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"## A complex (multistep) reaction `A <-> C` derived from 2 coupled elementary reactions: \n",
"## `A <-> B` (fast) and `B <-> C` (slow) \n",
"A repeat of experiment `cascade_2_b`, but with the fast/slow elementary reactions in reverse order.\n",
"\n",
"In PART 1, a time evolution of [A], [B] and [C] is obtained by simulation \n",
"In PART 2, the time functions generated in Part 1 are taken as a _starting point,_ to explore how to model the composite reaction `A <-> C` \n",
"\n",
"**Background**: please see experiment `cascade_2_b` \n",
"\n",
"LAST REVISED: June 14, 2024 (using v. 1.0 beta33)"
]
},
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"cell_type": "code",
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"id": "4d9b4808-b2ec-4b90-a604-f7fa69af39b8",
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"name": "stdout",
"output_type": "stream",
"text": [
"Added 'D:\\Docs\\- MY CODE\\BioSimulations\\life123-Win7' to sys.path\n"
]
}
],
"source": [
"import set_path # Importing this module will add the project's home directory to sys.path"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "3924c013",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"from experiments.get_notebook_info import get_notebook_basename\n",
"\n",
"from src.modules.reactions.uniform_compartment import UniformCompartment\n",
"from src.modules.visualization.plotly_helper import PlotlyHelper"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "75411c8b-f0c5-411d-9e12-1eaa423449f9",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "9329208b-070f-4902-8f37-0f11ddf75ed6",
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"source": [
"# PART 1 - We'll generate the time evolution of [A] and [C] by simulating coupled elementary reactions of KNOWN rate constants...\n",
"## but pretend you don't see this section! (because we later assume that those time evolutions are just GIVEN to us)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "72b4245c-de4e-480d-a501-3495b7ed8bc4",
"metadata": {
"tags": []
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"name": "stdout",
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"text": [
"Number of reactions: 2 (at temp. 25 C)\n",
"0: A <-> B (kF = 80 / kR = 0.1 / delta_G = -16,571 / K = 800) | 1st order in all reactants & products\n",
"1: B <-> C (kF = 8 / kR = 2 / delta_G = -3,436.6 / K = 4) | 1st order in all reactants & products\n",
"Set of chemicals involved in the above reactions: {'A', 'B', 'C'}\n"
]
}
],
"source": [
"# Instantiate the simulator and specify the chemicals\n",
"dynamics = UniformCompartment(names=[\"A\", \"B\", \"C\"], preset=\"mid\")\n",
"\n",
"# Reaction A <-> B (much faster, and with a much larger K)\n",
"dynamics.add_reaction(reactants=\"A\", products=\"B\",\n",
" forward_rate=80., reverse_rate=0.1) # <===== SPEEDS of 2 reactions ARE REVERSED, relative to experiment `cascade_2_b`\n",
"\n",
"# Reaction B <-> C (much slower, and with a much smaller K)\n",
"dynamics.add_reaction(reactants=\"B\", products=\"C\", \n",
" forward_rate=8., reverse_rate=2.) # <===== SPEEDS of 2 reactions ARE REVERSED, relative to experiment `cascade_2_b`\n",
" \n",
"dynamics.describe_reactions()"
]
},
{
"cell_type": "markdown",
"id": "98a9fbe5-2090-4d38-9c5f-94fbf7c3eae2",
"metadata": {},
"source": [
"### Run the simulation"
]
},
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"cell_type": "code",
"execution_count": 4,
"id": "ae304704-c8d9-4cef-9e0b-2587bb3909ef",
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"SYSTEM STATE at Time t = 0:\n",
"3 species:\n",
" Species 0 (A). Conc: 50.0\n",
" Species 1 (B). Conc: 0.0\n",
" Species 2 (C). Conc: 0.0\n",
"Set of chemicals involved in reactions: {'A', 'B', 'C'}\n"
]
}
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"dynamics.set_conc({\"A\": 50.}, snapshot=True)\n",
"dynamics.describe_state()"
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},
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"Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n",
"152 total step(s) taken\n",
"Number of step re-do's because of negative concentrations: 0\n",
"Number of step re-do's because of elective soft aborts: 4\n",
"Norm usage: {'norm_A': 46, 'norm_B': 44, 'norm_C': 42, 'norm_D': 42}\n"
]
}
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"dynamics.single_compartment_react(initial_step=0.01, duration=0.8,\n",
" snapshots={\"initial_caption\": \"1st reaction step\",\n",
" \"final_caption\": \"last reaction step\"},\n",
" variable_steps=True)"
]
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"plot_curves() WARNING: Excessive number of vertical lines (153) - only showing 1 every 2 lines\n"
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_history(colors=['darkturquoise', 'orange', 'green'], show_intervals=True)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "042a23ff-84de-4273-ae7b-09b73b740b4c",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0: A <-> B\n",
"Final concentrations: [A] = 0.01218 ; [B] = 9.998\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 821.034\n",
" Formula used: [B] / [A]\n",
"2. Ratio of forward/reverse reaction rates: 800\n",
"Discrepancy between the two values: 2.629 %\n",
"Reaction IS in equilibrium (within 3% tolerance)\n",
"\n",
"1: B <-> C\n",
"Final concentrations: [B] = 9.998 ; [C] = 39.99\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.99992\n",
" Formula used: [C] / [B]\n",
"2. Ratio of forward/reverse reaction rates: 4\n",
"Discrepancy between the two values: 0.001889 %\n",
"Reaction IS in equilibrium (within 3% tolerance)\n",
"\n"
]
},
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dynamics.is_in_equilibrium(tolerance=3)"
]
},
{
"cell_type": "markdown",
"id": "b56568ac-1e46-4242-9141-ca197b654c55",
"metadata": {},
"source": [
"#### A profoundly different plot than we got in experiment `cascade_2_b`"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "f2c169b6-3b95-42f5-9a5c-c323c200d829",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "bed9100c-f575-4591-bf8e-a32de741fa7a",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "1f447754-5017-4b48-a4f5-fc9049b7de64",
"metadata": {},
"source": [
"# PART 2 - This is the starting point of fitting the data from part 1. \n",
"### We're given the data of the time evolution of `A` and `C`, and we want to try to model the complex reaction `A <-> C`"
]
},
{
"cell_type": "markdown",
"id": "b5f75cfb-45b4-4fd2-ad4c-c2a2084ca62d",
"metadata": {},
"source": [
"Let's start by taking stock of the actual data (saved during the simulation of part 1):"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "f26c98c3-802c-4c38-a726-06ac4a77211a",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" SYSTEM TIME | \n",
" A | \n",
" C | \n",
" caption | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 0.000000 | \n",
" 50.000000 | \n",
" 0.000000 | \n",
" Initialized state | \n",
"
\n",
" \n",
" | 1 | \n",
" 0.000256 | \n",
" 48.976000 | \n",
" 0.000000 | \n",
" 1st reaction step | \n",
"
\n",
" \n",
" | 2 | \n",
" 0.000563 | \n",
" 47.772397 | \n",
" 0.002517 | \n",
" | \n",
"
\n",
" \n",
" | 3 | \n",
" 0.000717 | \n",
" 47.185404 | \n",
" 0.005250 | \n",
" | \n",
"
\n",
" \n",
" | 4 | \n",
" 0.000794 | \n",
" 46.895519 | \n",
" 0.006975 | \n",
" | \n",
"
\n",
" \n",
" | ... | \n",
" ... | \n",
" ... | \n",
" ... | \n",
" ... | \n",
"
\n",
" \n",
" | 148 | \n",
" 0.450771 | \n",
" 0.012844 | \n",
" 39.746776 | \n",
" | \n",
"
\n",
" \n",
" | 149 | \n",
" 0.516094 | \n",
" 0.012619 | \n",
" 39.905478 | \n",
" | \n",
"
\n",
" \n",
" | 150 | \n",
" 0.594482 | \n",
" 0.012517 | \n",
" 39.971659 | \n",
" | \n",
"
\n",
" \n",
" | 151 | \n",
" 0.688547 | \n",
" 0.012538 | \n",
" 39.988899 | \n",
" | \n",
"
\n",
" \n",
" | 152 | \n",
" 0.801426 | \n",
" 0.012177 | \n",
" 39.990107 | \n",
" last reaction step | \n",
"
\n",
" \n",
"
\n",
"
153 rows × 4 columns
\n",
"
A(t)=%{x}
value=%{y}",
"legendgroup": "wide_variable_0",
"line": {
"color": "green",
"dash": "solid"
},
"marker": {
"symbol": "circle"
},
"mode": "lines",
"name": "C'(t)",
"orientation": "v",
"showlegend": true,
"type": "scatter",
"x": [
50,
48.976,
47.77239728128,
47.18540424081068,
46.89551869293061,
46.607416414927755,
46.321086435338806,
46.03651785020284,
45.753699822646006,
45.472621582468776,
45.19327242573572,
44.91564171436782,
44.63971887573729,
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QIRAAARAAARAAARAAARAAARAAAcgqYgAEQAAEQAAEQAAEQAAEQAAEQCB0BCCroWsSVAgEQAAEQAAEQAAEQAAEQAAEQACyihgAARAAARAAARAAARAAARAAARAIHQHIauiaBBUCARAAARAAARAAARAAARAAARCArCIGQAAEQAAEQAAEQAAEQAAEQAAEQkcAshq6JkGFQAAEQAAEQAAEQAAEQAAEQAAEIKuIARAAARAAARAAARAAARAAARAAgdARgKyGrklQIRAAARAAARAAARAAARAAARAAAcgqYgAEQAAEQAAEQAAEQAAEQAAEQCB0BCCroWsSVAgEQAAEQAAEQAAEQAAEQAAEQACyihgAARAAARAAARAAARAAARAAARAIHQHIauiaBBUCARAAARAAARAAARAAARAAARCArBrGwKaaA4YlRDd7QX4e9ejagbbuPBjdizS8sm5d2tPhIw20/1CDYUnRzJ6fl0fl3TvQllrEUKoW7tq5HdU3NNG+g/XRDALDq0IMyQARQzKjvmVFhL/3qTkVFxXqF/ccwH0oFSXEkL/3mZwKKeJGALJq2OL445UaIGRVDi7IqjcjiIYcQxANxJAcJd4pEEMyQYiGNyPIKmJIJiCn4PcZDhBwEoCsGsYEZBWyahJCkFWIhkn8cF6IBmIIMWRKQM4PWYWsylHinQIxJBOErMqM4pgCsmrY6pBVyKpJCEFWIRom8QNZlemhd15mhC88ZEYQDciqHCWQ1SAYmZaB/NEjAFk1bFPIKmTVJIQgq5BVk/iBrMr0IKsyI8iqzAiyClmVowSyGgQj0zKQP3oEIKuGbQpZhayahBBkFbJqEj+QVZkeZFVmBFmVGUFWIatylEBWg2BkWgbyR49A5GX1rp/8hua8urBFyy2fN6vF/6fPvJtWr9uofzd0YD96Ydb9vl+HrEJWTW4LkFXIqkn8QFZlepBVmRFkVWYEWYWsylECWQ2CkWkZyB89ApGXVRbRH995M40eOVi33sOPP0fPvPgWzZ/9sP7/TXc8SDW1dUlB5fRlpSX0xM/u9PU6ZBWyanJbgKxCVk3iB7Iq04OsyowgqzIjyCpkVY4SyGoQjEzLQP7oEYi8rDqbbNmKNXTNbffRU4/cowV28ozb6fu3Xk0zpk7SSWfPXUAPPfp0Umal1yGrkFWT2wJkFbJqEj+QVZkeZFVmBFmVGUFWIatylEBWg2BkWoY9P3dIvbd0RYsiS7sVJz/jB3musJblxoDryhzYf+5+4DG6/we3aA9yduCF5ZpiJ6vcEKvWbNCB6hRXbhT77/j/drF1vs6yC1mFrJq8mSGrkFWT+IGsyvQgqzIjyKrMCLIKWZWjBLIaBCPTMqz8o6bM1EJmjaS0fs8e0KtHd/r3f/lOUKcKdTnpCGg6aVvzomMjq9xDWrtrj2ZrzVkNQlYbGptas70CPVd9Yz2t3PEFrd65mj7b9hmt2bmG+Hcb6jbo81TtXtfifJVdBx5z/m4duxE/nEdlt0r9K/6g2NiUYNS1Q1edtn9Jf+rWoRuVdepBvbv0po6FHQO9rlwqjPk0KT65G0XZp12Qn0e5/D7LNiGFR8dP89ss26fLyfIRQ97NhhiSwxox5M1I/SnTB+5DqTkhhvy9z+RUcgp7x5RXap76d/xxlS3ENdX0QC7H6qUdP3akfu5cA4ddY9K40cnynL2a1qhOtzpZa+xIZbKE2w+3tXbsr3sJqN2D/vf5149Z44ev05oWydfGh1P+5dYwTxEbWbVQ8ZzVR5+cowMsCFnduvOgeStkuYTNezfSiprltG7XV7Subg2trv2S1u7+itaq/4fh6FDQkco796LSojIa1HUIDeo2hIZ0O07/5P/z76N6lHRuR0fqG+nAoYaoXqLRdbHMl3VtT9t3HTIqJ8qZizu1o4aGJtp/qD7Kl5nxtSGGZHSIIZlRr+4dKRf+3stXkp0UXToW6oL3HsR9KBVhxJAce8woiIOF7pLzJoq9p35llRdhvfX6S+j2my9LVo/PYf8dTyPkIbWWbDol0e4fqa5RKtP5OpfDEuklkH5llUeLeqWFrAYRmWmUwY3tNWfVHmxuc1btr4dtGPAn25bSvKpXaXnNMvpq50olpGvoUIO7ULMkDuo2mIZ0H66lcEi3YZpiRUmiV7RPl35UkJf4A8RH7cEa2n9k7zGkD9Yfou37txzze/6QuLdxB9Xu3Zd8bfO+jVR7oEaXxRLNz/e5lGkvrET1yHL9BvJDi+yw5P9zXWQxDNj7jYshnPKNDUM4EUNylHinQAzJBDEM2JtRcVHis8KeA5DVVKQQQ/7eZ3Iq7xRWR5Q1D9MrtV9ZtS+8apXnFDv+Px/cE+nWGcavsVNcNe2sFtJrr18mZUq8Us1ZZQ/iwz7dEcOAJZpZet35jQN3sy9YsiwyqwGziL7w5Z/o9aq5NL/6Tao7tPsYkuWdemkhHdr9uGSPJT9n+cvmwUNeenTtIH4bzdewbd9WLa+rd35JVar3l3t+dU/w7jWeMpvrIgtZhWiYvgchGoghxJApATk/RAOyKkeJdwrEkEyQGZkerSWrzp5U7gizBNl6ze1anD209jReZXI6+1abfheKCqpn1bRdTPJHfhiwvWEtUFHYZ/WLms/pD8sfoz+v/L8Wgsq9ohP6nUET+k6i4WWjdA8kC11bHH5lVarbtv1btbhGUWQhqxANKf6l1yGriCEpRqTXEUMSISKIBmRVjhLIahCMTMvg/EEPA3brWeXzWD2lFf3KW+wk4pTOdK4pVZn2Mqz5ram8xp4WspoO/Yimbc1hwFYv6pPLH6elW5YkiZ5UPpauHHEdnVV5btZ7S9NpxqBk1eucpiI7VPU4H99jNI3qcaJ6nNTq82MhqxCNdN5TbmkhGoghxJApATk/ZBWyKkcJZDUIRqZlcH5pgSWWPV4NmDu0nCKaaoEla6EhpzR+/mWVLoMPK006vbvO6+W6uZWZiovbPFbIahBRFKEyWkNW3XpRO7frQpcNv4auPX4msayG8WgNWQ1aZHmerhbXnifRiT1PphFlx2f1CwDIKkTD9L0LWUUMIYZMCcj5IauQVTlKIKtBMDItw8rvtnWN1eNpLb7knBpovW5fYddNaK1zWFLK/3fOkbXmitpHc/L5xo89Xu9pmupIVSbX7XdP/ZVemHV/MqtVX69VhtPpWfVaBAoLLAUVmW1QTjZllXsN/33RPfScGurLW8rwwWLKgsqiysIa5qOtZdWPyFbvqaJl2z8i/kLgk20fus755WHUI9SQamZ/fNloGtt7nJr/OzwQ9JBViIZpIEFWEUOIIVMCcn7IKmRVjhLIahCMTMuw53dbXMgplfatLVlSuZe0prYuKYVessrn4tdrd9W5rsjrdn7nVES3601VpnPbGs7rJar8ejqyal0Pr37MB7auCTIa27CsbMgqi+mvP/xP+sUHP9Ur+fKqvVeNvC7UvahuTRBmWU0VMrzIE6+ovFJt9fNps8SuU4s9OQ8W2FOUtI7tNY5OVg9+nsncYMgqRMP09gVZRQwhhkwJyPkhq5BVOUogq0EwMi0D+aNHIPILLGW7yYKWVe5N/fvXbtYr+/Jx+fBr6Z/G35PcTibb1xNk+bkoq27Xzyssf6HklSX2o63v09KtS6i6ruqYpDxk+MTyU5TAnqp7X3k4sXRAViEaUoxIr0NWEUNSjEivI4YkQlhgSSKErWskQoghmVCCEQ4QcBKArBrGRJCy+tyXT9ETnzyihYjnS9500m164aRcPaIiq278V9auoBVqL9sVOz6jz3eonzWf6a137Ef/4gE0suwEGqkWcDpe/zzhmOHDkFWIhun7G6KBGEIMmRKQ86Nn1ZsRZBUxJBOQU0BWZUZxTAFZNWz1IGS19kANPfHpI/S7ZY/QroM7afqwK+mmE2+jr/U5zbB2bZs9yrLqJMvtxvL6uZLXL2pZYD/TIsvDuK2jXUH7ZmkdrSX2eCWv4wecTMWF3Wn/oYa2bayQnj0/L4/Ku3egLbVHOYa0qm1WLcgqZNU0+BBDMkHIKmRVjhLvFIghmSBkVWYUxxSQVcNWN5VV+7DfwvxC+oev3Ul/rx78PNePOMmqW1vx8OElmxeqYcNq6LDaaogf+47sbZG0Y2FHGtPrFBpTfiqd2meCXsSJVyTGkSAAWZUjAaIBWZWjxDsFYkgmCNGArMpRAlkNgpFpGcgfPQKQVcM2NZFVFtUrn59Kq3eupPJOveiX5z5OkyvONqxReLLHXVbdWoJXHWZp/WhbQl75/86DZZXnvJ7ae4JeuGlUzxP1IltxPCCrcqtDNCCrcpRAVk0ZQVYhq4ghUwJyfvSsyozimAKyatjqmcoqD/299LlztKjyNih/unSuFtYoHZBVuTXzCvfTexvep0XVi3QPLPfEco+s/eBedl6saVzfiWrlYbV4k1p9uKKkUi48Aikgq3IjQlYhq3KUQFZNGUFWIauIIVMCcn7Iqswojikgq4atnqmsXvfidHqr6rXIiipjhazKweW2wBJ/gWGtPLxk00JaWft5cp9dq8TSojIa1ychr9z7eqIaPhz2fXdlGsemgKzK1CCrkFU5SiCrpowgq5BVxJApATk/ZFVmFMcUkFXDVs9EVn/x/gP00/fuoxN6nkQ/mvwfdFrfSYa1CGd2yKrcLn5WA960Z4NatGl5YtVhXrhJLeTEqxHbj64du6nFm0bTiLJRavGmo6sPdyzM7WXgIatyDEFWIatylEBWTRlBViGriCFTAnJ+yKrMKI4pIKuGrZ6urM5e9Qzd884/0pHGI3SfEtVc3ppGQgdZlQgR+ZFVZykNTQ16q5wVSl4/1z8Tz3cc2N4i6aCuQ/WKw9b2Obx1TmXJILlSIUoBWZUbA7IKWZWjBLJqygiyCllFDJkSkPPHXVaXrVhD19x2Hz31yD00euRgDWz23AV09wOP0a3XX0K333zZMRAffvw5evTJOXT/D26hGVOj2fkFWZXfO54p0pFVXlDp/KdOI/75/XF30x3qEeUDsiq3biay6lYqb5GzfPun9KFatOn9LWr+q/rp3PeV840oO14v3nRy+Tg1B3bCMfu+yjVu3RSQVZk3ZBWyKkcJZNWUEWQVsooYMiUg54+LrI6aMvMYGMvnzdK/49fssjp5xu30/Vuv1iLqJrOW0D706NM0f/bDMuQcTAFZNWw0v7Ja31hP1704g+ZXv0lnVZ5Lsy76cyS2p/HCB1mVgysoWXU7E38pwtL6/mZevGkJfbJ1aYt9XzkPL+o1od8Zeu7rxP5n6IWcwnRAVuXWgKxCVuUogayaMoKsQlYRQ6YE5PxRl9VUvaR3/eQ3Gs6//8t3iOXUkk7uNX19/of0wqz79eupZJVfmz7zbjpn8imuva8y+XCngKwato9fWf33RffQrz78T72H5qtXLyZeICfqB2RVbuFsyqrz7PyFCS/WxIs2fdS88nB1XVWLZCUdutJEJa+n9Z0cCnmFrMoxBFmFrMpRAlk1ZQRZhawihkwJyPmjLqssoldNO8u3UDoFlPPX7tqTBDl0YL+kyDrFVqadOykgq4Zt5UdWWQ54mxregmTOFfPoJLVyaxwOyKrcyq0pq261YVldtPEdWrRpgf7plFdeYZiHC2t5VRLLqw5zHLfWAVmVSUNWIatylEBWTRlBViGriCFTAnL+IGV13a51xI/WPgZ2G0j8cB5evaKp6ugcEuxVhvWaNZy4ta87m+eDrBrSlWSVe7MueXaK3ookDvNU7Tghq3JwtbWsOmvI81x5r9dFG+frB2+jYz9YXidXnEVTBpyrfw7sOkS+SIMUkFUZHmQVsipHCWTVlBFkFbKKGDIlIOcPUlZ/9PaP6N5598onDTjFvVPupR+e+cNjSrWGAKcjkyyr9vSS8DrTB3xpbVYcZNUQvSSrc9e8SDf/5Wo9N3DxjSuoQ0FHwzPmTnbIqtxWYZNVZ4153qvueVXiOr/6LVq3+6sWSSpKKhPi2v8sJa9nEw8jDvKArMo0IauQVTlKIKumjCCrkOljGlgAACAASURBVFXEkCkBOX+Qsjrr41n0+09+L5804BQ3nnQjzRwz85hSJdF0qwZkNUEFsmoYpJKs3vrK9fTiqj/TXRPuo++e8o+GZ8ut7JBVub3CLqvOK/h46wdq0ab36eNtH6h5rx/Qml2rkklYVMeqhZrGqMfY3upn+deorKiHDMEjBWRVxgdZhazKUQJZNWUEWYWsIoZMCcj5g5RV+Wytn4LnnE4aN1ovpOTnwDBgyKqfOBHTeMkq90jd8NLl+gM7r/7L24bE6YCsyq2da7Jqv6Ldh3ZpYf1IrTj8kZbX96n2QE0yCe/pOqbX1/RKwyern/w83fmukFU5hiCrkFU5SiCrpowgq5BVxJApATl/1GU11WrAvDjSpq07jpFYtxV+WWDd9lTFAktyfMU2hZes3rfgLvrvj39B3zrxVvrxGT+LHSPIqtzkuSyrzqurqlurhdXe+9rQ2JBMdmLPk7WwWr2uw0pHiIAgqyIigqxCVuUogayaMoKsQlYRQ6YE5PxRl1UmYA0HttMo7Vbsukeqm4Dy7x59co7Obl8NGFvXyPEV2xSpZJXn9t3w4uXEH+B/f/Gf1by+c2LHCLIqN3mUZNV5tbyomBbXZoG1L9ZU3L6kRa/ryWrYcM+i8mOAQVblGIKsQlblKIGsmjKCrEJWEUOmBOT8cZBVmULLFDx0+Pu3Xk0zpk5KmZV7bB969GlX4U33fGFMjzmrhq2SSlZ/+/Gv6N4F/0wXDL6EHrvwKcOz5GZ2yKrcblGWVfvV7zlUp4YKt+x13b5/WzJJ/+IBxMLKw4VPLk/8bFfQniCrcgxBViGrcpRAVk0ZQVYhq4ghUwJyfsjqsYxSDR22Ulo9rW5Dg2XiuZECsmrYTm6yerjxkO5VnV/9Jj109iN0zfE3Gp4lN7NDVuV2i4usOknwfq6619UmsPWNR5LJRvU4Uc915SHD5xx3OpUVZHeLHLmlwpsCsgpZNY1OxJBMELIKWZWjxDsFYkgmCFmVGcUxBWTVsNXdZPXlr2bTd/76DT3MkYcA9yjqaXiW3MwOWZXbLa6y6iTz2Y5P1EJN7ycWbFLDhr+sXZFM0rldZ73CsO51bf7Zq3MfGW5MUkA0IKumoY4YkglCNCCrcpRAVoNgZFoG8kePAGTVsE3dZJX3VeX9Vf95/D30D6f+wPAMuZsdsiq3HWTVnRHPd+WRCW+vf13NeV1CB+sPJhPyXsUT+0+mSWpv1ykDzovdKttOYhANyKp8p/FOgRiSCUJWIatylEBWg2BkWgbyR48AZNWwTZ2yuu/IXhr92AA61HCQPpi5ivp06Wd4htzNDlmV2w6yKotGSXETPb/sNVqw4S2at/5V+qLm8xaZyjv1oimV5yl5nUKTK84m/n+cDoiGHEPl3TvQltqjX3jEKT78XCtiSKYEWYWsylECWQ2CkWkZyB89ApBVwzZ1yir3qHLP6ri+E+n5y143LD23s0NW5faDrKYvGtv2b6V5Va8qeZ2ne1/5//aD9zPmHlfueeUeWO6JjfIB0Ug/hqIcD5lcG2JIpgZZhazKUQJZDYKRaRnIHz0CkFXDNnXKKq8AzCsBf/eUf6S7JtxnWHpuZ4esyu0HWTUXjeU7PqW3lLwu3jSfFm6Yr0c1WAeLKn9xxL2uZ6neV164KWoHRMM8hqIWE+leD2JIJgZZhazKUQJZDYKRaRnIHz0CkFXDNnXK6lWzL6R3VY/Po+c/SdOGXW5Yem5nh6zK7QdZDVY0tuzblFikiRdr2pb4eaB+f/Ik3OuaWKwpsWBTFOQVohFsDMnv2uilQAzJbQpZhazKUQJZDYKRaRnIHz0CkFXDNrXL6ua9G+ncp8fT/sP76bVrF9OQbscZlp7b2SGrcvtBVrMrGjy/9SO1QJPeJkeJ6+c1y5In5H1cx6o9XXnVbt4iZ0z516h/yQC50UKWAqKR3RgKWXNnpTqIIRkrZBWyKkcJZDUIRqZl5GL+ZSvW0DW33UdPPXIPjR45ONSX0BZ1hawahoRdVt+omqv2V71M99q8dOXbhiXnfnbIqtyGkNXWEw3e/5iFVYur2h6Hf27cU52sAC/MxOJq9bqerAS2S7tiuRHbOAVEo/ViqI2bOmunRwzJaCGrkFU5SiCrQTAyLSOs+dtC8jJlYdXVmX/owH70wqz7k79urWuCrGbaks357LL6yw9+Sg8uvpeuG3UTPXjWrwxLzv3skFW5DSGrbScavDAT7+lq9bp+rIYN7z28J1mhYd1HEAurtb/r6J5j5AZtgxQQjbaLoTZo7qycEjEkY4WsQlblKIGsBsHItIyw5m8tsQvi+v3W1W860zpBVg0J2mXV2l/1gSm/pOtPuMWw5NzPDlmV2xCyGh7RqD1QQ/M3vKm2x3ldrzLMw/rtx9Duw9XWOLy367k0od9k6tyui9zArZACohGeGGqF5s7KKRBDMlbIKmRVjhLIahCMTMsIa34vsbO/xvXnIcG3Xn8JPfrknOTl3P+DW2jG1EnJ/990x4P03tIVyf/bhxDf9ZPf0JxXF7ZAYb1unctevnP4sd+6/u1dP6faXUe/5Hf2vAbVFpBVQ5J2WR352z5Ud2g3vXHtB8QLucT9gKzKEQBZDa9orN65Ukkr7+36Gi3aOJ94D2XrsFYZnjLgHDpn4AXEIttWB0QjvDHUVjGR7nkRQzIxyCpkVY4SyGoQjEzLSOZft46IH619DBxIxA/H4VcAORvLql38Hn78OS2uy+fN0qWyjC5Ysozmz35Y/3/23AX00KNPJ//vPLc9vVUPL7FMt67ZnmsLWTUMYktW+YPtmX88mUo6dKUV395sWGo0skNW5XaErHozys/Lo/LuHWhL7dHtaGSqwaeob6yn9zcvVD2vib1dl25Z0uIkfbr0U1vjnEtTKtRD/WzNXleIRm7EUPBRGVyJiCGZJWTVm1FxUaFOsOdAvQwzpikQQ3LDM6PAjh/9iOjeewMrzndBfM4f/vCY5CYC6Mw7aspMcva0Tp95N33rmgta9L5albDys+z6Gbqbas4qSykf1mJQ9ufZXBgKsuo7+twTWrL6h+VP0J1vfZcuHDKdfnvB/xmWGo3skFW5HSGruSkavMowC+tStdLw0q3v0cqao0Nxyjr2UKsLj6NT+oynU9TPsb3GUcfCAP8AO5BBNHIzhuS7Q+ulQAzJrCEakFU5SrxTIIZkgoHK6qxZRL//vXzSoFPceCPRzJlZl1W3atsFdvKM21sM0eX06cqqW4+p25Bl9KwGHUQBl2fJ6g/m/T09+dlj9P1xd9Md6oGDCLIqRwFkNRqiweLKw4XfUo9Uva7nD5qm57zyEOIgD4hGNGIoyJhItyzEkEwMogFZlaMEshoEI9Mywpo/6J5VL0F09rxm2rMKWQ1rNKVZL0tWpz07RX9I/cO0F/RwQByQVT8xAFmNnmjwvPW31r+qF2qaV/Uq8arD1sHDg1lYzx90sZrreiGVFpX5CRPPNBCN6MWQcVCkWQBiSAYGWYWsylECWQ2CkWkZYc0fpKzy4ko1tXXHbCNjXTsP07X3sloLLgXds8pDf92GJAfdBhgGbEjUklVrcaUPZq4inr+GA7LqJwYgq9EXjSWbFtK86tfp5dXPE89tt47C/EI9XJjFdergaTSw6xA/IXNMGohG9GMoo8BIIxNiSIYFWYWsylECWQ2CkWkZYc2fah7o+LEj6XvfvtJzHqib6Hqt+GstyGSx4HPwysHZkFX7ubAacEijj2WVe1JYVnl435rbakNa09avFoYBy8whq/ESjXW7v6LX1v6VXln7kl6wiRdusg5eUfiioZeqRZrOoXF9J8rB05wCohGvGPIdGGkkRAzJsCCrkFU5SiCrQTAyLQP5o0cAPauGbcqyunzHp3TeU6fR8NKR9OY3PjQsMTrZIatyW0JW4ysaq3Z+QUs2LyLueX1fParq1iZhjOxxAo3rM1FLK//s26V/SlAQjfjGkHyH8ZcCMSRzgqxCVuUogawGwci0DOSPHgHIqmGbsqy+VfUaXffidJqk5qI9Pf1lwxKjkx2yKrclZBWiwQS27tuselqVuKreVpbXZds/ToLpXzKAxvVOiOupvSfQiB6jWkCDaCCG5DuNdwrEkEwQsgpZlaMEshoEI9MykD96BCCrhm3KsvrMiifpe2/8DV163NX0q/N+Z1hidLJDVuW2hKxCNJwEDtTvbxbXRK8rC+yRhsM6WXH7khY9riywEA3EkHyngayaMoKsQlYRQ6YE5PyBbl0jnw4pcoQAZNWwoVhWf730IfrJwn+j75z89/TD0x8wLDE62SGrcltCViEaUpR8vPWDFr2uOw5sT2ZhWZ08YJLudT2px2laZnG0JJCfl0fl3TvQltqDQJOCAL7wkEMDsgpZlaPEOwViSCYIWZUZxTEFZNWw1VlW713wz/Tbj39F/3r6/XTbyd8zLDE62SGrcltCViGrcpQcTbFm16rEHNcti/VP/r918PBgHias57mqYcM8fBgHEWRVjgLIqswIogFZlaMEshoEI9MykD96BCCrhm3Ksvp3r86k2V8+Q78457d0xYhvGpYYneyQVbktIauQVTlK3FNwDysL6yfbF9OijQvpw83vJxPygkz2BZp4waa4HpBVueUhqzIjyCpkVY4SyGoQjEzLQP7oEYCsGrYpy+qVz19ACze+Tf97yRw6c8A5hiVGJztkVW5LyCpkVY4S7xQsGvsPH6J5a99p0evKc1/54KHBp/aZoB/W6sL5efmmp82Z/JBVuakgqzIjyCpkVY4SyGoQjEzLQP7oEYCsGrYpy+qUP44l3obi9WuWUJx7MJwoIatycEFWIatylMiyWt/QRPsOHt2zlVcTthZn4lWGebVh6/han9Na9Lp27dDNtAqhzg9ZlZsHsiozgqxCVuUogawGwci0DOSPHgHIqmGb7r3uRnqy6mlaUXKYvnftLOo89ESqHzSEqLDQsOTczw5ZldsQsgpZlaMkfVm15+D9W3kf14S8LtJfrFkH7w19qm0/14qSStPqhC4/ZFVuEsiqzAiyClmVowSyGgQj0zKQP3oEIKuGbdpQUkIFe/a0KKWpuITqBwyghv7qUaEeAyr183p+rh6NPXoanjU3skNW5XaCrEJW5Sgxk1V77l0Hdyb3cuUtcT7c8l7y5d6d+yaHCfNw4VE9TjStWijyQ1blZoCsyowgq5BVOUogq0EwMi0D+aNHALJq2KZLf/Fj+tNL/0Zf219K0xpHUOGaryh/21bPUhv69qP6YcNVD+zghMyqntj6weqh/t/UuYthjcKTHbIqtwVkFbIqR0lwsmovqbGpMSmu7ytxXbJpEe09kvjirXO7Lkpc1RxX1et6Kq8urH4W5BWYVrVN8kNWZeyQVZkRZBWyKkcJZDUIRqZlIH/0CEBWDdv09x/+mWa+dAWdVXku/WHaC7o0ltXC6vVUsL6KCjaon83PC/Xzasrbt9f1rE3t2il5Vb2wzT2w/NPqjdW/719hWNvWzQ5ZlXlDViGrcpRkR1adpa7Y8VmLXtdNezckk5zSZ3xiWxweMqwe3YtKTavdavkhqzJqyKrMCLIKWZWjBLIaBCPTMpA/egQgq4Zt+p/vPEL/9Nbf0lUjr6eff/2/xdLya2qSAquFtloJrf6ZeJ6/e7d7GWpjey2xPJyYhxXr5xWJIcYster3YZsnC1kVw4Egq5BVOUpaR1btZ9lQt17t5boouUjTFzXLky8P6z5CCWtiZWHuda0sGWR6CVnND1mV8UJWZUaQVciqHCWQ1SAYmZaB/NEjAFk1bNM75/6QfvreffTdU/6R7ppwn1Fp+XV1SWm1BLbQJrP5NTtSls9Diy2ZZYHVPbI8Z5bnzqrnTR06GtUtk8yQVZkaZBWyKkdJ68uq/Yx7DtXpHldeVdhaYbiJmnSSXp37JOe58tY4o3uOMb2cwPNDVmWkkFWZEWQVsipHCWQ1CEamZSB/9AhEXlZvuuNBem/pihYtt3zerBb/nz7zblq9bqP+3dCB/eiFWff7fv2GP3+bnvzsMbp30k/p22O+m7UIydu/r1lkq9UQY1tvLA8t5uHGW7ekPHdjz3Jbb+zRRZ+4N7ahooKauhRnpd6QVRkrZBWyKkdJ28qq8+zrdn9Fc9e8SK+sfYmWbllC9Y1Ht8w5qXwsnT/oYjpn0IWhWaAJsipHGGRVZgRZhazKUQJZDYKRaRnIHz0CkZfVyTNup/mzH0623F0/+Q0tWLIs+TuW2ZrauqSgsriWlZbQEz+7U+eRXr/0f6+m2aueoV+d9zu69Lir2yRC8g4fTgwtZmlVc2L5eaF+rn7Hv99QnVpkS0uTqxbr4cWOFYwbu2W+ByNkVQ4HyCpkVY6ScMmqvTYra1aoHtfmXtctC2n97nXJl0/udWqL/VxLi8pMLzWj/JBVGRtkVWYEWYWsylECWQ2CkWkZyB89ApGXVWeTLVuxhq657T566pF7aPTIwcQy+/1br6YZUyfppLPnLqCHHn06KbPS6+fMuoDeqJpLsy5+ls4deGH4IqSxUUurXtwpKbBKaNVzPWdW/Z4aGlzr7bkFjxLbxrIentcLWZXDAbIKWZWjJLyyaq/Zln2bksOEecjwZ9s/Sb48tPtwtZ8rL9CUmOs6sKvai7qVDsiqDBqyKjOCrEJW5SiBrAbByLQM5I8egdjJ6sOPP0fPvPiWllGnuHLz2n/H/7eLrfN1lt2Jj51Jiza+Q89eOpcm9Dsj5yKkYOOGoz2wLLV6BWMls80rGOcdPuQuskWdmlctrlDzY+0rGDc/792HIKtyOEBWIatylOSGrDpryUOEX1df5L2yZg59UfN58uUOBR21sF40ZAadM/AC6tOlnykCz/yQVRkvZFVmBFmFrMpRAlkNgpFpGcgfPQKxklVLRO//wS26JzUIWR3/2ARasnExvfHN+WplzPGRipA8NQ82f/16yqtSqxTzSsXWcyW0eUpm8/a6b8FDaguexspKalK9r/mDBtLhfmpeLPfE8kJPlQPVz9zagiebjdqxfQE1NDbRkfrGbJ4mZ8vOU6tgd+5YQHsPHJ0XmbMXk6WKd1Ax1BjyGPpg8xL1pd67tGgDPxZSzYHEYnFF7YrotH6nq8cE9WXf6frRobBDoKQQQzLOXIgh+Sqym6K4Uzvas/9Idk+Sw6W3b5eva3/4CP6WpWpGxJAc4MwIBwg4CcRGVi0xvfX6S+j2my/THIKQ1TGPjqVPtn5E8294j07qdXJsIixPrUys5VU98lle1YN/WkKbt3uXOwslH41qhWItr+qR+DkgIbeqh5afh20Lnmw2KmTVmy5EQ46+XBONVTu/bJZWJa5KYNfs/Cp5kWN7f40m9E9I64T+E6lnp3IZgJACMSQjzLUYkq8o+BQQDW+mkFU55hBD/hjJqZAibgRiIas8D/XuBx5LzlO1N7LbnFROa60YLL0+8lej9BC3N7/xIQ0vHRm3+HG9XmsLnnYbqqhkxybav3JNixWMc20Lnmw2KoYBe9PFEE45+nJ5COf2A9v0PFdepIl/frJtafKCB3cb1rwtTmKe66CuQ2UYLikQQzK2XI4h+eqCSYFhwN4ci4sKdYI9GAWTEhRiSH4vMiMcIOAkEHlZdS6Y5AQgrfYrvT74v4bR2t2racH1n2b8YSqqYek2ZzUXt+DJZvtAViGrpvEVFdE41HDQtpdrYk9X/h0fPYp6Ht3PVYnrmPJTfGODrMqoohJD8pVmngKiAVnNPHoSORFDMkHIqswojikiLavWMF+3hrXmrfJrJvusVvy8kjbUraf3bviC+peoIaw4kgTSXWAprFvwZLNJIauQVdP4iqpocC8rryq8hLfGUeK6bf9Wjap9foeEuPKjeXVhXrQp1QFZlSMsqjEkX7n/FBANyKr/aHFPiRiSCUJWZUZxTBFpWW2NBu31H731h6iPblpL5Z16tcYpc+Yc6cqq54W14RY82QQOWYWsmsZXHERj3e6vEsOFt3CP6yJavXNlEttJ5WObt8WZqBa5m3jMfRiyKkdYHGJIpuCdAqIBWUUMmRKQ80NWZUZxTAFZNWz17g+W0q6DO2n5LRupW8fuhqVFK3ugsiqgyeYWPNlsFcgqZNU0vuImGrUHahK9rc29rrxFjnXw/q32Htch3Y4jyKocYXGLIZnIsSkgq5DVTOLGngcxJBOErMqM4pgCsmrY6p3v70L76/fRqlu3U6fCzoalRSt7a8qqF7n8bVvVAk/rqUDvIat+Nj8v1M+rKW+f+xY8TWoLnoYWe8gOUHvKDmjeX1btJ9vffAseyCpk1fRdH2fRqG+sTy7OZPW67juSeD+XFfXQ4jq+z+l03nFnUGWnk0xRRzZ/nGPIb6NCNCCrfmMlVTrEkEwQsiozimMKyKphq7f7cXu1x2EDrb11JxUWYH8oO86wyKqnyNbUJAVWC63aT1bLbPPz/N273bOrLXgaWFz7K4FV2+8knldQQ/PzevV7P1vwQFYhq4a3IIJoHCW4fMeneriw1fO6ee9G/WK7/HZqqHDLea5FhZ1M0UcmP2JIbkqIBmRVjhLvFIghmSBkVWYUxxSQVcNWz/tRHvHiHmtuqzUsKXrZc0FWPUW2ri4prZbAFtpkNogteCCrkFXTdz5Ew51gdV1VUlqXbl1Ey7cvTyYc3XPM0dWF1SJNvTr3MW2GnM6PGJKbD6IBWZWjBLIaBCPTMpA/egQgq4ZtyrJa3KGEvvj2FsOSopc912XVq0WC2oKncPAgqu9XQQf6VhD3xjZUVFBTl+LoBUOGV4T5hjI4iIb8hUf7ogP00udvteh1tXJVlgzSCzNZc12HdR8hQ49YCsSQ3KCQVciqHCWQ1SAYmZaB/NEjAFk1bFOW1T5d+tEHM1cZlhS97FGWVU+RPXw4MbSY58iqObH8vFA/V7/j32+oTpm9sbRUDy3mYcV6eHHzcz28WD1v7NYteoHicUWQVbm5IRqyrJZ370BbahN7tvLBqwu/tPp5eqNqrhZY6yjML9TDhc8fdDGdO+gC4gWb4nAghuRWhqxCVuUogawGwci0DOSPHgHIqmGbsqxWlFTS4htWGJYUvexxlVXPlnRswdN560ZqWlelHusSi0ApmaWGBtcimopLlMAm5snqObLNAqsXfVLPG8t6RC6IIKtyk0I00pdVew5eXXjumheVuP6V5le/RdYCTZxmVI8T6ZxBF9JFQ2bo51E9EENyy0JWIatylEBWg2BkWgbyR48AZNWwTSGrqQFCVuXgcs5ZzdUteOQrzSwFZFXmBtEwk1V77kMNB7WwvrL2RS2wLLLWwSNoLh56KX29cipN6HcGcS9sVA7EkNySkFXIqhwlkNUgGJmWgfzRIwBZNWxTyCpk1SSE0llgKcxb8Jgw8MoLWZXJQjSCk1VnSTxE+C9rZtNra/+qhw5bR2lRGZ014Dy6UPW4nlV5rl5kL5cPxJDcepBVyKocJZDVIBiZloH80SMAWTVsU5ZVntf07vXLDEuKXnb0rMptmo6sekpdG2/BI19pZikgqzI3iEb2ZNVeMm+L8/rav9DLX80mfm4dndt1oamDp+W0uCKG5PcZZBWyKkcJZDUIRqZlIH/0CEBWDduUZZWHhD176VzDkqKXHbIqt2lQsuopsq2wBY98pZmlgKzK3CAarSOr9rPwtjg8TJh7Xe0LNOWquCKG5PcZZBWyKkcJZDUIRqZlIH/0CEBWDduUZZW3PHj+stcNS4pedsiq3KatIatetQhqCx77ok9BbsEDWZVjCKLR+rJqPyP3si7c8A4t2qgem+ZT3aHd+uUBXQfSaX0n08R+k/UXmv2LB8iN2UYpEEMyeMgqZFWOEshqEIxMy0D+6BGArBq2KcvqpIqz6OnpLxuWFL3skFW5TdtaVj1FNgRb8EBW5RiCaLStrKYS14VKXvccrkuKKwvrhD6TEuJaEi5xRQzJ7zPIKmRVjhLIahCMTMtA/ugRgKwatinL6tmV59GT02YblhS97JBVuU3DLKuetXdswZPYQ1btKav2kw1yCx7IqhxDEI3wyKovcS0ZqIWVe1y55zUM4ooYkt9nkFXIqhwlkNUgGJmWgfzRIxC4rN71k9/QnFePbrJuR3bJeRPp3//lO5GiyLLKi2s8fuHTkbquIC4GsipTzFlZFS4tqC14GisqqcuIwVRT2jext2zvPjLUmKWAaIRTVu21+mz7J2qY8Hw9VHjhJtXjeqi5x9Umriyw/Yor2iR6EUMydsgqZFWOEshqEIxMy0D+6BEITFZvuuNBem/pCk1o+bxZrqRGTZmpfz9+7Eh64md3RoImy+q0YZfTo+c/GYnrCfIiIKsyzajKqteVx3ELHjkSMk8B0Qi/rLYQ1x1KXNUcVx4mzHNcLXGtLBlEp6neVmuOa2uKK2JIfv9BViGrcpRAVoNgZFoG8kePQCCyyhJa2q2Y5s9+2BehyTNup9pde1JKra9CQpKIZfWKEd+gX5zzWEhqFJ5qQFbltoijrHqKrGMLHh5SXLR1A9V/tZYKqqsof3di8Zpjjry8RM9r/wFUP6Cy+XkFNTQ/50WfqLBQbpAcTAHRyC1ZTSmuqufVmuPK4jqhv5rj2jcxxzXb4ooYkt/4kFXIqhwlkNUgGJmWgfzRIxCIrHKvaro9pZnkCSN+ltVrj59J/3n2/wtj9dq0TpBVGT9k1b9o5OfwFjxyJGSeAqLhP4Yyp5z9nJ/Ze1zdxJVXFVZzXLMhroghuX0hq5BVOUogq0EwMi0D+aNHIBBZjR4W/1fEsnrj6O/QT878L/+ZYpISsio3NGQ1GNEI+xY8ciRkngKiEUwMZd4Cwedctv1jWqyEVQ8VTiGuE1WPa98u/QM5OWJIxghZhazKUQJZDYKRaRnIHz0CgcsqDwm+/we30Iypk1rQevjx5+iZF9/yPVQ4V1CzrH57zHfp3kk/zZUqt1o9Iasyashq9kUjLwRb8MiRkHkKiEb2Yyjz1jHPyeJqzXFdvGnB0aHCXQerIcK8hyvPczUTV8SQ3E6QVciqHCWQMdZ/3QAAIABJREFU1SAYmZaB/NEj0GqyOnvuArr7gcciMU/VHgYsq3879g66e+KPoxcdhlcEWZUBQlbbWDRaaQseORIyTwHRaOMYyrzp0s5pF1fucd17ZI8uo1KJ60Q1x/U0tY+rFtfi9HpcEUNyU0BWIatylEBWg2BkWgbyR49Aq8kqb2mzYMmySPas/n+n3kX/NP7fohcdhlcEWZUBQlbDLRpBbcGjF3/Sj+bFnwLcggeiEe4Yku8CmaVIKa4lCXHVva5qjqsfcUUMyW0AWYWsylECWQ2CkWkZyB89AoHIqtVrKuFxGx4s5Qn769yz+s/j76F/OPUHYa9qq9cPsiojh6zmrmiEZQseiEbuxpB8h/CX4tNtHx2d46q2w9l7uLnH1Sau3OPap0s/1wIRQzJnyCpkVY4SyGoQjEzLQP7oEQhEVu1YUs1ZjR66xBWxrP7r6ffTbSd/L6qXmPF1QVZldJDVaIpGvmMLHt52p0Btw5N4BLsFD0QjmjEk3z3cU3y6/SO1KJPax1Xt5cpzXC1xHdh1SIs5rnZxRQzJtCGrkFU5SiCrQTAyLQP5o0cgcFmNHiLvK2JZfWDKL+n6E26J26WL1wtZFRERZDV+ohH0Fjwdhw6iI2p48d7yvtTUoaMcdDFLka/24C3v3oG21B6M2ZUTbd67kV5a/Tz9Zc1sWrJpYfL6O7frQlMHT6MLh8ygsyrPpfKSYqpvaKJ9B+tjx8jvBUNWIat+YyVVOsSQTJAZ4QABJwHIqmFMsKzef+bPaebovzEsKXrZIatym0JW4yerXlcc5y145HdLZiniLKt2YvYeV16cad+Rvfpl7nGdMvBMNc/1TBrbc2LKocKZ0Y9OLogGZNU0mhFDMkHIqswojikCkdWb7niQnvjZnWnxyyRPWidopcToWU0NGrIqByFkFbIqR0kiRaoteNpvqqa89WpocXV1yqIaS0upoX9ikaf6AWqRp+bnDc3PG7t181uNnEsHWT22yT7ZtlQNEVb7uKqhwk5xndift8M5Q68q3Ltz35xr72xVGKIBWTWNLcSQTBCyKjOKY4pAZJXnqZZ2K/a90u/kGbdT7a49kdjGhmX1p2f/mr55/LfiGD+e1wxZlUMCsgpZlaPEO4Web3ikgQ6uWkOFG9ScWCWuem7shmr9vFA/X0/U0OBaUFNxiRJYJbIOga3n1YuVzDaW9TCtYpvmh6x642dx/Wj7u/RO1du0oPqdZI/roG5DlbROgrg244NoQFZNb2SIIZkgZFVmFMcUgcgqg+Oe0veWrtAMl8+b5cqSpZaP8WNHpt0TG9bGYVn9+df/m64aeX1Yq9hm9YKsyughq5BVOUp8yKow3zAXtuAx5ZAqP2RVJmstsLR6R5WvOa4dCuI3NxqiAVmV30neKRBDMkHIqswojikCk1UL3sOPP0ePPjnHleWt119Ct998WaQ4s6z+1zm/oStHXBep6wriYiCrMkXIKmRVjhJzWfUqISxb8JhygKxmTtBtNWDucbVWFeahwvvr9+kTDOo6VA0RVkOFeS9XtY9r7y7xGCoM0YCsZv4OS+REDMkEIasyozimCFxW4waRZfUX5/yWrhjxzbhduni9kFUREVYDFhChV0yOoWxuO9KaW/DIV5pZCsSQzE2KoY+3fpiY46q2xNHieuRYceU5rr0695FPlqMpIBqQVdPQRQzJBCGrMqM4poCsGra6ltVzH6Mrhn/DsKToZYesym2KnlVvRhANOYYk0ZBLyCxF0Fvw6DmzPHdWzZUNcgsexJDcvunE0MfbPmyxj6slroO7DVM9rWqOq+pxjaK4QjQgq/I7yTsFYkgmCFmVGcUxBWTVsNVZVn957uN0+fBrDUuKXnbIqtymkFXIqhwl3inSEQ3Tc/nNH6YteCCrcqtlGkN2ceUe1wP1+/XJWFx5qPBp6hEVcYVoQFbldxJkNQhGpmUgf/QIBCKr1sJJFp5UCyxFD5/aTkLJ6sPnPUGXHXdNFC/P6JogqzI+yCpkVY6S3JNVrxqn2oInsYJxYhXjVEcmW/BAVuUIy1RW7SVL4mrNcc3VocKQVciq/E6CrAbByLQM5I8egUBkNXpY/F8Ry+qvzvsdXXrc1f4zxSQlZFVuaMgqZFWOkmjJqufVNDbqbXeC3IKnUW2/0330MNpSUGyKOrL5g5DVFuK69YPk/Fa3HldrqHB5p945wxSyClk1DVbEkEwQw4BlRnFMAVk1bHWW1V+fP4tmDLvKsKToZYesym0KWYWsylESI1kVYGS6BQ916kT1eh/ZCqqvqNTzYhOP5ue9o7swkJ/4ClpW3cWVF2dakBwqPKT7cS3muIZdXCEakFU/7yWvNIghmSBkVWYUxxSByaq1ZY3b9jRer+U6dJbV/3f+72n6sCtz/VICrz9kVUYKWYWsylECWfXDKPUWPNW6p5b27nUtpqldu6PS2iyx9XaZ7V/h5/Q5nSabsppKXBdumE8HGw7olxPiqrbDaZ7jWt45fD2uEA3IqumbHDEkE4SsyozimCIwWZ0+824qKy2hJ352pyvHm+54kGpq6+iFWfdHijPL6iPn/w9dMuyKSF1XEBcDWZUpQlYhq3KUQFZNGOk5qw17qGbZqsQQY54bW12lnyceVZS/e7f7KVRe3QOremXr1XDixPMKtWpx4jn31lJhoUn1QpG3tWTVl7h2U+LK0sr7uKrtcMo79QoFI4gGZNU0EBFDMkHIqswojikCk1VeZOn+H9xCM6ZOcuU4e+4CuvuBxyhqiy+xrD56/pM0bdjlcYwfz2uGrMohAVmFrMpRAlk1YSQtsJQrW/CYMJDytoWs2uv00Zb39RzXxZvVXq7c41rf3OMaInGFaEBWpfeR9DpiSCJEBFmVGcUxBWTVsNVZVv976h/o4qGXGZYUveyQVblNIauQVTlKIKsmjCRZ9So7TFvwmDCQ8ra1rLYQ160JcV2kHwuS4jq0+3A6Te3j2lY9rhANyKr0PpJeRwxJhCCrMqF4pghMVifPuJ2+f+vVnj2rDz36NM2f/XCkSLOs/mbqH+mioZdG6rqCuBjIqkwRsgpZlaMEsmrCyERWPUX28OHEVjvreUhxtX5eqJ9nZwseEwZS3jDJaipx5R7XQw0H9cssrjxUOPFonaHCEA3IqvQ+kl5HDEmEIKsyoXimCExW7/rJb+jzL6tSzkmV5rTmKn4tqxf8L100ZEauXkLW6g1ZldFCViGrcpRAVk0YZUtWPeuUhS149KJPaq5sY1kPExyuecMqq+mI60QlrbwlTs+i8sD5cIEQDciqaWAhhmSCGAYsM4pjisBkleFx7yofzt5T/n3trj2Rm6/K18qy+tsL/o8uHDI9jvHjec2QVTkkIKuQVTlKIKsmjNpEVoUKZ7oFT1NRp+Ytd4LdgicXZNWOdOmWJYk5rpsSc1ydPa7ZEFeIBmTV5D6ELzz80YOs+uMUt1SByirD4x7WOa8ubMFx/NiRKVcJznXgLKuPXfgUXTD4kly/lMDrD1mVkUJWIatylEBWTRiFUVa9rif1Fjy8cnE15e0LfgueXJNVN3G15rha4jqsdERijmtAPa6QVciqyX0IsuqPHmTVH6e4pQpcVmMHUMnq4xc+TVMHT4vbpYvXC1kVERFkFbIqRwlk1YRRrsmqp8jW1CTmyQa8BU/n4UOoPq+A9h2sN0Hd5nmtHlcWV+5xPdx4SNdpWPcRifmtvJcrDxXulP5QYcgqZNU0wBFDMkHIqswojikgq4atzj2rT1z0DJ0/6GLDkqKXHbIqtylkFbIqRwlk1YRRlGTVU2Tr6pL7xlp7yBba9pPNr9mRMntTv/7UqObEHu6X2ENWz49Ve8g2DFAP9bypQ0eTJmiTvB9ufo8WqWHCqcTV6nHtUdTTV/0gGpBVX4HikQgxJBOErMqM4pgCsmrY6iyrv7voT3TeoIsMS4pedsiq3KaQVciqHCWQVRNGcZFVL0Zx2YInFQMW14Wbjs5xPdzQssfVj7hCNCCrJvchzosYkglCVmVGcUwBWTVsdZbVWRc/S+cOvNCwpOhlh6zKbQpZhazKUQJZNWEEWfWml6e24OlWs5ka166lI1+ty+ktePzEyYdblLjqPVy511UNFW4W1+NKR7aY4+rscYVoQFb9xJdXGsSQTBCyKjOKYwrIqmGrs6z+/uI/0zkDLzAsKXrZIatym0JWIatylEBWTRhBVmV6KRdYyrEteOQrbZnCLq4ssEcaDusELK48x5V7XE9TP1lcIRqQ1XTjy5keMSQThKzKjOKYArJq2Oosq/8z7Tn6euVUw5Kilx2yKrcpZBWyKkcJZNWEEWRVppfpasBh24JHvtLUKT7YvLh5jqvaDsdFXC8acQ6N6HoalXUMfp9bk3qHJW9xUaGuyp4Dub1IVzZ5QlZlupBVmVEcU0BWDVudZfXJac/T2ZXnG5YUveyQVblNIauQVTlKIKsmjCCrMr1MZdWr5LbYgke+Un8pWFwT+7gucBVXa44rxPUoT8iqHFuQVX+M5FRIETcCkFXDFk/I6mwlq+cZlhS97JBVuU0hq5BVOUogqyaMIKsyvWzIqqfIZmkLnnq1gjEVJnr4gjoscV267V2aV/V2cqjw8DKe45oYKjxBPcqK4t3jClmVIw6y6o+RnAop4kYAsmrY4lpWL1ayOhCy6kQJWZWDC7IKWZWjBLJqwgiyKtNrbVn1FFmDLXga+vbTW+0ktt0JdgseFo05n72VXJyJe17rG4/oSxmu57iekZzjGkdxhazK7zPIqj9GciqkiBsByKphi7Os/mHaC3RW5bmGJUUvO2RVblPIKmRVjhLIqgkjyKpML0yy6lXbttyCxyka729a1GKOq5u4ssCWFpXJDRCBFJBVuREhq/4YyamQIm4EIKuGLc6y+sdpc2hK5TmGJUUvO2RVblPIKmRVjhLIqgkjyKpML1dk1VNk1RY8BRvWU8H6Kiqorg58Cx4v0Xh/sxJX3g6neY5rfcOxPa5RF1fIqvw+g6z6YySnQoq4EYiNrC5bsYauue0+euqRe2j0yMEt2nn6zLtp9bqN+ndDB/ajF2bd7/t1ltX/vWQOnTkAsup880BW5dsJZBWyKkcJZNWEEWRVphcFWfW8ygC24Gk3eBDt66WGGavhxTzMuJ6HG6vnjWUt56pa4rpQ7+PKQ4UTq+OOKDu+xRzXqPW4Qlbl9xlk1R8jORVSxI1ALGR18ozbqXbXHt22Tlm96Y4Hqaa2LimoLK5lpSX0xM/u1Oml11lW/++SF+mMAV+PW+yI1wtZFRERZBWyKkcJZNWEEWRVphd5WRUQZGsLnsVN67Swuokr97Tqh1qkKQriClmV32eQVX+M5FRIETcCsZBVbtRUPassst+/9WqaMXWSbvvZcxfQQ48+TfNnP6z/L73OsvrU9JdocsXZcYsd8XohqyIiyKqACKIhx1DcRUMihBiSCBEhhlIzsrbg6bFzM9WtWK2GGCeGGhfykGM13Dhv317XzE3t2qnFnlQvLPfAqkdVtzxaVrSL5udX0V/qP6U1xUd7XC1x5ZWFu3cslRsshCkgq3KjQFb9MZJTIUXcCMRaVt0E1v47Dgbn0GFnHpbVp6e/TJMqzopb7IjXC1kVEUFWIatykAgpIBregCCrcoghhmRGbqKRb7AFz87yrkpgiT4t2k3rujbp541qWHGvkafTsDEX0GkDzsopcYWsZhZDcq54peD3GQ4QcBKArDrmsWYiq89fMVf1rE5BdDkI8IfErl3a0c49h8EmBYEuRe3oSH0jHTrSAEYuBPJUDHVXMVSLGEoZH507FlJDYxMdPIwYcoOEGJJvLYghmVFZSQeqqTskJ2xOkVe3m/K5F7aqSv9s+Vz9bseOlGVtKCHa3qMTHenfjzoOHUW9R06kjkNGapltVL20TR07+q5HayUs6lCgT3XgEO5DqZinG0Ot1XZhOg8zwgECkFXbAktB9ay+8o036MyBkNVjgiuPqF1BPh1WMobDnUBhQR41NTUp2QAhV9FQv2zXTsXQEQBKFSGJGCItrDiOJaBuQ4ghITAQQ/I7p4O6Dx0K6j60bx/lqaHEeVXr1WNd8/Mq2rPqM8pfv56KaxJrbLgdjeU9iQaqRSIHKGmtrKQmJbBNlQPVQ/1fPafiYvlispCiMJ/faaQWlMJ9KBXeQGMoC20YhiKZEQ4QOMYn1AflWNxZ0pmzevcDj9HyebM0K7c5q/bXeRjws5fO1Qsl4GhJAMOA5YjAAkvejDCEU44hDOFEDMlR4p0CMSQTbK35hnnNW/Cs+ugvtOXzd2nvV8uosLqKBuxqospdylF3p65rY2mpXqmY58jWN69arOfMNj9v7KbGGmfpwDBgGWxrxZBck/CmwDDg8LZNW9Ys1sOAGby02q/0upbVy17RK/rhgKymGwOQVYhGujHjTA/RQAwhhkwJyPnbUjTe2/wuLdrwDr2ntsPZtHw+9d/ZQAOVuJ5yuJzGHCylIbsLqGz7Xmq/cYMaYuE+DLepuEQJrBLXZpmVtuCRibRMAVmVibVlDMm1C0cKyGo42iFstYiFrNq3ruEGKO1WnFztl/9vus/qny97Ve2fllhNGMdRAuhZlaMBsgrRkKPEOwVkFTGEGDIlIOcPi2hY4mpth9PYlJgiMbLHCXRxh7F0RtNgOvlQGRVvqaFCNdS4YEN1cgXjvMPuc26bijo1r1pcofaPPbqCcXI14959RECQVRERhSWG5Jq2XQrIatuxD/OZYyGr2WwA7ll97vLXaHyf07N5mpwsG7IqNxtkFaIhRwlk1YQRhpLL9PCFh8wojKLhJa68DY61j2u3jt3J2oKHt90p0NvuZLYFjx5i3Lwdj5bZ/hUaHmQ1N2NIrnXrpoCsti7vXDkbZNWwpVhWn7/sdRrXd6JhSdHLDlmV2xSyClmVowSyasIIsirTg6zKjMIoq/ZaL960gBarYcJuPa6WuPLPrh2OnbdqsgWPnhOrhhbnDVKLPKm5sft790vMkWWpVb+nwkIZbkxShD2GwtAMkNUwtEL46gBZNWwTltXZl79Bp/aZYFhS9LJDVuU2haxCVuUogayaMIKsyvQgqzKjXBINFlee48riunjTfLKGCh/fY7TqbZ2se1xTiauTRH5dXaIXVi3ylPi5Xi/4ZD3Pr0m9BU9DXyWuzTLLAqt7ZHnOLM+d5S14OoRvCx45EjJPkUsxlPlVmuWErJrxi2puyKphy7KsvnD5m/S1PqcZlhS97JBVuU0hq5BVOUogqyaMIKsyPciqzChXRcMuros2vkNN6h8fLK4srKepxSG1uHZMf6XgvP37mqW1mjpvqdbb7jSsXZcYZszDjbduSQm2sWd5YsViS2CbVy3m3tiGigpq6tI2W/DIkZB5ilyNocyvOP2ckNX0mcUhB2TVsJVZVudc8Rad0nu8YUnRyw5ZldsUsgpZlaMEsmrCCLIq04OsyoyiIBopxbVMiWv/o3NcMxFX55xVawseLa3VapEnJbB6wSfunWWZVQs/pTracgseORIyTxGFGMr86v3lhKz64xS3VJBVwxZnWX3xink0tvc4w5Kilx2yKrcpZBWyKkcJZNWEEWRVpgdZlRlFTTQW8RBhnuOqhgnzkOFkj6tNXLnHtaRDVxmOSpHWAkuNjYnhxFYPrBZYJbRKZgubZbattuDxdbEZJopaDGWIwTMbZDUbVHO/TMiqYRuyrL505dt0cq9TDUuKXnbIqtymkFXIqhwlkFUTRpBVmR5kVWYUZdFY1Cys1hzXpqbEUOFRPU5sMcfVS1zTklUBd4HaLzbZA8tS24pb8MiRkHmKKMdQ5lRa5oSsBkUyWuVAVg3bk2X12Uvn6gULcLQkAFmVIwKyClmVowSyasIIsirTg6zKjOIiGut2f0UvfPknevmr2bR8x6dJMKVFZTR18DS6ZOgVNLni7GOABSmrXq2R7S145EjIPEVcYihzQqT3osUBAk4CkFXDmICspgYIWZWDC7IKWZWjBLJqwgiyKtODrMqM4igafsSVv6gvzC9MbxiwjDujFEFswXN00aeKwLfgiWMMpduQkNV0icUjPWTVsJ0hq5BVkxCCrEJWTeKH80I0EEOIIVMCcv64i4YlrnNWP0tf1HyeBGb1uF496mrV43omHTgks2yLFGHYgifuMeSn3SGrfijFLw1k1bDNIauQVZMQgqxCNEziB7Iq00PPqswIX3jIjCAaRxml6nHtV9yPLhxyqR4qnEuLTtq34LHvIRv0FjyIIX/vMzkVUsSNAGTVsMUhq5BVkxCCrEJWTeIHsirTg6zKjCCrMiOIhjsjFtfnVj5Fz696itbs/CqZaGDXITT9uCvpqhHfJH6eq0eQW/B0GT6Eakv7JIYXq/1kG7ulv7dtrnL0W2/0rPolFa90kFXD9mZZfeWaRXRCj5MMS4pedsxZldsUsgpZlaPEOwVEAzGEGDIlIOeHrHoz6ti+id6pfoteXf0GvbthHn26/SOdgeeznt5/inqcSZP6n0UnlY+VYedKiphuwZPN5oGsZpNu7pYNWTVsO5bVV69ZrJd4x9GSAGRVjgjIKkRDjhLIqgkj9KzK9PCFh8wIsurNyL4a8J7DdTRfiStL67sb36ZVtV/ozMXtS5LSyvJ6XOlIGXwOp3BuwVOybSMdWr02sS2P2o4n77D7BN+mok7UUDFAPSqovkL1wurn/Gh+3rtPDlPxrjpkNbJNa3RhkFUjfEQsq69d+x4drzbSxgFZTTcGIKuQ1XRjxpkeooEYQgyZEpDzQ1b9y6o95dZ9m2kBS+uGt9XPt2jjnmr9cnmnXrqnlaWVe14rSirlRsjxFPYYyuUteLLZDJDVbNLN3bIhq4Ztx7L6+jVLaGSPEwxLil529KzKbQpZhWjIUeKdArKKGEIMmRKQ80NWM5NVey6e37qgWVq517X2QI1+ubLrYJrUT0lrxRSaVHEWlXXsITdIDqbwG0Nh34Inm+ghq9mkm7tlQ1YN245l9Y1r36cRZaMMS4pedsiq3KaQVYiGHCWQVRNGGAYs08MXHjIjv6IhlxTNFPZhwH6ucMWOz3SPK/e2cq/rgfr9Oht/lpqkelpZWrnXtVNhZz/F5USaIGIoDFvwZBM2ZDWbdHO3bMiqYdslZPUDdYM93rCk6GWHrMptClmFrMpRAlk1YQRZlelBVmVGQYiGfJbcTZGurNqvdOmWJVpaudeVe1yt4+Rep6q9W5uHCvebQnl5ebkLSNU82zHUWlvwZLMRIKvZpJu7ZUNWDduOZfXNb3xIwyO+UEAmmCCrMjXIKmRVjhLIqgkjyKpMD7IqM8q2aMg1CHcKE1m1X9kCXphJLcrEva4ssdbB81onNc9vPaX3+HDDSFG7toyhILfg4W139IJPWdiCB7Kak6Gd9UpDVg0Rs6y+pWQ16qvaZYIJsipTg6xCVuUogayaMIKsyvQgqzKjthQNuXZtnyIoWbWuZP+RfVpauaeVVxb+oma5fqmosFPzisK8Hc4UOr5H7ixuGdoYCtEWPJDVtn8vh7EGkFXDVmFZnffNpTSs+wjDkqKXHbIqtylkFbIqRwlk1YQRZFWmB1mVGYVWNOSqt0qKoGXVXumagzvo3Wo1v1VJKw8Vrqpbo18uLSrTwjpJDRGepBZnGth1SKtca6YnydUYcm7BU6i23SnYUJ2VLXggq5lGV7TzQVYN25dl9e1vfkRDuw83LCl62SGrcptCViGrcpRAVk0YQVZlepBVmVGuioZ8ZcGkyKas2mu4Yc96La16K5yN82jbvi365X7FFQlxbX706hy+vUijGEN5+/aqPWPXU+Har/SjYO0a9VM9Vq2kgk0bPYOrsbwX1Q8eQvWDhlDDwEH6efdbbggmIFFKpAhAVg2bk2X1nes+piHdjjMsKXrZIatym0JWIatylEBWTRhBVmV6kFWZURRFQ75q/ylaS1btNfqydoWWVh4qzHNc9xyu0y9z5wFLqyWvJR26+r+QLKaMWwzl19aq3lfVC1utZFY9rOf8f36ev3t3S9r5+UQNDVlsARSdqwQgq4Ytx7I6/7pPaHC3YYYlRS87ZFVuU8gqZFWOEsiqCSPIqkwPsioziptoyERapmgLWbXX4JNtS5PSyvJa31ivXz6x/GQ6XQ0TZnGdrIYKF+a3S/fSAkuPGGqJUvfEruGeWNUru24N5W/dSkXPPRMYbxQUHQKQVcO2ZFldcP2nNKjrUMOSopcdsiq3KWQVsipHCWTVhBFkVaYHWZUZQTS8GbW1rNprt3jTAjVUeJ5aoGkeLdm0MPnS+D6n0+lKWHl+Kz9v7QMxJBPHnFWZURxTQFYNW51l9d3rl4V+Yr/hZWaUHbIqY4OsQlblKIGsmjCCrMr0IKsyI4hG7siqVdMjDYfVSsIJaeXe1mXbP9YvFRa0U4synamklfdwnUIn9jxZDoAAUiCGZIiQVZlRHFNAVg1bnWV14Q2fUWXJYMOSopcdsiq3KWQVsipHCWTVhBFkVaYHWZUZQTRyT1btNa47tJvmb+CFmVhc36bVO1fql4vbl6jhwQlpPV0J7LDS7O3sgBjy9z6TUyFF3AhAVg1bPCGry5WsDjIsKXrZIatym0JWIatylEBWTRhBVmV6kFWZEUQjt2XVXvstezfplYT1isJqZeFNezfol3kF4cTCTGfqea79SwbIgZFGCsSQDAs9qzKjOKaArBq2Osvqohs+pwElAw1Lil52yKrcppBVyKocJZBVE0aQVZkeZFVmBNGIjqzar2Tt7tVaWufr7XDm0c6Dtfpl3rN1UrO08nBh3tPV9EAMyQQhqzKjOKaArBq2Osvq4htWUEVJpWFJ0csOWZXbFLIKWZWjBLJqwgiyKtODrMqMIBrRlFX7VX1es4wWrH9Lb4Pz7sa36WD9Af3yyB4nNO/fysOFz6Siwk5ywLikQAzJ2CCrMqM4poCsGrY6y+p7N35B/YuDHS5iWK1QZIesys0AWYWsylECWTVhBFmV6UFWZUYQjejLqv0KP9i8OLEVjpLWharn1To9Snk1AAAZ3ElEQVTG9h6nxPWsRK+rGjKczoEYkmlBVmVGcUwBWTVsdZbVJTeupH7FFYYlRS87ZFVuU8gqZFWOEsiqCSPIqkwPsiozgmjES1atq21sakwuysQLNH289YMkCL2aMK8qrKSVJVY6EEMSISLIqswojikgq4atzrL6/swvqW+X/oYlRS87ZFVuU8gqZFWOEsiqCSPIqkwPsiozgmjEU1btV73vyN7EokzNqwp/UfO5frlTu85aWrmnlVcWHlE2yhUWYsjf+0xOhRRxIwBZNWxxltUPZq6iPl36GZYUveyQVblNIauQVTlKIKsmjCCrMj3IqswIogFZtRPYcWC7XklY7+Fa/TZV1a3VL5d17EGnV0zRe7jyUGH7toaIIX/vMzkVUsSNAGTVsMVZVj/81mrq3bmvYUnRyw5ZldsUsgpZlaMEsmrCCLIq04OsyowgGpDVVASq66qae1sTW+FsP7BNJ+W1TPRQYSWtk9RWOGMGDKJNNYlFm3C4E8AwYESGGwHIqmFcsKwu/dZXen8uHC0JQFbliICsQlblKIGsmjCCrMr0IKsyI8gqZFWOEqKVNSsSva28OFP1PNp7ZI/OdlzpSDpv6NdpTI9JWlyLO5T4KS52aSCrsWtyXxcMWfWFKXUiltWPblpD5Z16G5YUveyQVblNIauQVTlKIKsmjCCrMj3IqswIsgpZlaOkZYqPt32YlFYW2IbGBp3gpPKxen7r6UpaJ6khw4X5hekWHdn0kNXINq3RhUFWjfARJWR1rZLVXoYlRS87ZFVuU8gqZFWOEsiqCSPIqkwPsiozgqxCVuUoSZ1i0ab59MmOBTR31ev0/uZFyYSn9Z2UGCastsMZ13eiySkikReyGolmDPwiIKuGSFlWP755HfUsKjcsKXrZIatym0JWIatylEBWTRhBVmV6kFWZEWQVsipHiXcKjqF123fp4cH84N7Wz7Z/ojO1K2ivF2RiaeVe19E9x5ieLifzQ1ZzstmyXmnIqiFiltVPbq6iHkU9DUuKXnbIqtymkFXIqhwlkFUTRpBVmR5kVWYEWYWsylEiy6p9gaVdB3cmhgk3P9bsWqULKOnQlSY3Syv3ug7tPtz01DmTH7KaM03VqhWFrBriZln99Jb1erlyHC0JQFbliICsQlblKIGsmjCCrMr0IKsyI8gqZFWOkvRk1Z56896NWlznqwf/5P/z0btLX70gE0sr97j2K64wrUao80NWQ908bVY5yKohepbVZTdXU2lRmWFJ0csOWZXbFLIKWZWjBLJqwgiyKtODrMqMIKuQVTlKMpdVe07uYdVDhZtXFeYeWD4GdR2qpXWy3g5nCnXvWGpapdDlh6yGrklCUSHIqmEzsKwuvmEFVZRUGpYUveyQVblNIauQVTlKIKsmjCCrMj3IqswIsgpZlaMkGFm1l7Jt/1Z64cs/0ZzVz9LSLUuSL3EHyeXDr6VLhl5BY3uPM61aaPJDVkPTFKGqCGTVsDkgq6kBQlbl4IKsQlblKIGsmjCCrMr0IKsyI8gqZFWOkuBl1V7iut1faXF97sunafXOlcmXBnYdosT1GrpyxHU533ECWTWNsmjmh6watitkFbJqEkKQVciqSfxwXogGYggxZEpAzg9ZhazKUZJdWbWXvnzHp/SnL/5AL61+Pjm/lV8/Z+AFdMtJf6eGCp9tWt02yQ9ZbRPsoT8pZNWwiVhWV3x7s169DUdLAuhZlSMCsgrRkKPEOwVkFTGEGDIlIOeHrEJW5ShpPVm1zlTfWE+LNr6jxPWP9MKqPxH/n48RZcfTzSd+ly4fcQ11KOhoWvVWyw9ZbTXUOXUiyKphc7GsfvGdLVTcvsSwpOhlh6zKbQpZhWjIUQJZNWGEYcAyPXzhITOCrEJW5ShpfVm1n/GjLe/Tq+v+Qq+ufYm+qFmuXzq+x2g6d9BFdJ56jCk/xfQSsp4fspp1xDl5AsiqYbNBVlMDhKzKwQVZhazKUQJZNWEEWZXpQVZlRpBVyKocJW0rq9bZq+uqlLC+TK8pcZ1f/ab+dXmnXlpYzxt8MX29cqrppWQtP2Q1a2hzumDIqmHzsayu/Jut1KVdsWFJ0csOWZXbFLIKWZWjBLJqwgiyKtODrMqMIKuQVTlKwiGrVi0O1O9PSOta7m19mfYd2Uv5eflaWs8deKH6eXHotl2ErJpGWTTzQ1YN25Vl9cu/2Uad23UxLCl62SGrcptCViGrcpRAVk0YQVZlepBVmRFkFbIqR0m4ZNVem4Ub39bC+qoS16rda/RLp/Qe3yyuF9HwspGmlxdIfshqIBgjVwhk1bBJWVZX3bqdOhV2Niwpetkhq3KbQlYhq3KUQFZNGEFWZXqQVZkRZBWyKkdJeGXVqtnKmhVqeDBL68v04Zb39K8rSwar4cE8r/VCmtjvTNPLNMoPWTXCF9nMkFXDpmVZ3fjd/YalRDM7ZFVuV8gqZFWOEsiqCSPIqkwPsiozgqxCVuUoCb+sWjXkVYNfWfMiPfrxL2jpliXJip9VeS5dN+oWvQVOYX6h6SWnnR+ymjayWGSArBo2M8vqV7fVUMeCIsOSopcdsiq3KWQVsipHCWTVhBFkVaYHWZUZQVYhq3KU5I6s2mv6+rq/qnmtid7Wbfu36pfG9PqaWojpfDp74NRWXUUYsmoaZdHMD1k1bFeW1TW31ebUPlaGl+w7O2RVRgVZhazKUQJZNWEEWZXpQVZlRpBVyKocJbkpq1atV+z4jN6omktvrnuF3tv8rv51WcceWlgT4np+1tdngayaRlk080NWDduVZXXt3+6k9vkdDEuKXnbIqtymkFXIqhwlkFUTRpBVmR5kVWYEWYWsylGS27Jq1X7vkT1aWN+oeoXeVPJae6BGv3Ra30laWHnrmxFlo0xxuOaHrGYFa84XClk1bEKW1XW37aJ2Be0NS4pedsiq3KaQVciqHCWQVRNGkFWZHmRVZgRZhazKURINWbVfxcdbP0hI67q59PG2D/VLfbv0p7NVT+vXVY8r/wxybitk1TTKopkfsmrYriyrVX+7W71Z2xmWFL3skFW5TSGrkFU5SiCrJowgqzI9yKrMCLIKWZWjJHqyal1RzcEdWlgT4vqK3rOVjzMHnNMsrufToK5DTRERZNUYYSQLgKz6aNbpM++m1es26pRDB/ajF2bdn8yVkNW6QL9Z8lGlnEgCWZWbCbIKWZWjBLJqwgiyKtODrMqMIKuQVTlKoiur9itbvGlB8zDhufRFzXL90qBuQxPzWtWDBTbTA7KaKblo54OsCu170x0PUk1tXVJQWVzLSkvoiZ/dqXNi65rUACGr8s0DsgpZlaMEsmrCCLIq04Osyowgq5BVOUriIavWVR5qOEgvrX6eZi377xbb34ztPY4uGXoFXTz0UurTpV9a2CCraeGKTWLIqtDUk2fcTt+/9WqaMXWSTjl77gJ66NGnaf7shyGrAjvIqnwfgaxCVuUogayaMIKsyvQgqzIjyCpkVY6SeMmq/Wq/qPlcSeuj9NzKp5JDhPn1cX0n0oWDZ9DUwdOooqRSRAhZFRHFMgFk1aPZl61YQ9fcdh899cg9NHrkYJ3S+TvuWd35/UOxDB7povlDYpdOhVS374iUNLavd+pYSPUNjXT4SGNsGXhdeJ6KoRIVQ7sRQykxFXUopMbGJjp0pAEx5EIAMSSHBWJIZsRfLO7ae1hOGNMUHdsX6Cs/eBj3oVQhEIcY4rms86repDmrnqeXV81pIa6jy0+iS4ZdSpeNuIoGdxviiokZ4QABJwHIqqGsfuuFb9Hvpv8OkQUCIAACIAACIAACIAACIMBfXNQfpLmr59KfV/yZZn8xm/YeTizKxMeY3mNoxogZNH34dP0cBwh4EYCsGsrq/kP4FjEVQtUpRh3bFdABfNOaMsraF+brXrF69cBxLAEVQtSxg4ohvM88YiiPOHzqGxBDbpAQQ/KdpX0hYkii1Endh/D3PjWldgX8TiM6gvtQSkhxjqEt+zbT/Kp3aEH1OzRfPVbuWJHkNLH/6XR6xRk0ecAZNG3EVOmtiNdjSACyKjS625zVux94jJbPm6Vzbqo5EMOw8XfJmLMqc8KcVW9GmG8oxxDmGyKG5CjxToEYkglizqo3o+KiQp1gz4F6GWZMUyCGEg2/48B2WrxxPi1Sj8Wb5qsVhT9PRkTTD/Gla0zfHp6XDVkVokJaDRiymhogZFW+5UBWIRpylEA0TBjhCw+ZHmRVZgTRgKzKUeKdAjF0LJ/6xnolre/QnNXP0idbl9Jnf/eJKWbkjyAByKqPRvXaZxWyCln1EUIpk0BWIasm8cN5IRqIIcSQKQE5P0QDsipHCWQ1CEamZSB/9AhAVg3bFLIKWTUJIcgqRMMkfiCrMj30rMqM8IWHzAiyClmVowSyGgQj0zKQP3oEIKuGbQpZhayahBBkFbJqEj+QVZkeZFVmBFmVGUFWIatylEBWg2BkWgbyR48AZNWwTSGrkFWTEIKsQlZN4geyKtODrMqMIKsyI8gqZFWOEshqEIxMy0D+6BGArBq2KWQVsmoSQpBVyKpJ/EBWZXqQVZkRZFVmBFmFrMpRAlkNgpFpGcgfPQKQVcM2haxCVk1CCLIKWTWJH8iqTA+yKjOCrMqMIKuQVTlKIKtBMDItA/mjRwCyatimkFXIqkkIQVYhqybxA1mV6UFWZUaQVZkRZBWyKkcJZDUIRqZlIH/0CEBWDdsUsgpZNQkhyCpk1SR+IKsyPciqzAiyKjOCrEJW5SiBrAbByLQM5I8eAciqYZtCViGrJiEEWYWsmsQPZFWmB1mVGUFWZUaQVciqHCWQ1SAYmZaB/NEjAFk1bFPIKmTVJIQgq5BVk/iBrMr0IKsyI8iqzAiyClmVowSyGgQj0zKQP3oEIKvRa1NcEQiAAAiAAAiAAAiAAAiAAAjkPAHIas43IS4ABEAABEAABEAABEAABEAABKJHALIavTbFFYEACIAACIAACIAACIAACIBAzhOArOZ8E+ICQAAEQAAEQAAEQAAEQAAEQCB6BCCr0WvTNr+i2XMX0N0PPHZMPZbPm9XmdWvrCixbsYauue0+euqRe2j0yMEtqjN95t20et1G/buhA/vRC7Pub+vqtvr5U/FBTBHddMeD9N7SFS3axPmeinMMSXwQQ0R3/eQ3NOfVhYihFHc2iQ9iqCU4i5fz71mc70N2Qm58EENEfhgghlr941eoTwhZDXXz5Gbl+Eb00KNP0/zZD+fmBWSp1pNn3E61u/bo0p1/3PmDdk1tXVJQ+UZdVlpCT/zszizVJnzFevFBTBExH/t7ij8ILViyLPm7uMeQxAcxRMT3lR/feXPyi7KHH3+OnnnxLcRQ8+1Q4oMYOvp3g1n87qm/6i9Y7X/P4n4fsgil4oMYSsiq12dExFD4Pp+1dY0gq23dAhE8v3QjiuAl+76kVD2H/EH7+7deTTOmTtJlxZWhV88qvgBpGWZOVoghbz5xfU953ZwQQ963bicfxNBRXqOmzNSS6hwphPtQglEqPogh+fMNYsj3R8rYJISsxqapW+9C3YZ4YAhwgr+bjPn9Xeu1YNudKZ1hwHGPKXuvGGLo2Jh19hrivnQsI+7BWLVmg+5ZRQx587G+RHROcYnjfYh7oL91zQU0pLJvC1lFDCViKBUfxFCCj9e9GDHUdp+/wnxmyGqYWycidXMO6YjIZWV0GX5vxF5zWzM6cY5k8nvdcY8pi9P9P7hF98b7jascCQPjajr5uBUY5xiyD7m3ZAsxdDRK3PgghhIEePrB1h079RQVZ8wghrz5IIbcb+32ezFiyPjPXyQLgKxGslnDdVHWzSeO30A7W8LvjdivtIWrpc1r4/e64xxT1rXfev0ldPvNl2nofuPKvIXCX4IbH7daxzmGLB7c+/zok3OI782IoWOjxM4HMXTs8E3IasuocA7x9fP3DPeho3+/cB8K/9/XtqohZLWtyMfovNaQD8iqu1RwKLjN0eDhZnFj5uePO/OKa0xZ1+22mjRi6GhcuPFx3nLjGkNODtbcOl6dHDF07B9mO5+4x1CqVVyZi/XlWZxjyA+fuMeQ20df5704zjEUIzVI61Ihq2nhQmI/BJyrcsZxZdtUnFLJGFa/SxBLxQcxJS9KEfcYkhYuQQxhRWnp75e0ojRiqCVBt/t13O9DdkJufBBDx96HnJ8REUPSnSp+r0NW49fmWb9i+/5YfLLxY0fGaguWVIDt86A4TWm34hZbkcR9XzEvPnGPKetDj1tsWfNW+bW4xpAfPnGPIWd8WLGEvXqPvqucMcKv2PkghmRZjfN9yHl/dpNVxFDLv1OpPiPG9W9Z1j+g5+gJIKs52nCoNgiAAAiAAAiAAAiAAAiAAAj8/+3dz4tVZRgH8PcvaGFLBWWwYJLZFBSEgoFIm0ZpEW2EwSRs4aZNPwQXwphu2rgwwmKgjbQItU2IYKC4CFpJBSVikIFgEv4F8QrnOs09dzyKlzvP+3xmNzP3nvs8n+/dfDnnntuygLLacrp2I0CAAAECBAgQIECAQFABZTVocMYmQIAAAQIECBAgQIBAywLKasvp2o0AAQIECBAgQIAAAQJBBZTVoMEZmwABAgQIECBAgAABAi0LKKstp2s3AgQIECBAgAABAgQIBBVQVoMGZ2wCBAgQIECAAAECBAi0LKCstpyu3QgQIECAAAECBAgQIBBUQFkNGpyxCRAgQIAAAQIECBAg0LKAstpyunYjQIAAAQIECBAgQIBAUAFlNWhwxiZAgAABAgQIECBAgEDLAspqy+najQABAgQIECBAgAABAkEFlNWgwRmbAAECBAgQIECAAAECLQsoqy2nazcCBAgQIECAAAECBAgEFVBWgwZnbAIECBAgQIAAAQIECLQsoKy2nK7dCBAgQIAAAQIECBAgEFRAWQ0anLEJECBAgAABAgQIECDQsoCy2nK6diNAgAABAgQIECBAgEBQAWU1aHDGJkCAAIFhAvuWjpabt++Uc2eOlYX5ud4n3fjtVnn3g+Nl+7bN5cLK8rADexQBAgQIECAwVQFldaq8Dk6AAAEC0xLoCmY9/qQievqr78oX31wsv/y4Mhrj4Ienyj/3H/SW0h27l8rhA4vlyHtvT2tsxyVAgAABAgQGCiirA6E8jAABAgQ2lsAnJ74sv/7+Z7n/74Oy89WF8tmn748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"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.estimate_rate_constants(t=t_arr, reactant_conc=A_conc, product_conc=C_conc, reactant_name=\"A\", product_name=\"C\")"
]
},
{
"cell_type": "markdown",
"id": "8951650d-cb8c-4def-99c3-4e465a12b9d4",
"metadata": {},
"source": [
"### A terrible fit! But it looks like we'll do much better if split it into 3 portions, one where A(t) ranges from 0 to about 0.04, one from about 0.04 to 5, and one from about 5 to 50 \n",
"\n",
"This is a larger numer of splits than we did in experiments `cascade_2_a` and `cascade_2_b`\n",
"\n",
"Let's visually locate at what times those [A] values occur:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "6ef1f912-d7c9-401c-b037-2e4d2b6cf8fa",
"metadata": {},
"outputs": [
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_history(chemicals='A', colors='darkturquoise', xrange=[0, 0.15], \n",
" vertical_lines=[0.028, 0.1], title=\"[A] as a function of time\")"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "781a0677-4d2a-4222-b5f8-4ce031157faf",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" SYSTEM TIME | \n",
" A | \n",
"
\n",
" \n",
" \n",
" \n",
" | 72 | \n",
" 0.020462 | \n",
" 9.428805 | \n",
"
\n",
" \n",
" | 73 | \n",
" 0.021645 | \n",
" 8.540614 | \n",
"
\n",
" \n",
" | 74 | \n",
" 0.022828 | \n",
" 7.736565 | \n",
"
\n",
" \n",
" | 75 | \n",
" 0.024012 | \n",
" 7.008682 | \n",
"
\n",
" \n",
" | 76 | \n",
" 0.025195 | \n",
" 6.349747 | \n",
"
\n",
" \n",
" | 77 | \n",
" 0.026378 | \n",
" 5.753223 | \n",
"
\n",
" \n",
" | 78 | \n",
" 0.027561 | \n",
" 5.213195 | \n",
"
\n",
" \n",
" | 79 | \n",
" 0.028745 | \n",
" 4.724310 | \n",
"
\n",
" \n",
" | 80 | \n",
" 0.029928 | \n",
" 4.281718 | \n",
"
\n",
" \n",
"
\n",
"
\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" SYSTEM TIME | \n",
" A | \n",
"
\n",
" \n",
" \n",
" \n",
" | 126 | \n",
" 0.090918 | \n",
" 0.062461 | \n",
"
\n",
" \n",
" | 127 | \n",
" 0.093371 | \n",
" 0.057137 | \n",
"
\n",
" \n",
" | 128 | \n",
" 0.095825 | \n",
" 0.052750 | \n",
"
\n",
" \n",
" | 129 | \n",
" 0.098769 | \n",
" 0.048391 | \n",
"
\n",
" \n",
" | 130 | \n",
" 0.101714 | \n",
" 0.044909 | \n",
"
\n",
" \n",
" | 131 | \n",
" 0.105247 | \n",
" 0.041540 | \n",
"
\n",
" \n",
" | 132 | \n",
" 0.109487 | \n",
" 0.038396 | \n",
"
\n",
" \n",
"
\n",
"
A(t)=%{x}
value=%{y}",
"legendgroup": "wide_variable_0",
"line": {
"color": "green",
"dash": "solid"
},
"marker": {
"symbol": "circle"
},
"mode": "lines",
"name": "C'(t)",
"orientation": "v",
"showlegend": true,
"type": "scatter",
"x": [
50,
48.976,
47.77239728128,
47.18540424081068,
46.89551869293061,
46.607416414927755,
46.321086435338806,
46.03651785020284,
45.753699822646006,
45.472621582468776,
45.19327242573572,
44.91564171436782,
44.63971887573729,
44.365493402264846,
44.09295485101956,
43.82209284332105,
43.55289706434419,
43.28535726272624,
43.01946325017639,
42.75520490108773,
42.492572152151524,
42.23155500197398,
41.92026121243955,
41.61126534638508,
41.304550438435676,
41.000099648472606,
40.63745558315576,
40.278023883987196,
39.921776091028875,
39.56868399648809,
39.14872677168258,
38.73323359058411,
38.32215699422331,
37.91545002819503,
37.432589479113815,
36.955888117925646,
36.48526736785515,
36.020649654601975,
35.47022014134112,
34.92821584437163,
34.39450778065552,
33.868968941818565,
33.24797532833916,
32.63838797165015,
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"yaxis": {
"automargin": true,
"gridcolor": "white",
"linecolor": "white",
"ticks": "",
"title": {
"standoff": 15
},
"zerolinecolor": "white",
"zerolinewidth": 2
}
}
},
"title": {
"text": "d/dt C(t) as a function of A(t), alongside its least-square fit"
},
"xaxis": {
"anchor": "y",
"autorange": true,
"domain": [
0,
1
],
"range": [
5.213195469421105,
50
],
"title": {
"text": "A(t)"
},
"type": "linear"
},
"yaxis": {
"anchor": "x",
"autorange": true,
"domain": [
0,
1
],
"range": [
-21.635372886155253,
336.59935756422243
],
"title": {
"text": "C'(t)"
},
"type": "linear"
}
}
},
"image/png": 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""
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"source": [
"dynamics.estimate_rate_constants(t=t_arr_early, reactant_conc=A_conc_early, product_conc=C_conc_early, \n",
" reactant_name=\"A\", product_name=\"C\")"
]
},
{
"cell_type": "markdown",
"id": "49e2b683-f622-4d9a-a6e8-e687a7b44f34",
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"source": [
"Just as we saw in experiment `cascade_2_b`, trying to fit an elementary reaction to that region leads to a **negative** reverse rate constant! \n",
"We won't discuss this part any further."
]
},
{
"cell_type": "markdown",
"id": "a9250abb-943b-40b0-a546-a556e58b6a8e",
"metadata": {},
"source": [
"### II. Let's now consider the MID region (not seen in earlier experiments in this series), when 0.028 < t < 0.1"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "4f3723d4-6c1d-44de-9f74-a1d791e1b0a3",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Total REACTANT + PRODUCT has a median of 14.9, \n",
" with standard deviation 3.612 (ideally should be zero)\n",
"The sum of the time derivatives of reactant and product \n",
" has a median of 199 (ideally should be zero)\n",
"Least square fit: Y = 224.4 + 24.68 X\n",
" where X is the array [A] and Y is the time gradient of C\n",
"\n",
"-> ESTIMATED RATE CONSTANTS: kF = 39.74 , kR = -15.06\n"
]
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""
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"source": [
"dynamics.estimate_rate_constants(t=t_arr_mid, reactant_conc=A_conc_mid, product_conc=C_conc_mid, \n",
" reactant_name=\"A\", product_name=\"C\")"
]
},
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"For this region, too, trying to fit an elementary reaction to that region leads to a **negative** reverse rate! \n",
"We won't discuss this part any further."
]
},
{
"cell_type": "markdown",
"id": "652e8cc0-b053-40d1-9d1c-2f2a30f59469",
"metadata": {},
"source": [
"### III. And now let's consider the LATE region, when t > 0.1"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "2d61a783-e1e5-473a-9fd8-cba5cb842a85",
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"name": "stdout",
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"text": [
"Total REACTANT + PRODUCT has a median of 34.37, \n",
" with standard deviation 6.092 (ideally should be zero)\n",
"The sum of the time derivatives of reactant and product \n",
" has a median of 62.73 (ideally should be zero)\n",
"Least square fit: Y = -55.81 + 5,404 X\n",
" where X is the array [A] and Y is the time gradient of C\n",
"\n",
"-> ESTIMATED RATE CONSTANTS: kF = 5,402 , kR = 1.624\n"
]
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.estimate_rate_constants(t=t_arr_late, reactant_conc=A_conc_late, product_conc=C_conc_late, \n",
" reactant_name=\"A\", product_name=\"C\")"
]
},
{
"cell_type": "markdown",
"id": "5e2ab9aa-c84d-41d1-948f-16d1e437b2a6",
"metadata": {},
"source": [
"This time we have an adequate linear fit AND positive rate constants, but a **huge value of kF** relative to that of any of the elementary reactions! \n",
"\n",
"Let's see the time evolution again, but just for `A` and `C`:"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "ffa91f21-a726-46df-88dc-5fdc38fa4673",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.plotly.v1+json": {
"config": {
"plotlyServerURL": "https://plot.ly"
},
"data": [
{
"hovertemplate": "Chemical=A
SYSTEM TIME=%{x}
Concentration=%{y}",
"legendgroup": "A",
"line": {
"color": "darkturquoise",
"dash": "solid"
},
"marker": {
"symbol": "circle"
},
"mode": "lines",
"name": "A",
"orientation": "v",
"showlegend": true,
"type": "scatter",
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_history(chemicals=['A', 'C'], colors=['darkturquoise', 'green'], xrange=[0, 0.25], \n",
" vertical_lines=[0.028, 0.1], title='A <-> C compound reaction')"
]
},
{
"cell_type": "markdown",
"id": "1ddc931c-2bf1-4e8e-9156-fdb7268648a1",
"metadata": {},
"source": [
"For t > 0.1, the product [C] appears to have a lot of response to nearly non-existing changes in [A] ! \n",
"\n",
"That doesn't seem like a good fit to an elementary reaction..."
]
},
{
"cell_type": "markdown",
"id": "be6a8d74-8ad7-4930-9c24-681ced6e1bb0",
"metadata": {},
"source": [
"#### This time, modeling the compound reaction `A <-> C` as an elementary reaction is not a good fit at any time"
]
},
{
"cell_type": "markdown",
"id": "310322af-ca59-4d41-b533-ec3336d6f3a8",
"metadata": {},
"source": [
"### EXPANDED conclusion : "
]
},
{
"cell_type": "markdown",
"id": "d94c2e0d-4b50-4616-b248-74c07809aa21",
"metadata": {},
"source": [
"### While it's a well-known Chemistry notion that the slower reaction is the rate-determining step in a chain, we saw in this experiment that the complex reaction CANNOT always be modeled, not even roughly, with the rate constants of the slower reaction. "
]
},
{
"cell_type": "markdown",
"id": "7e352310-17ae-48bb-854b-d98b8c3ca89e",
"metadata": {},
"source": [
"We saw this in a scenario where the slower reaction is the later one."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "58f279e3-c420-4a57-a753-fab458bec80c",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
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