (aero_particle_mass), and the number concentration associated with each particle (aero_num_conc). From these fields the number size distribution of dimers comprising one \"1\" and one \"2\" particle is reconstructed as a function of time. The PartMC predicted πββ is then compared to the prediction from the simple semi-analytical programatic solution conjectured above. "
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"push!(LOAD_PATH, \"PartMC/\") # RunPartMC is a module that is located in the PartMC folder\n",
"using RunPartMC, Interpolations, LsqFit, ProgressMeter, DataFrames, Printf, Random, Statistics"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Module RunPartMC is a wrapper to initialize PartMC solutions and process the netCDF output produced by the model. Model runs are initialized as follows\n",
"```julia\n",
"ics = InitialConditionLogNormal(N1, N2, Dm, Οg)\n",
"```\n",
"where N1, N2 are number concentrations N1 and N2, Dm is the mode diameter, and Οg is the geometric standard deviation of a lognormal distribution. The simulation is executed via\n",
"```julia\n",
"x = runSimulation(ics,i,\"logn\"; verbose = true, repeat = 1)\n",
"```\n",
"The wrapper creates a copy of the PartMC input files hosted in directory PartMC/ and creates a copy in directory \"logn$i\" (i = 1 -> logn1/). Underlying parameters of the simulation can be changed in the relevant input files to PartMC. Verbose pipes the PartMC output to julia. Repeat sets the number of repeats of the Monte-Carlo simulation. Note that PartMC must be installed on the computer and executable from the shell (i.e. the executable should be in the /usr/bin or /usr/local/bin). PartMC or its dependencies are not provided by this package. Detailed documentation of PartMC and inputs/outputs is provided on the model source website (http://lagrange.mechse.illinois.edu/partmc/)."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"repeat t_sim n_part n_coag n_emit n_dil_in n_dil_out n_nuc t_wall t_rem\n",
" 1 0s 997678 0 0 0 0 0 0s 0s\n",
"repeat t_sim n_part n_coag n_emit n_dil_in n_dil_out n_nuc t_wall t_rem\n",
" 1 10s 997039 2987 0 0 0 0 21s 103s\n",
"repeat t_sim n_part n_coag n_emit n_dil_in n_dil_out n_nuc t_wall t_rem\n",
" 1 20s 996425 2964 0 0 0 0 21s 43s\n",
"repeat t_sim n_part n_coag n_emit n_dil_in n_dil_out n_nuc t_wall t_rem\n",
" 1 30s 995753 3044 0 0 0 0 22s 22s\n",
"repeat t_sim n_part n_coag n_emit n_dil_in n_dil_out n_nuc t_wall t_rem\n",
" 1 40s 995140 3048 0 0 0 0 23s 11s\n",
"repeat t_sim n_part n_coag n_emit n_dil_in n_dil_out n_nuc t_wall t_rem\n",
" 1 50s 994511 2968 0 0 0 0 24s 5s\n",
"repeat t_sim n_part n_coag n_emit n_dil_in n_dil_out n_nuc t_wall t_rem\n",
" 1 60s 993869 2979 0 0 0 0 25s 0s\n"
]
}
],
"source": [
"cd(\"PartMC\") # Descend into directory PartMC\n",
"Random.seed!(20) # Pick a random seed \n",
"ics = InitialConditionLogNormal(1e11, 1.5e11, 100.0, 1.1) # Set initial conditions\n",
"x = runSimulation(ics,1,\"logn\"; verbose = true, repeat = 1) # Run simulations\n",
"cd(\"..\") # Come back "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The variable x is a complex data-type that contains the output from the model simulation. See comment in the code below for description. "
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"Input PartMC Float64 String 2 rows Γ 2 columns
1 1.0e11 1.0E+11 2 1.5e11 1.5E+11
"
],
"text/latex": [
"\\begin{tabular}{r|cc}\n",
"\t& Input & PartMC\\\\\n",
"\t\\hline\n",
"\t& Float64 & String\\\\\n",
"\t\\hline\n",
"\t1 & 1.0e11 & 1.0E+11 \\\\\n",
"\t2 & 1.5e11 & 1.5E+11 \\\\\n",
"\\end{tabular}\n"
],
"text/plain": [
"2Γ2 DataFrame\n",
"β Row β Input β PartMC β\n",
"β β \u001b[90mFloat64\u001b[39m β \u001b[90mString\u001b[39m β\n",
"βββββββΌββββββββββΌββββββββββ€\n",
"β 1 β 1.0e11 β 1.0E+11 β\n",
"β 2 β 1.5e11 β 1.5E+11 β"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"π0 = lognormal([[0, 100, 1.1]]; d1 = 10.0, d2 = 1000.0, bins = 256); # empty size distribution\n",
"r = 1 # repeat number\n",
"Dm = ics.Dm # recover Dm from initial condition\n",
"Nβ = ics.Nt1 # recover Nβ from initial condition\n",
"Nβ = ics.Nt2 # recover Nβ from initial condition\n",
"t = x[r].r[end,end].t # end time of simulation. \n",
"\n",
"# Hack: The constructed D grid from PartMC causes an error. Adding an empty size distributio\n",
"# fixes the diameter grid by interpolating it onto the regular lognormal grid\n",
"πβ = (π0 + x[r].s1) # reconstructed size distribution for πβ from model output \n",
"πβ = (π0 + x[r].s2) # reconstructed size distribution for πβ from model output \n",
"πββ = (π0 + x[r].r[end,1].sc12) # reconstructed dimer size distribution πββ from model output \n",
"\n",
"DataFrame(Input = [Nβ,Nβ], PartMC = [@sprintf(\"%.1E\", sum(πβ.N)), @sprintf(\"%.1E\", sum(πβ.N))])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Table 1. Comparison of assumed input number concentration and reconstructed output number concentration from PartMC simulation."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"PartMC Analytical String String 1 rows Γ 2 columns
1 1.075E+09 1.097E+09
"
],
"text/latex": [
"\\begin{tabular}{r|cc}\n",
"\t& PartMC & Analytical\\\\\n",
"\t\\hline\n",
"\t& String & String\\\\\n",
"\t\\hline\n",
"\t1 & 1.075E+09 & 1.097E+09 \\\\\n",
"\\end{tabular}\n"
],
"text/plain": [
"1Γ2 DataFrame\n",
"β Row β PartMC β Analytical β\n",
"β β \u001b[90mString\u001b[39m β \u001b[90mString\u001b[39m β\n",
"βββββββΌββββββββββββΌβββββββββββββ€\n",
"β 1 β 1.075E+09 β 1.097E+09 β"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Ξ²ββ = Ξ²12(Dm*1e-9, Dm*1e-9, 0,0) # Zebel-Brownian coagulation rate for no charge\n",
"Ξ²ββαΆ»β½ΒΉβ»ΒΉβΎ = Ξ²12(Dm*1e-9, Dm*1e-9, 1,-1) # +1 -1 charge\n",
"Ξ²ββαΆ»β½Β²β»Β²βΎ = Ξ²12(Dm*1e-9, Dm*1e-9, 2,-2) # +1 -1 charge\n",
"f = 2.0^(1.0/3.0) # diameter shift for dimers particles\n",
"\n",
"πβα΅ = fβ
((Ξ²ββ*t)*(πβ*πβ)) # Semi-analytical estimate using Browninan Kernel\n",
"πβαΆ»ΒΉ = fβ
((Ξ²ββαΆ»β½ΒΉβ»ΒΉβΎ*t)*(πβ*πβ)) # Estimated enhancement for +1/-1 charged case\n",
"πβαΆ»Β² = fβ
((Ξ²ββαΆ»β½Β²β»Β²βΎ*t)*(πβ*πβ)) # Estimated enhancement for +2/-2 charged caseprintln()\n",
"\n",
"DataFrame(PartMC = [@sprintf(\"%.3E\",sum(πββ.N))], Analytical = [@sprintf(\"%.3E\",sum(πβα΅.N))])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Table 2. Comparison of assumed PartMC inferred number concentration and number concentration obtained from f$β
$((Ξ²ββ$*$t)$*$(πβ$.*$πβ))."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"application/vnd.plotly.v1+json": {
"data": [
{
"colorbar": {
"title": ""
},
"hoverinfo": "text",
"legendgroup": "πβ = ππ (Nβ,Dβ,Ο)",
"line": {
"color": "rgba(0, 0, 0, 1.000)",
"dash": "solid",
"shape": "linear",
"width": 1
},
"mode": "lines",
"name": "πβ = ππ (Nβ,Dβ,Ο)",
"showlegend": true,
"text": [
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null
],
"type": "scatter",
"x": [
10.090350448414474,
10.090350448414474,
10.273507681793024,
10.273507681793024,
10.459989534302535,
10.459989534302535,
10.649856353504289,
10.649856353504289,
10.84316958237171,
10.84316958237171,
11.039991779173976,
11.039991779173976,
11.240386637720556,
11.240386637720556,
11.44441900797323,
11.44441900797323,
11.652154917032231,
11.652154917032231,
11.863661590503344,
11.863661590503344,
12.079007474252842,
12.079007474252842,
12.298262256557319,
12.298262256557319,
12.521496890655566,
12.521496890655566,
12.748783617709826,
12.748783617709826,
12.98019599018381,
12.98019599018381,
13.215808895645086,
13.215808895645086,
13.455698580999508,
13.455698580999508,
13.699942677165545,
13.699942677165545,
13.948620224196498,
13.948620224196498,
14.201811696858716,
14.201811696858716,
14.459599030674116,
14.459599030674116,
14.722065648435406,
14.722065648435406,
14.989296487202608,
14.989296487202608,
15.261378025789629,
15.261378025789629,
15.538398312749738,
15.538398312749738,
15.820446994869037,
15.820446994869037,
16.10761534617715,
16.10761534617715,
16.39999629748447,
16.39999629748447,
16.69768446645562,
16.69768446645562,
17.00077618822873,
17.00077618822873,
17.309369546590553,
17.309369546590553,
17.623564405717435,
17.623564405717435,
17.94346244249247,
17.94346244249247,
18.269167179409244,
18.269167179409244,
18.600784018072822,
18.600784018072822,
18.938420273308882,
18.938420273308882,
19.282185207891956,
19.282185207891956,
19.632190067904055,
19.632190067904055,
19.988548118735103,
19.988548118735103,
20.35137468173687,
20.35137468173687,
20.72078717154221,
20.72078717154221,
21.096905134061714,
21.096905134061714,
21.479850285170084,
21.479850285170084,
21.869746550094703,
21.869746550094703,
22.266720103519187,
22.266720103519187,
22.67089941041491,
22.67089941041491,
23.08241526761366,
23.08241526761366,
23.501400846134892,
23.501400846134892,
23.927991734281377,
23.927991734281377,
24.36232598151701,
24.36232598151701,
24.804544143141136,
24.804544143141136,
25.25478932577379,
25.25478932577379,
25.713207233666548,
25.713207233666548,
26.179946215854002,
26.179946215854002,
26.65515731416115,
26.65515731416115,
27.138994312082165,
27.138994312082165,
27.6316137845464,
27.6316137845464,
28.133175148587764,
28.133175148587764,
28.6438407149338,
28.6438407149338,
29.163775740531204,
29.163775740531204,
29.693148482024785,
29.693148482024785,
30.232130250207152,
30.232130250207152,
30.78089546545674,
30.78089546545674,
31.339621714182158,
31.339621714182158,
31.90848980629108,
31.90848980629108,
32.48768383370232,
32.48768383370232,
33.07739122991996,
33.07739122991996,
33.6778028306889,
33.6778028306889,
34.289112935751355,
34.289112935751355,
34.911519371724424,
34.911519371724424,
35.54522355611888,
35.54522355611888,
36.19043056252011,
36.19043056252011,
36.847349186952165,
36.847349186952165,
37.51619201544639,
37.51619201544639,
38.19717549283665,
38.19717549283665,
38.89051999280318,
38.89051999280318,
39.59644988918792,
39.59644988918792,
40.31519362860439,
40.31519362860439,
41.04698380436544,
41.04698380436544,
41.792057231753,
41.792057231753,
42.55065502465411,
42.55065502465411,
43.323022673587985,
43.323022673587985,
44.10941012514944,
44.10941012514944,
44.910071862894306,
44.910071862894306,
45.72526698969311,
45.72526698969311,
46.55525931157958,
46.55525931157958,
47.400317423121166,
47.400317423121166,
48.26071479433915,
48.26071479433915,
49.13672985920654,
49.13672985920654,
50.02864610575234,
50.02864610575234,
50.93675216780135,
50.93675216780135,
51.861341918379274,
51.861341918379274,
52.80271456481317,
52.80271456481317,
53.76117474555825,
53.76117474555825,
54.73703262878217,
54.73703262878217,
55.73060401273886,
55.73060401273886,
56.74221042796429,
56.74221042796429,
57.77217924132721,
57.77217924132721,
58.8208437619687,
58.8208437619687,
59.888543349164614,
59.888543349164614,
60.975623522145916,
60.975623522145916,
62.08243607191253,
62.08243607191253,
63.20933917507671,
63.20933917507671,
64.35669750977287,
64.35669750977287,
65.52488237367147,
65.52488237367147,
66.71427180413495,
66.71427180413495,
67.92525070055476,
67.92525070055476,
69.15821094890896,
69.15821094890896,
70.41355154858087,
70.41355154858087,
71.69167874147956,
71.69167874147956,
72.9930061435042,
72.9930061435042,
74.31795487839462,
74.31795487839462,
75.66695371401163,
75.66695371401163,
77.04043920109092,
77.04043920109092,
78.43885581451562,
78.43885581451562,
79.8626560971533,
79.8626560971533,
81.31230080630368,
81.31230080630368,
82.78825906280481,
82.78825906280481,
84.29100850284559,
84.29100850284559,
85.82103543253415,
85.82103543253415,
87.37883498527172,
87.37883498527172,
88.9649112819833,
88.9649112819833,
90.5797775942566,
90.5797775942566,
92.22395651044235,
92.22395651044235,
93.8979801047696,
93.8979801047696,
95.60239010953076,
95.60239010953076,
97.33773809039202,
97.33773809039202,
99.10458562488608,
99.10458562488608,
100.90350448414475,
100.90350448414475,
102.73507681793026,
102.73507681793026,
104.59989534302535,
104.59989534302535,
106.4985635350429,
106.4985635350429,
108.4316958237171,
108.4316958237171,
110.39991779173975,
110.39991779173975,
112.40386637720557,
112.40386637720557,
114.44419007973231,
114.44419007973231,
116.5215491703223,
116.5215491703223,
118.63661590503344,
118.63661590503344,
120.79007474252845,
120.79007474252845,
122.98262256557321,
122.98262256557321,
125.21496890655568,
125.21496890655568,
127.48783617709826,
127.48783617709826,
129.8019599018381,
129.8019599018381,
132.15808895645085,
132.15808895645085,
134.55698580999507,
134.55698580999507,
136.99942677165546,
136.99942677165546,
139.48620224196497,
139.48620224196497,
142.01811696858715,
142.01811696858715,
144.59599030674116,
144.59599030674116,
147.22065648435404,
147.22065648435404,
149.89296487202606,
149.89296487202606,
152.6137802578963,
152.6137802578963,
155.38398312749737,
155.38398312749737,
158.20446994869036,
158.20446994869036,
161.07615346177147,
161.07615346177147,
163.9999629748447,
163.9999629748447,
166.9768446645562,
166.9768446645562,
170.0077618822873,
170.0077618822873,
173.0936954659055,
173.0936954659055,
176.23564405717434,
176.23564405717434,
179.43462442492472,
179.43462442492472,
182.69167179409243,
182.69167179409243,
186.00784018072818,
186.00784018072818,
189.3842027330888,
189.3842027330888,
192.8218520789196,
192.8218520789196,
196.32190067904054,
196.32190067904054,
199.88548118735102,
199.88548118735102,
203.51374681736868,
203.51374681736868,
207.2078717154221,
207.2078717154221,
210.96905134061717,
210.96905134061717,
214.79850285170085,
214.79850285170085,
218.69746550094703,
218.69746550094703,
222.66720103519188,
222.66720103519188,
226.70899410414913,
226.70899410414913,
230.82415267613658,
230.82415267613658,
235.01400846134894,
235.01400846134894,
239.27991734281375,
239.27991734281375,
243.6232598151701,
243.6232598151701,
248.04544143141135,
248.04544143141135,
252.5478932577379,
252.5478932577379,
257.13207233666543,
257.13207233666543,
261.79946215854,
261.79946215854,
266.5515731416115,
266.5515731416115,
271.3899431208216,
271.3899431208216,
276.31613784546397,
276.31613784546397,
281.33175148587765,
281.33175148587765,
286.438407149338,
286.438407149338,
291.637757405312,
291.637757405312,
296.9314848202479,
296.9314848202479,
302.32130250207155,
302.32130250207155,
307.8089546545674,
307.8089546545674,
313.3962171418216,
313.3962171418216,
319.08489806291084,
319.08489806291084,
324.8768383370232,
324.8768383370232,
330.7739122991996,
330.7739122991996,
336.7780283068889,
336.7780283068889,
342.89112935751353,
342.89112935751353,
349.1151937172442,
349.1151937172442,
355.4522355611888,
355.4522355611888,
361.9043056252011,
361.9043056252011,
368.4734918695216,
368.4734918695216,
375.16192015446387,
375.16192015446387,
381.97175492836647,
381.97175492836647,
388.9051999280318,
388.9051999280318,
395.96449889187926,
395.96449889187926,
403.15193628604396,
403.15193628604396,
410.4698380436544,
410.4698380436544,
417.92057231753,
417.92057231753,
425.5065502465411,
425.5065502465411,
433.23022673587985,
433.23022673587985,
441.09410125149435,
441.09410125149435,
449.100718628943,
449.100718628943,
457.2526698969311,
457.2526698969311,
465.55259311579584,
465.55259311579584,
474.0031742312117,
474.0031742312117,
482.6071479433915,
482.6071479433915,
491.36729859206537,
491.36729859206537,
500.2864610575233,
500.2864610575233,
509.36752167801353,
509.36752167801353,
518.6134191837928,
518.6134191837928,
528.0271456481318,
528.0271456481318,
537.6117474555825,
537.6117474555825,
547.3703262878216,
547.3703262878216,
557.3060401273885,
557.3060401273885,
567.4221042796428,
567.4221042796428,
577.7217924132722,
577.7217924132722,
588.2084376196871,
588.2084376196871,
598.8854334916462,
598.8854334916462,
609.7562352214592,
609.7562352214592,
620.8243607191254,
620.8243607191254,
632.093391750767,
632.093391750767,
643.5669750977287,
643.5669750977287,
655.2488237367147,
655.2488237367147,
667.1427180413494,
667.1427180413494,
679.2525070055476,
679.2525070055476,
691.5821094890896,
691.5821094890896,
704.1355154858088,
704.1355154858088,
716.9167874147956,
716.9167874147956,
729.9300614350419,
729.9300614350419,
743.1795487839462,
743.1795487839462,
756.6695371401163,
756.6695371401163,
770.4043920109092,
770.4043920109092,
784.3885581451563,
784.3885581451563,
798.626560971533,
798.626560971533,
813.1230080630369,
813.1230080630369,
827.8825906280481,
827.8825906280481,
842.9100850284559,
842.9100850284559,
858.2103543253414,
858.2103543253414,
873.7883498527173,
873.7883498527173,
889.649112819833,
889.649112819833,
905.797775942566,
905.797775942566,
922.2395651044235,
922.2395651044235,
938.9798010476961,
938.9798010476961,
956.0239010953076,
956.0239010953076,
973.3773809039202,
973.3773809039202,
991.0458562488608
],
"xaxis": "x1",
"y": [
9.46810013300733e-125,
1.118864971142895e-122,
1.118864971142895e-122,
1.363302303709405e-120,
1.363302303709405e-120,
6.763368967718927e-119,
6.763368967718927e-119,
6.921642113440284e-117,
6.921642113440284e-117,
7.490161991817119e-115,
7.490161991817119e-115,
3.4914078111390584e-113,
3.4914078111390584e-113,
3.109184027556042e-111,
3.109184027556042e-111,
2.9883087630538943e-109,
2.9883087630538943e-109,
1.3033674066253193e-107,
1.3033674066253193e-107,
1.0141223954540685e-105,
1.0141223954540685e-105,
8.657647309437534e-104,
8.657647309437534e-104,
3.520471800253454e-102,
3.520471800253454e-102,
2.4018274462999074e-100,
2.4018274462999074e-100,
1.8214592571433225e-98,
1.8214592571433225e-98,
6.883368905350908e-97,
6.883368905350908e-97,
4.1304896160103184e-95,
4.1304896160103184e-95,
2.782846223431059e-93,
2.782846223431059e-93,
9.746171372690099e-92,
9.746171372690099e-92,
5.1578697857150745e-90,
5.1578697857150745e-90,
3.087551390201621e-88,
3.087551390201621e-88,
9.99634572620211e-87,
9.99634572620211e-87,
4.676803386597052e-85,
4.676803386597052e-85,
2.487708675460908e-83,
2.487708675460908e-83,
7.42922965696115e-82,
7.42922965696115e-82,
3.0792044423065615e-80,
3.0792044423065615e-80,
1.4556277298315473e-78,
1.4556277298315473e-78,
4.001714360189491e-77,
4.001714360189491e-77,
1.4721069496157113e-75,
1.4721069496157113e-75,
6.185456537901593e-74,
6.185456537901593e-74,
1.5625683585062754e-72,
1.5625683585062754e-72,
5.110370115974353e-71,
5.110370115974353e-71,
1.9088378260232217e-69,
1.9088378260232217e-69,
4.423867536309373e-68,
4.423867536309373e-68,
1.2881848819564272e-66,
1.2881848819564272e-66,
4.27806477793269e-65,
4.27806477793269e-65,
9.082498835588321e-64,
9.082498835588321e-64,
2.3578575070179084e-62,
2.3578575070179084e-62,
6.963249672294262e-61,
6.963249672294262e-61,
1.3524172173683435e-59,
1.3524172173683435e-59,
3.1337983791499518e-58,
3.1337983791499518e-58,
8.231294024757341e-57,
8.231294024757341e-57,
1.4607410621586074e-55,
1.4607410621586074e-55,
3.0244002397218106e-54,
3.0244002397218106e-54,
7.066771609999281e-53,
7.066771609999281e-53,
1.1445696132031421e-51,
1.1445696132031421e-51,
2.1194477717334809e-50,
2.1194477717334809e-50,
4.406320112009501e-49,
4.406320112009501e-49,
6.506714522178695e-48,
6.506714522178695e-48,
1.0785043108457884e-46,
1.0785043108457884e-46,
1.995438421156521e-45,
1.995438421156521e-45,
2.683932451619709e-44,
2.683932451619709e-44,
3.985081112294821e-43,
3.985081112294821e-43,
6.5631622777763e-42,
6.5631622777763e-42,
8.033550971697025e-41,
8.033550971697025e-41,
1.069224467106965e-39,
1.069224467106965e-39,
1.5678542484224666e-38,
1.5678542484224666e-38,
1.7450268938517384e-37,
1.7450268938517384e-37,
2.0831344450435357e-36,
2.0831344450435357e-36,
2.7203271308599854e-35,
2.7203271308599854e-35,
2.7509629557618237e-34,
2.7509629557618237e-34,
2.947016424180495e-33,
2.947016424180495e-33,
3.4281877799755936e-32,
3.4281877799755936e-32,
3.1476191606086345e-31,
3.1476191606086345e-31,
3.0273644710590498e-30,
3.0273644710590498e-30,
3.1379148957991224e-29,
3.1379148957991224e-29,
2.6140796929146927e-28,
2.6140796929146927e-28,
2.2582067502413968e-27,
2.2582067502413968e-27,
2.0861993376576747e-26,
2.0861993376576747e-26,
1.5758573848904716e-25,
1.5758573848904716e-25,
1.2231489500464135e-24,
1.2231489500464135e-24,
1.0074266682860554e-23,
1.0074266682860554e-23,
6.895992024618724e-23,
6.895992024618724e-23,
4.810733793676508e-22,
4.810733793676508e-22,
3.533612313151644e-21,
3.533612313151644e-21,
2.1906696786115542e-20,
2.1906696786115542e-20,
1.3739127860402545e-19,
1.3739127860402545e-19,
9.002785093704714e-19,
9.002785093704714e-19,
5.052127661241261e-18,
5.052127661241261e-18,
2.849195359943896e-17,
2.849195359943896e-17,
1.6660651616020206e-16,
1.6660651616020206e-16,
8.45871750646986e-16,
8.45871750646986e-16,
4.2904188860307456e-15,
4.2904188860307456e-15,
2.2395906875965263e-14,
2.2395906875965263e-14,
1.0282097024322746e-13,
1.0282097024322746e-13,
4.691271295169864e-13,
4.691271295169864e-13,
2.1868107325213744e-12,
2.1868107325213744e-12,
9.0744186391138e-12,
9.0744186391138e-12,
3.724719324296586e-11,
3.724719324296586e-11,
1.5510427002566308e-10,
1.5510427002566308e-10,
5.814705235980484e-10,
5.814705235980484e-10,
2.1473717348711747e-09,
2.1473717348711747e-09,
7.991168479665367e-09,
7.991168479665367e-09,
2.705323354169442e-08,
2.705323354169442e-08,
8.989382438232592e-08,
8.989382438232592e-08,
2.9907118050803023e-07,
2.9907118050803023e-07,
9.139092854791069e-07,
9.139092854791069e-07,
2.7324952253275947e-06,
2.7324952253275947e-06,
8.130554229340444e-06,
8.130554229340444e-06,
2.241756225038273e-05,
2.241756225038273e-05,
6.03105895249467e-05,
6.03105895249467e-05,
0.000160564816591912,
0.000160564816591912,
0.0003992851830055348,
0.0003992851830055348,
0.000966561929535367,
0.000966561929535367,
0.0023033948141853444,
0.0023033948141853444,
0.005164102804948146,
0.005164102804948146,
0.011247725916358534,
0.011247725916358534,
0.024003634530457153,
0.024003634530457153,
0.048498698350334796,
0.048498698350334796,
0.09503755917777496,
0.09503755917777496,
0.1817100113783823,
0.1817100113783823,
0.330746135935819,
0.330746135935819,
0.5830656846151003,
0.5830656846151003,
0.9992548603205159,
0.9992548603205159,
1.637926159811997,
1.637926159811997,
2.5973294015005415,
2.5973294015005415,
3.991823233515128,
3.991823233515128,
5.890246522595441,
5.890246522595441,
8.400769958454076,
8.400769958454076,
11.584191185919952,
11.584191185919952,
15.382129396012955,
15.382129396012955,
19.728237157097524,
19.728237157097524,
24.420861435117214,
24.420861435117214,
29.170710125549853,
29.170710125549853,
33.637879107291646,
33.637879107291646,
37.398850055780336,
37.398850055780336,
40.17245163943608,
40.17245163943608,
41.64217652148391,
41.64217652148391,
41.6062303655233,
41.6062303655233,
40.17568251579937,
40.17568251579937,
37.42789137344088,
37.42789137344088,
33.62496708511679,
33.62496708511679,
29.17790907617099,
29.17790907617099,
24.423408559611943,
24.423408559611943,
19.740990883383123,
19.740990883383123,
15.388739403308893,
15.388739403308893,
11.570634025292449,
11.570634025292449,
8.419367907022663,
8.419367907022663,
5.894019106972982,
5.894019106972982,
3.9795875689489413,
3.9795875689489413,
2.608513194573175,
2.608513194573175,
1.6393849923284536,
1.6393849923284536,
0.9936605079054143,
0.9936605079054143,
0.5870955956861574,
0.5870955956861574,
0.3311404907044538,
0.3311404907044538,
0.1801129550042376,
0.1801129550042376,
0.09598994408993576,
0.09598994408993576,
0.048574265962994426,
0.048574265962994426,
0.02369984432214786,
0.02369984432214786,
0.011400984642326632,
0.011400984642326632,
0.0051744390059736516,
0.0051744390059736516,
0.0022637316801655994,
0.0022637316801655994,
0.0009836870224181594,
0.0009836870224181594,
0.00040029812939628497,
0.00040029812939628497,
0.00015695208864050338,
0.00015695208864050338,
6.165487488761766e-05,
6.165487488761766e-05,
2.2488841378601263e-05,
2.2488841378601263e-05,
7.898671476316832e-06,
7.898671476316832e-06,
2.807187534703152e-06,
2.807187534703152e-06,
9.175158900731644e-07,
9.175158900731644e-07,
2.885134372243777e-07,
2.885134372243777e-07,
9.284666031940775e-08,
9.284666031940775e-08,
2.718458261953615e-08,
2.718458261953615e-08,
7.648587582026529e-09,
7.648587582026529e-09,
2.230740408986155e-09,
2.230740408986155e-09,
5.849162690587626e-10,
5.849162690587626e-10,
1.4715515641826652e-10,
1.4715515641826652e-10,
3.8932869839440156e-11,
3.8932869839440156e-11,
9.139573402418744e-12,
9.139573402418744e-12,
2.0545749467370086e-12,
2.0545749467370086e-12,
4.935883611477953e-13,
4.935883611477953e-13,
1.0370947423478672e-13,
1.0370947423478672e-13,
2.081570026210523e-14,
2.081570026210523e-14,
4.545594817490605e-15,
4.545594817490605e-15,
8.546143564588019e-16,
8.546143564588019e-16,
1.5302046786914372e-16,
1.5302046786914372e-16,
3.040813648934722e-17,
3.040813648934722e-17,
5.11422726470359e-18,
5.11422726470359e-18,
8.161323812529787e-19,
8.161323812529787e-19,
1.4776033905001372e-19,
1.4776033905001372e-19,
2.2225251696138786e-20,
2.2225251696138786e-20,
3.1577885276299982e-21,
3.1577885276299982e-21,
5.215433655598911e-22,
5.215433655598911e-22,
7.014049449417065e-23,
7.014049449417065e-23,
8.862792404225321e-24,
8.862792404225321e-24,
1.337157956159709e-24,
1.337157956159709e-24,
1.6074778292564793e-25,
1.6074778292564793e-25,
1.80414384589141e-26,
1.80414384589141e-26,
2.490174636187103e-27,
2.490174636187103e-27,
2.675307352892012e-28,
2.675307352892012e-28,
2.663336160576891e-29,
2.663336160576891e-29,
3.368422617252095e-30,
3.368422617252095e-30,
3.2333545178332518e-31,
3.2333545178332518e-31,
2.8508102543711136e-32,
2.8508102543711136e-32,
3.3095406063189995e-33,
3.3095406063189995e-33,
2.8378033081296692e-34,
2.8378033081296692e-34,
2.2121880290553455e-35,
2.2121880290553455e-35,
2.3618251841857804e-36,
2.3618251841857804e-36,
1.8086682213331358e-37,
1.8086682213331358e-37,
1.2442278138921776e-38,
1.2442278138921776e-38,
1.224224458252515e-39,
1.224224458252515e-39,
8.371079512386546e-41,
8.371079512386546e-41,
5.071089322174979e-42,
5.071089322174979e-42,
4.608948452067579e-43,
4.608948452067579e-43,
2.8135084708099284e-44,
2.8135084708099284e-44,
1.497301296682379e-45,
1.497301296682379e-45,
1.2602718735360864e-46,
1.2602718735360864e-46,
6.866847820641572e-48,
6.866847820641572e-48,
3.2017463174718112e-49,
3.2017463174718112e-49,
2.5028925641327795e-50,
2.5028925641327795e-50,
1.217046779329446e-51,
1.217046779329446e-51,
4.956475174964421e-53,
4.956475174964421e-53,
3.610186272068931e-54,
3.610186272068931e-54,
1.5663758430695064e-55,
1.5663758430695064e-55,
5.552324057533861e-57,
5.552324057533861e-57,
3.781988619119448e-58,
3.781988619119448e-58,
1.4639348021619084e-59,
1.4639348021619084e-59,
4.572782487496749e-61,
4.572782487496749e-61,
2.8774494611534463e-62,
2.8774494611534463e-62,
9.935340163184449e-64,
9.935340163184449e-64,
2.7464134341600177e-65,
2.7464134341600177e-65,
1.589958038125516e-66,
1.589958038125516e-66,
4.8964033690527995e-68,
4.8964033690527995e-68,
1.1976067194742777e-69,
1.1976067194742777e-69,
6.380395606675256e-71,
6.380395606675256e-71,
1.7522790817419308e-72,
1.7522790817419308e-72,
3.791647933952443e-74,
3.791647933952443e-74,
1.8594606150880922e-75,
1.8594606150880922e-75,
4.5536454607032246e-77,
4.5536454607032246e-77,
8.715846636155748e-79,
8.715846636155748e-79,
3.935475147804347e-80,
3.935475147804347e-80,
8.592968511727324e-82,
8.592968511727324e-82,
1.4546585917370767e-83,
1.4546585917370767e-83,
6.048831675423223e-85,
6.048831675423223e-85,
1.1774799708755907e-86,
1.1774799708755907e-86,
1.7627245104506166e-88,
1.7627245104506166e-88,
6.751545903832128e-90,
6.751545903832128e-90,
1.1716243472710903e-91,
1.1716243472710903e-91,
1.550891672389114e-93,
1.550891672389114e-93,
5.4724973824508386e-95,
5.4724973824508386e-95,
8.465372389150157e-97,
8.465372389150157e-97,
9.90726476154769e-99,
9.90726476154769e-99,
3.2211553633848863e-100,
3.2211553633848863e-100,
4.44145078867102e-102,
4.44145078867102e-102,
4.595183398628425e-104,
4.595183398628425e-104,
1.3768120627174189e-105,
1.3768120627174189e-105,
1.6920884436809173e-107,
1.6920884436809173e-107,
1.5474978860729683e-109,
1.5474978860729683e-109,
4.273341383576945e-111,
4.273341383576945e-111,
4.681004029571688e-113,
4.681004029571688e-113,
3.783873906031635e-115,
3.783873906031635e-115,
9.631267675837815e-117,
9.631267675837815e-117,
9.403100503442765e-119,
9.403100503442765e-119,
6.717748684999947e-121,
6.717748684999947e-121,
1.576214074138538e-122,
1.576214074138538e-122,
1.3715689034155284e-124,
1.3715689034155284e-124
],
"yaxis": "y1",
"zmax": 0.1,
"zmin": -0.1
},
{
"colorbar": {
"title": ""
},
"hoverinfo": "text",
"legendgroup": "πβ = ππ (Nβ,Dβ,Ο)",
"line": {
"color": "rgba(204, 0, 0, 1.000)",
"dash": "solid",
"shape": "linear",
"width": 1
},
"mode": "lines",
"name": "πβ = ππ (Nβ,Dβ,Ο)",
"showlegend": true,
"text": [
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null
],
"type": "scatter",
"x": [
10.090350448414474,
10.090350448414474,
10.273507681793024,
10.273507681793024,
10.459989534302535,
10.459989534302535,
10.649856353504289,
10.649856353504289,
10.84316958237171,
10.84316958237171,
11.039991779173976,
11.039991779173976,
11.240386637720556,
11.240386637720556,
11.44441900797323,
11.44441900797323,
11.652154917032231,
11.652154917032231,
11.863661590503344,
11.863661590503344,
12.079007474252842,
12.079007474252842,
12.298262256557319,
12.298262256557319,
12.521496890655566,
12.521496890655566,
12.748783617709826,
12.748783617709826,
12.98019599018381,
12.98019599018381,
13.215808895645086,
13.215808895645086,
13.455698580999508,
13.455698580999508,
13.699942677165545,
13.699942677165545,
13.948620224196498,
13.948620224196498,
14.201811696858716,
14.201811696858716,
14.459599030674116,
14.459599030674116,
14.722065648435406,
14.722065648435406,
14.989296487202608,
14.989296487202608,
15.261378025789629,
15.261378025789629,
15.538398312749738,
15.538398312749738,
15.820446994869037,
15.820446994869037,
16.10761534617715,
16.10761534617715,
16.39999629748447,
16.39999629748447,
16.69768446645562,
16.69768446645562,
17.00077618822873,
17.00077618822873,
17.309369546590553,
17.309369546590553,
17.623564405717435,
17.623564405717435,
17.94346244249247,
17.94346244249247,
18.269167179409244,
18.269167179409244,
18.600784018072822,
18.600784018072822,
18.938420273308882,
18.938420273308882,
19.282185207891956,
19.282185207891956,
19.632190067904055,
19.632190067904055,
19.988548118735103,
19.988548118735103,
20.35137468173687,
20.35137468173687,
20.72078717154221,
20.72078717154221,
21.096905134061714,
21.096905134061714,
21.479850285170084,
21.479850285170084,
21.869746550094703,
21.869746550094703,
22.266720103519187,
22.266720103519187,
22.67089941041491,
22.67089941041491,
23.08241526761366,
23.08241526761366,
23.501400846134892,
23.501400846134892,
23.927991734281377,
23.927991734281377,
24.36232598151701,
24.36232598151701,
24.804544143141136,
24.804544143141136,
25.25478932577379,
25.25478932577379,
25.713207233666548,
25.713207233666548,
26.179946215854002,
26.179946215854002,
26.65515731416115,
26.65515731416115,
27.138994312082165,
27.138994312082165,
27.6316137845464,
27.6316137845464,
28.133175148587764,
28.133175148587764,
28.6438407149338,
28.6438407149338,
29.163775740531204,
29.163775740531204,
29.693148482024785,
29.693148482024785,
30.232130250207152,
30.232130250207152,
30.78089546545674,
30.78089546545674,
31.339621714182158,
31.339621714182158,
31.90848980629108,
31.90848980629108,
32.48768383370232,
32.48768383370232,
33.07739122991996,
33.07739122991996,
33.6778028306889,
33.6778028306889,
34.289112935751355,
34.289112935751355,
34.911519371724424,
34.911519371724424,
35.54522355611888,
35.54522355611888,
36.19043056252011,
36.19043056252011,
36.847349186952165,
36.847349186952165,
37.51619201544639,
37.51619201544639,
38.19717549283665,
38.19717549283665,
38.89051999280318,
38.89051999280318,
39.59644988918792,
39.59644988918792,
40.31519362860439,
40.31519362860439,
41.04698380436544,
41.04698380436544,
41.792057231753,
41.792057231753,
42.55065502465411,
42.55065502465411,
43.323022673587985,
43.323022673587985,
44.10941012514944,
44.10941012514944,
44.910071862894306,
44.910071862894306,
45.72526698969311,
45.72526698969311,
46.55525931157958,
46.55525931157958,
47.400317423121166,
47.400317423121166,
48.26071479433915,
48.26071479433915,
49.13672985920654,
49.13672985920654,
50.02864610575234,
50.02864610575234,
50.93675216780135,
50.93675216780135,
51.861341918379274,
51.861341918379274,
52.80271456481317,
52.80271456481317,
53.76117474555825,
53.76117474555825,
54.73703262878217,
54.73703262878217,
55.73060401273886,
55.73060401273886,
56.74221042796429,
56.74221042796429,
57.77217924132721,
57.77217924132721,
58.8208437619687,
58.8208437619687,
59.888543349164614,
59.888543349164614,
60.975623522145916,
60.975623522145916,
62.08243607191253,
62.08243607191253,
63.20933917507671,
63.20933917507671,
64.35669750977287,
64.35669750977287,
65.52488237367147,
65.52488237367147,
66.71427180413495,
66.71427180413495,
67.92525070055476,
67.92525070055476,
69.15821094890896,
69.15821094890896,
70.41355154858087,
70.41355154858087,
71.69167874147956,
71.69167874147956,
72.9930061435042,
72.9930061435042,
74.31795487839462,
74.31795487839462,
75.66695371401163,
75.66695371401163,
77.04043920109092,
77.04043920109092,
78.43885581451562,
78.43885581451562,
79.8626560971533,
79.8626560971533,
81.31230080630368,
81.31230080630368,
82.78825906280481,
82.78825906280481,
84.29100850284559,
84.29100850284559,
85.82103543253415,
85.82103543253415,
87.37883498527172,
87.37883498527172,
88.9649112819833,
88.9649112819833,
90.5797775942566,
90.5797775942566,
92.22395651044235,
92.22395651044235,
93.8979801047696,
93.8979801047696,
95.60239010953076,
95.60239010953076,
97.33773809039202,
97.33773809039202,
99.10458562488608,
99.10458562488608,
100.90350448414475,
100.90350448414475,
102.73507681793026,
102.73507681793026,
104.59989534302535,
104.59989534302535,
106.4985635350429,
106.4985635350429,
108.4316958237171,
108.4316958237171,
110.39991779173975,
110.39991779173975,
112.40386637720557,
112.40386637720557,
114.44419007973231,
114.44419007973231,
116.5215491703223,
116.5215491703223,
118.63661590503344,
118.63661590503344,
120.79007474252845,
120.79007474252845,
122.98262256557321,
122.98262256557321,
125.21496890655568,
125.21496890655568,
127.48783617709826,
127.48783617709826,
129.8019599018381,
129.8019599018381,
132.15808895645085,
132.15808895645085,
134.55698580999507,
134.55698580999507,
136.99942677165546,
136.99942677165546,
139.48620224196497,
139.48620224196497,
142.01811696858715,
142.01811696858715,
144.59599030674116,
144.59599030674116,
147.22065648435404,
147.22065648435404,
149.89296487202606,
149.89296487202606,
152.6137802578963,
152.6137802578963,
155.38398312749737,
155.38398312749737,
158.20446994869036,
158.20446994869036,
161.07615346177147,
161.07615346177147,
163.9999629748447,
163.9999629748447,
166.9768446645562,
166.9768446645562,
170.0077618822873,
170.0077618822873,
173.0936954659055,
173.0936954659055,
176.23564405717434,
176.23564405717434,
179.43462442492472,
179.43462442492472,
182.69167179409243,
182.69167179409243,
186.00784018072818,
186.00784018072818,
189.3842027330888,
189.3842027330888,
192.8218520789196,
192.8218520789196,
196.32190067904054,
196.32190067904054,
199.88548118735102,
199.88548118735102,
203.51374681736868,
203.51374681736868,
207.2078717154221,
207.2078717154221,
210.96905134061717,
210.96905134061717,
214.79850285170085,
214.79850285170085,
218.69746550094703,
218.69746550094703,
222.66720103519188,
222.66720103519188,
226.70899410414913,
226.70899410414913,
230.82415267613658,
230.82415267613658,
235.01400846134894,
235.01400846134894,
239.27991734281375,
239.27991734281375,
243.6232598151701,
243.6232598151701,
248.04544143141135,
248.04544143141135,
252.5478932577379,
252.5478932577379,
257.13207233666543,
257.13207233666543,
261.79946215854,
261.79946215854,
266.5515731416115,
266.5515731416115,
271.3899431208216,
271.3899431208216,
276.31613784546397,
276.31613784546397,
281.33175148587765,
281.33175148587765,
286.438407149338,
286.438407149338,
291.637757405312,
291.637757405312,
296.9314848202479,
296.9314848202479,
302.32130250207155,
302.32130250207155,
307.8089546545674,
307.8089546545674,
313.3962171418216,
313.3962171418216,
319.08489806291084,
319.08489806291084,
324.8768383370232,
324.8768383370232,
330.7739122991996,
330.7739122991996,
336.7780283068889,
336.7780283068889,
342.89112935751353,
342.89112935751353,
349.1151937172442,
349.1151937172442,
355.4522355611888,
355.4522355611888,
361.9043056252011,
361.9043056252011,
368.4734918695216,
368.4734918695216,
375.16192015446387,
375.16192015446387,
381.97175492836647,
381.97175492836647,
388.9051999280318,
388.9051999280318,
395.96449889187926,
395.96449889187926,
403.15193628604396,
403.15193628604396,
410.4698380436544,
410.4698380436544,
417.92057231753,
417.92057231753,
425.5065502465411,
425.5065502465411,
433.23022673587985,
433.23022673587985,
441.09410125149435,
441.09410125149435,
449.100718628943,
449.100718628943,
457.2526698969311,
457.2526698969311,
465.55259311579584,
465.55259311579584,
474.0031742312117,
474.0031742312117,
482.6071479433915,
482.6071479433915,
491.36729859206537,
491.36729859206537,
500.2864610575233,
500.2864610575233,
509.36752167801353,
509.36752167801353,
518.6134191837928,
518.6134191837928,
528.0271456481318,
528.0271456481318,
537.6117474555825,
537.6117474555825,
547.3703262878216,
547.3703262878216,
557.3060401273885,
557.3060401273885,
567.4221042796428,
567.4221042796428,
577.7217924132722,
577.7217924132722,
588.2084376196871,
588.2084376196871,
598.8854334916462,
598.8854334916462,
609.7562352214592,
609.7562352214592,
620.8243607191254,
620.8243607191254,
632.093391750767,
632.093391750767,
643.5669750977287,
643.5669750977287,
655.2488237367147,
655.2488237367147,
667.1427180413494,
667.1427180413494,
679.2525070055476,
679.2525070055476,
691.5821094890896,
691.5821094890896,
704.1355154858088,
704.1355154858088,
716.9167874147956,
716.9167874147956,
729.9300614350419,
729.9300614350419,
743.1795487839462,
743.1795487839462,
756.6695371401163,
756.6695371401163,
770.4043920109092,
770.4043920109092,
784.3885581451563,
784.3885581451563,
798.626560971533,
798.626560971533,
813.1230080630369,
813.1230080630369,
827.8825906280481,
827.8825906280481,
842.9100850284559,
842.9100850284559,
858.2103543253414,
858.2103543253414,
873.7883498527173,
873.7883498527173,
889.649112819833,
889.649112819833,
905.797775942566,
905.797775942566,
922.2395651044235,
922.2395651044235,
938.9798010476961,
938.9798010476961,
956.0239010953076,
956.0239010953076,
973.3773809039202,
973.3773809039202,
991.0458562488608
],
"xaxis": "x1",
"y": [
1.4202150199510995e-124,
1.6782974567143423e-122,
1.6782974567143423e-122,
2.0449534555641076e-120,
2.0449534555641076e-120,
1.014505345157839e-118,
1.014505345157839e-118,
1.0382463170160425e-116,
1.0382463170160425e-116,
1.1235242987725681e-114,
1.1235242987725681e-114,
5.237111716708587e-113,
5.237111716708587e-113,
4.663776041334063e-111,
4.663776041334063e-111,
4.482463144580841e-109,
4.482463144580841e-109,
1.9550511099379785e-107,
1.9550511099379785e-107,
1.5211835931811033e-105,
1.5211835931811033e-105,
1.2986470964156302e-103,
1.2986470964156302e-103,
5.280707700380181e-102,
5.280707700380181e-102,
3.602741169449861e-100,
3.602741169449861e-100,
2.732188885714984e-98,
2.732188885714984e-98,
1.0325053358026363e-96,
1.0325053358026363e-96,
6.195734424015478e-95,
6.195734424015478e-95,
4.174269335146588e-93,
4.174269335146588e-93,
1.4619257059035145e-91,
1.4619257059035145e-91,
7.736804678572611e-90,
7.736804678572611e-90,
4.631327085302431e-88,
4.631327085302431e-88,
1.4994518589303162e-86,
1.4994518589303162e-86,
7.015205079895578e-85,
7.015205079895578e-85,
3.731563013191362e-83,
3.731563013191362e-83,
1.1143844485441725e-81,
1.1143844485441725e-81,
4.6188066634598426e-80,
4.6188066634598426e-80,
2.1834415947473206e-78,
2.1834415947473206e-78,
6.002571540284237e-77,
6.002571540284237e-77,
2.2081604244235665e-75,
2.2081604244235665e-75,
9.27818480685239e-74,
9.27818480685239e-74,
2.3438525377594127e-72,
2.3438525377594127e-72,
7.66555517396153e-71,
7.66555517396153e-71,
2.863256739034833e-69,
2.863256739034833e-69,
6.635801304464058e-68,
6.635801304464058e-68,
1.9322773229346407e-66,
1.9322773229346407e-66,
6.4170971668990354e-65,
6.4170971668990354e-65,
1.3623748253382482e-63,
1.3623748253382482e-63,
3.5367862605268624e-62,
3.5367862605268624e-62,
1.0444874508441393e-60,
1.0444874508441393e-60,
2.0286258260525147e-59,
2.0286258260525147e-59,
4.700697568724928e-58,
4.700697568724928e-58,
1.234694103713601e-56,
1.234694103713601e-56,
2.191111593237911e-55,
2.191111593237911e-55,
4.5366003595827154e-54,
4.5366003595827154e-54,
1.0600157414998921e-52,
1.0600157414998921e-52,
1.716854419804713e-51,
1.716854419804713e-51,
3.179171657600222e-50,
3.179171657600222e-50,
6.609480168014251e-49,
6.609480168014251e-49,
9.760071783268042e-48,
9.760071783268042e-48,
1.6177564662686821e-46,
1.6177564662686821e-46,
2.993157631734781e-45,
2.993157631734781e-45,
4.025898677429563e-44,
4.025898677429563e-44,
5.977621668442231e-43,
5.977621668442231e-43,
9.844743416664452e-42,
9.844743416664452e-42,
1.2050326457545537e-40,
1.2050326457545537e-40,
1.6038367006604474e-39,
1.6038367006604474e-39,
2.3517813726336996e-38,
2.3517813726336996e-38,
2.6175403407776073e-37,
2.6175403407776073e-37,
3.1247016675653036e-36,
3.1247016675653036e-36,
4.0804906962899773e-35,
4.0804906962899773e-35,
4.126444433642735e-34,
4.126444433642735e-34,
4.4205246362707417e-33,
4.4205246362707417e-33,
5.142281669963391e-32,
5.142281669963391e-32,
4.721428740912952e-31,
4.721428740912952e-31,
4.5410467065885745e-30,
4.5410467065885745e-30,
4.706872343698685e-29,
4.706872343698685e-29,
3.921119539372039e-28,
3.921119539372039e-28,
3.3873101253620954e-27,
3.3873101253620954e-27,
3.129299006486512e-26,
3.129299006486512e-26,
2.3637860773357074e-25,
2.3637860773357074e-25,
1.8347234250696204e-24,
1.8347234250696204e-24,
1.5111400024290828e-23,
1.5111400024290828e-23,
1.0343988036928088e-22,
1.0343988036928088e-22,
7.216100690514762e-22,
7.216100690514762e-22,
5.300418469727466e-21,
5.300418469727466e-21,
3.286004517917331e-20,
3.286004517917331e-20,
2.0608691790603819e-19,
2.0608691790603819e-19,
1.3504177640557073e-18,
1.3504177640557073e-18,
7.578191491861891e-18,
7.578191491861891e-18,
4.2737930399158443e-17,
4.2737930399158443e-17,
2.4990977424030313e-16,
2.4990977424030313e-16,
1.268807625970479e-15,
1.268807625970479e-15,
6.4356283290461176e-15,
6.4356283290461176e-15,
3.3593860313947895e-14,
3.3593860313947895e-14,
1.5423145536484121e-13,
1.5423145536484121e-13,
7.036906942754797e-13,
7.036906942754797e-13,
3.2802160987820615e-12,
3.2802160987820615e-12,
1.36116279586707e-11,
1.36116279586707e-11,
5.587078986444879e-11,
5.587078986444879e-11,
2.3265640503849465e-10,
2.3265640503849465e-10,
8.722057853970727e-10,
8.722057853970727e-10,
3.221057602306762e-09,
3.221057602306762e-09,
1.1986752719498052e-08,
1.1986752719498052e-08,
4.0579850312541633e-08,
4.0579850312541633e-08,
1.3484073657348888e-07,
1.3484073657348888e-07,
4.486067707620454e-07,
4.486067707620454e-07,
1.3708639282186604e-06,
1.3708639282186604e-06,
4.098742837991392e-06,
4.098742837991392e-06,
1.2195831344010667e-05,
1.2195831344010667e-05,
3.36263433755741e-05,
3.36263433755741e-05,
9.046588428742004e-05,
9.046588428742004e-05,
0.00024084722488786802,
0.00024084722488786802,
0.0005989277745083023,
0.0005989277745083023,
0.0014498428943030507,
0.0014498428943030507,
0.003455092221278016,
0.003455092221278016,
0.007746154207422218,
0.007746154207422218,
0.0168715888745378,
0.0168715888745378,
0.03600545179568573,
0.03600545179568573,
0.0727480475255022,
0.0727480475255022,
0.14255633876666246,
0.14255633876666246,
0.27256501706757347,
0.27256501706757347,
0.4961192039037285,
0.4961192039037285,
0.8745985269226506,
0.8745985269226506,
1.4988822904807737,
1.4988822904807737,
2.4568892397179956,
2.4568892397179956,
3.8959941022508118,
3.8959941022508118,
5.987734850272692,
5.987734850272692,
8.83536978389316,
8.83536978389316,
12.601154937681114,
12.601154937681114,
17.376286778879926,
17.376286778879926,
23.073194094019435,
23.073194094019435,
29.59235573564629,
29.59235573564629,
36.631292152675826,
36.631292152675826,
43.75606518832477,
43.75606518832477,
50.456818660937465,
50.456818660937465,
56.09827508367051,
56.09827508367051,
60.25867745915413,
60.25867745915413,
62.46326478222587,
62.46326478222587,
62.40934554828494,
62.40934554828494,
60.26352377369906,
60.26352377369906,
56.141837060161315,
56.141837060161315,
50.43745062767519,
50.43745062767519,
43.766863614256486,
43.766863614256486,
36.63511283941791,
36.63511283941791,
29.611486325074683,
29.611486325074683,
23.08310910496334,
23.08310910496334,
17.355951037938674,
17.355951037938674,
12.629051860533995,
12.629051860533995,
8.841028660459473,
8.841028660459473,
5.969381353423412,
5.969381353423412,
3.9127697918597626,
3.9127697918597626,
2.4590774884926803,
2.4590774884926803,
1.4904907618581216,
1.4904907618581216,
0.880643393529236,
0.880643393529236,
0.4967107360566806,
0.4967107360566806,
0.2701694325063564,
0.2701694325063564,
0.14398491613490363,
0.14398491613490363,
0.07286139894449163,
0.07286139894449163,
0.03554976648322179,
0.03554976648322179,
0.017101476963489952,
0.017101476963489952,
0.0077616585089604765,
0.0077616585089604765,
0.0033955975202483997,
0.0033955975202483997,
0.0014755305336272388,
0.0014755305336272388,
0.0006004471940944275,
0.0006004471940944275,
0.00023542813296075507,
0.00023542813296075507,
9.248231233142651e-05,
9.248231233142651e-05,
3.373326206790189e-05,
3.373326206790189e-05,
1.1848007214475246e-05,
1.1848007214475246e-05,
4.210781302054727e-06,
4.210781302054727e-06,
1.3762738351097466e-06,
1.3762738351097466e-06,
4.327701558365666e-07,
4.327701558365666e-07,
1.3926999047911163e-07,
1.3926999047911163e-07,
4.077687392930422e-08,
4.077687392930422e-08,
1.1472881373039791e-08,
1.1472881373039791e-08,
3.3461106134792327e-09,
3.3461106134792327e-09,
8.773744035881437e-10,
8.773744035881437e-10,
2.2073273462739983e-10,
2.2073273462739983e-10,
5.839930475916024e-11,
5.839930475916024e-11,
1.3709360103628115e-11,
1.3709360103628115e-11,
3.081862420105513e-12,
3.081862420105513e-12,
7.403825417216929e-13,
7.403825417216929e-13,
1.5556421135218007e-13,
1.5556421135218007e-13,
3.1223550393157846e-14,
3.1223550393157846e-14,
6.818392226235908e-15,
6.818392226235908e-15,
1.281921534688203e-15,
1.281921534688203e-15,
2.295307018037156e-16,
2.295307018037156e-16,
4.561220473402082e-17,
4.561220473402082e-17,
7.671340897055385e-18,
7.671340897055385e-18,
1.224198571879468e-18,
1.224198571879468e-18,
2.216405085750206e-19,
2.216405085750206e-19,
3.3337877544208174e-20,
3.3337877544208174e-20,
4.736682791444998e-21,
4.736682791444998e-21,
7.823150483398365e-22,
7.823150483398365e-22,
1.0521074174125596e-22,
1.0521074174125596e-22,
1.329418860633798e-23,
1.329418860633798e-23,
2.005736934239564e-24,
2.005736934239564e-24,
2.411216743884719e-25,
2.411216743884719e-25,
2.7062157688371144e-26,
2.7062157688371144e-26,
3.7352619542806544e-27,
3.7352619542806544e-27,
4.0129610293380184e-28,
4.0129610293380184e-28,
3.995004240865337e-29,
3.995004240865337e-29,
5.052633925878142e-30,
5.052633925878142e-30,
4.850031776749878e-31,
4.850031776749878e-31,
4.27621538155667e-32,
4.27621538155667e-32,
4.9643109094784996e-33,
4.9643109094784996e-33,
4.2567049621945045e-34,
4.2567049621945045e-34,
3.3182820435830176e-35,
3.3182820435830176e-35,
3.542737776278671e-36,
3.542737776278671e-36,
2.713002331999704e-37,
2.713002331999704e-37,
1.866341720838266e-38,
1.866341720838266e-38,
1.8363366873787724e-39,
1.8363366873787724e-39,
1.255661926857982e-40,
1.255661926857982e-40,
7.60663398326247e-42,
7.60663398326247e-42,
6.91342267810137e-43,
6.91342267810137e-43,
4.2202627062148934e-44,
4.2202627062148934e-44,
2.2459519450235686e-45,
2.2459519450235686e-45,
1.8904078103041295e-46,
1.8904078103041295e-46,
1.0300271730962361e-47,
1.0300271730962361e-47,
4.802619476207716e-49,
4.802619476207716e-49,
3.754338846199169e-50,
3.754338846199169e-50,
1.825570168994169e-51,
1.825570168994169e-51,
7.434712762446631e-53,
7.434712762446631e-53,
5.415279408103395e-54,
5.415279408103395e-54,
2.3495637646042592e-55,
2.3495637646042592e-55,
8.328486086300793e-57,
8.328486086300793e-57,
5.672982928679171e-58,
5.672982928679171e-58,
2.1959022032428622e-59,
2.1959022032428622e-59,
6.859173731245125e-61,
6.859173731245125e-61,
4.3161741917301705e-62,
4.3161741917301705e-62,
1.4903010244776674e-63,
1.4903010244776674e-63,
4.119620151240026e-65,
4.119620151240026e-65,
2.3849370571882746e-66,
2.3849370571882746e-66,
7.344605053579199e-68,
7.344605053579199e-68,
1.7964100792114164e-69,
1.7964100792114164e-69,
9.570593410012883e-71,
9.570593410012883e-71,
2.628418622612896e-72,
2.628418622612896e-72,
5.687471900928664e-74,
5.687471900928664e-74,
2.789190922632138e-75,
2.789190922632138e-75,
6.830468191054835e-77,
6.830468191054835e-77,
1.3073769954233622e-78,
1.3073769954233622e-78,
5.9032127217065225e-80,
5.9032127217065225e-80,
1.2889452767590985e-81,
1.2889452767590985e-81,
2.181987887605615e-83,
2.181987887605615e-83,
9.073247513134835e-85,
9.073247513134835e-85,
1.766219956313386e-86,
1.766219956313386e-86,
2.6440867656759255e-88,
2.6440867656759255e-88,
1.0127318855748192e-89,
1.0127318855748192e-89,
1.7574365209066355e-91,
1.7574365209066355e-91,
2.3263375085836714e-93,
2.3263375085836714e-93,
8.208746073676256e-95,
8.208746073676256e-95,
1.2698058583725236e-96,
1.2698058583725236e-96,
1.486089714232154e-98,
1.486089714232154e-98,
4.831733045077329e-100,
4.831733045077329e-100,
6.6621761830065304e-102,
6.6621761830065304e-102,
6.892775097942637e-104,
6.892775097942637e-104,
2.0652180940761283e-105,
2.0652180940761283e-105,
2.538132665521376e-107,
2.538132665521376e-107,
2.3212468291094527e-109,
2.3212468291094527e-109,
6.410012075365417e-111,
6.410012075365417e-111,
7.021506044357532e-113,
7.021506044357532e-113,
5.6758108590474545e-115,
5.6758108590474545e-115,
1.4446901513756723e-116,
1.4446901513756723e-116,
1.4104650755164148e-118,
1.4104650755164148e-118,
1.0076623027499921e-120,
1.0076623027499921e-120,
2.364321111207807e-122,
2.364321111207807e-122,
2.0573533551232925e-124,
2.0573533551232925e-124
],
"yaxis": "y1",
"zmax": 0.1,
"zmin": -0.1
},
{
"colorbar": {
"title": ""
},
"hoverinfo": "text",
"legendgroup": "πββ (partMC)",
"line": {
"color": "rgba(0, 0, 204, 1.000)",
"dash": "solid",
"shape": "linear",
"width": 1.5
},
"mode": "lines",
"name": "πββ (partMC)",
"showlegend": true,
"text": [
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null
],
"type": "scatter",
"x": [
10.090350448414474,
10.090350448414474,
10.273507681793024,
10.273507681793024,
10.459989534302535,
10.459989534302535,
10.649856353504289,
10.649856353504289,
10.84316958237171,
10.84316958237171,
11.039991779173976,
11.039991779173976,
11.240386637720556,
11.240386637720556,
11.44441900797323,
11.44441900797323,
11.652154917032231,
11.652154917032231,
11.863661590503344,
11.863661590503344,
12.079007474252842,
12.079007474252842,
12.298262256557319,
12.298262256557319,
12.521496890655566,
12.521496890655566,
12.748783617709826,
12.748783617709826,
12.98019599018381,
12.98019599018381,
13.215808895645086,
13.215808895645086,
13.455698580999508,
13.455698580999508,
13.699942677165545,
13.699942677165545,
13.948620224196498,
13.948620224196498,
14.201811696858716,
14.201811696858716,
14.459599030674116,
14.459599030674116,
14.722065648435406,
14.722065648435406,
14.989296487202608,
14.989296487202608,
15.261378025789629,
15.261378025789629,
15.538398312749738,
15.538398312749738,
15.820446994869037,
15.820446994869037,
16.10761534617715,
16.10761534617715,
16.39999629748447,
16.39999629748447,
16.69768446645562,
16.69768446645562,
17.00077618822873,
17.00077618822873,
17.309369546590553,
17.309369546590553,
17.623564405717435,
17.623564405717435,
17.94346244249247,
17.94346244249247,
18.269167179409244,
18.269167179409244,
18.600784018072822,
18.600784018072822,
18.938420273308882,
18.938420273308882,
19.282185207891956,
19.282185207891956,
19.632190067904055,
19.632190067904055,
19.988548118735103,
19.988548118735103,
20.35137468173687,
20.35137468173687,
20.72078717154221,
20.72078717154221,
21.096905134061714,
21.096905134061714,
21.479850285170084,
21.479850285170084,
21.869746550094703,
21.869746550094703,
22.266720103519187,
22.266720103519187,
22.67089941041491,
22.67089941041491,
23.08241526761366,
23.08241526761366,
23.501400846134892,
23.501400846134892,
23.927991734281377,
23.927991734281377,
24.36232598151701,
24.36232598151701,
24.804544143141136,
24.804544143141136,
25.25478932577379,
25.25478932577379,
25.713207233666548,
25.713207233666548,
26.179946215854002,
26.179946215854002,
26.65515731416115,
26.65515731416115,
27.138994312082165,
27.138994312082165,
27.6316137845464,
27.6316137845464,
28.133175148587764,
28.133175148587764,
28.6438407149338,
28.6438407149338,
29.163775740531204,
29.163775740531204,
29.693148482024785,
29.693148482024785,
30.232130250207152,
30.232130250207152,
30.78089546545674,
30.78089546545674,
31.339621714182158,
31.339621714182158,
31.90848980629108,
31.90848980629108,
32.48768383370232,
32.48768383370232,
33.07739122991996,
33.07739122991996,
33.6778028306889,
33.6778028306889,
34.289112935751355,
34.289112935751355,
34.911519371724424,
34.911519371724424,
35.54522355611888,
35.54522355611888,
36.19043056252011,
36.19043056252011,
36.847349186952165,
36.847349186952165,
37.51619201544639,
37.51619201544639,
38.19717549283665,
38.19717549283665,
38.89051999280318,
38.89051999280318,
39.59644988918792,
39.59644988918792,
40.31519362860439,
40.31519362860439,
41.04698380436544,
41.04698380436544,
41.792057231753,
41.792057231753,
42.55065502465411,
42.55065502465411,
43.323022673587985,
43.323022673587985,
44.10941012514944,
44.10941012514944,
44.910071862894306,
44.910071862894306,
45.72526698969311,
45.72526698969311,
46.55525931157958,
46.55525931157958,
47.400317423121166,
47.400317423121166,
48.26071479433915,
48.26071479433915,
49.13672985920654,
49.13672985920654,
50.02864610575234,
50.02864610575234,
50.93675216780135,
50.93675216780135,
51.861341918379274,
51.861341918379274,
52.80271456481317,
52.80271456481317,
53.76117474555825,
53.76117474555825,
54.73703262878217,
54.73703262878217,
55.73060401273886,
55.73060401273886,
56.74221042796429,
56.74221042796429,
57.77217924132721,
57.77217924132721,
58.8208437619687,
58.8208437619687,
59.888543349164614,
59.888543349164614,
60.975623522145916,
60.975623522145916,
62.08243607191253,
62.08243607191253,
63.20933917507671,
63.20933917507671,
64.35669750977287,
64.35669750977287,
65.52488237367147,
65.52488237367147,
66.71427180413495,
66.71427180413495,
67.92525070055476,
67.92525070055476,
69.15821094890896,
69.15821094890896,
70.41355154858087,
70.41355154858087,
71.69167874147956,
71.69167874147956,
72.9930061435042,
72.9930061435042,
74.31795487839462,
74.31795487839462,
75.66695371401163,
75.66695371401163,
77.04043920109092,
77.04043920109092,
78.43885581451562,
78.43885581451562,
79.8626560971533,
79.8626560971533,
81.31230080630368,
81.31230080630368,
82.78825906280481,
82.78825906280481,
84.29100850284559,
84.29100850284559,
85.82103543253415,
85.82103543253415,
87.37883498527172,
87.37883498527172,
88.9649112819833,
88.9649112819833,
90.5797775942566,
90.5797775942566,
92.22395651044235,
92.22395651044235,
93.8979801047696,
93.8979801047696,
95.60239010953076,
95.60239010953076,
97.33773809039202,
97.33773809039202,
99.10458562488608,
99.10458562488608,
100.90350448414475,
100.90350448414475,
102.73507681793026,
102.73507681793026,
104.59989534302535,
104.59989534302535,
106.4985635350429,
106.4985635350429,
108.4316958237171,
108.4316958237171,
110.39991779173975,
110.39991779173975,
112.40386637720557,
112.40386637720557,
114.44419007973231,
114.44419007973231,
116.5215491703223,
116.5215491703223,
118.63661590503344,
118.63661590503344,
120.79007474252845,
120.79007474252845,
122.98262256557321,
122.98262256557321,
125.21496890655568,
125.21496890655568,
127.48783617709826,
127.48783617709826,
129.8019599018381,
129.8019599018381,
132.15808895645085,
132.15808895645085,
134.55698580999507,
134.55698580999507,
136.99942677165546,
136.99942677165546,
139.48620224196497,
139.48620224196497,
142.01811696858715,
142.01811696858715,
144.59599030674116,
144.59599030674116,
147.22065648435404,
147.22065648435404,
149.89296487202606,
149.89296487202606,
152.6137802578963,
152.6137802578963,
155.38398312749737,
155.38398312749737,
158.20446994869036,
158.20446994869036,
161.07615346177147,
161.07615346177147,
163.9999629748447,
163.9999629748447,
166.9768446645562,
166.9768446645562,
170.0077618822873,
170.0077618822873,
173.0936954659055,
173.0936954659055,
176.23564405717434,
176.23564405717434,
179.43462442492472,
179.43462442492472,
182.69167179409243,
182.69167179409243,
186.00784018072818,
186.00784018072818,
189.3842027330888,
189.3842027330888,
192.8218520789196,
192.8218520789196,
196.32190067904054,
196.32190067904054,
199.88548118735102,
199.88548118735102,
203.51374681736868,
203.51374681736868,
207.2078717154221,
207.2078717154221,
210.96905134061717,
210.96905134061717,
214.79850285170085,
214.79850285170085,
218.69746550094703,
218.69746550094703,
222.66720103519188,
222.66720103519188,
226.70899410414913,
226.70899410414913,
230.82415267613658,
230.82415267613658,
235.01400846134894,
235.01400846134894,
239.27991734281375,
239.27991734281375,
243.6232598151701,
243.6232598151701,
248.04544143141135,
248.04544143141135,
252.5478932577379,
252.5478932577379,
257.13207233666543,
257.13207233666543,
261.79946215854,
261.79946215854,
266.5515731416115,
266.5515731416115,
271.3899431208216,
271.3899431208216,
276.31613784546397,
276.31613784546397,
281.33175148587765,
281.33175148587765,
286.438407149338,
286.438407149338,
291.637757405312,
291.637757405312,
296.9314848202479,
296.9314848202479,
302.32130250207155,
302.32130250207155,
307.8089546545674,
307.8089546545674,
313.3962171418216,
313.3962171418216,
319.08489806291084,
319.08489806291084,
324.8768383370232,
324.8768383370232,
330.7739122991996,
330.7739122991996,
336.7780283068889,
336.7780283068889,
342.89112935751353,
342.89112935751353,
349.1151937172442,
349.1151937172442,
355.4522355611888,
355.4522355611888,
361.9043056252011,
361.9043056252011,
368.4734918695216,
368.4734918695216,
375.16192015446387,
375.16192015446387,
381.97175492836647,
381.97175492836647,
388.9051999280318,
388.9051999280318,
395.96449889187926,
395.96449889187926,
403.15193628604396,
403.15193628604396,
410.4698380436544,
410.4698380436544,
417.92057231753,
417.92057231753,
425.5065502465411,
425.5065502465411,
433.23022673587985,
433.23022673587985,
441.09410125149435,
441.09410125149435,
449.100718628943,
449.100718628943,
457.2526698969311,
457.2526698969311,
465.55259311579584,
465.55259311579584,
474.0031742312117,
474.0031742312117,
482.6071479433915,
482.6071479433915,
491.36729859206537,
491.36729859206537,
500.2864610575233,
500.2864610575233,
509.36752167801353,
509.36752167801353,
518.6134191837928,
518.6134191837928,
528.0271456481318,
528.0271456481318,
537.6117474555825,
537.6117474555825,
547.3703262878216,
547.3703262878216,
557.3060401273885,
557.3060401273885,
567.4221042796428,
567.4221042796428,
577.7217924132722,
577.7217924132722,
588.2084376196871,
588.2084376196871,
598.8854334916462,
598.8854334916462,
609.7562352214592,
609.7562352214592,
620.8243607191254,
620.8243607191254,
632.093391750767,
632.093391750767,
643.5669750977287,
643.5669750977287,
655.2488237367147,
655.2488237367147,
667.1427180413494,
667.1427180413494,
679.2525070055476,
679.2525070055476,
691.5821094890896,
691.5821094890896,
704.1355154858088,
704.1355154858088,
716.9167874147956,
716.9167874147956,
729.9300614350419,
729.9300614350419,
743.1795487839462,
743.1795487839462,
756.6695371401163,
756.6695371401163,
770.4043920109092,
770.4043920109092,
784.3885581451563,
784.3885581451563,
798.626560971533,
798.626560971533,
813.1230080630369,
813.1230080630369,
827.8825906280481,
827.8825906280481,
842.9100850284559,
842.9100850284559,
858.2103543253414,
858.2103543253414,
873.7883498527173,
873.7883498527173,
889.649112819833,
889.649112819833,
905.797775942566,
905.797775942566,
922.2395651044235,
922.2395651044235,
938.9798010476961,
938.9798010476961,
956.0239010953076,
956.0239010953076,
973.3773809039202,
973.3773809039202,
991.0458562488608
],
"xaxis": "x2",
"y": [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.001660429349534434,
0.001660429349534434,
0.00285707455268562,
0.00285707455268562,
0.005074205387940568,
0.005074205387940568,
0.015911629435727482,
0.015911629435727482,
0.023630103722488985,
0.023630103722488985,
0.05358106669684123,
0.05358106669684123,
0.07406248316300047,
0.07406248316300047,
0.13235319643972215,
0.13235319643972215,
0.2179175293910647,
0.2179175293910647,
0.3004779122703456,
0.3004779122703456,
0.39675690579819173,
0.39675690579819173,
0.5207364988538564,
0.5207364988538564,
0.5855901707876983,
0.5855901707876983,
0.6085888788531155,
0.6085888788531155,
0.6425247127634108,
0.6425247127634108,
0.547214360658466,
0.547214360658466,
0.5445809230674346,
0.5445809230674346,
0.3952345454823395,
0.3952345454823395,
0.32283374399326803,
0.32283374399326803,
0.22188514183780128,
0.22188514183780128,
0.14015032000210698,
0.14015032000210698,
0.08619421842064146,
0.08619421842064146,
0.0634584598940785,
0.0634584598940785,
0.03835521616850645,
0.03835521616850645,
0.022223937534490618,
0.022223937534490618,
0.007604436589863831,
0.007604436589863831,
0.002141637636578918,
0.002141637636578918,
0.00216143414043382,
0.00216143414043382,
0.00030154005301095304,
0.00030154005301095304,
0.000510872965720734,
0.000510872965720734,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
],
"yaxis": "y2",
"zmax": 0.1,
"zmin": -0.1
},
{
"colorbar": {
"title": ""
},
"hoverinfo": "text",
"legendgroup": "fβ
[(Ξ²ββα΅t)*(πβ*πβ)]",
"line": {
"color": "rgba(165, 42, 42, 1.000)",
"dash": "solid",
"shape": "linear",
"width": 1
},
"mode": "lines",
"name": "fβ
[(Ξ²ββα΅t)*(πβ*πβ)]",
"showlegend": true,
"text": [
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null
],
"type": "scatter",
"x": [
10.090350448414474,
10.273507681793024,
10.459989534302535,
10.649856353504289,
10.84316958237171,
11.039991779173976,
11.240386637720556,
11.44441900797323,
11.652154917032231,
11.863661590503344,
12.079007474252842,
12.298262256557319,
12.521496890655566,
12.748783617709826,
12.98019599018381,
13.215808895645086,
13.455698580999508,
13.699942677165545,
13.948620224196498,
14.201811696858716,
14.459599030674116,
14.722065648435406,
14.989296487202608,
15.261378025789629,
15.538398312749738,
15.820446994869037,
16.10761534617715,
16.39999629748447,
16.69768446645562,
17.00077618822873,
17.309369546590553,
17.623564405717435,
17.94346244249247,
18.269167179409244,
18.600784018072822,
18.938420273308882,
19.282185207891956,
19.632190067904055,
19.988548118735103,
20.35137468173687,
20.72078717154221,
21.096905134061714,
21.479850285170084,
21.869746550094703,
22.266720103519187,
22.67089941041491,
23.08241526761366,
23.501400846134892,
23.927991734281377,
24.36232598151701,
24.804544143141136,
25.25478932577379,
25.713207233666548,
26.179946215854002,
26.65515731416115,
27.138994312082165,
27.6316137845464,
28.133175148587764,
28.6438407149338,
29.163775740531204,
29.693148482024785,
30.232130250207152,
30.78089546545674,
31.339621714182158,
31.90848980629108,
32.48768383370232,
33.07739122991996,
33.6778028306889,
34.289112935751355,
34.911519371724424,
35.54522355611888,
36.19043056252011,
36.847349186952165,
37.51619201544639,
38.19717549283665,
38.89051999280318,
39.59644988918792,
40.31519362860439,
41.04698380436544,
41.792057231753,
42.55065502465411,
43.323022673587985,
44.10941012514944,
44.910071862894306,
45.72526698969311,
46.55525931157958,
47.400317423121166,
48.26071479433915,
49.13672985920654,
50.02864610575234,
50.93675216780135,
51.861341918379274,
52.80271456481317,
53.76117474555825,
54.73703262878217,
55.73060401273886,
56.74221042796429,
57.77217924132721,
58.8208437619687,
59.888543349164614,
60.975623522145916,
62.08243607191253,
63.20933917507671,
64.35669750977287,
65.52488237367147,
66.71427180413495,
67.92525070055476,
69.15821094890896,
70.41355154858087,
71.69167874147956,
72.9930061435042,
74.31795487839462,
75.66695371401163,
77.04043920109092,
78.43885581451562,
79.8626560971533,
81.31230080630368,
82.78825906280481,
84.29100850284559,
85.82103543253415,
87.37883498527172,
88.9649112819833,
90.5797775942566,
92.22395651044235,
93.8979801047696,
95.60239010953076,
97.33773809039202,
99.10458562488608,
100.90350448414475,
102.73507681793026,
104.59989534302535,
106.4985635350429,
108.4316958237171,
110.39991779173975,
112.40386637720557,
114.44419007973231,
116.5215491703223,
118.63661590503344,
120.79007474252845,
122.98262256557321,
125.21496890655568,
127.48783617709826,
129.8019599018381,
132.15808895645085,
134.55698580999507,
136.99942677165546,
139.48620224196497,
142.01811696858715,
144.59599030674116,
147.22065648435404,
149.89296487202606,
152.6137802578963,
155.38398312749737,
158.20446994869036,
161.07615346177147,
163.9999629748447,
166.9768446645562,
170.0077618822873,
173.0936954659055,
176.23564405717434,
179.43462442492472,
182.69167179409243,
186.00784018072818,
189.3842027330888,
192.8218520789196,
196.32190067904054,
199.88548118735102,
203.51374681736868,
207.2078717154221,
210.96905134061717,
214.79850285170085,
218.69746550094703,
222.66720103519188,
226.70899410414913,
230.82415267613658,
235.01400846134894,
239.27991734281375,
243.6232598151701,
248.04544143141135,
252.5478932577379,
257.13207233666543,
261.79946215854,
266.5515731416115,
271.3899431208216,
276.31613784546397,
281.33175148587765,
286.438407149338,
291.637757405312,
296.9314848202479,
302.32130250207155,
307.8089546545674,
313.3962171418216,
319.08489806291084,
324.8768383370232,
330.7739122991996,
336.7780283068889,
342.89112935751353,
349.1151937172442,
355.4522355611888,
361.9043056252011,
368.4734918695216,
375.16192015446387,
381.97175492836647,
388.9051999280318,
395.96449889187926,
403.15193628604396,
410.4698380436544,
417.92057231753,
425.5065502465411,
433.23022673587985,
441.09410125149435,
449.100718628943,
457.2526698969311,
465.55259311579584,
474.0031742312117,
482.6071479433915,
491.36729859206537,
500.2864610575233,
509.36752167801353,
518.6134191837928,
528.0271456481318,
537.6117474555825,
547.3703262878216,
557.3060401273885,
567.4221042796428,
577.7217924132722,
588.2084376196871,
598.8854334916462,
609.7562352214592,
620.8243607191254,
632.093391750767,
643.5669750977287,
655.2488237367147,
667.1427180413494,
679.2525070055476,
691.5821094890896,
704.1355154858088,
716.9167874147956,
729.9300614350419,
743.1795487839462,
756.6695371401163,
770.4043920109092,
784.3885581451563,
798.626560971533,
813.1230080630369,
827.8825906280481,
842.9100850284559,
858.2103543253414,
873.7883498527173,
889.649112819833,
905.797775942566,
922.2395651044235,
938.9798010476961,
956.0239010953076,
973.3773809039202,
991.0458562488608
],
"xaxis": "x2",
"y": [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1.428320220902363e-248,
2.6011538762290837e-245,
5.082517348795381e-241,
5.333453530973188e-237,
8.256990827587541e-234,
1.2596463430767196e-229,
1.0501110333470017e-225,
1.3819087591965063e-222,
1.6461145945762073e-218,
1.0902419946888113e-214,
1.2193933541752307e-211,
1.134276903471339e-207,
5.9688333253244175e-204,
5.67311209412967e-201,
4.121282512163238e-197,
1.7232711693791454e-193,
1.3916164336944924e-190,
7.896008557684633e-187,
2.623827738249029e-183,
1.7998966345091971e-180,
7.977257836743746e-177,
2.1069580605112442e-173,
1.2274860580461422e-170,
4.2499208336087735e-167,
8.92356765673105e-164,
4.414078714482218e-161,
1.19399240983854e-157,
1.9934653933464053e-154,
8.370172870759755e-152,
1.769011095491662e-148,
2.3490638517520287e-145,
8.369882593094965e-143,
1.3822468899352927e-139,
1.4602556651501059e-136,
4.413861213653756e-134,
5.696241846846968e-131,
4.789029011469954e-128,
1.227611536543043e-125,
1.238127749254181e-122,
8.286910955978269e-120,
1.816453503779961e-117,
1.4196305889495828e-114,
7.566823544376118e-112,
1.4526345665732377e-109,
8.589013958469697e-107,
3.6464304141581246e-104,
6.0874578375898365e-102,
2.7419057400268988e-99,
9.275211363929551e-97,
1.3381585506573132e-94,
4.619266050598122e-92,
1.2455531391372576e-89,
1.5444238019065183e-87,
4.1076164811640776e-85,
8.832422060039479e-83,
9.366417174621206e-81,
1.9284425108361593e-78,
3.308199634357488e-76,
2.987217774749749e-74,
4.7813272377619e-72,
6.546895542694674e-70,
5.01386298734379e-68,
6.262757572016024e-66,
6.848169283463627e-64,
4.4321270048756904e-62,
4.3354852483586696e-60,
3.787936153636911e-58,
2.064960170982087e-56,
1.5870019492096616e-54,
1.1085306515325207e-52,
5.07465479094339e-51,
3.0735047536851484e-49,
1.7174138497546534e-47,
6.583357779734459e-46,
3.151336370739219e-44,
1.4095791553500177e-42,
4.5123649624760346e-41,
1.7119343012929605e-39,
6.133894316887858e-38,
1.6355623662912352e-36,
4.931453950425548e-35,
1.4164385752346329e-33,
3.1379522056030814e-32,
7.539694001215332e-31,
1.7373472090240245e-29,
3.1898333394795165e-28,
6.124058053025845e-27,
1.1330115797770408e-25,
1.7197547799750305e-24,
2.645164964968553e-23,
3.932545307544117e-22,
4.9223554947964996e-21,
6.081344542540695e-20,
7.271375226082907e-19,
7.486858539907457e-18,
7.448099291086568e-17,
7.168487519931627e-16,
6.056499923561379e-15,
4.862843878104405e-14,
3.7704868232022443e-13,
2.6077019928529966e-12,
1.693342794847077e-11,
1.0585684443349417e-10,
5.979325890109996e-10,
3.1456639879122196e-09,
1.5866069876577182e-08,
7.303969390404848e-08,
3.117303446436826e-07,
1.2694132469024808e-06,
4.753731049931211e-06,
1.6474641098790166e-05,
5.419448726652532e-05,
0.00016483020672010724,
0.0004640766589280157,
0.0012338318538313835,
0.0030439046432489012,
0.006962780848393107,
0.014967643633200595,
0.029922938199832928,
0.05559265984962449,
0.09665830374904037,
0.15648860387315455,
0.23598381546840624,
0.33195213854204125,
0.43506310027781286,
0.5320529340673477,
0.6056463571168386,
0.6425065777813807,
0.6365349193130792,
0.5864627861802459,
0.5036393079239253,
0.40373359238330186,
0.30111829276190694,
0.20938676523234392,
0.1356489084107456,
0.0819110341811878,
0.04613782679568445,
0.024125036396816252,
0.011795847137814773,
0.0053846842398697,
0.0022697126500595224,
0.0008986909845210169,
0.00033266325534829364,
0.00011289753128085174,
3.620242626221446e-05,
1.0873450477077215e-05,
2.967590507696957e-06,
7.707221005141965e-07,
1.8795489084164763e-07,
4.120568213475952e-08,
8.66780131608724e-09,
1.7174993916086823e-09,
3.0213426440507495e-10,
5.147738047900595e-11,
8.293806506908903e-12,
1.1695352948718417e-12,
1.6139451048813152e-13,
2.1159476884437836e-14,
2.3894550204096556e-15,
2.6706298161388107e-16,
2.851332649168858e-17,
2.576178120284437e-18,
2.331819375593988e-19,
2.029070242811584e-20,
1.4654750865067167e-21,
1.0741103845887947e-22,
7.623956171982208e-24,
4.397974437265305e-25,
2.609771356747055e-26,
1.5122968327889706e-27,
6.962334002311575e-29,
3.344184633383014e-30,
1.5834912657305577e-31,
5.813655083137964e-33,
2.2597116000957406e-34,
8.751301802788624e-36,
2.5603948937773476e-37,
8.050741617911747e-39,
2.5525292850055857e-40,
5.94708792893869e-42,
1.5121224537390521e-43,
3.928961540724439e-45,
7.284878184353445e-47,
1.4971181712397808e-48,
3.1912870908882595e-50,
4.705926015592895e-52,
7.812567346009867e-54,
1.367761884822375e-55,
1.6030975208258373e-57,
2.148573917418882e-59,
3.0930706902904774e-61,
2.8797599984981886e-63,
3.1136857768233395e-65,
3.690492456711227e-67,
2.7278810924063497e-69,
2.377466492709984e-71,
2.3231437989926457e-73,
1.3625740258266482e-75,
9.563428524319065e-78,
7.715227593946453e-80,
3.5888409196291957e-82,
2.026344847409195e-84,
1.3517207829819662e-86,
4.98428155993595e-89,
2.2612586639333951e-91,
1.2493280094413272e-93,
3.650066200964439e-96,
1.328788059673696e-98,
6.091209998365277e-101,
1.4094343943122624e-103,
4.1110720789679417e-106,
1.5665896334487404e-108,
2.8696671854996758e-111,
6.695245450979264e-114,
2.1252937336457638e-116,
3.0807587518158134e-119,
5.738517351694725e-122,
1.5208366460802909e-124,
1.7438959750530325e-127,
2.5879425250696506e-130,
5.740295603789154e-133,
5.20496288561242e-136,
6.1393128785796325e-139,
1.1427796420942714e-141,
8.191180577079527e-145,
7.658965864707007e-148,
1.1999302075491526e-150,
6.796806756795694e-154,
5.0230193716995935e-157,
6.645132477893773e-160,
2.973656268263522e-163,
1.7311878139146936e-166,
1.9408615627645946e-169,
6.859650266448632e-173,
3.1341937793601447e-176,
2.9896337678381914e-179,
8.343274910716416e-183,
2.9792047952440938e-186,
2.4286411025674965e-189,
5.350477745989938e-193,
1.48602188838742e-196,
1.0404474537316912e-199,
1.8091230030634097e-203
],
"yaxis": "y2",
"zmax": 0.1,
"zmin": -0.1
},
{
"colorbar": {
"title": ""
},
"hoverinfo": "text",
"legendgroup": "fβ
[(Ξ²ββαΆ»β½ΒΉ β»ΒΉβΎt)*(πβ*πβ)]",
"line": {
"color": "rgba(165, 42, 42, 1.000)",
"dash": "dash",
"shape": "linear",
"width": 1
},
"mode": "lines",
"name": "fβ
[(Ξ²ββαΆ»β½ΒΉ β»ΒΉβΎt)*(πβ*πβ)]",
"showlegend": true,
"text": [
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null
],
"type": "scatter",
"x": [
10.090350448414474,
10.273507681793024,
10.459989534302535,
10.649856353504289,
10.84316958237171,
11.039991779173976,
11.240386637720556,
11.44441900797323,
11.652154917032231,
11.863661590503344,
12.079007474252842,
12.298262256557319,
12.521496890655566,
12.748783617709826,
12.98019599018381,
13.215808895645086,
13.455698580999508,
13.699942677165545,
13.948620224196498,
14.201811696858716,
14.459599030674116,
14.722065648435406,
14.989296487202608,
15.261378025789629,
15.538398312749738,
15.820446994869037,
16.10761534617715,
16.39999629748447,
16.69768446645562,
17.00077618822873,
17.309369546590553,
17.623564405717435,
17.94346244249247,
18.269167179409244,
18.600784018072822,
18.938420273308882,
19.282185207891956,
19.632190067904055,
19.988548118735103,
20.35137468173687,
20.72078717154221,
21.096905134061714,
21.479850285170084,
21.869746550094703,
22.266720103519187,
22.67089941041491,
23.08241526761366,
23.501400846134892,
23.927991734281377,
24.36232598151701,
24.804544143141136,
25.25478932577379,
25.713207233666548,
26.179946215854002,
26.65515731416115,
27.138994312082165,
27.6316137845464,
28.133175148587764,
28.6438407149338,
29.163775740531204,
29.693148482024785,
30.232130250207152,
30.78089546545674,
31.339621714182158,
31.90848980629108,
32.48768383370232,
33.07739122991996,
33.6778028306889,
34.289112935751355,
34.911519371724424,
35.54522355611888,
36.19043056252011,
36.847349186952165,
37.51619201544639,
38.19717549283665,
38.89051999280318,
39.59644988918792,
40.31519362860439,
41.04698380436544,
41.792057231753,
42.55065502465411,
43.323022673587985,
44.10941012514944,
44.910071862894306,
45.72526698969311,
46.55525931157958,
47.400317423121166,
48.26071479433915,
49.13672985920654,
50.02864610575234,
50.93675216780135,
51.861341918379274,
52.80271456481317,
53.76117474555825,
54.73703262878217,
55.73060401273886,
56.74221042796429,
57.77217924132721,
58.8208437619687,
59.888543349164614,
60.975623522145916,
62.08243607191253,
63.20933917507671,
64.35669750977287,
65.52488237367147,
66.71427180413495,
67.92525070055476,
69.15821094890896,
70.41355154858087,
71.69167874147956,
72.9930061435042,
74.31795487839462,
75.66695371401163,
77.04043920109092,
78.43885581451562,
79.8626560971533,
81.31230080630368,
82.78825906280481,
84.29100850284559,
85.82103543253415,
87.37883498527172,
88.9649112819833,
90.5797775942566,
92.22395651044235,
93.8979801047696,
95.60239010953076,
97.33773809039202,
99.10458562488608,
100.90350448414475,
102.73507681793026,
104.59989534302535,
106.4985635350429,
108.4316958237171,
110.39991779173975,
112.40386637720557,
114.44419007973231,
116.5215491703223,
118.63661590503344,
120.79007474252845,
122.98262256557321,
125.21496890655568,
127.48783617709826,
129.8019599018381,
132.15808895645085,
134.55698580999507,
136.99942677165546,
139.48620224196497,
142.01811696858715,
144.59599030674116,
147.22065648435404,
149.89296487202606,
152.6137802578963,
155.38398312749737,
158.20446994869036,
161.07615346177147,
163.9999629748447,
166.9768446645562,
170.0077618822873,
173.0936954659055,
176.23564405717434,
179.43462442492472,
182.69167179409243,
186.00784018072818,
189.3842027330888,
192.8218520789196,
196.32190067904054,
199.88548118735102,
203.51374681736868,
207.2078717154221,
210.96905134061717,
214.79850285170085,
218.69746550094703,
222.66720103519188,
226.70899410414913,
230.82415267613658,
235.01400846134894,
239.27991734281375,
243.6232598151701,
248.04544143141135,
252.5478932577379,
257.13207233666543,
261.79946215854,
266.5515731416115,
271.3899431208216,
276.31613784546397,
281.33175148587765,
286.438407149338,
291.637757405312,
296.9314848202479,
302.32130250207155,
307.8089546545674,
313.3962171418216,
319.08489806291084,
324.8768383370232,
330.7739122991996,
336.7780283068889,
342.89112935751353,
349.1151937172442,
355.4522355611888,
361.9043056252011,
368.4734918695216,
375.16192015446387,
381.97175492836647,
388.9051999280318,
395.96449889187926,
403.15193628604396,
410.4698380436544,
417.92057231753,
425.5065502465411,
433.23022673587985,
441.09410125149435,
449.100718628943,
457.2526698969311,
465.55259311579584,
474.0031742312117,
482.6071479433915,
491.36729859206537,
500.2864610575233,
509.36752167801353,
518.6134191837928,
528.0271456481318,
537.6117474555825,
547.3703262878216,
557.3060401273885,
567.4221042796428,
577.7217924132722,
588.2084376196871,
598.8854334916462,
609.7562352214592,
620.8243607191254,
632.093391750767,
643.5669750977287,
655.2488237367147,
667.1427180413494,
679.2525070055476,
691.5821094890896,
704.1355154858088,
716.9167874147956,
729.9300614350419,
743.1795487839462,
756.6695371401163,
770.4043920109092,
784.3885581451563,
798.626560971533,
813.1230080630369,
827.8825906280481,
842.9100850284559,
858.2103543253414,
873.7883498527173,
889.649112819833,
905.797775942566,
922.2395651044235,
938.9798010476961,
956.0239010953076,
973.3773809039202,
991.0458562488608
],
"xaxis": "x2",
"y": [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1.5732759659204021e-248,
2.865136835034455e-245,
5.598326113580841e-241,
5.874729022832347e-237,
9.09496696172356e-234,
1.3874839046037687e-229,
1.1566835126572157e-225,
1.5221543503495396e-222,
1.8131736083393208e-218,
1.2008872395556997e-214,
1.3431457659508242e-211,
1.2493911132915762e-207,
6.574591522190305e-204,
6.248858469585925e-201,
4.5395385644391197e-197,
1.8981605622266735e-193,
1.532847226323116e-190,
8.697349732022197e-187,
2.8901117962851175e-183,
1.982562505784135e-180,
8.786844745900319e-177,
2.3207866340437384e-173,
1.3520597729872665e-170,
4.681231986169679e-167,
9.82919258521041e-164,
4.862049736149758e-161,
1.315166959341652e-157,
2.1957759516031867e-154,
9.219635495915501e-152,
1.9485424901604065e-148,
2.587462983643151e-145,
9.219315758879804e-143,
1.5225267969178134e-139,
1.608452438367332e-136,
4.861810161843534e-134,
6.274335588452742e-131,
5.275052564250058e-128,
1.3521979859037573e-125,
1.3637814561009984e-122,
9.127923590220106e-120,
2.000799679852932e-117,
1.5637044504409351e-114,
8.334756762882346e-112,
1.6000578983689258e-109,
9.460686080099219e-107,
4.016495214477758e-104,
6.705254864615232e-102,
3.020173164585054e-99,
1.0216523510731468e-96,
1.4739640701928723e-94,
5.0880608922604226e-92,
1.3719604255433364e-89,
1.701162535667157e-87,
4.5244856107625845e-85,
9.728796907423441e-83,
1.0316985513448765e-80,
2.1241541004306202e-78,
3.64393845234029e-76,
3.2903811492739954e-74,
5.266569161654115e-72,
7.211319463226327e-70,
5.522704236044751e-68,
6.898345219963355e-66,
7.543168532208407e-64,
4.881929690999143e-62,
4.7754800653427166e-60,
4.1723619281906805e-58,
2.2745265102643113e-56,
1.7480618057644e-54,
1.2210319548934095e-52,
5.589665609361849e-51,
3.385425123408298e-49,
1.891708801581497e-47,
7.251482138485623e-46,
3.471155627470285e-44,
1.5526329283313823e-42,
4.970310747571603e-41,
1.8856731509110673e-39,
6.75640403673532e-38,
1.801550467460475e-36,
5.431931764115308e-35,
1.560188489253011e-33,
3.456413145340268e-32,
8.304873927369243e-31,
1.9136651350420328e-29,
3.5135595329765977e-28,
6.745569521265967e-27,
1.2479973758591597e-25,
1.8942873054769956e-24,
2.913614471305719e-23,
4.331647012140946e-22,
5.421909934725303e-21,
6.6985211504014e-20,
8.009324320254985e-19,
8.246676360599879e-18,
8.203983557029185e-17,
7.895994863101304e-16,
6.671155128867437e-15,
5.356358670474777e-14,
4.1531417198700846e-13,
2.8723494995026073e-12,
1.8651948507137323e-11,
1.1659992397935515e-10,
6.586148944508096e-10,
3.4649075722788668e-09,
1.7476267608017636e-08,
8.045226364213006e-08,
3.433668808288298e-07,
1.3982420209040605e-06,
5.236172323165322e-06,
1.8146600817228667e-05,
5.969451601541946e-05,
0.00018155830807086435,
0.0005111743453263036,
0.0013590495837085988,
0.0033528209904859782,
0.007669411665842796,
0.016486662899513577,
0.03295972346437623,
0.06123458475421324,
0.10646785221518915,
0.17237014208097676,
0.2599330736829342,
0.3656409212453299,
0.4792162914934256,
0.5860493196944037,
0.6671115087183952,
0.7077125577138437,
0.7011348543337653,
0.6459810572598257,
0.5547520836391356,
0.44470724998212635,
0.3316778450437379,
0.23063677213345496,
0.1494154912062625,
0.09022392845459581,
0.050820210310815565,
0.026573410769251085,
0.012992970713437474,
0.005931158975894991,
0.002500058677057859,
0.000989896317397939,
0.0003664242070686813,
0.0001243551480799574,
3.987649709976416e-05,
1.1976962905001612e-05,
3.268761972370269e-06,
8.489402722147429e-07,
2.070298439460171e-07,
4.538751773815595e-08,
9.547469319840617e-09,
1.8918030248103318e-09,
3.3279692446644827e-10,
5.67016585713494e-11,
9.135518949014434e-12,
1.288227768388695e-12,
1.7777393379059562e-13,
2.330688591155216e-14,
2.6319533254828372e-15,
2.9416636704528097e-16,
3.1407054679569386e-17,
2.8376263678553356e-18,
2.5684684196180106e-19,
2.234994225708688e-20,
1.6142015624476302e-21,
1.183118482878768e-22,
8.39768760189669e-24,
4.844311086284616e-25,
2.874628876656008e-26,
1.6657751010913355e-27,
7.668919470752191e-29,
3.683575456194203e-30,
1.7441948340161891e-31,
6.403664726298915e-33,
2.489042651861459e-34,
9.639444009372735e-36,
2.8202413511308685e-37,
8.867786165831724e-39,
2.8115774863638156e-40,
6.550639253642664e-42,
1.6655830248578813e-43,
4.327699540052858e-45,
8.024197651462494e-47,
1.6490560047285504e-48,
3.51516082106195e-50,
5.183515705640888e-52,
8.605440333153465e-54,
1.5065717540101453e-55,
1.7657908665246558e-57,
2.3666259539076025e-59,
3.406976745629566e-61,
3.1720178199212646e-63,
3.4296839927180594e-65,
4.0650289757055894e-67,
3.004725199409589e-69,
2.61874811966089e-71,
2.5589123859235715e-73,
1.500857395455868e-75,
1.0533990927891025e-77,
8.49822187456911e-80,
3.9530611425477057e-82,
2.2319922384641897e-84,
1.4889026909925733e-86,
5.4901206822328675e-89,
2.490746722361833e-91,
1.3761183956098156e-93,
4.0204999858979725e-96,
1.4636425974323134e-98,
6.709387820434158e-101,
1.5524734759493684e-103,
4.528291906362931e-106,
1.7255779080183136e-108,
3.1609007189471863e-111,
7.374724938997852e-114,
2.3409831372083358e-116,
3.3934153070861544e-119,
6.320901501859826e-122,
1.6751815932826968e-124,
1.920878514821369e-127,
2.850584705230299e-130,
6.322860223188958e-133,
5.7331982643698045e-136,
6.762372511279591e-139,
1.2587567682225912e-141,
9.022477835041553e-145,
8.436250318668557e-148,
1.321707365541812e-150,
7.486593383601638e-154,
5.532789873166524e-157,
7.31952615725239e-160,
3.275443327975789e-163,
1.9068806422173105e-166,
2.1378335230366943e-169,
7.555814684192475e-173,
3.452273288191175e-176,
3.2930423339329056e-179,
9.190007746165005e-183,
3.2815549575789044e-186,
2.6751162803687965e-189,
5.893480972102932e-193,
1.6368335948885183e-196,
1.1460392066178312e-199,
1.992725229581391e-203
],
"yaxis": "y2",
"zmax": 0.1,
"zmin": -0.1
},
{
"colorbar": {
"title": ""
},
"hoverinfo": "text",
"legendgroup": "fβ
[(Ξ²ββαΆ»β½Β² β»Β²βΎt)*(πβ*πβ)]",
"line": {
"color": "rgba(165, 42, 42, 1.000)",
"dash": "dot",
"shape": "linear",
"width": 1
},
"mode": "lines",
"name": "fβ
[(Ξ²ββαΆ»β½Β² β»Β²βΎt)*(πβ*πβ)]",
"showlegend": true,
"text": [
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null
],
"type": "scatter",
"x": [
10.090350448414474,
10.273507681793024,
10.459989534302535,
10.649856353504289,
10.84316958237171,
11.039991779173976,
11.240386637720556,
11.44441900797323,
11.652154917032231,
11.863661590503344,
12.079007474252842,
12.298262256557319,
12.521496890655566,
12.748783617709826,
12.98019599018381,
13.215808895645086,
13.455698580999508,
13.699942677165545,
13.948620224196498,
14.201811696858716,
14.459599030674116,
14.722065648435406,
14.989296487202608,
15.261378025789629,
15.538398312749738,
15.820446994869037,
16.10761534617715,
16.39999629748447,
16.69768446645562,
17.00077618822873,
17.309369546590553,
17.623564405717435,
17.94346244249247,
18.269167179409244,
18.600784018072822,
18.938420273308882,
19.282185207891956,
19.632190067904055,
19.988548118735103,
20.35137468173687,
20.72078717154221,
21.096905134061714,
21.479850285170084,
21.869746550094703,
22.266720103519187,
22.67089941041491,
23.08241526761366,
23.501400846134892,
23.927991734281377,
24.36232598151701,
24.804544143141136,
25.25478932577379,
25.713207233666548,
26.179946215854002,
26.65515731416115,
27.138994312082165,
27.6316137845464,
28.133175148587764,
28.6438407149338,
29.163775740531204,
29.693148482024785,
30.232130250207152,
30.78089546545674,
31.339621714182158,
31.90848980629108,
32.48768383370232,
33.07739122991996,
33.6778028306889,
34.289112935751355,
34.911519371724424,
35.54522355611888,
36.19043056252011,
36.847349186952165,
37.51619201544639,
38.19717549283665,
38.89051999280318,
39.59644988918792,
40.31519362860439,
41.04698380436544,
41.792057231753,
42.55065502465411,
43.323022673587985,
44.10941012514944,
44.910071862894306,
45.72526698969311,
46.55525931157958,
47.400317423121166,
48.26071479433915,
49.13672985920654,
50.02864610575234,
50.93675216780135,
51.861341918379274,
52.80271456481317,
53.76117474555825,
54.73703262878217,
55.73060401273886,
56.74221042796429,
57.77217924132721,
58.8208437619687,
59.888543349164614,
60.975623522145916,
62.08243607191253,
63.20933917507671,
64.35669750977287,
65.52488237367147,
66.71427180413495,
67.92525070055476,
69.15821094890896,
70.41355154858087,
71.69167874147956,
72.9930061435042,
74.31795487839462,
75.66695371401163,
77.04043920109092,
78.43885581451562,
79.8626560971533,
81.31230080630368,
82.78825906280481,
84.29100850284559,
85.82103543253415,
87.37883498527172,
88.9649112819833,
90.5797775942566,
92.22395651044235,
93.8979801047696,
95.60239010953076,
97.33773809039202,
99.10458562488608,
100.90350448414475,
102.73507681793026,
104.59989534302535,
106.4985635350429,
108.4316958237171,
110.39991779173975,
112.40386637720557,
114.44419007973231,
116.5215491703223,
118.63661590503344,
120.79007474252845,
122.98262256557321,
125.21496890655568,
127.48783617709826,
129.8019599018381,
132.15808895645085,
134.55698580999507,
136.99942677165546,
139.48620224196497,
142.01811696858715,
144.59599030674116,
147.22065648435404,
149.89296487202606,
152.6137802578963,
155.38398312749737,
158.20446994869036,
161.07615346177147,
163.9999629748447,
166.9768446645562,
170.0077618822873,
173.0936954659055,
176.23564405717434,
179.43462442492472,
182.69167179409243,
186.00784018072818,
189.3842027330888,
192.8218520789196,
196.32190067904054,
199.88548118735102,
203.51374681736868,
207.2078717154221,
210.96905134061717,
214.79850285170085,
218.69746550094703,
222.66720103519188,
226.70899410414913,
230.82415267613658,
235.01400846134894,
239.27991734281375,
243.6232598151701,
248.04544143141135,
252.5478932577379,
257.13207233666543,
261.79946215854,
266.5515731416115,
271.3899431208216,
276.31613784546397,
281.33175148587765,
286.438407149338,
291.637757405312,
296.9314848202479,
302.32130250207155,
307.8089546545674,
313.3962171418216,
319.08489806291084,
324.8768383370232,
330.7739122991996,
336.7780283068889,
342.89112935751353,
349.1151937172442,
355.4522355611888,
361.9043056252011,
368.4734918695216,
375.16192015446387,
381.97175492836647,
388.9051999280318,
395.96449889187926,
403.15193628604396,
410.4698380436544,
417.92057231753,
425.5065502465411,
433.23022673587985,
441.09410125149435,
449.100718628943,
457.2526698969311,
465.55259311579584,
474.0031742312117,
482.6071479433915,
491.36729859206537,
500.2864610575233,
509.36752167801353,
518.6134191837928,
528.0271456481318,
537.6117474555825,
547.3703262878216,
557.3060401273885,
567.4221042796428,
577.7217924132722,
588.2084376196871,
598.8854334916462,
609.7562352214592,
620.8243607191254,
632.093391750767,
643.5669750977287,
655.2488237367147,
667.1427180413494,
679.2525070055476,
691.5821094890896,
704.1355154858088,
716.9167874147956,
729.9300614350419,
743.1795487839462,
756.6695371401163,
770.4043920109092,
784.3885581451563,
798.626560971533,
813.1230080630369,
827.8825906280481,
842.9100850284559,
858.2103543253414,
873.7883498527173,
889.649112819833,
905.797775942566,
922.2395651044235,
938.9798010476961,
956.0239010953076,
973.3773809039202,
991.0458562488608
],
"xaxis": "x2",
"y": [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
3.4014950734334996e-248,
6.194557750954432e-245,
1.210383880979135e-240,
1.270143462544449e-236,
1.9663737312127937e-233,
2.9998040828246994e-229,
2.5008030091678994e-225,
3.290967786881761e-222,
3.9201648214575713e-218,
2.5963735019038184e-214,
2.9039429856871925e-211,
2.7012411100850096e-207,
1.4214569571387848e-203,
1.3510319714599338e-200,
9.814691380966712e-197,
4.1039105286417724e-193,
3.314086277046756e-190,
1.880407055484024e-186,
6.248554767049204e-183,
4.286391416558319e-180,
1.8997562895279827e-176,
5.017647554014364e-173,
2.9232154793092955e-170,
1.012103908244734e-166,
2.12511669145487e-163,
1.0511975382924509e-160,
2.843451517627441e-157,
4.747368702967826e-154,
1.993327642290815e-151,
4.2128385764661194e-148,
5.594214099879671e-145,
1.993258513671598e-142,
3.2917730335101606e-139,
3.477548226421826e-136,
1.0511457412244227e-133,
1.3565402418580048e-130,
1.1404906512318214e-127,
2.923514301998202e-125,
2.9485582978785626e-122,
1.9734991060291822e-119,
4.3258210265518024e-117,
3.380801016285266e-114,
1.8020127861436616e-111,
3.45939884445271e-109,
2.0454438884110249e-106,
8.683847576939683e-104,
1.449706973357442e-101,
6.529753433462085e-99,
2.20885942086074e-96,
3.186778182456965e-94,
1.1000621908203173e-91,
2.9662416063803852e-89,
3.677991725244619e-87,
9.782146202065816e-85,
2.1034106836861306e-82,
2.230579768384783e-80,
4.592518963194965e-78,
7.878362704332755e-76,
7.113955536990774e-74,
1.1386565005321909e-71,
1.55912046954644e-69,
1.1940340828855556e-67,
1.4914539971899662e-65,
1.630867766124868e-63,
1.0554956760600804e-61,
1.032480776889016e-59,
9.02083858823795e-58,
4.917631036543387e-56,
3.7793901064816147e-54,
2.6399273039456963e-52,
1.2085114400932087e-50,
7.319444984983604e-49,
4.089961525081738e-47,
1.567803824850255e-45,
7.504798281879118e-44,
3.356863875741063e-42,
1.0746040674057907e-40,
4.0769121704452035e-39,
1.4607656598654314e-37,
3.895035055737107e-36,
1.1744086565293632e-34,
3.3731993463187955e-33,
7.4729243567562e-32,
1.795551979522328e-30,
4.1374321289137766e-29,
7.596477477899683e-28,
1.4584231877378234e-26,
2.698227785587135e-25,
4.095536369220563e-24,
6.299368632529133e-23,
9.36522027337435e-22,
1.1722418908737938e-20,
1.4482511133417538e-19,
1.731652793725879e-18,
1.782969397639689e-17,
1.773739016945999e-16,
1.7071504433097123e-15,
1.4423344534903596e-14,
1.1580694057386093e-13,
8.979283612932251e-13,
6.210151863612472e-12,
4.032637142578253e-11,
2.5209440401415455e-10,
1.4239557250553572e-09,
7.4912896988889e-09,
3.778449519242514e-08,
1.7394149809260089e-07,
7.423750052879047e-07,
3.023063625579781e-06,
1.132084564100994e-05,
3.923378645351438e-05,
0.00012906229201731763,
0.00039253742116544344,
0.0011051824695458333,
0.002938327771906313,
0.00724895334848043,
0.01658162112851951,
0.03564492425030253,
0.07126043962682542,
0.13239199153681125,
0.23018839836986,
0.3726721832634534,
0.5619872728670797,
0.7905325061862674,
1.0360876857801242,
1.267065611444308,
1.4423257962940346,
1.5301071335328935,
1.5158858359814786,
1.3966407873746358,
1.1993995461384674,
0.961477549203783,
0.7171027717462723,
0.49864732008767176,
0.32304317121848275,
0.1950682873138426,
0.10987563450253544,
0.057452937548087744,
0.02809140089111316,
0.012823438782054348,
0.00540524196486532,
0.002140201413977114,
0.0007922260061995731,
0.0002688615555775097,
8.62148226813347e-05,
2.5894745231314318e-05,
7.067213881157565e-06,
1.835447954541397e-06,
4.476080544611282e-07,
9.812990303414067e-08,
2.0642068244013595e-08,
4.090165240040606e-09,
7.195222729816473e-10,
1.2259159642925062e-10,
1.9751412575702656e-11,
2.7852077464813146e-12,
3.8435542973533095e-13,
5.0390560411848496e-14,
5.690404267314493e-15,
6.360012292496802e-16,
6.790349822773354e-17,
6.135078854305247e-18,
5.553146977929623e-19,
4.832160417230357e-20,
3.489978097378542e-21,
2.5579566318779283e-22,
1.8156187232780984e-23,
1.0473623605211858e-24,
6.215079981962805e-26,
3.601482462420734e-27,
1.6580556980072493e-28,
7.964059731590068e-30,
3.7710295355229457e-31,
1.3845017969039305e-32,
5.381424811202486e-34,
2.0840921757383737e-35,
6.0974916477243354e-37,
1.9172561971791062e-38,
6.078759973205438e-40,
1.416278366400275e-41,
3.601067184760634e-43,
9.356685656974558e-45,
1.7348684764111657e-46,
3.565335006321382e-48,
7.599939536465034e-50,
1.1206999609561633e-51,
1.8605358202890384e-53,
3.2572774961585146e-55,
3.8177211521080144e-57,
5.116754274045682e-59,
7.366040584483057e-61,
6.85804856937053e-63,
7.4151346981515156e-65,
8.788779803254528e-67,
6.4963542215138e-69,
5.661854004347277e-71,
5.5324863931134136e-73,
3.2449227898696937e-75,
2.2774973381006535e-77,
1.8373546958991762e-79,
8.546700192862236e-82,
4.825669982593419e-84,
3.21907616841415e-86,
1.1869893685336623e-88,
5.385109090081311e-91,
2.9752313291009884e-93,
8.692506077133651e-96,
3.164462683138269e-98,
1.4506005374340135e-100,
3.356519132349811e-103,
9.790375588399215e-106,
3.7307788843746574e-108,
6.834012885222729e-111,
1.59444948574251e-113,
5.061313323722332e-116,
7.336720129970745e-119,
1.366608006730486e-121,
3.6218197316222555e-124,
4.153027788107529e-127,
6.1630953763240275e-130,
1.3670314912999827e-132,
1.239543860943849e-135,
1.4620560715413245e-138,
2.7214900872494755e-141,
1.9507012482773482e-144,
1.823956160190571e-147,
2.857592176958675e-150,
1.618635958518749e-153,
1.1962146440665103e-156,
1.582515254988729e-159,
7.08165927959263e-163,
4.122763743062259e-166,
4.622094504682853e-169,
1.6336019224079033e-172,
7.463973794996921e-176,
7.119709140746799e-179,
1.986921986385795e-182,
7.094872904179773e-186,
5.783724563041208e-189,
1.274197720312498e-192,
3.5389095935159225e-196,
2.4777895294368316e-199,
4.308363693309402e-203
],
"yaxis": "y2",
"zmax": 0.1,
"zmin": -0.1
},
{
"colorbar": {
"title": ""
},
"hoverinfo": "text",
"legendgroup": "f*Dβ",
"line": {
"color": "rgba(128, 128, 128, 1.000)",
"dash": "dashdot",
"shape": "linear",
"width": 1
},
"mode": "lines",
"name": "f*Dβ",
"showlegend": true,
"text": [
null,
null
],
"type": "scatter",
"x": [
125.99210498948732,
125.99210498948732
],
"xaxis": "x2",
"y": [
0,
1.6066124902095382
],
"yaxis": "y2",
"zmax": 0.1,
"zmin": -0.1
}
],
"layout": {
"annotations": [],
"height": 288,
"legend": {
"bgcolor": "rgba(255, 255, 255, 1.000)",
"bordercolor": "rgba(0, 0, 0, 1.000)",
"font": {
"color": "rgba(0, 0, 0, 1.000)",
"family": "Nimbus Sans L",
"size": 14
},
"tracegroupgap": 0,
"x": 1,
"y": 1
},
"margin": {
"b": 20,
"l": 0,
"r": 0,
"t": 20
},
"paper_bgcolor": "rgba(255, 255, 255, 1.000)",
"plot_bgcolor": "rgba(255, 255, 255, 1.000)",
"showlegend": true,
"width": 792,
"xaxis1": {
"anchor": "y1",
"domain": [
0.09890572390572391,
0.4971334075664785
],
"gridcolor": "rgba(0, 0, 0, 0.100)",
"gridwidth": 0.5,
"linecolor": "rgba(0, 0, 0, 1.000)",
"mirror": false,
"range": [
1.6020599913279623,
2.6020599913279625
],
"showgrid": true,
"showline": true,
"showticklabels": true,
"tickangle": 0,
"tickcolor": "rgb(0, 0, 0)",
"tickfont": {
"color": "rgba(0, 0, 0, 1.000)",
"family": "Nimbus Sans L",
"size": 17
},
"tickmode": "array",
"ticks": "inside",
"ticktext": [
"10^1.7781513",
"10^1.9030900",
"10^2.0000000",
"10^2.0791812",
"10^2.1461280",
"10^2.2041200"
],
"tickvals": [
60,
79.99999999999999,
100,
119.99999999999996,
140.00000000000006,
159.99999999999991
],
"title": "Diameter (nm)",
"titlefont": {
"color": "rgba(0, 0, 0, 1.000)",
"family": "Nimbus Sans L",
"size": 17
},
"type": "log",
"visible": true,
"zeroline": false,
"zerolinecolor": "rgba(0, 0, 0, 1.000)"
},
"xaxis2": {
"anchor": "y2",
"domain": [
0.5968013468013469,
0.9950290304621014
],
"gridcolor": "rgba(0, 0, 0, 0.100)",
"gridwidth": 0.5,
"linecolor": "rgba(0, 0, 0, 1.000)",
"mirror": false,
"range": [
1.954242509439325,
2.255272505103306
],
"showgrid": true,
"showline": true,
"showticklabels": true,
"tickangle": 0,
"tickcolor": "rgb(0, 0, 0)",
"tickfont": {
"color": "rgba(0, 0, 0, 1.000)",
"family": "Nimbus Sans L",
"size": 17
},
"tickmode": "array",
"ticks": "inside",
"ticktext": [
"10^2.0000000",
"10^2.0791812",
"10^2.1461280",
"10^2.2041200"
],
"tickvals": [
100,
119.99999999999996,
140.00000000000006,
159.99999999999991
],
"title": "Diameter (nm)",
"titlefont": {
"color": "rgba(0, 0, 0, 1.000)",
"family": "Nimbus Sans L",
"size": 17
},
"type": "log",
"visible": true,
"zeroline": false,
"zerolinecolor": "rgba(0, 0, 0, 1.000)"
},
"yaxis1": {
"anchor": "x1",
"domain": [
0.1294109069699621,
0.9863298337707787
],
"gridcolor": "rgba(0, 0, 0, 0.100)",
"gridwidth": 0.5,
"linecolor": "rgba(0, 0, 0, 1.000)",
"mirror": false,
"range": [
-1.873897943466776,
64.33716272569265
],
"showgrid": true,
"showline": true,
"showticklabels": true,
"tickangle": 0,
"tickcolor": "rgb(0, 0, 0)",
"tickfont": {
"color": "rgba(0, 0, 0, 1.000)",
"family": "Nimbus Sans L",
"size": 17
},
"tickmode": "array",
"ticks": "inside",
"ticktext": [
"0",
"10",
"20",
"30",
"40",
"50",
"60"
],
"tickvals": [
0,
10,
20,
30,
40,
50,
60
],
"title": "dN/dlnD (mβ»Β³) Γ 10β»ΒΉβ°",
"titlefont": {
"color": "rgba(0, 0, 0, 1.000)",
"family": "Nimbus Sans L",
"size": 17
},
"type": "-",
"visible": true,
"zeroline": false,
"zerolinecolor": "rgba(0, 0, 0, 1.000)"
},
"yaxis2": {
"anchor": "x2",
"domain": [
0.1294109069699621,
0.9863298337707787
],
"gridcolor": "rgba(0, 0, 0, 0.100)",
"gridwidth": 0.5,
"linecolor": "rgba(0, 0, 0, 1.000)",
"mirror": false,
"range": [
-0.04819837470628614,
1.6548108649158244
],
"showgrid": true,
"showline": true,
"showticklabels": true,
"tickangle": 0,
"tickcolor": "rgb(0, 0, 0)",
"tickfont": {
"color": "rgba(0, 0, 0, 1.000)",
"family": "Nimbus Sans L",
"size": 17
},
"tickmode": "array",
"ticks": "inside",
"ticktext": [
"0.0",
"0.5",
"1.0",
"1.5"
],
"tickvals": [
0,
0.5,
1,
1.5
],
"title": "",
"titlefont": {
"color": "rgba(0, 0, 0, 1.000)",
"family": "Nimbus Sans L",
"size": 17
},
"type": "-",
"visible": true,
"zeroline": false,
"zerolinecolor": "rgba(0, 0, 0, 1.000)"
}
}
},
"image/svg+xml": [
"4 5 6 7 8 9 100 2 3 4 0 10 20 30 40 50 60 100 120 140 160 180 0.0 0.5 1.0 1.5 πβ = ππ (Nβ,Dβ,Ο) πβ = ππ (Nβ,Dβ,Ο) πββ (partMC) fβ
[(Ξ²ββα΅t)*(πβ*πβ)] fβ
[(Ξ²ββαΆ»β½ΒΉ β»ΒΉβΎt)*(πβ*πβ)] fβ
[(Ξ²ββαΆ»β½Β² β»Β²βΎt)*(πβ*πβ)] f*Dβ Diameter (nm) Diameter (nm) dN/dlnD (mβ»Β³) Γ 10β»ΒΉβ° "
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"figure(\"Nimbus Sans L\", 2, 5.5, 2, 8)\n",
"pre = 1e-10\n",
"p1 = plot(πβ.Dp, pre*πβ.S, xlim = (40, 400), color = :black, label = \"πβ = ππ (Nβ,Dβ,Ο)\", \n",
" xlabel = \"Diameter (nm)\", ylabel = \"dN/dlnD (mβ»Β³) Γ 10β»ΒΉβ°\", t = :steppre, \n",
" xticks = [60,80,100,120,140,160])\n",
"\n",
"p1 = plot!(πβ.Dp, pre*πβ.S, color = RGBA(0.8,0,0,1), label = \"πβ = ππ (Nβ,Dβ,Ο)\", t = :steppre)\n",
"\n",
"p2 = plot(πββ.Dp, pre*πββ.S, color = RGBA(0.0,0.0,0.8), xlim = (90, 180), label = \"πββ (partMC)\", \n",
" xlabel = \"Diameter (nm)\", t = :steppre, lw = 1.5, xticks = [60,80,100,120,140, 160])\n",
"p2 = plot!(πβα΅.Dp,pre*πβα΅.S, color = :brown, label = \"fβ
[(Ξ²ββα΅t)*(πβ*πβ)]\", lw = 1)\n",
"p2 = plot!(πβαΆ»ΒΉ.Dp,pre*πβαΆ»ΒΉ.S, color = :brown, label = \"fβ
[(Ξ²ββαΆ»β½ΒΉ β»ΒΉβΎt)*(πβ*πβ)]\", lw = 1, ls = :dash)\n",
"p2 = plot!(πβαΆ»Β².Dp,pre*πβαΆ»Β².S, color = :brown, label = \"fβ
[(Ξ²ββαΆ»β½Β² β»Β²βΎt)*(πβ*πβ)]\", lw = 1, ls = :dot)\n",
"p2 = plot!([f*Dm, f*Dm], [0,1.05*maximum(pre*πβαΆ»Β².S)], color = :grey, ls = :dashdot, label = \"f*Dβ\") \n",
"\n",
"plot(p1,p2, layout = grid(1,2), left_margin = 35px, xaxis = :log10, fmt = :svg)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Figure 3. Comparison of assumed PartMC inferred size distribution and size distribution obtained from πβα΅ = f$β
$((Ξ²ββ$*$t)$*$(πβ$.*$πβ)). Left: Input size distributions to PartMC. Right: Blue histogram shows output size distribution from PartMC. The dark-red solid line corresponds to the analytical prediction. Note that the diameter is shifted by f$*$Dm due to the larger sphere equivalent volume of the dimers. Enhancement of concentration due to +1/-1 charge on the input size distribution is negligible and approximately a factor of two for +2/-2 charges. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The DMA particle size distribution is not lognormal. To test of the analytical approximation holds, the model as also initialized with DMA type size distributions."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"t,p = 295.15, 1e5 # Temperature [K], Pressure [Pa]\n",
"qsa,Ξ² = 1.66e-5, 1/3 # Qsample [m3 s-1], Sample-to-sheath ratio,\n",
"rβ,rβ,l = 9.37e-3,1.961e-2,0.44369 # DMA geometry [m]\n",
"leff = 13.0 # DMA effective diffusion length [m]\n",
"n = 6 # Upper number of charges\n",
"Ξ = DMAconfig(t,p,qsa,qsa/Ξ²,rβ,rβ,l,leff,:-,n,:cylindrical) # Specify DMA with negative polarity\n",
"bins,zβ,zβ = 512, dtoz(Ξ,500e-9),dtoz(Ξ,20e-9) # bins, upper, lower mobility limit\n",
"Ξ΄ = setupDMA(Ξ, zβ, zβ, bins); # Compute matrices"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The API for Triangular size distributions is\n",
"```julia\n",
"ics = InitialConditionTriangular(N1, N2, Dm, Ξ, Ξ΄)\n",
"```\n",
"where N1, N2, Dm are as above, and Ξ, Ξ΄ define the DMA. The width of the distribution is set by Ξ²."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"repeat t_sim n_part n_coag n_emit n_dil_in n_dil_out n_nuc t_wall t_rem\n",
" 1 0s 999372 0 0 0 0 0 0s 0s\n",
"repeat t_sim n_part n_coag n_emit n_dil_in n_dil_out n_nuc t_wall t_rem\n",
" 1 10s 998722 2984 0 0 0 0 19s 97s\n",
"repeat t_sim n_part n_coag n_emit n_dil_in n_dil_out n_nuc t_wall t_rem\n",
" 1 20s 998050 2965 0 0 0 0 20s 40s\n",
"repeat t_sim n_part n_coag n_emit n_dil_in n_dil_out n_nuc t_wall t_rem\n",
" 1 30s 997444 2951 0 0 0 0 21s 21s\n",
"repeat t_sim n_part n_coag n_emit n_dil_in n_dil_out n_nuc t_wall t_rem\n",
" 1 40s 996810 2938 0 0 0 0 21s 11s\n",
"repeat t_sim n_part n_coag n_emit n_dil_in n_dil_out n_nuc t_wall t_rem\n",
" 1 50s 996200 2908 0 0 0 0 22s 4s\n",
"repeat t_sim n_part n_coag n_emit n_dil_in n_dil_out n_nuc t_wall t_rem\n",
" 1 60s 995468 2994 0 0 0 0 23s 0s\n"
]
}
],
"source": [
"cd(\"PartMC\") # Descend into directory PartMC\n",
"Random.seed!(30) # Pick a random seed \n",
"ics = InitialConditionTriangular(1e11, 1.5e11, 100.0, Ξ, Ξ΄) # Set initial conditions\n",
"x = runSimulation(ics,1,\"triangular\"; verbose = true, repeat = 1) # Run simulations\n",
"cd(\"..\") # Come back "
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"Input PartMC Float64 String 2 rows Γ 2 columns
1 1.0e11 1.0E+11 2 1.5e11 1.5E+11
"
],
"text/latex": [
"\\begin{tabular}{r|cc}\n",
"\t& Input & PartMC\\\\\n",
"\t\\hline\n",
"\t& Float64 & String\\\\\n",
"\t\\hline\n",
"\t1 & 1.0e11 & 1.0E+11 \\\\\n",
"\t2 & 1.5e11 & 1.5E+11 \\\\\n",
"\\end{tabular}\n"
],
"text/plain": [
"2Γ2 DataFrame\n",
"β Row β Input β PartMC β\n",
"β β \u001b[90mFloat64\u001b[39m β \u001b[90mString\u001b[39m β\n",
"βββββββΌββββββββββΌββββββββββ€\n",
"β 1 β 1.0e11 β 1.0E+11 β\n",
"β 2 β 1.5e11 β 1.5E+11 β"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"r = 1 # repeat number\n",
"Dm = ics.Dm # recover Dm from initial condition\n",
"Nβ = ics.Nt1 # recover Nβ from initial condition\n",
"Nβ = ics.Nt2 # recover Nβ from initial condition\n",
"t = x[r].r[end,end].t # end time of simulation. \n",
"πβ = (π0 + x[r].s1) # reconstructed size distribution for πβ from model output \n",
"πβ = (π0 + x[r].s2) # reconstructed size distribution for πβ from model output \n",
"πββ = (π0 + x[r].r[end,1].sc12) # reconstructed dimer size distribution πββ from model output \n",
"\n",
"DataFrame(Input = [Nβ,Nβ], PartMC = [@sprintf(\"%.1E\", sum(πβ.N)), @sprintf(\"%.1E\", sum(πβ.N))])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Table 3. Comparison of assumed input number concentration and reconstructed output number concentration from PartMC simulation."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"PartMC Analytical String String 1 rows Γ 2 columns
1 1.046E+09 1.097E+09
"
],
"text/latex": [
"\\begin{tabular}{r|cc}\n",
"\t& PartMC & Analytical\\\\\n",
"\t\\hline\n",
"\t& String & String\\\\\n",
"\t\\hline\n",
"\t1 & 1.046E+09 & 1.097E+09 \\\\\n",
"\\end{tabular}\n"
],
"text/plain": [
"1Γ2 DataFrame\n",
"β Row β PartMC β Analytical β\n",
"β β \u001b[90mString\u001b[39m β \u001b[90mString\u001b[39m β\n",
"βββββββΌββββββββββββΌβββββββββββββ€\n",
"β 1 β 1.046E+09 β 1.097E+09 β"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Ξ²ββ = Ξ²12(Dm*1e-9, Dm*1e-9, 0,0) # Zebel-Brownian coagulation rate for no charge\n",
"Ξ²ββαΆ»β½ΒΉβ»ΒΉβΎ = Ξ²12(Dm*1e-9, Dm*1e-9, 1,-1) # +1 -1 charge\n",
"Ξ²ββαΆ»β½Β²β»Β²βΎ = Ξ²12(Dm*1e-9, Dm*1e-9, 2,-2) # +1 -1 charge\n",
"f = (Dm^3.0+Dm^3.0)^(1.0/3.0)/Dm \t # diameter shift for larger particles\n",
"\n",
"πβα΅ = fβ
((Ξ²ββ*t)*(πβ*πβ)) # Semi-analytical estimate using Browninan Kernel\n",
"πβαΆ»ΒΉ = fβ
((Ξ²ββαΆ»β½ΒΉβ»ΒΉβΎ*t)*(πβ*πβ)) # Estimated enhancement for +1/-1 charged case\n",
"πβαΆ»Β² = fβ
((Ξ²ββαΆ»β½Β²β»Β²βΎ*t)*(πβ*πβ)) # Estimated enhancement for +2/-2 charged caseprintln()\n",
"\n",
"DataFrame(PartMC = [@sprintf(\"%.3E\",sum(πββ.N))], Analytical = [@sprintf(\"%.3E\",sum(πβα΅.N))])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Table 4. Comparison of assumed PartMC inferred number concentration and number concentration obtained from f$β
$((Ξ²ββ$*$t)$*$(πβ$.*$πβ))."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.plotly.v1+json": {
"data": [
{
"colorbar": {
"title": ""
},
"hoverinfo": "text",
"legendgroup": "πβ = Ξ(Nβ,Dβ,Ξ²)",
"line": {
"color": "rgba(0, 0, 0, 1.000)",
"dash": "solid",
"shape": "linear",
"width": 1
},
"mode": "lines",
"name": "πβ = Ξ(Nβ,Dβ,Ξ²)",
"showlegend": true,
"text": [
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null
],
"type": "scatter",
"x": [
10.090350448414474,
10.090350448414474,
10.273507681793024,
10.273507681793024,
10.459989534302535,
10.459989534302535,
10.649856353504289,
10.649856353504289,
10.84316958237171,
10.84316958237171,
11.039991779173976,
11.039991779173976,
11.240386637720556,
11.240386637720556,
11.44441900797323,
11.44441900797323,
11.652154917032231,
11.652154917032231,
11.863661590503344,
11.863661590503344,
12.079007474252842,
12.079007474252842,
12.298262256557319,
12.298262256557319,
12.521496890655566,
12.521496890655566,
12.748783617709826,
12.748783617709826,
12.98019599018381,
12.98019599018381,
13.215808895645086,
13.215808895645086,
13.455698580999508,
13.455698580999508,
13.699942677165545,
13.699942677165545,
13.948620224196498,
13.948620224196498,
14.201811696858716,
14.201811696858716,
14.459599030674116,
14.459599030674116,
14.722065648435406,
14.722065648435406,
14.989296487202608,
14.989296487202608,
15.261378025789629,
15.261378025789629,
15.538398312749738,
15.538398312749738,
15.820446994869037,
15.820446994869037,
16.10761534617715,
16.10761534617715,
16.39999629748447,
16.39999629748447,
16.69768446645562,
16.69768446645562,
17.00077618822873,
17.00077618822873,
17.309369546590553,
17.309369546590553,
17.623564405717435,
17.623564405717435,
17.94346244249247,
17.94346244249247,
18.269167179409244,
18.269167179409244,
18.600784018072822,
18.600784018072822,
18.938420273308882,
18.938420273308882,
19.282185207891956,
19.282185207891956,
19.632190067904055,
19.632190067904055,
19.988548118735103,
19.988548118735103,
20.35137468173687,
20.35137468173687,
20.72078717154221,
20.72078717154221,
21.096905134061714,
21.096905134061714,
21.479850285170084,
21.479850285170084,
21.869746550094703,
21.869746550094703,
22.266720103519187,
22.266720103519187,
22.67089941041491,
22.67089941041491,
23.08241526761366,
23.08241526761366,
23.501400846134892,
23.501400846134892,
23.927991734281377,
23.927991734281377,
24.36232598151701,
24.36232598151701,
24.804544143141136,
24.804544143141136,
25.25478932577379,
25.25478932577379,
25.713207233666548,
25.713207233666548,
26.179946215854002,
26.179946215854002,
26.65515731416115,
26.65515731416115,
27.138994312082165,
27.138994312082165,
27.6316137845464,
27.6316137845464,
28.133175148587764,
28.133175148587764,
28.6438407149338,
28.6438407149338,
29.163775740531204,
29.163775740531204,
29.693148482024785,
29.693148482024785,
30.232130250207152,
30.232130250207152,
30.78089546545674,
30.78089546545674,
31.339621714182158,
31.339621714182158,
31.90848980629108,
31.90848980629108,
32.48768383370232,
32.48768383370232,
33.07739122991996,
33.07739122991996,
33.6778028306889,
33.6778028306889,
34.289112935751355,
34.289112935751355,
34.911519371724424,
34.911519371724424,
35.54522355611888,
35.54522355611888,
36.19043056252011,
36.19043056252011,
36.847349186952165,
36.847349186952165,
37.51619201544639,
37.51619201544639,
38.19717549283665,
38.19717549283665,
38.89051999280318,
38.89051999280318,
39.59644988918792,
39.59644988918792,
40.31519362860439,
40.31519362860439,
41.04698380436544,
41.04698380436544,
41.792057231753,
41.792057231753,
42.55065502465411,
42.55065502465411,
43.323022673587985,
43.323022673587985,
44.10941012514944,
44.10941012514944,
44.910071862894306,
44.910071862894306,
45.72526698969311,
45.72526698969311,
46.55525931157958,
46.55525931157958,
47.400317423121166,
47.400317423121166,
48.26071479433915,
48.26071479433915,
49.13672985920654,
49.13672985920654,
50.02864610575234,
50.02864610575234,
50.93675216780135,
50.93675216780135,
51.861341918379274,
51.861341918379274,
52.80271456481317,
52.80271456481317,
53.76117474555825,
53.76117474555825,
54.73703262878217,
54.73703262878217,
55.73060401273886,
55.73060401273886,
56.74221042796429,
56.74221042796429,
57.77217924132721,
57.77217924132721,
58.8208437619687,
58.8208437619687,
59.888543349164614,
59.888543349164614,
60.975623522145916,
60.975623522145916,
62.08243607191253,
62.08243607191253,
63.20933917507671,
63.20933917507671,
64.35669750977287,
64.35669750977287,
65.52488237367147,
65.52488237367147,
66.71427180413495,
66.71427180413495,
67.92525070055476,
67.92525070055476,
69.15821094890896,
69.15821094890896,
70.41355154858087,
70.41355154858087,
71.69167874147956,
71.69167874147956,
72.9930061435042,
72.9930061435042,
74.31795487839462,
74.31795487839462,
75.66695371401163,
75.66695371401163,
77.04043920109092,
77.04043920109092,
78.43885581451562,
78.43885581451562,
79.8626560971533,
79.8626560971533,
81.31230080630368,
81.31230080630368,
82.78825906280481,
82.78825906280481,
84.29100850284559,
84.29100850284559,
85.82103543253415,
85.82103543253415,
87.37883498527172,
87.37883498527172,
88.9649112819833,
88.9649112819833,
90.5797775942566,
90.5797775942566,
92.22395651044235,
92.22395651044235,
93.8979801047696,
93.8979801047696,
95.60239010953076,
95.60239010953076,
97.33773809039202,
97.33773809039202,
99.10458562488608,
99.10458562488608,
100.90350448414475,
100.90350448414475,
102.73507681793026,
102.73507681793026,
104.59989534302535,
104.59989534302535,
106.4985635350429,
106.4985635350429,
108.4316958237171,
108.4316958237171,
110.39991779173975,
110.39991779173975,
112.40386637720557,
112.40386637720557,
114.44419007973231,
114.44419007973231,
116.5215491703223,
116.5215491703223,
118.63661590503344,
118.63661590503344,
120.79007474252845,
120.79007474252845,
122.98262256557321,
122.98262256557321,
125.21496890655568,
125.21496890655568,
127.48783617709826,
127.48783617709826,
129.8019599018381,
129.8019599018381,
132.15808895645085,
132.15808895645085,
134.55698580999507,
134.55698580999507,
136.99942677165546,
136.99942677165546,
139.48620224196497,
139.48620224196497,
142.01811696858715,
142.01811696858715,
144.59599030674116,
144.59599030674116,
147.22065648435404,
147.22065648435404,
149.89296487202606,
149.89296487202606,
152.6137802578963,
152.6137802578963,
155.38398312749737,
155.38398312749737,
158.20446994869036,
158.20446994869036,
161.07615346177147,
161.07615346177147,
163.9999629748447,
163.9999629748447,
166.9768446645562,
166.9768446645562,
170.0077618822873,
170.0077618822873,
173.0936954659055,
173.0936954659055,
176.23564405717434,
176.23564405717434,
179.43462442492472,
179.43462442492472,
182.69167179409243,
182.69167179409243,
186.00784018072818,
186.00784018072818,
189.3842027330888,
189.3842027330888,
192.8218520789196,
192.8218520789196,
196.32190067904054,
196.32190067904054,
199.88548118735102,
199.88548118735102,
203.51374681736868,
203.51374681736868,
207.2078717154221,
207.2078717154221,
210.96905134061717,
210.96905134061717,
214.79850285170085,
214.79850285170085,
218.69746550094703,
218.69746550094703,
222.66720103519188,
222.66720103519188,
226.70899410414913,
226.70899410414913,
230.82415267613658,
230.82415267613658,
235.01400846134894,
235.01400846134894,
239.27991734281375,
239.27991734281375,
243.6232598151701,
243.6232598151701,
248.04544143141135,
248.04544143141135,
252.5478932577379,
252.5478932577379,
257.13207233666543,
257.13207233666543,
261.79946215854,
261.79946215854,
266.5515731416115,
266.5515731416115,
271.3899431208216,
271.3899431208216,
276.31613784546397,
276.31613784546397,
281.33175148587765,
281.33175148587765,
286.438407149338,
286.438407149338,
291.637757405312,
291.637757405312,
296.9314848202479,
296.9314848202479,
302.32130250207155,
302.32130250207155,
307.8089546545674,
307.8089546545674,
313.3962171418216,
313.3962171418216,
319.08489806291084,
319.08489806291084,
324.8768383370232,
324.8768383370232,
330.7739122991996,
330.7739122991996,
336.7780283068889,
336.7780283068889,
342.89112935751353,
342.89112935751353,
349.1151937172442,
349.1151937172442,
355.4522355611888,
355.4522355611888,
361.9043056252011,
361.9043056252011,
368.4734918695216,
368.4734918695216,
375.16192015446387,
375.16192015446387,
381.97175492836647,
381.97175492836647,
388.9051999280318,
388.9051999280318,
395.96449889187926,
395.96449889187926,
403.15193628604396,
403.15193628604396,
410.4698380436544,
410.4698380436544,
417.92057231753,
417.92057231753,
425.5065502465411,
425.5065502465411,
433.23022673587985,
433.23022673587985,
441.09410125149435,
441.09410125149435,
449.100718628943,
449.100718628943,
457.2526698969311,
457.2526698969311,
465.55259311579584,
465.55259311579584,
474.0031742312117,
474.0031742312117,
482.6071479433915,
482.6071479433915,
491.36729859206537,
491.36729859206537,
500.2864610575233,
500.2864610575233,
509.36752167801353,
509.36752167801353,
518.6134191837928,
518.6134191837928,
528.0271456481318,
528.0271456481318,
537.6117474555825,
537.6117474555825,
547.3703262878216,
547.3703262878216,
557.3060401273885,
557.3060401273885,
567.4221042796428,
567.4221042796428,
577.7217924132722,
577.7217924132722,
588.2084376196871,
588.2084376196871,
598.8854334916462,
598.8854334916462,
609.7562352214592,
609.7562352214592,
620.8243607191254,
620.8243607191254,
632.093391750767,
632.093391750767,
643.5669750977287,
643.5669750977287,
655.2488237367147,
655.2488237367147,
667.1427180413494,
667.1427180413494,
679.2525070055476,
679.2525070055476,
691.5821094890896,
691.5821094890896,
704.1355154858088,
704.1355154858088,
716.9167874147956,
716.9167874147956,
729.9300614350419,
729.9300614350419,
743.1795487839462,
743.1795487839462,
756.6695371401163,
756.6695371401163,
770.4043920109092,
770.4043920109092,
784.3885581451563,
784.3885581451563,
798.626560971533,
798.626560971533,
813.1230080630369,
813.1230080630369,
827.8825906280481,
827.8825906280481,
842.9100850284559,
842.9100850284559,
858.2103543253414,
858.2103543253414,
873.7883498527173,
873.7883498527173,
889.649112819833,
889.649112819833,
905.797775942566,
905.797775942566,
922.2395651044235,
922.2395651044235,
938.9798010476961,
938.9798010476961,
956.0239010953076,
956.0239010953076,
973.3773809039202,
973.3773809039202,
991.0458562488608
],
"xaxis": "x1",
"y": [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
2.879295754192845e-13,
2.879295754192845e-13,
7.98629143769524e-16,
7.98629143769524e-16,
0,
0,
0,
0,
0,
0,
0,
0,
2.0087932375700155e-13,
2.0087932375700155e-13,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
9.359918905212538e-14,
9.359918905212538e-14,
0,
0,
0,
0,
0,
0,
0,
0,
2.6255915461265948e-14,
2.6255915461265948e-14,
2.0358201742982285e-13,
2.0358201742982285e-13,
1.333308304749645e-13,
1.333308304749645e-13,
1.86137851517955e-13,
1.86137851517955e-13,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
2.0212451720925313e-13,
2.0212451720925313e-13,
0,
0,
0,
0,
0,
0,
0,
0,
8.313697342016117e-14,
8.313697342016117e-14,
0,
0,
7.322080843553106e-14,
7.322080843553106e-14,
0,
0,
0,
0,
0,
0,
0,
0,
6.737762009220397e-14,
6.737762009220397e-14,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
3.4219734445789547e-14,
3.4219734445789547e-14,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
3.039573917254629e-15,
3.039573917254629e-15,
0,
0,
0,
0,
0,
0,
2.3081375380844478e-14,
2.3081375380844478e-14,
2.89999938679599e-14,
2.89999938679599e-14,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
8.513176103683918e-15,
8.513176103683918e-15,
0,
0,
0,
0,
3.0749467209554194e-13,
3.0749467209554194e-13,
1.4877283676497799e-05,
1.4877283676497799e-05,
0.15249772700137998,
0.15249772700137998,
3.95853958122214,
3.95853958122214,
10.312317667014637,
10.312317667014637,
16.482380694456616,
16.482380694456616,
22.417865417197365,
22.417865417197365,
28.126708857190987,
28.126708857190987,
33.616585927342946,
33.616585927342946,
38.894909460793784,
38.894909460793784,
43.96782178223359,
43.96782178223359,
48.465718459647704,
48.465718459647704,
48.36290607467809,
48.36290607467809,
44.0142833576386,
44.0142833576386,
39.43661932049587,
39.43661932049587,
35.02538714336563,
35.02538714336563,
30.7772868764537,
30.7772868764537,
26.68670909293412,
26.68670909293412,
22.748235855983808,
22.748235855983808,
18.956634756585085,
18.956634756585085,
15.30685247797967,
15.30685247797967,
11.794008609168017,
11.794008609168017,
8.416117069953417,
8.416117069953417,
5.174681296364537,
5.174681296364537,
2.2693618968384763,
2.2693618968384763,
0.5025988361859374,
0.5025988361859374,
0.03927658173121001,
0.03927658173121001,
0.0008562116243944005,
0.0008562116243944005,
5.404597596774551e-06,
5.404597596774551e-06,
1.798489140322821e-08,
1.798489140322821e-08,
1.539350030326486e-11,
1.539350030326486e-11,
0,
0,
0,
0,
2.1040632136072264e-16,
2.1040632136072264e-16,
0,
0,
5.17730690154359e-15,
5.17730690154359e-15,
0,
0,
0,
0,
0,
0,
5.444968921673138e-15,
5.444968921673138e-15,
2.1817475890228234e-15,
2.1817475890228234e-15,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
7.0884971447365185e-15,
7.0884971447365185e-15,
0,
0,
0,
0,
7.79839610527883e-15,
7.79839610527883e-15,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1.839858959450457e-14,
1.839858959450457e-14,
0,
0,
3.246957681480402e-17,
3.246957681480402e-17,
9.468813230051754e-15,
9.468813230051754e-15,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1.6730660139569572e-14,
1.6730660139569572e-14,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1.1796209897745128e-14,
1.1796209897745128e-14,
0,
0,
0,
0,
0,
0,
1.829709332412506e-14,
1.829709332412506e-14,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
4.6850625794977315e-15,
4.6850625794977315e-15,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5.53291155730977e-15,
5.53291155730977e-15,
9.549144450367065e-15,
9.549144450367065e-15,
0,
0,
0,
0,
0,
0,
0,
0,
1.7052628737853258e-14,
1.7052628737853258e-14,
0,
0,
1.60044287284556e-14,
1.60044287284556e-14,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
],
"yaxis": "y1",
"zmax": 0.1,
"zmin": -0.1
},
{
"colorbar": {
"title": ""
},
"hoverinfo": "text",
"legendgroup": "πβ = Ξ(Nβ,Dβ,,Ξ²)",
"line": {
"color": "rgba(204, 0, 0, 1.000)",
"dash": "solid",
"shape": "linear",
"width": 1
},
"mode": "lines",
"name": "πβ = Ξ(Nβ,Dβ,,Ξ²)",
"showlegend": true,
"text": [
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null
],
"type": "scatter",
"x": [
10.090350448414474,
10.090350448414474,
10.273507681793024,
10.273507681793024,
10.459989534302535,
10.459989534302535,
10.649856353504289,
10.649856353504289,
10.84316958237171,
10.84316958237171,
11.039991779173976,
11.039991779173976,
11.240386637720556,
11.240386637720556,
11.44441900797323,
11.44441900797323,
11.652154917032231,
11.652154917032231,
11.863661590503344,
11.863661590503344,
12.079007474252842,
12.079007474252842,
12.298262256557319,
12.298262256557319,
12.521496890655566,
12.521496890655566,
12.748783617709826,
12.748783617709826,
12.98019599018381,
12.98019599018381,
13.215808895645086,
13.215808895645086,
13.455698580999508,
13.455698580999508,
13.699942677165545,
13.699942677165545,
13.948620224196498,
13.948620224196498,
14.201811696858716,
14.201811696858716,
14.459599030674116,
14.459599030674116,
14.722065648435406,
14.722065648435406,
14.989296487202608,
14.989296487202608,
15.261378025789629,
15.261378025789629,
15.538398312749738,
15.538398312749738,
15.820446994869037,
15.820446994869037,
16.10761534617715,
16.10761534617715,
16.39999629748447,
16.39999629748447,
16.69768446645562,
16.69768446645562,
17.00077618822873,
17.00077618822873,
17.309369546590553,
17.309369546590553,
17.623564405717435,
17.623564405717435,
17.94346244249247,
17.94346244249247,
18.269167179409244,
18.269167179409244,
18.600784018072822,
18.600784018072822,
18.938420273308882,
18.938420273308882,
19.282185207891956,
19.282185207891956,
19.632190067904055,
19.632190067904055,
19.988548118735103,
19.988548118735103,
20.35137468173687,
20.35137468173687,
20.72078717154221,
20.72078717154221,
21.096905134061714,
21.096905134061714,
21.479850285170084,
21.479850285170084,
21.869746550094703,
21.869746550094703,
22.266720103519187,
22.266720103519187,
22.67089941041491,
22.67089941041491,
23.08241526761366,
23.08241526761366,
23.501400846134892,
23.501400846134892,
23.927991734281377,
23.927991734281377,
24.36232598151701,
24.36232598151701,
24.804544143141136,
24.804544143141136,
25.25478932577379,
25.25478932577379,
25.713207233666548,
25.713207233666548,
26.179946215854002,
26.179946215854002,
26.65515731416115,
26.65515731416115,
27.138994312082165,
27.138994312082165,
27.6316137845464,
27.6316137845464,
28.133175148587764,
28.133175148587764,
28.6438407149338,
28.6438407149338,
29.163775740531204,
29.163775740531204,
29.693148482024785,
29.693148482024785,
30.232130250207152,
30.232130250207152,
30.78089546545674,
30.78089546545674,
31.339621714182158,
31.339621714182158,
31.90848980629108,
31.90848980629108,
32.48768383370232,
32.48768383370232,
33.07739122991996,
33.07739122991996,
33.6778028306889,
33.6778028306889,
34.289112935751355,
34.289112935751355,
34.911519371724424,
34.911519371724424,
35.54522355611888,
35.54522355611888,
36.19043056252011,
36.19043056252011,
36.847349186952165,
36.847349186952165,
37.51619201544639,
37.51619201544639,
38.19717549283665,
38.19717549283665,
38.89051999280318,
38.89051999280318,
39.59644988918792,
39.59644988918792,
40.31519362860439,
40.31519362860439,
41.04698380436544,
41.04698380436544,
41.792057231753,
41.792057231753,
42.55065502465411,
42.55065502465411,
43.323022673587985,
43.323022673587985,
44.10941012514944,
44.10941012514944,
44.910071862894306,
44.910071862894306,
45.72526698969311,
45.72526698969311,
46.55525931157958,
46.55525931157958,
47.400317423121166,
47.400317423121166,
48.26071479433915,
48.26071479433915,
49.13672985920654,
49.13672985920654,
50.02864610575234,
50.02864610575234,
50.93675216780135,
50.93675216780135,
51.861341918379274,
51.861341918379274,
52.80271456481317,
52.80271456481317,
53.76117474555825,
53.76117474555825,
54.73703262878217,
54.73703262878217,
55.73060401273886,
55.73060401273886,
56.74221042796429,
56.74221042796429,
57.77217924132721,
57.77217924132721,
58.8208437619687,
58.8208437619687,
59.888543349164614,
59.888543349164614,
60.975623522145916,
60.975623522145916,
62.08243607191253,
62.08243607191253,
63.20933917507671,
63.20933917507671,
64.35669750977287,
64.35669750977287,
65.52488237367147,
65.52488237367147,
66.71427180413495,
66.71427180413495,
67.92525070055476,
67.92525070055476,
69.15821094890896,
69.15821094890896,
70.41355154858087,
70.41355154858087,
71.69167874147956,
71.69167874147956,
72.9930061435042,
72.9930061435042,
74.31795487839462,
74.31795487839462,
75.66695371401163,
75.66695371401163,
77.04043920109092,
77.04043920109092,
78.43885581451562,
78.43885581451562,
79.8626560971533,
79.8626560971533,
81.31230080630368,
81.31230080630368,
82.78825906280481,
82.78825906280481,
84.29100850284559,
84.29100850284559,
85.82103543253415,
85.82103543253415,
87.37883498527172,
87.37883498527172,
88.9649112819833,
88.9649112819833,
90.5797775942566,
90.5797775942566,
92.22395651044235,
92.22395651044235,
93.8979801047696,
93.8979801047696,
95.60239010953076,
95.60239010953076,
97.33773809039202,
97.33773809039202,
99.10458562488608,
99.10458562488608,
100.90350448414475,
100.90350448414475,
102.73507681793026,
102.73507681793026,
104.59989534302535,
104.59989534302535,
106.4985635350429,
106.4985635350429,
108.4316958237171,
108.4316958237171,
110.39991779173975,
110.39991779173975,
112.40386637720557,
112.40386637720557,
114.44419007973231,
114.44419007973231,
116.5215491703223,
116.5215491703223,
118.63661590503344,
118.63661590503344,
120.79007474252845,
120.79007474252845,
122.98262256557321,
122.98262256557321,
125.21496890655568,
125.21496890655568,
127.48783617709826,
127.48783617709826,
129.8019599018381,
129.8019599018381,
132.15808895645085,
132.15808895645085,
134.55698580999507,
134.55698580999507,
136.99942677165546,
136.99942677165546,
139.48620224196497,
139.48620224196497,
142.01811696858715,
142.01811696858715,
144.59599030674116,
144.59599030674116,
147.22065648435404,
147.22065648435404,
149.89296487202606,
149.89296487202606,
152.6137802578963,
152.6137802578963,
155.38398312749737,
155.38398312749737,
158.20446994869036,
158.20446994869036,
161.07615346177147,
161.07615346177147,
163.9999629748447,
163.9999629748447,
166.9768446645562,
166.9768446645562,
170.0077618822873,
170.0077618822873,
173.0936954659055,
173.0936954659055,
176.23564405717434,
176.23564405717434,
179.43462442492472,
179.43462442492472,
182.69167179409243,
182.69167179409243,
186.00784018072818,
186.00784018072818,
189.3842027330888,
189.3842027330888,
192.8218520789196,
192.8218520789196,
196.32190067904054,
196.32190067904054,
199.88548118735102,
199.88548118735102,
203.51374681736868,
203.51374681736868,
207.2078717154221,
207.2078717154221,
210.96905134061717,
210.96905134061717,
214.79850285170085,
214.79850285170085,
218.69746550094703,
218.69746550094703,
222.66720103519188,
222.66720103519188,
226.70899410414913,
226.70899410414913,
230.82415267613658,
230.82415267613658,
235.01400846134894,
235.01400846134894,
239.27991734281375,
239.27991734281375,
243.6232598151701,
243.6232598151701,
248.04544143141135,
248.04544143141135,
252.5478932577379,
252.5478932577379,
257.13207233666543,
257.13207233666543,
261.79946215854,
261.79946215854,
266.5515731416115,
266.5515731416115,
271.3899431208216,
271.3899431208216,
276.31613784546397,
276.31613784546397,
281.33175148587765,
281.33175148587765,
286.438407149338,
286.438407149338,
291.637757405312,
291.637757405312,
296.9314848202479,
296.9314848202479,
302.32130250207155,
302.32130250207155,
307.8089546545674,
307.8089546545674,
313.3962171418216,
313.3962171418216,
319.08489806291084,
319.08489806291084,
324.8768383370232,
324.8768383370232,
330.7739122991996,
330.7739122991996,
336.7780283068889,
336.7780283068889,
342.89112935751353,
342.89112935751353,
349.1151937172442,
349.1151937172442,
355.4522355611888,
355.4522355611888,
361.9043056252011,
361.9043056252011,
368.4734918695216,
368.4734918695216,
375.16192015446387,
375.16192015446387,
381.97175492836647,
381.97175492836647,
388.9051999280318,
388.9051999280318,
395.96449889187926,
395.96449889187926,
403.15193628604396,
403.15193628604396,
410.4698380436544,
410.4698380436544,
417.92057231753,
417.92057231753,
425.5065502465411,
425.5065502465411,
433.23022673587985,
433.23022673587985,
441.09410125149435,
441.09410125149435,
449.100718628943,
449.100718628943,
457.2526698969311,
457.2526698969311,
465.55259311579584,
465.55259311579584,
474.0031742312117,
474.0031742312117,
482.6071479433915,
482.6071479433915,
491.36729859206537,
491.36729859206537,
500.2864610575233,
500.2864610575233,
509.36752167801353,
509.36752167801353,
518.6134191837928,
518.6134191837928,
528.0271456481318,
528.0271456481318,
537.6117474555825,
537.6117474555825,
547.3703262878216,
547.3703262878216,
557.3060401273885,
557.3060401273885,
567.4221042796428,
567.4221042796428,
577.7217924132722,
577.7217924132722,
588.2084376196871,
588.2084376196871,
598.8854334916462,
598.8854334916462,
609.7562352214592,
609.7562352214592,
620.8243607191254,
620.8243607191254,
632.093391750767,
632.093391750767,
643.5669750977287,
643.5669750977287,
655.2488237367147,
655.2488237367147,
667.1427180413494,
667.1427180413494,
679.2525070055476,
679.2525070055476,
691.5821094890896,
691.5821094890896,
704.1355154858088,
704.1355154858088,
716.9167874147956,
716.9167874147956,
729.9300614350419,
729.9300614350419,
743.1795487839462,
743.1795487839462,
756.6695371401163,
756.6695371401163,
770.4043920109092,
770.4043920109092,
784.3885581451563,
784.3885581451563,
798.626560971533,
798.626560971533,
813.1230080630369,
813.1230080630369,
827.8825906280481,
827.8825906280481,
842.9100850284559,
842.9100850284559,
858.2103543253414,
858.2103543253414,
873.7883498527173,
873.7883498527173,
889.649112819833,
889.649112819833,
905.797775942566,
905.797775942566,
922.2395651044235,
922.2395651044235,
938.9798010476961,
938.9798010476961,
956.0239010953076,
956.0239010953076,
973.3773809039202,
973.3773809039202,
991.0458562488608
],
"xaxis": "x1",
"y": [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
4.318943631289267e-13,
4.318943631289267e-13,
1.197943715654286e-15,
1.197943715654286e-15,
0,
0,
0,
0,
0,
0,
0,
0,
3.0131898563550233e-13,
3.0131898563550233e-13,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1.4039878357818805e-13,
1.4039878357818805e-13,
0,
0,
0,
0,
0,
0,
0,
0,
3.938387319189893e-14,
3.938387319189893e-14,
3.0537302614473423e-13,
3.0537302614473423e-13,
1.9999624571244673e-13,
1.9999624571244673e-13,
2.792067772769325e-13,
2.792067772769325e-13,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
3.0318677581387974e-13,
3.0318677581387974e-13,
0,
0,
0,
0,
0,
0,
0,
0,
1.2470546013024176e-13,
1.2470546013024176e-13,
0,
0,
1.0983121265329658e-13,
1.0983121265329658e-13,
0,
0,
0,
0,
0,
0,
0,
0,
1.0106643013830595e-13,
1.0106643013830595e-13,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
5.132960166868431e-14,
5.132960166868431e-14,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
4.559360875881943e-15,
4.559360875881943e-15,
0,
0,
0,
0,
0,
0,
3.462206307126671e-14,
3.462206307126671e-14,
4.3499990801939846e-14,
4.3499990801939846e-14,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1.2769764155525873e-14,
1.2769764155525873e-14,
0,
0,
0,
0,
4.612420081433129e-13,
4.612420081433129e-13,
2.23159255147467e-05,
2.23159255147467e-05,
0.22874659050206997,
0.22874659050206997,
5.93780937183321,
5.93780937183321,
15.468476500521952,
15.468476500521952,
24.72357104168492,
24.72357104168492,
33.62679812579604,
33.62679812579604,
42.19006328578648,
42.19006328578648,
50.42487889101441,
50.42487889101441,
58.342364191190676,
58.342364191190676,
65.95173267335039,
65.95173267335039,
72.69857768947155,
72.69857768947155,
72.54435911201713,
72.54435911201713,
66.02142503645791,
66.02142503645791,
59.154928980743804,
59.154928980743804,
52.53808071504844,
52.53808071504844,
46.16593031468055,
46.16593031468055,
40.03006363940118,
40.03006363940118,
34.12235378397572,
34.12235378397572,
28.434952134877626,
28.434952134877626,
22.9602787169695,
22.9602787169695,
17.69101291375203,
17.69101291375203,
12.624175604930123,
12.624175604930123,
7.762021944546807,
7.762021944546807,
3.4040428452577145,
3.4040428452577145,
0.753898254278906,
0.753898254278906,
0.058914872596815014,
0.058914872596815014,
0.0012843174365916006,
0.0012843174365916006,
8.106896395161825e-06,
8.106896395161825e-06,
2.697733710484231e-08,
2.697733710484231e-08,
2.309025045489729e-11,
2.309025045489729e-11,
0,
0,
0,
0,
3.1560948204108392e-16,
3.1560948204108392e-16,
0,
0,
7.765960352315384e-15,
7.765960352315384e-15,
0,
0,
0,
0,
0,
0,
8.167453382509707e-15,
8.167453382509707e-15,
3.2726213835342358e-15,
3.2726213835342358e-15,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1.0632745717104777e-14,
1.0632745717104777e-14,
0,
0,
0,
0,
1.1697594157918246e-14,
1.1697594157918246e-14,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
2.759788439175685e-14,
2.759788439175685e-14,
0,
0,
4.870436522220602e-17,
4.870436522220602e-17,
1.4203219845077629e-14,
1.4203219845077629e-14,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
2.5095990209354358e-14,
2.5095990209354358e-14,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1.769431484661769e-14,
1.769431484661769e-14,
0,
0,
0,
0,
0,
0,
2.744563998618759e-14,
2.744563998618759e-14,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
7.027593869246598e-15,
7.027593869246598e-15,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
8.299367335964653e-15,
8.299367335964653e-15,
1.4323716675550596e-14,
1.4323716675550596e-14,
0,
0,
0,
0,
0,
0,
0,
0,
2.5578943106779885e-14,
2.5578943106779885e-14,
0,
0,
2.4006643092683396e-14,
2.4006643092683396e-14,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
],
"yaxis": "y1",
"zmax": 0.1,
"zmin": -0.1
},
{
"colorbar": {
"title": ""
},
"hoverinfo": "text",
"legendgroup": "πββ (partMC)",
"line": {
"color": "rgba(0, 0, 204, 1.000)",
"dash": "solid",
"shape": "linear",
"width": 1.5
},
"mode": "lines",
"name": "πββ (partMC)",
"showlegend": true,
"text": [
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null
],
"type": "scatter",
"x": [
10.090350448414474,
10.090350448414474,
10.273507681793024,
10.273507681793024,
10.459989534302535,
10.459989534302535,
10.649856353504289,
10.649856353504289,
10.84316958237171,
10.84316958237171,
11.039991779173976,
11.039991779173976,
11.240386637720556,
11.240386637720556,
11.44441900797323,
11.44441900797323,
11.652154917032231,
11.652154917032231,
11.863661590503344,
11.863661590503344,
12.079007474252842,
12.079007474252842,
12.298262256557319,
12.298262256557319,
12.521496890655566,
12.521496890655566,
12.748783617709826,
12.748783617709826,
12.98019599018381,
12.98019599018381,
13.215808895645086,
13.215808895645086,
13.455698580999508,
13.455698580999508,
13.699942677165545,
13.699942677165545,
13.948620224196498,
13.948620224196498,
14.201811696858716,
14.201811696858716,
14.459599030674116,
14.459599030674116,
14.722065648435406,
14.722065648435406,
14.989296487202608,
14.989296487202608,
15.261378025789629,
15.261378025789629,
15.538398312749738,
15.538398312749738,
15.820446994869037,
15.820446994869037,
16.10761534617715,
16.10761534617715,
16.39999629748447,
16.39999629748447,
16.69768446645562,
16.69768446645562,
17.00077618822873,
17.00077618822873,
17.309369546590553,
17.309369546590553,
17.623564405717435,
17.623564405717435,
17.94346244249247,
17.94346244249247,
18.269167179409244,
18.269167179409244,
18.600784018072822,
18.600784018072822,
18.938420273308882,
18.938420273308882,
19.282185207891956,
19.282185207891956,
19.632190067904055,
19.632190067904055,
19.988548118735103,
19.988548118735103,
20.35137468173687,
20.35137468173687,
20.72078717154221,
20.72078717154221,
21.096905134061714,
21.096905134061714,
21.479850285170084,
21.479850285170084,
21.869746550094703,
21.869746550094703,
22.266720103519187,
22.266720103519187,
22.67089941041491,
22.67089941041491,
23.08241526761366,
23.08241526761366,
23.501400846134892,
23.501400846134892,
23.927991734281377,
23.927991734281377,
24.36232598151701,
24.36232598151701,
24.804544143141136,
24.804544143141136,
25.25478932577379,
25.25478932577379,
25.713207233666548,
25.713207233666548,
26.179946215854002,
26.179946215854002,
26.65515731416115,
26.65515731416115,
27.138994312082165,
27.138994312082165,
27.6316137845464,
27.6316137845464,
28.133175148587764,
28.133175148587764,
28.6438407149338,
28.6438407149338,
29.163775740531204,
29.163775740531204,
29.693148482024785,
29.693148482024785,
30.232130250207152,
30.232130250207152,
30.78089546545674,
30.78089546545674,
31.339621714182158,
31.339621714182158,
31.90848980629108,
31.90848980629108,
32.48768383370232,
32.48768383370232,
33.07739122991996,
33.07739122991996,
33.6778028306889,
33.6778028306889,
34.289112935751355,
34.289112935751355,
34.911519371724424,
34.911519371724424,
35.54522355611888,
35.54522355611888,
36.19043056252011,
36.19043056252011,
36.847349186952165,
36.847349186952165,
37.51619201544639,
37.51619201544639,
38.19717549283665,
38.19717549283665,
38.89051999280318,
38.89051999280318,
39.59644988918792,
39.59644988918792,
40.31519362860439,
40.31519362860439,
41.04698380436544,
41.04698380436544,
41.792057231753,
41.792057231753,
42.55065502465411,
42.55065502465411,
43.323022673587985,
43.323022673587985,
44.10941012514944,
44.10941012514944,
44.910071862894306,
44.910071862894306,
45.72526698969311,
45.72526698969311,
46.55525931157958,
46.55525931157958,
47.400317423121166,
47.400317423121166,
48.26071479433915,
48.26071479433915,
49.13672985920654,
49.13672985920654,
50.02864610575234,
50.02864610575234,
50.93675216780135,
50.93675216780135,
51.861341918379274,
51.861341918379274,
52.80271456481317,
52.80271456481317,
53.76117474555825,
53.76117474555825,
54.73703262878217,
54.73703262878217,
55.73060401273886,
55.73060401273886,
56.74221042796429,
56.74221042796429,
57.77217924132721,
57.77217924132721,
58.8208437619687,
58.8208437619687,
59.888543349164614,
59.888543349164614,
60.975623522145916,
60.975623522145916,
62.08243607191253,
62.08243607191253,
63.20933917507671,
63.20933917507671,
64.35669750977287,
64.35669750977287,
65.52488237367147,
65.52488237367147,
66.71427180413495,
66.71427180413495,
67.92525070055476,
67.92525070055476,
69.15821094890896,
69.15821094890896,
70.41355154858087,
70.41355154858087,
71.69167874147956,
71.69167874147956,
72.9930061435042,
72.9930061435042,
74.31795487839462,
74.31795487839462,
75.66695371401163,
75.66695371401163,
77.04043920109092,
77.04043920109092,
78.43885581451562,
78.43885581451562,
79.8626560971533,
79.8626560971533,
81.31230080630368,
81.31230080630368,
82.78825906280481,
82.78825906280481,
84.29100850284559,
84.29100850284559,
85.82103543253415,
85.82103543253415,
87.37883498527172,
87.37883498527172,
88.9649112819833,
88.9649112819833,
90.5797775942566,
90.5797775942566,
92.22395651044235,
92.22395651044235,
93.8979801047696,
93.8979801047696,
95.60239010953076,
95.60239010953076,
97.33773809039202,
97.33773809039202,
99.10458562488608,
99.10458562488608,
100.90350448414475,
100.90350448414475,
102.73507681793026,
102.73507681793026,
104.59989534302535,
104.59989534302535,
106.4985635350429,
106.4985635350429,
108.4316958237171,
108.4316958237171,
110.39991779173975,
110.39991779173975,
112.40386637720557,
112.40386637720557,
114.44419007973231,
114.44419007973231,
116.5215491703223,
116.5215491703223,
118.63661590503344,
118.63661590503344,
120.79007474252845,
120.79007474252845,
122.98262256557321,
122.98262256557321,
125.21496890655568,
125.21496890655568,
127.48783617709826,
127.48783617709826,
129.8019599018381,
129.8019599018381,
132.15808895645085,
132.15808895645085,
134.55698580999507,
134.55698580999507,
136.99942677165546,
136.99942677165546,
139.48620224196497,
139.48620224196497,
142.01811696858715,
142.01811696858715,
144.59599030674116,
144.59599030674116,
147.22065648435404,
147.22065648435404,
149.89296487202606,
149.89296487202606,
152.6137802578963,
152.6137802578963,
155.38398312749737,
155.38398312749737,
158.20446994869036,
158.20446994869036,
161.07615346177147,
161.07615346177147,
163.9999629748447,
163.9999629748447,
166.9768446645562,
166.9768446645562,
170.0077618822873,
170.0077618822873,
173.0936954659055,
173.0936954659055,
176.23564405717434,
176.23564405717434,
179.43462442492472,
179.43462442492472,
182.69167179409243,
182.69167179409243,
186.00784018072818,
186.00784018072818,
189.3842027330888,
189.3842027330888,
192.8218520789196,
192.8218520789196,
196.32190067904054,
196.32190067904054,
199.88548118735102,
199.88548118735102,
203.51374681736868,
203.51374681736868,
207.2078717154221,
207.2078717154221,
210.96905134061717,
210.96905134061717,
214.79850285170085,
214.79850285170085,
218.69746550094703,
218.69746550094703,
222.66720103519188,
222.66720103519188,
226.70899410414913,
226.70899410414913,
230.82415267613658,
230.82415267613658,
235.01400846134894,
235.01400846134894,
239.27991734281375,
239.27991734281375,
243.6232598151701,
243.6232598151701,
248.04544143141135,
248.04544143141135,
252.5478932577379,
252.5478932577379,
257.13207233666543,
257.13207233666543,
261.79946215854,
261.79946215854,
266.5515731416115,
266.5515731416115,
271.3899431208216,
271.3899431208216,
276.31613784546397,
276.31613784546397,
281.33175148587765,
281.33175148587765,
286.438407149338,
286.438407149338,
291.637757405312,
291.637757405312,
296.9314848202479,
296.9314848202479,
302.32130250207155,
302.32130250207155,
307.8089546545674,
307.8089546545674,
313.3962171418216,
313.3962171418216,
319.08489806291084,
319.08489806291084,
324.8768383370232,
324.8768383370232,
330.7739122991996,
330.7739122991996,
336.7780283068889,
336.7780283068889,
342.89112935751353,
342.89112935751353,
349.1151937172442,
349.1151937172442,
355.4522355611888,
355.4522355611888,
361.9043056252011,
361.9043056252011,
368.4734918695216,
368.4734918695216,
375.16192015446387,
375.16192015446387,
381.97175492836647,
381.97175492836647,
388.9051999280318,
388.9051999280318,
395.96449889187926,
395.96449889187926,
403.15193628604396,
403.15193628604396,
410.4698380436544,
410.4698380436544,
417.92057231753,
417.92057231753,
425.5065502465411,
425.5065502465411,
433.23022673587985,
433.23022673587985,
441.09410125149435,
441.09410125149435,
449.100718628943,
449.100718628943,
457.2526698969311,
457.2526698969311,
465.55259311579584,
465.55259311579584,
474.0031742312117,
474.0031742312117,
482.6071479433915,
482.6071479433915,
491.36729859206537,
491.36729859206537,
500.2864610575233,
500.2864610575233,
509.36752167801353,
509.36752167801353,
518.6134191837928,
518.6134191837928,
528.0271456481318,
528.0271456481318,
537.6117474555825,
537.6117474555825,
547.3703262878216,
547.3703262878216,
557.3060401273885,
557.3060401273885,
567.4221042796428,
567.4221042796428,
577.7217924132722,
577.7217924132722,
588.2084376196871,
588.2084376196871,
598.8854334916462,
598.8854334916462,
609.7562352214592,
609.7562352214592,
620.8243607191254,
620.8243607191254,
632.093391750767,
632.093391750767,
643.5669750977287,
643.5669750977287,
655.2488237367147,
655.2488237367147,
667.1427180413494,
667.1427180413494,
679.2525070055476,
679.2525070055476,
691.5821094890896,
691.5821094890896,
704.1355154858088,
704.1355154858088,
716.9167874147956,
716.9167874147956,
729.9300614350419,
729.9300614350419,
743.1795487839462,
743.1795487839462,
756.6695371401163,
756.6695371401163,
770.4043920109092,
770.4043920109092,
784.3885581451563,
784.3885581451563,
798.626560971533,
798.626560971533,
813.1230080630369,
813.1230080630369,
827.8825906280481,
827.8825906280481,
842.9100850284559,
842.9100850284559,
858.2103543253414,
858.2103543253414,
873.7883498527173,
873.7883498527173,
889.649112819833,
889.649112819833,
905.797775942566,
905.797775942566,
922.2395651044235,
922.2395651044235,
938.9798010476961,
938.9798010476961,
956.0239010953076,
956.0239010953076,
973.3773809039202,
973.3773809039202,
991.0458562488608
],
"xaxis": "x2",
"y": [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.015792948989228776,
0.015792948989228776,
0.03787796640629062,
0.03787796640629062,
0.08601540799184956,
0.08601540799184956,
0.21552412829822407,
0.21552412829822407,
0.2731740555921125,
0.2731740555921125,
0.46298713017445164,
0.46298713017445164,
0.577338420459175,
0.577338420459175,
0.619159822923045,
0.619159822923045,
0.6330471575141582,
0.6330471575141582,
0.6604623925544546,
0.6604623925544546,
0.5942497468911792,
0.5942497468911792,
0.5132919805738363,
0.5132919805738363,
0.40359186313669176,
0.40359186313669176,
0.3079567853992242,
0.3079567853992242,
0.201887132529441,
0.201887132529441,
0.1180648644587022,
0.1180648644587022,
0.06352676076991295,
0.06352676076991295,
0.022126315209840944,
0.022126315209840944,
0.00724152242500706,
0.00724152242500706,
0.001750072303297965,
0.001750072303297965,
0.0012775751129169397,
0.0012775751129169397,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
],
"yaxis": "y2",
"zmax": 0.1,
"zmin": -0.1
},
{
"colorbar": {
"title": ""
},
"hoverinfo": "text",
"legendgroup": "fβ
[(Ξ²ββα΅t)*(πβ*πβ)]",
"line": {
"color": "rgba(165, 42, 42, 1.000)",
"dash": "solid",
"shape": "linear",
"width": 1
},
"mode": "lines",
"name": "fβ
[(Ξ²ββα΅t)*(πβ*πβ)]",
"showlegend": true,
"text": [
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null
],
"type": "scatter",
"x": [
10.090350448414474,
10.273507681793024,
10.459989534302535,
10.649856353504289,
10.84316958237171,
11.039991779173976,
11.240386637720556,
11.44441900797323,
11.652154917032231,
11.863661590503344,
12.079007474252842,
12.298262256557319,
12.521496890655566,
12.748783617709826,
12.98019599018381,
13.215808895645086,
13.455698580999508,
13.699942677165545,
13.948620224196498,
14.201811696858716,
14.459599030674116,
14.722065648435406,
14.989296487202608,
15.261378025789629,
15.538398312749738,
15.820446994869037,
16.10761534617715,
16.39999629748447,
16.69768446645562,
17.00077618822873,
17.309369546590553,
17.623564405717435,
17.94346244249247,
18.269167179409244,
18.600784018072822,
18.938420273308882,
19.282185207891956,
19.632190067904055,
19.988548118735103,
20.35137468173687,
20.72078717154221,
21.096905134061714,
21.479850285170084,
21.869746550094703,
22.266720103519187,
22.67089941041491,
23.08241526761366,
23.501400846134892,
23.927991734281377,
24.36232598151701,
24.804544143141136,
25.25478932577379,
25.713207233666548,
26.179946215854002,
26.65515731416115,
27.138994312082165,
27.6316137845464,
28.133175148587764,
28.6438407149338,
29.163775740531204,
29.693148482024785,
30.232130250207152,
30.78089546545674,
31.339621714182158,
31.90848980629108,
32.48768383370232,
33.07739122991996,
33.6778028306889,
34.289112935751355,
34.911519371724424,
35.54522355611888,
36.19043056252011,
36.847349186952165,
37.51619201544639,
38.19717549283665,
38.89051999280318,
39.59644988918792,
40.31519362860439,
41.04698380436544,
41.792057231753,
42.55065502465411,
43.323022673587985,
44.10941012514944,
44.910071862894306,
45.72526698969311,
46.55525931157958,
47.400317423121166,
48.26071479433915,
49.13672985920654,
50.02864610575234,
50.93675216780135,
51.861341918379274,
52.80271456481317,
53.76117474555825,
54.73703262878217,
55.73060401273886,
56.74221042796429,
57.77217924132721,
58.8208437619687,
59.888543349164614,
60.975623522145916,
62.08243607191253,
63.20933917507671,
64.35669750977287,
65.52488237367147,
66.71427180413495,
67.92525070055476,
69.15821094890896,
70.41355154858087,
71.69167874147956,
72.9930061435042,
74.31795487839462,
75.66695371401163,
77.04043920109092,
78.43885581451562,
79.8626560971533,
81.31230080630368,
82.78825906280481,
84.29100850284559,
85.82103543253415,
87.37883498527172,
88.9649112819833,
90.5797775942566,
92.22395651044235,
93.8979801047696,
95.60239010953076,
97.33773809039202,
99.10458562488608,
100.90350448414475,
102.73507681793026,
104.59989534302535,
106.4985635350429,
108.4316958237171,
110.39991779173975,
112.40386637720557,
114.44419007973231,
116.5215491703223,
118.63661590503344,
120.79007474252845,
122.98262256557321,
125.21496890655568,
127.48783617709826,
129.8019599018381,
132.15808895645085,
134.55698580999507,
136.99942677165546,
139.48620224196497,
142.01811696858715,
144.59599030674116,
147.22065648435404,
149.89296487202606,
152.6137802578963,
155.38398312749737,
158.20446994869036,
161.07615346177147,
163.9999629748447,
166.9768446645562,
170.0077618822873,
173.0936954659055,
176.23564405717434,
179.43462442492472,
182.69167179409243,
186.00784018072818,
189.3842027330888,
192.8218520789196,
196.32190067904054,
199.88548118735102,
203.51374681736868,
207.2078717154221,
210.96905134061717,
214.79850285170085,
218.69746550094703,
222.66720103519188,
226.70899410414913,
230.82415267613658,
235.01400846134894,
239.27991734281375,
243.6232598151701,
248.04544143141135,
252.5478932577379,
257.13207233666543,
261.79946215854,
266.5515731416115,
271.3899431208216,
276.31613784546397,
281.33175148587765,
286.438407149338,
291.637757405312,
296.9314848202479,
302.32130250207155,
307.8089546545674,
313.3962171418216,
319.08489806291084,
324.8768383370232,
330.7739122991996,
336.7780283068889,
342.89112935751353,
349.1151937172442,
355.4522355611888,
361.9043056252011,
368.4734918695216,
375.16192015446387,
381.97175492836647,
388.9051999280318,
395.96449889187926,
403.15193628604396,
410.4698380436544,
417.92057231753,
425.5065502465411,
433.23022673587985,
441.09410125149435,
449.100718628943,
457.2526698969311,
465.55259311579584,
474.0031742312117,
482.6071479433915,
491.36729859206537,
500.2864610575233,
509.36752167801353,
518.6134191837928,
528.0271456481318,
537.6117474555825,
547.3703262878216,
557.3060401273885,
567.4221042796428,
577.7217924132722,
588.2084376196871,
598.8854334916462,
609.7562352214592,
620.8243607191254,
632.093391750767,
643.5669750977287,
655.2488237367147,
667.1427180413494,
679.2525070055476,
691.5821094890896,
704.1355154858088,
716.9167874147956,
729.9300614350419,
743.1795487839462,
756.6695371401163,
770.4043920109092,
784.3885581451563,
798.626560971533,
813.1230080630369,
827.8825906280481,
842.9100850284559,
858.2103543253414,
873.7883498527173,
889.649112819833,
905.797775942566,
922.2395651044235,
938.9798010476961,
956.0239010953076,
973.3773809039202,
991.0458562488608
],
"xaxis": "x2",
"y": [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1.2948692500253121e-32,
7.066063534901799e-32,
1.47003690501054e-32,
8.021948292657387e-32,
0,
0,
0,
4.6097193984596395e-33,
2.67026832968744e-32,
8.445096972341087e-33,
0,
0,
0,
0,
1.1096253157011322e-33,
6.0551928162063975e-33,
0,
0,
0,
0,
1.6924263187054677e-32,
9.235520803261726e-32,
0,
0,
7.034456481825688e-33,
3.838682278779354e-32,
0,
0,
0,
0,
1.415049780713496e-32,
7.721885167460305e-32,
0,
0,
0,
0,
0,
4.532488016685056e-33,
2.473370752179979e-32,
2.908375257307287e-37,
1.7112545975806762e-32,
9.338266169084031e-32,
0,
0,
0,
0,
0,
0,
3.0743700821115573e-33,
1.6776747404866052e-32,
0,
2.5401180553342097e-33,
1.3861349757739948e-32,
0,
0,
0,
0,
2.4063266085478563e-34,
2.811900148395201e-33,
8.178769995138152e-33,
0,
0,
1.3550439573819136e-33,
7.39443514876823e-33,
2.2380157104004096e-36,
1.2212786118358615e-35,
0,
1.1978993607162498e-26,
1.635170109544413e-20,
1.4767212840645759e-15,
3.7068261758588255e-11,
7.81875695597435e-08,
1.3195493810636216e-05,
0.0003300324363077736,
0.002774377513328843,
0.010967646657888314,
0.026571658608021666,
0.05021701445382377,
0.08280154781138495,
0.125293521122834,
0.17875817201440947,
0.2443516634288891,
0.3233281947564421,
0.41704764612945167,
0.5269726234677785,
0.6526637679853796,
0.7639858859297045,
0.7457145030778874,
0.6097715209846679,
0.4744614812412556,
0.35174146169420495,
0.24364620567228734,
0.15237272345425376,
0.08032002002725151,
0.030128762841548234,
0.0043239957934242765,
6.415402754945914e-06,
6.10582668683794e-14,
2.6083890896977585e-29,
0,
3.663775031190361e-33,
1.999311293203752e-32,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
4.2514920969691745e-32,
2.5893469754032075e-31,
1.469672448944772e-31,
0,
0,
4.670581795834117e-34,
2.5487227929519276e-33,
0,
0,
0,
0,
0,
0,
5.919688222234659e-32,
3.2303565077557613e-31,
0,
0,
0,
0,
0,
2.29496939114495e-31,
1.2523580684434624e-30,
0,
0,
0,
2.710282764317869e-31,
1.4789933585838696e-30,
3.4940891703857583e-31,
1.9067142164412235e-30,
0,
0,
0,
2.065301950112675e-30,
1.1270292192024783e-29,
0,
0,
0,
0,
0,
1.7515194225687576e-30,
1.0456673564784727e-29,
6.999283832116371e-30,
1.1468265943096313e-29,
1.9017416376797924e-31,
0,
0,
0,
4.428837400659248e-31,
2.4168035852420076e-30,
0,
0,
0,
0,
0,
0,
2.0399336376869543e-30,
1.1131858054856826e-29,
0,
0,
0,
3.2243031906369405e-35,
4.1911803575261916e-30,
2.2870188185520317e-29,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
],
"yaxis": "y2",
"zmax": 0.1,
"zmin": -0.1
},
{
"colorbar": {
"title": ""
},
"hoverinfo": "text",
"legendgroup": "fβ
[(Ξ²ββαΆ»β½ΒΉ β»ΒΉβΎt)*(πβ*πβ)]",
"line": {
"color": "rgba(165, 42, 42, 1.000)",
"dash": "dash",
"shape": "linear",
"width": 1
},
"mode": "lines",
"name": "fβ
[(Ξ²ββαΆ»β½ΒΉ β»ΒΉβΎt)*(πβ*πβ)]",
"showlegend": true,
"text": [
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null
],
"type": "scatter",
"x": [
10.090350448414474,
10.273507681793024,
10.459989534302535,
10.649856353504289,
10.84316958237171,
11.039991779173976,
11.240386637720556,
11.44441900797323,
11.652154917032231,
11.863661590503344,
12.079007474252842,
12.298262256557319,
12.521496890655566,
12.748783617709826,
12.98019599018381,
13.215808895645086,
13.455698580999508,
13.699942677165545,
13.948620224196498,
14.201811696858716,
14.459599030674116,
14.722065648435406,
14.989296487202608,
15.261378025789629,
15.538398312749738,
15.820446994869037,
16.10761534617715,
16.39999629748447,
16.69768446645562,
17.00077618822873,
17.309369546590553,
17.623564405717435,
17.94346244249247,
18.269167179409244,
18.600784018072822,
18.938420273308882,
19.282185207891956,
19.632190067904055,
19.988548118735103,
20.35137468173687,
20.72078717154221,
21.096905134061714,
21.479850285170084,
21.869746550094703,
22.266720103519187,
22.67089941041491,
23.08241526761366,
23.501400846134892,
23.927991734281377,
24.36232598151701,
24.804544143141136,
25.25478932577379,
25.713207233666548,
26.179946215854002,
26.65515731416115,
27.138994312082165,
27.6316137845464,
28.133175148587764,
28.6438407149338,
29.163775740531204,
29.693148482024785,
30.232130250207152,
30.78089546545674,
31.339621714182158,
31.90848980629108,
32.48768383370232,
33.07739122991996,
33.6778028306889,
34.289112935751355,
34.911519371724424,
35.54522355611888,
36.19043056252011,
36.847349186952165,
37.51619201544639,
38.19717549283665,
38.89051999280318,
39.59644988918792,
40.31519362860439,
41.04698380436544,
41.792057231753,
42.55065502465411,
43.323022673587985,
44.10941012514944,
44.910071862894306,
45.72526698969311,
46.55525931157958,
47.400317423121166,
48.26071479433915,
49.13672985920654,
50.02864610575234,
50.93675216780135,
51.861341918379274,
52.80271456481317,
53.76117474555825,
54.73703262878217,
55.73060401273886,
56.74221042796429,
57.77217924132721,
58.8208437619687,
59.888543349164614,
60.975623522145916,
62.08243607191253,
63.20933917507671,
64.35669750977287,
65.52488237367147,
66.71427180413495,
67.92525070055476,
69.15821094890896,
70.41355154858087,
71.69167874147956,
72.9930061435042,
74.31795487839462,
75.66695371401163,
77.04043920109092,
78.43885581451562,
79.8626560971533,
81.31230080630368,
82.78825906280481,
84.29100850284559,
85.82103543253415,
87.37883498527172,
88.9649112819833,
90.5797775942566,
92.22395651044235,
93.8979801047696,
95.60239010953076,
97.33773809039202,
99.10458562488608,
100.90350448414475,
102.73507681793026,
104.59989534302535,
106.4985635350429,
108.4316958237171,
110.39991779173975,
112.40386637720557,
114.44419007973231,
116.5215491703223,
118.63661590503344,
120.79007474252845,
122.98262256557321,
125.21496890655568,
127.48783617709826,
129.8019599018381,
132.15808895645085,
134.55698580999507,
136.99942677165546,
139.48620224196497,
142.01811696858715,
144.59599030674116,
147.22065648435404,
149.89296487202606,
152.6137802578963,
155.38398312749737,
158.20446994869036,
161.07615346177147,
163.9999629748447,
166.9768446645562,
170.0077618822873,
173.0936954659055,
176.23564405717434,
179.43462442492472,
182.69167179409243,
186.00784018072818,
189.3842027330888,
192.8218520789196,
196.32190067904054,
199.88548118735102,
203.51374681736868,
207.2078717154221,
210.96905134061717,
214.79850285170085,
218.69746550094703,
222.66720103519188,
226.70899410414913,
230.82415267613658,
235.01400846134894,
239.27991734281375,
243.6232598151701,
248.04544143141135,
252.5478932577379,
257.13207233666543,
261.79946215854,
266.5515731416115,
271.3899431208216,
276.31613784546397,
281.33175148587765,
286.438407149338,
291.637757405312,
296.9314848202479,
302.32130250207155,
307.8089546545674,
313.3962171418216,
319.08489806291084,
324.8768383370232,
330.7739122991996,
336.7780283068889,
342.89112935751353,
349.1151937172442,
355.4522355611888,
361.9043056252011,
368.4734918695216,
375.16192015446387,
381.97175492836647,
388.9051999280318,
395.96449889187926,
403.15193628604396,
410.4698380436544,
417.92057231753,
425.5065502465411,
433.23022673587985,
441.09410125149435,
449.100718628943,
457.2526698969311,
465.55259311579584,
474.0031742312117,
482.6071479433915,
491.36729859206537,
500.2864610575233,
509.36752167801353,
518.6134191837928,
528.0271456481318,
537.6117474555825,
547.3703262878216,
557.3060401273885,
567.4221042796428,
577.7217924132722,
588.2084376196871,
598.8854334916462,
609.7562352214592,
620.8243607191254,
632.093391750767,
643.5669750977287,
655.2488237367147,
667.1427180413494,
679.2525070055476,
691.5821094890896,
704.1355154858088,
716.9167874147956,
729.9300614350419,
743.1795487839462,
756.6695371401163,
770.4043920109092,
784.3885581451563,
798.626560971533,
813.1230080630369,
827.8825906280481,
842.9100850284559,
858.2103543253414,
873.7883498527173,
889.649112819833,
905.797775942566,
922.2395651044235,
938.9798010476961,
956.0239010953076,
973.3773809039202,
991.0458562488608
],
"xaxis": "x2",
"y": [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1.4262814740431077e-32,
7.783176188673087e-32,
1.619226345621548e-32,
8.836070696192152e-32,
0,
0,
0,
5.077545380301215e-33,
2.9412654978738427e-32,
9.302163409867192e-33,
0,
0,
0,
0,
1.222237713099467e-33,
6.669715367281501e-33,
0,
0,
0,
0,
1.8641853642793655e-32,
1.0172804879391818e-31,
0,
0,
7.748361434789117e-33,
4.2282581186120113e-32,
0,
0,
0,
0,
1.5586587503263117e-32,
8.505555104364089e-32,
0,
0,
0,
0,
0,
4.992476027516997e-33,
2.724385402005191e-32,
3.2035371517098355e-37,
1.88492446619819e-32,
1.0285977550542415e-31,
0,
0,
0,
0,
0,
0,
3.386378271306068e-33,
1.8479366945962677e-32,
0,
2.7979066798711667e-33,
1.526809472408889e-32,
0,
0,
0,
0,
2.650537158251073e-34,
3.097271086201747e-33,
9.008807742014997e-33,
0,
0,
1.4925631239525545e-33,
8.144873209009443e-33,
2.465144914283145e-36,
1.3452223525058784e-35,
0,
1.319470414425449e-26,
1.8011184018051594e-20,
1.626589101367016e-15,
4.083020352844236e-11,
8.612258107244344e-08,
1.4534663142701882e-05,
0.00036352639444475786,
0.0030559403964418507,
0.012080718761134467,
0.029268333004647793,
0.05531338194635767,
0.09120481752359505,
0.13800916810066624,
0.19689977893364863,
0.26915014832071155,
0.35614176041936324,
0.4593725053368092,
0.5804534242861155,
0.7189005693343318,
0.8415204203132075,
0.821394732050716,
0.6716553225451287,
0.5226130907257439,
0.3874386008143147,
0.26837309586623287,
0.16783655385132326,
0.08847144725801528,
0.033186436604235224,
0.004762824581617655,
7.0664818843490216e-06,
6.725487910833257e-14,
2.873106327653819e-29,
0,
4.0356000823607255e-33,
2.202215133524822e-32,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
4.6829627121265575e-32,
2.85213168882878e-31,
1.618824902051321e-31,
0,
0,
5.144584511734268e-34,
2.8073846853554364e-33,
0,
0,
0,
0,
0,
0,
6.520458836534596e-32,
3.558195270662707e-31,
0,
0,
0,
0,
0,
2.5278786456795127e-31,
1.3794559658084426e-30,
0,
0,
0,
2.9853408721300264e-31,
1.6290917616120178e-30,
3.8486933350826274e-31,
2.100220669501246e-30,
0,
0,
0,
2.274902975488242e-30,
1.24140788424958e-29,
0,
0,
0,
0,
0,
1.929275642145079e-30,
1.1517888609430811e-29,
7.709619223038836e-30,
1.2632144329412435e-29,
2.0947434392978796e-31,
0,
0,
0,
4.878306235155431e-31,
2.6620774104908702e-30,
0,
0,
0,
0,
0,
0,
2.2469601125004645e-30,
1.2261595458390467e-29,
0,
0,
0,
3.5515276213514633e-35,
4.616530123173534e-30,
2.519121194379243e-29,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
],
"yaxis": "y2",
"zmax": 0.1,
"zmin": -0.1
},
{
"colorbar": {
"title": ""
},
"hoverinfo": "text",
"legendgroup": "fβ
[(Ξ²ββαΆ»β½Β² β»Β²βΎ*t)*(πβ*πβ)]",
"line": {
"color": "rgba(165, 42, 42, 1.000)",
"dash": "dot",
"shape": "linear",
"width": 1
},
"mode": "lines",
"name": "fβ
[(Ξ²ββαΆ»β½Β² β»Β²βΎ*t)*(πβ*πβ)]",
"showlegend": true,
"text": [
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null,
null
],
"type": "scatter",
"x": [
10.090350448414474,
10.273507681793024,
10.459989534302535,
10.649856353504289,
10.84316958237171,
11.039991779173976,
11.240386637720556,
11.44441900797323,
11.652154917032231,
11.863661590503344,
12.079007474252842,
12.298262256557319,
12.521496890655566,
12.748783617709826,
12.98019599018381,
13.215808895645086,
13.455698580999508,
13.699942677165545,
13.948620224196498,
14.201811696858716,
14.459599030674116,
14.722065648435406,
14.989296487202608,
15.261378025789629,
15.538398312749738,
15.820446994869037,
16.10761534617715,
16.39999629748447,
16.69768446645562,
17.00077618822873,
17.309369546590553,
17.623564405717435,
17.94346244249247,
18.269167179409244,
18.600784018072822,
18.938420273308882,
19.282185207891956,
19.632190067904055,
19.988548118735103,
20.35137468173687,
20.72078717154221,
21.096905134061714,
21.479850285170084,
21.869746550094703,
22.266720103519187,
22.67089941041491,
23.08241526761366,
23.501400846134892,
23.927991734281377,
24.36232598151701,
24.804544143141136,
25.25478932577379,
25.713207233666548,
26.179946215854002,
26.65515731416115,
27.138994312082165,
27.6316137845464,
28.133175148587764,
28.6438407149338,
29.163775740531204,
29.693148482024785,
30.232130250207152,
30.78089546545674,
31.339621714182158,
31.90848980629108,
32.48768383370232,
33.07739122991996,
33.6778028306889,
34.289112935751355,
34.911519371724424,
35.54522355611888,
36.19043056252011,
36.847349186952165,
37.51619201544639,
38.19717549283665,
38.89051999280318,
39.59644988918792,
40.31519362860439,
41.04698380436544,
41.792057231753,
42.55065502465411,
43.323022673587985,
44.10941012514944,
44.910071862894306,
45.72526698969311,
46.55525931157958,
47.400317423121166,
48.26071479433915,
49.13672985920654,
50.02864610575234,
50.93675216780135,
51.861341918379274,
52.80271456481317,
53.76117474555825,
54.73703262878217,
55.73060401273886,
56.74221042796429,
57.77217924132721,
58.8208437619687,
59.888543349164614,
60.975623522145916,
62.08243607191253,
63.20933917507671,
64.35669750977287,
65.52488237367147,
66.71427180413495,
67.92525070055476,
69.15821094890896,
70.41355154858087,
71.69167874147956,
72.9930061435042,
74.31795487839462,
75.66695371401163,
77.04043920109092,
78.43885581451562,
79.8626560971533,
81.31230080630368,
82.78825906280481,
84.29100850284559,
85.82103543253415,
87.37883498527172,
88.9649112819833,
90.5797775942566,
92.22395651044235,
93.8979801047696,
95.60239010953076,
97.33773809039202,
99.10458562488608,
100.90350448414475,
102.73507681793026,
104.59989534302535,
106.4985635350429,
108.4316958237171,
110.39991779173975,
112.40386637720557,
114.44419007973231,
116.5215491703223,
118.63661590503344,
120.79007474252845,
122.98262256557321,
125.21496890655568,
127.48783617709826,
129.8019599018381,
132.15808895645085,
134.55698580999507,
136.99942677165546,
139.48620224196497,
142.01811696858715,
144.59599030674116,
147.22065648435404,
149.89296487202606,
152.6137802578963,
155.38398312749737,
158.20446994869036,
161.07615346177147,
163.9999629748447,
166.9768446645562,
170.0077618822873,
173.0936954659055,
176.23564405717434,
179.43462442492472,
182.69167179409243,
186.00784018072818,
189.3842027330888,
192.8218520789196,
196.32190067904054,
199.88548118735102,
203.51374681736868,
207.2078717154221,
210.96905134061717,
214.79850285170085,
218.69746550094703,
222.66720103519188,
226.70899410414913,
230.82415267613658,
235.01400846134894,
239.27991734281375,
243.6232598151701,
248.04544143141135,
252.5478932577379,
257.13207233666543,
261.79946215854,
266.5515731416115,
271.3899431208216,
276.31613784546397,
281.33175148587765,
286.438407149338,
291.637757405312,
296.9314848202479,
302.32130250207155,
307.8089546545674,
313.3962171418216,
319.08489806291084,
324.8768383370232,
330.7739122991996,
336.7780283068889,
342.89112935751353,
349.1151937172442,
355.4522355611888,
361.9043056252011,
368.4734918695216,
375.16192015446387,
381.97175492836647,
388.9051999280318,
395.96449889187926,
403.15193628604396,
410.4698380436544,
417.92057231753,
425.5065502465411,
433.23022673587985,
441.09410125149435,
449.100718628943,
457.2526698969311,
465.55259311579584,
474.0031742312117,
482.6071479433915,
491.36729859206537,
500.2864610575233,
509.36752167801353,
518.6134191837928,
528.0271456481318,
537.6117474555825,
547.3703262878216,
557.3060401273885,
567.4221042796428,
577.7217924132722,
588.2084376196871,
598.8854334916462,
609.7562352214592,
620.8243607191254,
632.093391750767,
643.5669750977287,
655.2488237367147,
667.1427180413494,
679.2525070055476,
691.5821094890896,
704.1355154858088,
716.9167874147956,
729.9300614350419,
743.1795487839462,
756.6695371401163,
770.4043920109092,
784.3885581451563,
798.626560971533,
813.1230080630369,
827.8825906280481,
842.9100850284559,
858.2103543253414,
873.7883498527173,
889.649112819833,
905.797775942566,
922.2395651044235,
938.9798010476961,
956.0239010953076,
973.3773809039202,
991.0458562488608
],
"xaxis": "x2",
"y": [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
3.0836862142293453e-32,
1.6827585264704841e-31,
3.5008419099463216e-32,
1.9103991666220086e-31,
0,
0,
0,
1.0977886887203248e-32,
6.359151425048833e-32,
2.0111705572534927e-32,
0,
0,
0,
0,
2.6425342087014404e-33,
1.442023170406682e-32,
0,
0,
0,
0,
4.030454586429442e-32,
2.1994072514803946e-31,
0,
0,
1.675231416390349e-32,
9.141688725442343e-32,
0,
0,
0,
0,
3.369891980328644e-32,
1.838940173943734e-31,
0,
0,
0,
0,
0,
1.0793963029810305e-32,
5.890246672416055e-32,
6.926194815877269e-37,
4.07529347962581e-32,
2.223875704040836e-31,
0,
0,
0,
0,
0,
0,
7.321505734622415e-33,
3.995324214470464e-32,
0,
6.0492030601514694e-33,
3.301032375100296e-32,
0,
0,
0,
0,
5.730583369376658e-34,
6.69644268965861e-33,
1.947745711226605e-32,
0,
0,
3.2269901930034256e-33,
1.7609590875544977e-32,
5.3297568022837284e-36,
2.9084326614272287e-35,
0,
2.852755785653752e-26,
3.894100909897603e-20,
3.5167605268562618e-15,
8.827677988968301e-11,
1.8620098544371634e-07,
3.1424610904160506e-05,
0.0007859608018886166,
0.006607083835493665,
0.026119070169291308,
0.06327948349778419,
0.11959007844844952,
0.19718901464207947,
0.298382175506279,
0.4257063875066126,
0.5819150125967889,
0.7699948831301777,
0.9931845064828351,
1.254967027931271,
1.554296129763026,
1.8194058931132775,
1.775893228484047,
1.4521497309889189,
1.1299135637500808,
0.8376600930001976,
0.5802349894139761,
0.36287035678025226,
0.19127934228094357,
0.07175060387328795,
0.010297446030406136,
1.5278059181472533e-05,
1.4540814511046376e-13,
6.211788160920476e-29,
0,
8.725153180908847e-33,
4.76129051074843e-32,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
1.0124780991650371e-31,
6.166440026088529e-31,
3.4999739704646493e-31,
0,
0,
1.1122828575906534e-33,
6.069694944384797e-33,
0,
0,
0,
0,
0,
0,
1.409753221268016e-31,
7.692981997848636e-31,
0,
0,
0,
0,
0,
5.465390017883007e-31,
2.9824473095353093e-30,
0,
0,
0,
6.454444413462624e-31,
3.5221713935308016e-30,
8.321052187930162e-31,
4.5407737836078595e-30,
0,
0,
0,
4.918444971690339e-30,
2.6839810013407973e-29,
0,
0,
0,
0,
0,
4.1711827639930745e-30,
2.4902205468075447e-29,
1.6668551718371314e-29,
2.7311277636063006e-29,
4.528931759731322e-31,
0,
0,
0,
1.0547122682239366e-30,
5.755533926043227e-30,
0,
0,
0,
0,
0,
0,
4.858031215394923e-30,
2.6510133916493e-29,
0,
0,
0,
7.678566233052846e-35,
9.981150675714703e-30,
5.446456004970482e-29,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
],
"yaxis": "y2",
"zmax": 0.1,
"zmin": -0.1
},
{
"colorbar": {
"title": ""
},
"hoverinfo": "text",
"legendgroup": "f*Dβ",
"line": {
"color": "rgba(128, 128, 128, 1.000)",
"dash": "dashdot",
"shape": "linear",
"width": 1
},
"mode": "lines",
"name": "f*Dβ",
"showlegend": true,
"text": [
null,
null
],
"type": "scatter",
"x": [
125.9921049894873,
125.9921049894873
],
"xaxis": "x2",
"y": [
0,
1.9103761877689414
],
"yaxis": "y2",
"zmax": 0.1,
"zmin": -0.1
}
],
"layout": {
"annotations": [],
"height": 288,
"legend": {
"bgcolor": "rgba(255, 255, 255, 1.000)",
"bordercolor": "rgba(0, 0, 0, 1.000)",
"font": {
"color": "rgba(0, 0, 0, 1.000)",
"family": "Nimbus Sans L",
"size": 14
},
"tracegroupgap": 0,
"x": 1,
"y": 1
},
"margin": {
"b": 20,
"l": 0,
"r": 0,
"t": 20
},
"paper_bgcolor": "rgba(255, 255, 255, 1.000)",
"plot_bgcolor": "rgba(255, 255, 255, 1.000)",
"showlegend": true,
"width": 792,
"xaxis1": {
"anchor": "y1",
"domain": [
0.09890572390572391,
0.4971334075664785
],
"gridcolor": "rgba(0, 0, 0, 0.100)",
"gridwidth": 0.5,
"linecolor": "rgba(0, 0, 0, 1.000)",
"mirror": false,
"range": [
1.6020599913279623,
2.6020599913279625
],
"showgrid": true,
"showline": true,
"showticklabels": true,
"tickangle": 0,
"tickcolor": "rgb(0, 0, 0)",
"tickfont": {
"color": "rgba(0, 0, 0, 1.000)",
"family": "Nimbus Sans L",
"size": 17
},
"tickmode": "array",
"ticks": "inside",
"ticktext": [
"10^1.7781513",
"10^1.9030900",
"10^2.0000000",
"10^2.0791812",
"10^2.1461280",
"10^2.2041200"
],
"tickvals": [
60,
79.99999999999999,
100,
119.99999999999996,
140.00000000000006,
159.99999999999991
],
"title": "Diameter (nm)",
"titlefont": {
"color": "rgba(0, 0, 0, 1.000)",
"family": "Nimbus Sans L",
"size": 17
},
"type": "log",
"visible": true,
"zeroline": false,
"zerolinecolor": "rgba(0, 0, 0, 1.000)"
},
"xaxis2": {
"anchor": "y2",
"domain": [
0.5968013468013469,
0.9950290304621014
],
"gridcolor": "rgba(0, 0, 0, 0.100)",
"gridwidth": 0.5,
"linecolor": "rgba(0, 0, 0, 1.000)",
"mirror": false,
"range": [
1.954242509439325,
2.255272505103306
],
"showgrid": true,
"showline": true,
"showticklabels": true,
"tickangle": 0,
"tickcolor": "rgb(0, 0, 0)",
"tickfont": {
"color": "rgba(0, 0, 0, 1.000)",
"family": "Nimbus Sans L",
"size": 17
},
"tickmode": "array",
"ticks": "inside",
"ticktext": [
"10^2.0000000",
"10^2.0791812",
"10^2.1461280",
"10^2.2041200"
],
"tickvals": [
100,
119.99999999999996,
140.00000000000006,
159.99999999999991
],
"title": "Diameter (nm)",
"titlefont": {
"color": "rgba(0, 0, 0, 1.000)",
"family": "Nimbus Sans L",
"size": 17
},
"type": "log",
"visible": true,
"zeroline": false,
"zerolinecolor": "rgba(0, 0, 0, 1.000)"
},
"yaxis1": {
"anchor": "x1",
"domain": [
0.1294109069699621,
0.9863298337707787
],
"gridcolor": "rgba(0, 0, 0, 0.100)",
"gridwidth": 0.5,
"linecolor": "rgba(0, 0, 0, 1.000)",
"mirror": false,
"range": [
-2.1809573306841465,
74.8795350201557
],
"showgrid": true,
"showline": true,
"showticklabels": true,
"tickangle": 0,
"tickcolor": "rgb(0, 0, 0)",
"tickfont": {
"color": "rgba(0, 0, 0, 1.000)",
"family": "Nimbus Sans L",
"size": 17
},
"tickmode": "array",
"ticks": "inside",
"ticktext": [
"0",
"20",
"40",
"60"
],
"tickvals": [
0,
20,
40,
60
],
"title": "dN/dlnD (mβ»Β³) Γ 10β»ΒΉβ°",
"titlefont": {
"color": "rgba(0, 0, 0, 1.000)",
"family": "Nimbus Sans L",
"size": 17
},
"type": "-",
"visible": true,
"zeroline": false,
"zerolinecolor": "rgba(0, 0, 0, 1.000)"
},
"yaxis2": {
"anchor": "x2",
"domain": [
0.1294109069699621,
0.9863298337707787
],
"gridcolor": "rgba(0, 0, 0, 0.100)",
"gridwidth": 0.5,
"linecolor": "rgba(0, 0, 0, 1.000)",
"mirror": false,
"range": [
-0.05731128563306824,
1.9676874734020096
],
"showgrid": true,
"showline": true,
"showticklabels": true,
"tickangle": 0,
"tickcolor": "rgb(0, 0, 0)",
"tickfont": {
"color": "rgba(0, 0, 0, 1.000)",
"family": "Nimbus Sans L",
"size": 17
},
"tickmode": "array",
"ticks": "inside",
"ticktext": [
"0.0",
"0.5",
"1.0",
"1.5"
],
"tickvals": [
0,
0.5,
1,
1.5
],
"title": "",
"titlefont": {
"color": "rgba(0, 0, 0, 1.000)",
"family": "Nimbus Sans L",
"size": 17
},
"type": "-",
"visible": true,
"zeroline": false,
"zerolinecolor": "rgba(0, 0, 0, 1.000)"
}
}
},
"image/svg+xml": [
"4 5 6 7 8 9 100 2 3 4 0 20 40 60 100 120 140 160 180 0.0 0.5 1.0 1.5 πβ = Ξ(Nβ,Dβ,Ξ²) πβ = Ξ(Nβ,Dβ,,Ξ²) πββ (partMC) fβ
[(Ξ²ββα΅t)*(πβ*πβ)] fβ
[(Ξ²ββαΆ»β½ΒΉ β»ΒΉβΎt)*(πβ*πβ)] fβ
[(Ξ²ββαΆ»β½Β² β»Β²βΎ*t)*(πβ*πβ)] f*Dβ Diameter (nm) Diameter (nm) dN/dlnD (mβ»Β³) Γ 10β»ΒΉβ° "
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pre = 1e-10\n",
"p1 = plot(πβ.Dp, pre*πβ.S, xlim = (40, 400), color = :black, label = \"πβ = Ξ(Nβ,Dβ,Ξ²)\", \n",
" xlabel = \"Diameter (nm)\", ylabel = \"dN/dlnD (mβ»Β³) Γ 10β»ΒΉβ°\", t = :steppre, \n",
" xticks = [60,80,100,120,140,160])\n",
"\n",
"p1 = plot!(πβ.Dp, pre*πβ.S, color = RGBA(0.8,0.0,0.0,1.0), label = \"πβ = Ξ(Nβ,Dβ,,Ξ²)\", t = :steppre)\n",
"\n",
"p2 = plot(πββ.Dp, pre*πββ.S, color = RGBA(0.0,0.0,0.8), xlim = (90, 180), label = \"πββ (partMC)\", \n",
" xlabel = \"Diameter (nm)\", t = :steppre, lw = 1.5, xticks = [60,80,100,120,140, 160])\n",
"p2 = plot!(πβα΅.Dp,pre*πβα΅.S, color = :brown, label = \"fβ
[(Ξ²ββα΅t)*(πβ*πβ)]\", lw = 1)\n",
"p2 = plot!(πβαΆ»ΒΉ.Dp,pre*πβαΆ»ΒΉ.S, color = :brown, label = \"fβ
[(Ξ²ββαΆ»β½ΒΉ β»ΒΉβΎt)*(πβ*πβ)]\", lw = 1, ls = :dash)\n",
"p2 = plot!(πβαΆ»Β².Dp,pre*πβαΆ»Β².S, color = :brown, label = \"fβ
[(Ξ²ββαΆ»β½Β² β»Β²βΎ*t)*(πβ*πβ)]\", lw = 1, ls = :dot)\n",
"p2 = plot!([f*Dm, f*Dm], [0,1.05*maximum(pre*πβαΆ»Β².S)], color = :grey, ls = :dashdot, \n",
" label = \"f*Dβ\") \n",
"\n",
"plot(p1,p2, layout = grid(1,2), left_margin = 35px, xaxis = :log10, fmt = :svg)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Figure 4. Comparison of assumed PartMC inferred size distribution and size distribution obtained from πβα΅ = f$β
$((kββ$*$t)$*$(πβ$.*$πβ)). Left: Input size distributions to PartMC. Right: Blue histogram shows output size distribution from PartMC. The dark-red solid line corresponds to the analytical prediction. Note that the diameter is shifted by f$*$Dm due to the larger sphere equivalent volume of the dimers. Enhancement of concentration due to +1/-1 charge on the input size distribution is negligible and approximately a factor of two for +2/-2 charges. Fpr the triangular case, the number concentration is predicted well (Table 4). However, the shape of the analytical prediction of the size distribution does not fit exactly the modeled shape. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Generalization \n",
"The predicted number of dimers by the analytical approximation is \n",
" $N = Ξ²_{1,2}^B N_1N_2t$ \n",
"How accurate is this estimate relative to the PartMC prediction? The average coagulation coefficient is enhanced for polydisperse coagulation because coagulation is more efficient for particles of dissimilar size (e.g. Table 12.4, Hinds 1999). To test how this might affect the dimer formation rate, a Monte-Carlo simulation is used. PartMC is is run for a range of sizes and geometric standard deviations. Number concentration for N1 and N2 are picked randomly within an interval where coagulated number concentration after time t remains small relative to the total particle number. This assumption mimicks the physics in the coagulation system described in Notebook 9a. After the simulation is completed the effective coagulation rate concentration is computed from the dimer size distribution \n",
"\n",
"```julia\n",
"Ξ²12eff = sum(πββ)/(Nβ*Nβ*t) \n",
"```\n",
"where sum(πββ) is the number concentration of the dimers formed, Nβ and Nβ are the initial concentrations, and t is the total simulation time. This effectively observed coagulation rate is compared to the underlying Brownian coagulation rate computed from Eq. (15.33). The calculations are performed for lognormal distributions and triangular distributions.\n",
"\n",
"### Step 1. Monte-Carlo Simulations"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"\u001b[32mSimulate...100%|ββββββββββββββββββββββββββββββββββββββββ| Time: 0:57:56\u001b[39m\n"
]
}
],
"source": [
"Random.seed!(10)\n",
"Narr = exp10.(range(10, stop=12, length=100))\n",
"Dgs = collect([20:20:100;200:200:1000])\n",
"Οs = collect(1.05:0.05:1.3)\n",
"\n",
"ics = InitialConditionLogNormal[]\n",
"for Dg in Dgs\n",
" for Ο in Οs\n",
" N = Narr[randperm(100)]\n",
" push!(ics, InitialConditionLogNormal(N[1], N[2], Dg, Ο))\n",
" end\n",
"end\n",
"\n",
"cd(\"PartMC\") # Descend into directory PartMC\n",
"l = Simulation[]\n",
"@showprogress 1 \"Simulate...\" for i = 1:length(ics)\n",
" x = runSimulation(ics[i],1,\"logn\"; verbose = false, repeat=2)\n",
" push!(l,x[1])\n",
"end\n",
"cd(\"..\") # Come back "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Step 2. Collate the Results\n",
"The code below extracts the effective $\\beta$12 from the five repeats and multiple 5 time steps (10..60s) in the model and computes an average $\\beta$12eff from these points for each simulation. "
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/html": [
"Dβ Οβ Οβ Οβ Οβ Οβ
Οβ Float64 Float64 Float64 Float64 Float64 Float64 Float64 11 rows Γ 7 columns
1 NaN 1.05 1.1 1.15 1.2 1.25 1.3 2 20.0 1.21 1.2 1.21 1.24 1.16 1.25 3 40.0 0.85 0.93 0.94 0.96 1.02 1.01 4 60.0 0.91 0.84 0.94 0.91 1.01 0.91 5 80.0 0.92 0.91 0.88 0.95 0.96 0.94 6 100.0 0.91 0.92 0.94 0.96 0.98 1.04 7 200.0 0.99 0.97 1.04 1.01 1.04 1.03 8 400.0 1.01 1.01 1.01 1.0 1.03 1.06 9 600.0 0.95 0.97 1.0 1.01 1.03 1.04 10 800.0 0.97 0.98 0.99 0.99 1.05 1.04 11 1000.0 0.96 0.98 1.01 1.0 1.07 1.05
"
],
"text/latex": [
"\\begin{tabular}{r|ccccccc}\n",
"\t& Dβ & Οβ & Οβ & Οβ & Οβ & Οβ
& Οβ\\\\\n",
"\t\\hline\n",
"\t& Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64\\\\\n",
"\t\\hline\n",
"\t1 & NaN & 1.05 & 1.1 & 1.15 & 1.2 & 1.25 & 1.3 \\\\\n",
"\t2 & 20.0 & 1.21 & 1.2 & 1.21 & 1.24 & 1.16 & 1.25 \\\\\n",
"\t3 & 40.0 & 0.85 & 0.93 & 0.94 & 0.96 & 1.02 & 1.01 \\\\\n",
"\t4 & 60.0 & 0.91 & 0.84 & 0.94 & 0.91 & 1.01 & 0.91 \\\\\n",
"\t5 & 80.0 & 0.92 & 0.91 & 0.88 & 0.95 & 0.96 & 0.94 \\\\\n",
"\t6 & 100.0 & 0.91 & 0.92 & 0.94 & 0.96 & 0.98 & 1.04 \\\\\n",
"\t7 & 200.0 & 0.99 & 0.97 & 1.04 & 1.01 & 1.04 & 1.03 \\\\\n",
"\t8 & 400.0 & 1.01 & 1.01 & 1.01 & 1.0 & 1.03 & 1.06 \\\\\n",
"\t9 & 600.0 & 0.95 & 0.97 & 1.0 & 1.01 & 1.03 & 1.04 \\\\\n",
"\t10 & 800.0 & 0.97 & 0.98 & 0.99 & 0.99 & 1.05 & 1.04 \\\\\n",
"\t11 & 1000.0 & 0.96 & 0.98 & 1.01 & 1.0 & 1.07 & 1.05 \\\\\n",
"\\end{tabular}\n"
],
"text/plain": [
"11Γ7 DataFrame\n",
"β Row β Dβ β Οβ β Οβ β Οβ β Οβ β Οβ
β Οβ β\n",
"β β \u001b[90mFloat64\u001b[39m β \u001b[90mFloat64\u001b[39m β \u001b[90mFloat64\u001b[39m β \u001b[90mFloat64\u001b[39m β \u001b[90mFloat64\u001b[39m β \u001b[90mFloat64\u001b[39m β \u001b[90mFloat64\u001b[39m β\n",
"βββββββΌββββββββββΌββββββββββΌββββββββββΌββββββββββΌββββββββββΌββββββββββΌββββββββββ€\n",
"β 1 β NaN β 1.05 β 1.1 β 1.15 β 1.2 β 1.25 β 1.3 β\n",
"β 2 β 20.0 β 1.21 β 1.2 β 1.21 β 1.24 β 1.16 β 1.25 β\n",
"β 3 β 40.0 β 0.85 β 0.93 β 0.94 β 0.96 β 1.02 β 1.01 β\n",
"β 4 β 60.0 β 0.91 β 0.84 β 0.94 β 0.91 β 1.01 β 0.91 β\n",
"β 5 β 80.0 β 0.92 β 0.91 β 0.88 β 0.95 β 0.96 β 0.94 β\n",
"β 6 β 100.0 β 0.91 β 0.92 β 0.94 β 0.96 β 0.98 β 1.04 β\n",
"β 7 β 200.0 β 0.99 β 0.97 β 1.04 β 1.01 β 1.04 β 1.03 β\n",
"β 8 β 400.0 β 1.01 β 1.01 β 1.01 β 1.0 β 1.03 β 1.06 β\n",
"β 9 β 600.0 β 0.95 β 0.97 β 1.0 β 1.01 β 1.03 β 1.04 β\n",
"β 10 β 800.0 β 0.97 β 0.98 β 0.99 β 0.99 β 1.05 β 1.04 β\n",
"β 11 β 1000.0 β 0.96 β 0.98 β 1.01 β 1.0 β 1.07 β 1.05 β"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Ξ²12eff = Array{Float64}(undef,length(Dgs)+1, length(Οs)+1)\n",
"Dm = Array{Float64}(undef,length(Dgs)+1, length(Οs)+1)\n",
"Οk = Array{Float64}(undef,length(Dgs)+1, length(Οs)+1)\n",
"mDm, mΟ = Float64[], Float64[]\n",
"for i = 1:length(l)\n",
" push!(mDm, l[i].case.Dm)\n",
" push!(mΟ, l[i].case.Ο)\n",
"end\n",
"Ξ²12eff[2:end,1] = map(x -> x, mDm[1:length(Οs):end])\n",
"Ξ²12eff[1,2:end] = map(x -> x, mΟ[1:length(Οs)])\n",
"Ξ²12eff[1,1] = NaN\n",
"\n",
"# Compute the Browninan Kernel\n",
"f = collect([10e-9:20e-9:100e-9; 200e-9:200e-9:1000e-9])\n",
"g = map(x->Ξ²12brown(x, x), f)\n",
"\n",
"for i = 1:length(Οs)\n",
" Ξ²12eff[2:end,i+1] = map(x -> mean(x.k12), l[i:length(Οs):end]) # average the different runs\n",
" Ξ²12eff[2:end,i+1] = Ξ²12eff[2:end,i+1]./g # Compute the ratio\n",
"end\n",
"table = DataFrame(round.(Ξ²12eff,digits=2))\n",
"rename!(table,f => t for (f, t) = zip([:x1, :x2, :x3, :x4, :x5, :x6, :x7],[:Dβ, :Οβ, :Οβ, :Οβ, :Οβ, :Οβ
, :Οβ]))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Table 5. Column Dβ: Mode diameter for simulation. Row 1: List of geometric standard deviation for simulation. All other entries, ratio of effective $\\beta_{1,2}$ derived as average from five PartMC repeat runs and Brownian coagulation kernel computed via Eq. (15.33) in Jacobson (2005), the same kernel that is used in PartMC. The table shows that the analytical approximation of number concentrion fir distributions with Οg < 1.3 and sizes 10 < D < 1000 nm is within a few % of the model simulation."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"\u001b[32mSimulate...100%|ββββββββββββββββββββββββββββββββββββββββ| Time: 0:10:48\u001b[39m\n"
]
}
],
"source": [
"Random.seed!(10)\n",
"Narr = exp10.(range(10, stop=12, length=100))\n",
"\n",
"t,p = 295.15, 1e5 # Temperature [K], Pressure [Pa]\n",
"qsa,Ξ² = 1.66e-5, 1/3 # Qsample [m3 s-1], Sample-to-sheath ratio,\n",
"rβ,rβ,l = 9.37e-3,1.961e-2,0.44369 # DMA geometry [m]\n",
"leff = 13.0 # DMA effective diffusion length [m]\n",
"m = 6 # Upper number of charges\n",
"Ξ = DMAconfig(t,p,qsa,qsa/Ξ²,rβ,rβ,l,leff,:-,m,:cylindrical) # Specify DMA with negative polarity\n",
"bins,zβ,zβ = 512, dtoz(Ξ,900e-9),dtoz(Ξ,10e-9) # bins, upper, lower mobility limit\n",
"Ξ΄ = setupDMA(Ξ, zβ, zβ, bins); # Compute matrices\n",
"\n",
"Dgs = collect([40:20:100;200:200:600]) # Stay within grid for simulations\n",
"\n",
"Ξs,Ξ΄s = DMAconfig[], DifferentialMobilityAnalyzer[]\n",
"Ξ² = [1.0/10.0, 1.0/5.0, 1.0/3.0] # Three sheath-to-sample flow ratios\n",
"for i = 1:length(Ξ²)\n",
" push!(Ξs, DMAconfig(t,p,qsa,qsa/Ξ²[i],rβ,rβ,l,leff,:-,n,:cylindrical))\n",
" push!(Ξ΄s, setupDMA(Ξs[i], zβ, zβ, bins)) \n",
"end\n",
"\n",
"# Setup simulation initial conditions as a list\n",
"ics = InitialConditionTriangular[]\n",
"for Dg in Dgs\n",
" for i in 1:length(Ξs)\n",
" N = Narr[randperm(100)]\n",
" push!(ics, InitialConditionTriangular(N[1], N[2], Dg, Ξs[i], Ξ΄s[i]))\n",
" end\n",
"end\n",
"\n",
"# Run simulations\n",
"cd(\"PartMC\") # Descend into directory PartMC\n",
"l = Simulation[]\n",
"@showprogress 1 \"Simulate...\" for i = 1:length(ics)\n",
" x = runSimulation(ics[i],1,\"triangular\"; verbose = false)\n",
" push!(l,x[1])\n",
"end\n",
"cd(\"..\")"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"Dβ Ξ²β Ξ²β Ξ²β Float64 Float64 Float64 Float64 8 rows Γ 4 columns
1 NaN 0.1 0.2 0.33 2 40.0 0.96 0.97 0.96 3 60.0 0.97 0.91 0.96 4 80.0 0.93 0.98 0.99 5 100.0 0.98 1.01 1.01 6 200.0 0.99 0.94 0.99 7 400.0 0.97 0.93 0.97 8 600.0 1.03 0.99 0.91
"
],
"text/latex": [
"\\begin{tabular}{r|cccc}\n",
"\t& Dβ & Ξ²β & Ξ²β & Ξ²β\\\\\n",
"\t\\hline\n",
"\t& Float64 & Float64 & Float64 & Float64\\\\\n",
"\t\\hline\n",
"\t1 & NaN & 0.1 & 0.2 & 0.33 \\\\\n",
"\t2 & 40.0 & 0.96 & 0.97 & 0.96 \\\\\n",
"\t3 & 60.0 & 0.97 & 0.91 & 0.96 \\\\\n",
"\t4 & 80.0 & 0.93 & 0.98 & 0.99 \\\\\n",
"\t5 & 100.0 & 0.98 & 1.01 & 1.01 \\\\\n",
"\t6 & 200.0 & 0.99 & 0.94 & 0.99 \\\\\n",
"\t7 & 400.0 & 0.97 & 0.93 & 0.97 \\\\\n",
"\t8 & 600.0 & 1.03 & 0.99 & 0.91 \\\\\n",
"\\end{tabular}\n"
],
"text/plain": [
"8Γ4 DataFrame\n",
"β Row β Dβ β Ξ²β β Ξ²β β Ξ²β β\n",
"β β \u001b[90mFloat64\u001b[39m β \u001b[90mFloat64\u001b[39m β \u001b[90mFloat64\u001b[39m β \u001b[90mFloat64\u001b[39m β\n",
"βββββββΌββββββββββΌββββββββββΌββββββββββΌββββββββββ€\n",
"β 1 β NaN β 0.1 β 0.2 β 0.33 β\n",
"β 2 β 40.0 β 0.96 β 0.97 β 0.96 β\n",
"β 3 β 60.0 β 0.97 β 0.91 β 0.96 β\n",
"β 4 β 80.0 β 0.93 β 0.98 β 0.99 β\n",
"β 5 β 100.0 β 0.98 β 1.01 β 1.01 β\n",
"β 6 β 200.0 β 0.99 β 0.94 β 0.99 β\n",
"β 7 β 400.0 β 0.97 β 0.93 β 0.97 β\n",
"β 8 β 600.0 β 1.03 β 0.99 β 0.91 β"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Ξ²12eff = Array{Float64}(undef,length(Dgs)+1, length(Ξ²)+1)\n",
"Dm = Array{Float64}(undef,length(Dgs)+1, length(Ξ²)+1)\n",
"mDm = Float64[]\n",
"for i = 1:length(l)\n",
" push!(mDm, l[i].case.Dm)\n",
"end\n",
"\n",
"Ξ²12eff[2:end,1] = map(x -> x, mDm[1:length(Ξ²):end])\n",
"Ξ²12eff[1,2:end] = map(x -> x, Ξ²[1:length(Ξ²)])\n",
"Ξ²12eff[1,1] = NaN\n",
"\n",
"# Compute the Browninan Kernel\n",
"f = collect([40:20:100; 200:200:600])\n",
"g = map(x->Ξ²12brown(x*1e-9, x*1e-9), f)\n",
"\n",
"for i = 1:length(Ξ²)\n",
" Ξ²12eff[2:end,i+1] = (map(x -> mean(x.k12), l[i:length(Ξ²):end])) # Average rate\n",
" Ξ²12eff[2:end,i+1] = Ξ²12eff[2:end,i+1]./g # Compute the ratio\n",
"end\n",
"\n",
"table = DataFrame(round.(Ξ²12eff,digits=2))\n",
"rename!(table, f => t for (f, t) = zip([:x1, :x2, :x3, :x4], [:Dβ, :Ξ²β, :Ξ²β, :Ξ²β]))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Table 6. Column Dβ: Mode diameter for simulation. Row 1: List of sample-to-sheath flow ratios. All other entries, ratio of effective $\\beta_{1,2}$ derived as average from five PartMC repeat runs and Brownian coagulation kernel computed via Eq. (15.33) in Jacobson (2005), the same kernel that is used in PartMC. The table shows that the analytical approximation of number concentrion fir distributions with sheath-to-sample flow ratio < 1/10 and sizes 40 < D < 600 nm is within a few % of the model simulation."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### References\n",
"\n",
"Jacobson, M. Z. (2005) Fundamentals of Atmospheric Modeling. Second Edition, Cambridge University Press. \n",
"\n",
"Hinds, W. C. (1999) Aerosol Technology, Properties, Behavior, and Measurement of Airborne Particles, Second Edition, John Wiley & Sons, Inc.\n",
"\n",
"Riemer, N., M. West, R. A. Zaveri, and R. C. Easter (2009) Simulating the evolution of soot mixing state with a particle-resolved aerosol model, Journal of Geophysical Research 114(D09202), DOI:10.1029/2008JD011073. \n",
"\n",
"Tian, J., B. T. Brem, M. West, T. C. Bond, M. J. Rood & N. Riemer (2017) Simulating aerosol chamber experiments with the particle-resolved aerosol model PartMC, Aerosol Science and Technology, 51:7, 856-867, DOI:10.1080/02786826.2017.1311988\n",
"\n",
"Zebel, G. (1957) Zur Theorie des Verhaltens elektrisch geladener Aerosole, Kolloid-Zeitschrift, (1), 37β50, DOI:10.1007/BF01734032."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.1.0",
"language": "julia",
"name": "julia-1.1"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.1.0"
}
},
"nbformat": 4,
"nbformat_minor": 2
}