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"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-warning\">\n",
"이 노트북을 처음 열어보면 아마도 그림이나 표의 수식 등이 제대로 표시되지 않고 있을 것입니다. 이때는 오른쪽 상단의 \"Not Trusted\"버튼을 눌러서 나오는 안내창의 \"Trust\"를 선택해주세요. 노트북에 저장되어 있던 결과들이 제대로 표시될 것입니다. Jupyter Notebook이 아닌 Jupyter Lab 환경이라면 상단 \"View\" 메뉴의 \"Activate Command Palette\" 항목을 선택한 다음 \"Trust Notebook\"이라는 기능을 검색하여 실행하면 됩니다. 검색을 할 때에는 앞 글자 \"tr\"만 입력하여도 해당 항목이 나옵니다.\n",
"</div>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 2. 광합성"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"지난 시간에는 식물의 성장을 logistic, exponential, Gompertz 등 간단한 성장 곡선 모형으로 모의해보았습니다. 이번 시간에는 실제 식물이 어떻게 그러한 곡선의 형태로 성장을 할 수 있는지 조금 더 고민해보면서 특히 광합성을 표현하는 방법에 대해 살펴보겠습니다. 다른 기작들과 마찬가지로 광합성 역시 그 구현 방식에 따라 상대적으로 단순한 모형에서 부터 꽤나 복잡한 기체교환 모형까지 다양하게 생각해볼 수 있습니다. 하지만 작물모형 관점에서는 결국 성장량 변화($\\frac{dW}{dt}$)를 표현하는 방식의 차이일뿐이며 기본적으로는 시간에 따라 생체량($W$)이 누적되어 수량이 결정된다는 기본 가정을 계속 가지고 간다는 점을 기억해주세요."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
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"text/html": [
"<div style=\"padding: 1em; background-color: #f8d6da; border: 1px solid #f5c6cb; font-weight: bold;\">\n",
"<p>The WebIO Jupyter extension was not detected. See the\n",
"<a href=\"https://juliagizmos.github.io/WebIO.jl/latest/providers/ijulia/\" target=\"_blank\">\n",
" WebIO Jupyter integration documentation\n",
"</a>\n",
"for more information.\n",
"</div>\n"
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"text/plain": [
"WebIO._IJuliaInit()"
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"kernelId": "cf1f84de-2548-4892-ac97-3dc4528bd326"
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"output_type": "display_data"
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"source": [
"using Cropbox"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.webio.node+json": {
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" WebIO Jupyter integration documentation\n",
"</a>\n",
"for more information.\n",
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"source": [
"Cropbox.Interact.WebIO.setup(:ijulia)"
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},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 2.1. 복습"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"식물이 지수적 성장을 계속할 수는 없기 때문에 언젠가 성장이 둔화되는 상황을 표현해야 하는데요. Logistic 모형에서는 주어진 최종 생체량(`Wf`)에 따라 S자 형태로 성장이 둔화되도록 처리하여 해결하고자 하였습니다. 이와는 달리 Gompertz 모형에서는 성장률(`r`)이 시간에 따른 성장 효율 저하도(`α`)에 따라 감소하는 접근 방식을 택하고 있었습니다."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"\\begin{align}\n",
"\\frac{dW}{dt} &= r_t W_t \\\\\n",
"\\frac{dr}{dt} &= -\\alpha r_t \\\\\n",
"W_{t = 0} &= W_0 \\\\\n",
"r_{t = 0} &= r_0\n",
"\\end{align}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"| 이름 | 값 | 단위 | 설명 |\n",
"| :- | :- | :- | :- |\n",
"| $\\alpha$ | 0.005 | $\\mathrm{d^{-1}}$ | 시간에 따른 성장 효율 저하도 |\n",
"| $r_0$ | 0.05 | $\\mathrm{g}\\ \\mathrm{g^{-1}}\\ \\mathrm{d^{-1}}$ | 효율 저하 이전의 초기 최적 성장률 |\n",
"| $r$ | - | $$\\mathrm{g}\\ \\mathrm{g^{-1}}\\ \\mathrm{d^{-1}}$$ | 상대성장률 |\n",
"| $$W_0$$ | 0.25 | $\\mathrm{g}$ | 최초 생체량 |\n",
"| $W$ | - | $\\mathrm{g}$ | 시간별 생체량 |\n",
"| $t$ | - | $\\mathrm{d}$ | 시간 |"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"이쯤에서 지난 시간의 기억을 되살려 Gompertz 모형을 Cropbox 기반으로 다시 한번 만들어보겠습니다."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Gompertz"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"@system Gompertz(Controller) begin\n",
" α: decay_rate ~ preserve(parameter, u\"d^-1\")\n",
" r0: initial_growth_rate ~ preserve(parameter, u\"g/g/d\")\n",
" W0: initial_biomass ~ preserve(parameter, u\"g\")\n",
"\n",
" r(r, α): growth_rate => (-α * r) ~ accumulate(init = r0, u\"g/g/d\")\n",
" W(W, r): biomass => (r * W) ~ accumulate(init = W0, u\"g\")\n",
"\n",
" t(context.clock.time): time ~ track(u\"d\")\n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"코드가 올바로 만들어졌다면 이제 모수에 따라 움직이는 그래프를 그려서 Gompertz 모형이 실제 어떤 식으로 작동하는지 살펴보겠습니다."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
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" '<p>Please read ' +\n",
" '<a href=\"https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/\" target=\"_blank\">the troubleshooting guide</a> ' +\n",
" 'for more information on how to resolve this issue.</p>' +\n",
" '<p><a href=\"https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/\" target=\"_blank\">https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/</a></p>' +\n",
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"Gadfly.Plot(Gadfly.Layer[Gadfly.Layer(nothing, Dict{Symbol, Any}(:y => [0.55, 0.5511458333333333, 0.552293575394242, 0.5534432283663927, 0.5545947944341898, 0.5557482757827715, 0.5569036745980084, 0.5580609930665001, 0.5592202333755733, 0.5603813977132784 … 63.424648447324756, 63.43124764017109, 63.43784476969889, 63.44443983626741, 63.45103284023605, 63.457623781964436, 63.46421266181234, 63.470799480139746, 63.477384237306815, 63.483966933673884], :x => [0.0, 0.041666666666666664, 0.08333333333333333, 0.125, 0.16666666666666666, 0.20833333333333331, 0.25, 0.29166666666666663, 0.3333333333333333, 0.375 … 299.625, 299.66666666666663, 299.7083333333333, 299.75, 299.79166666666663, 299.8333333333333, 299.875, 299.91666666666663, 299.9583333333333, 300.0]), Gadfly.StatisticElement[], Gadfly.Geom.LineGeometry(Gadfly.Stat.Identity(), false, 2, Symbol(\"\")), Gadfly.Theme(LCHab{Float32}(70.0f0,60.0f0,240.0f0), 0.7mm, 0.45mm, 1.8mm, Gadfly.Scale.default_discrete_sizes, Gadfly.Scale.default_continuous_sizes, Gadfly.Scale.default_discrete_colors, Function[Compose.circle, Gadfly.Shape.square, Gadfly.Shape.diamond, Gadfly.Shape.cross, Gadfly.Shape.xcross, Gadfly.Shape.utriangle, Gadfly.Shape.dtriangle, Gadfly.Shape.star1, Gadfly.Shape.star2, Gadfly.Shape.hexagon, Gadfly.Shape.octagon, Gadfly.Shape.hline, Gadfly.Shape.vline, Gadfly.Shape.ltriangle, Gadfly.Shape.rtriangle], 0.3mm, [:solid, :dash, :dot, :dashdot, :dashdotdot, :ldash, :ldashdash, :ldashdot, :ldashdashdot], [1.0, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, 0.0], nothing, nothing, 0.3mm, 0.0, RGB{N0f8}(1.0,1.0,1.0), Measures.AbsoluteLength[5.0mm, 5.0mm, 5.0mm, 0.0mm], RGB{N0f8}(0.816,0.816,0.878), Measures.AbsoluteLength[0.5mm, 0.5mm], RGB{N0f8}(0.627,0.627,0.627), 0.2mm, 0, \"'PT Sans Caption','Helvetica Neue','Helvetica',sans-serif\", 2.822222222222222mm, RGB{N0f8}(0.424,0.376,0.42), \"'PT Sans','Helvetica Neue','Helvetica',sans-serif\", 3.5277777777777777mm, RGB{N0f8}(0.337,0.29,0.333), \"'PT Sans Caption','Helvetica Neue','Helvetica',sans-serif\", 2.822222222222222mm, RGB{N0f8}(0.298,0.251,0.294), \"'PT Sans','Helvetica Neue','Helvetica',sans-serif\", 3.175mm, RGB{N0f8}(0.212,0.165,0.208), \"'PT Sans','Helvetica Neue','Helvetica',sans-serif\", 2.822222222222222mm, RGB{N0f8}(0.298,0.251,0.294), 40, -0.05mm, 1.0mm, 3.0mm, Gadfly.default_stroke_color, 0.3mm, Cropbox.var\"#504#513\"(), Gadfly.default_continuous_highlight_color, Gadfly.default_lowlight_color, Gadfly.default_middle_color, 0.6mm, :left, :square, nothing, nothing, nothing, :right, nothing, 2.0mm, 1000, 10.0, 0.5, 0.2, 1.0mm, 4, Gadfly.Scale.DiscreteColorScale(Gadfly.Scale.default_discrete_colors, nothing, nothing, true), Gadfly.Scale.ContinuousColorScale(Gadfly.Scale.var\"#69#73\"{Int64, Int64, Int64, Int64, Float64, Int64}(100, 40, 260, 10, 1.5, 70), Gadfly.Scale.ContinuousScaleTransform(identity, identity, Gadfly.Scale.identity_formatter), nothing, nothing)), 0)], nothing, Data(\n",
" titles=Dict{Symbol, AbstractString}()\n",
")\n",
", Gadfly.ScaleElement[], Gadfly.StatisticElement[], Gadfly.Coord.Cartesian([:x, :xmin, :xmax, :xintercept], [:y, :ymin, :ymax, :yintercept, :middle, :lower_hinge, :upper_hinge, :lower_fence, :upper_fence, :outliers], 0.0, 300.0, 0, 400, false, false, false, nothing, false), Gadfly.GuideElement[Gadfly.Guide.Title(\"\"), Gadfly.Guide.XLabel(\"t (d)\", :auto), Gadfly.Guide.YLabel(\"W (g)\", :auto)], Gadfly.Theme(LCHab{Float32}(70.0f0,60.0f0,240.0f0), 0.7mm, 0.45mm, 1.8mm, Gadfly.Scale.default_discrete_sizes, Gadfly.Scale.default_continuous_sizes, Gadfly.Scale.default_discrete_colors, Function[Compose.circle, Gadfly.Shape.square, Gadfly.Shape.diamond, Gadfly.Shape.cross, Gadfly.Shape.xcross, Gadfly.Shape.utriangle, Gadfly.Shape.dtriangle, Gadfly.Shape.star1, Gadfly.Shape.star2, Gadfly.Shape.hexagon, Gadfly.Shape.octagon, Gadfly.Shape.hline, Gadfly.Shape.vline, Gadfly.Shape.ltriangle, Gadfly.Shape.rtriangle], 0.3mm, [:solid, :dash, :dot, :dashdot, :dashdotdot, :ldash, :ldashdash, :ldashdot, :ldashdashdot], [1.0, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, 0.0], nothing, nothing, 0.3mm, 0.0, RGB{N0f8}(1.0,1.0,1.0), Measures.AbsoluteLength[5.0mm, 5.0mm, 5.0mm, 0.0mm], RGB{N0f8}(0.816,0.816,0.878), Measures.AbsoluteLength[0.5mm, 0.5mm], RGB{N0f8}(0.627,0.627,0.627), 0.2mm, 0, \"'PT Sans Caption','Helvetica Neue','Helvetica',sans-serif\", 2.822222222222222mm, RGB{N0f8}(0.424,0.376,0.42), \"'PT Sans','Helvetica Neue','Helvetica',sans-serif\", 3.5277777777777777mm, RGB{N0f8}(0.337,0.29,0.333), \"'PT Sans Caption','Helvetica Neue','Helvetica',sans-serif\", 2.822222222222222mm, RGB{N0f8}(0.298,0.251,0.294), \"'PT Sans','Helvetica Neue','Helvetica',sans-serif\", 3.175mm, RGB{N0f8}(0.212,0.165,0.208), \"'PT Sans','Helvetica Neue','Helvetica',sans-serif\", 2.822222222222222mm, RGB{N0f8}(0.298,0.251,0.294), 40, -0.05mm, 1.0mm, 3.0mm, Gadfly.default_stroke_color, 0.3mm, Cropbox.var\"#504#513\"(), Gadfly.default_continuous_highlight_color, Gadfly.default_lowlight_color, Gadfly.default_middle_color, 0.6mm, :left, :square, nothing, nothing, nothing, :right, nothing, 2.0mm, 1000, 10.0, 0.5, 0.2, 1.0mm, 4, Gadfly.Scale.DiscreteColorScale(Gadfly.Scale.default_discrete_colors, nothing, nothing, true), Gadfly.Scale.ContinuousColorScale(Gadfly.Scale.var\"#69#73\"{Int64, Int64, Int64, Int64, Float64, Int64}(100, 40, 260, 10, 1.5, 70), Gadfly.Scale.ContinuousScaleTransform(identity, identity, Gadfly.Scale.identity_formatter), nothing, nothing)), Dict{Symbol, Any}())], Dict{Symbol, Any}(:style => Dict(\"display\" => \"flex\", \"flex-direction\" => \"column\")))"
]
},
"execution_count": 4,
"metadata": {
"application/vnd.webio.node+json": {
"kernelId": "cf1f84de-2548-4892-ac97-3dc4528bd326"
}
},
"output_type": "execute_result"
}
],
"source": [
"manipulate(Gompertz, :t, :W;\n",
" parameters = :Gompertz => (;\n",
" α = 0:0.001:0.02,\n",
" r0 = 0:0.01:0.1,\n",
" W0 = 0.1:0.01:1,\n",
" ),\n",
" stop = 300u\"d\",\n",
" kind = :line,\n",
" ylim = (0, 400),\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"여기서 눈여겨보아야 할 것은 성장률(`r`)입니다. 성장 효율 저하도(`α`)에 따라 감소하도록 되어 있는 이 성장률은 실제 식물 성장에서 어떤 의미가 있는 것일까요?"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.webio.node+json": {
"children": [
{
"children": [
"Gompertz"
],
"instanceArgs": {
"namespace": "html",
"tag": "div"
},
"nodeType": "DOM",
"props": {
"style": {
"color": "darkorchid",
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}
},
"type": "node"
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{
"children": [
{
"children": [
{
"children": [
{
"children": [
{
"children": [
"α"
],
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"namespace": "html",
"tag": "label"
},
"nodeType": "DOM",
"props": {
"className": "interact ",
"style": {
"color": "royalblue",
"padding": "5px 10px 0px 10px"
}
},
"type": "node"
}
],
"instanceArgs": {
"namespace": "html",
"tag": "div"
},
"nodeType": "DOM",
"props": {
"className": "interact-flex-row-left"
},
"type": "node"
},
{
"children": [
{
"children": [],
"instanceArgs": {
"namespace": "html",
"tag": "input"
},
"nodeType": "DOM",
"props": {
"attributes": {
"data-bind": "numericValue: index, valueUpdate: 'input', event: {change: function (){this.changes(this.changes()+1)}}",
"orient": "horizontal",
"type": "range"
},
"className": "slider slider is-fullwidth",
"max": 21,
"min": 1,
"step": 1,
"style": {}
},
"type": "node"
}
],
"instanceArgs": {
"namespace": "html",
"tag": "div"
},
"nodeType": "DOM",
"props": {
"className": "interact-flex-row-center"
},
"type": "node"
},
{
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{
"children": [],
"instanceArgs": {
"namespace": "html",
"tag": "p"
},
"nodeType": "DOM",
"props": {
"attributes": {
"data-bind": "text: formatted_val"
}
},
"type": "node"
}
],
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},
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},
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],
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},
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"props": {
"className": "interact-flex-row interact-widget",
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"width": "25%"
}
},
"type": "node"
}
],
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"changes": [
"(function (val){return (val!=this.model[\"changes\"]()) ? (this.valueFromJulia[\"changes\"]=true, this.model[\"changes\"](val)) : undefined})"
],
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"(function (val){return (val!=this.model[\"index\"]()) ? (this.valueFromJulia[\"index\"]=true, this.model[\"index\"](val)) : undefined})"
]
},
"id": "13712546257730639579",
"imports": {
"data": [
{
"name": "knockout",
"type": "js",
"url": "/assetserver/c853cad7a3e123085fa7960dd53fd3d4c05dc309-knockout.js"
},
{
"name": "knockout_punches",
"type": "js",
"url": "/assetserver/fab584ebb4dc64eb3ddf5ca7c73b2e76fd533845-knockout_punches.js"
},
{
"name": null,
"type": "js",
"url": "/assetserver/f2016dce9a0d470782f38e7aa4873f823db566c0-all.js"
},
{
"name": null,
"type": "css",
"url": "/assetserver/805f638970bef13ab5dd6d32d993673e39af56c0-style.css"
},
{
"name": null,
"type": "css",
"url": "/assetserver/a99a2e54e5d65dd4545013d46edee359c5b0afdb-bulma_confined.min.css"
}
],
"type": "async_block"
},
"mount_callbacks": [
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],
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"sync": true,
"value": 0
},
"index": {
"id": "11452243288313603969",
"sync": true,
"value": 11
}
},
"systemjs_options": null
},
"nodeType": "Scope",
"props": {},
"type": "node"
}
],
"instanceArgs": {
"namespace": "html",
"tag": "div"
},
"nodeType": "DOM",
"props": {
"className": "field interact-widget"
},
"type": "node"
},
{
"children": [
{
"children": [
{
"children": [
{
"children": [
{
"children": [
"r0"
],
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},
"nodeType": "DOM",
"props": {
"className": "interact ",
"style": {
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}
},
"type": "node"
}
],
"instanceArgs": {
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},
"nodeType": "DOM",
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{
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{
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},
"nodeType": "DOM",
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"orient": "horizontal",
"type": "range"
},
"className": "slider slider is-fullwidth",
"max": 11,
"min": 1,
"step": 1,
"style": {}
},
"type": "node"
}
],
"instanceArgs": {
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},
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{
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{
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],
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"width": "25%"
}
},
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],
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},
"id": "3240076548114206083",
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{
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{
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{
"name": null,
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},
{
"name": null,
"type": "css",
"url": "/assetserver/805f638970bef13ab5dd6d32d993673e39af56c0-style.css"
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{
"name": null,
"type": "css",
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],
"type": "async_block"
},
"mount_callbacks": [
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7.09,5.09 7.11,5.09 7.12,5.09 7.14,5.1 7.15,5.1 7.17,5.1 7.18,5.11 7.2,5.11 7.22,5.11 7.23,5.12 7.25,5.12 7.26,5.12 7.28,5.12 7.29,5.13 7.31,5.13 7.32,5.13 7.34,5.14 7.36,5.14 7.37,5.14 7.39,5.14 7.4,5.15 7.42,5.15 7.43,5.15 7.45,5.16 7.47,5.16 7.48,5.16 7.5,5.17 7.51,5.17 7.53,5.17 7.54,5.17 7.56,5.18 7.57,5.18 7.59,5.18 7.61,5.19 7.62,5.19 7.64,5.19 7.65,5.19 7.67,5.2 7.68,5.2 7.7,5.2 7.71,5.21 7.73,5.21 7.75,5.21 7.76,5.22 7.78,5.22 7.79,5.22 7.81,5.22 7.82,5.23 7.84,5.23 7.86,5.23 7.87,5.24 7.89,5.24 7.9,5.24 7.92,5.24 7.93,5.25 7.95,5.25 7.96,5.25 7.98,5.26 8,5.26 8.01,5.26 8.03,5.26 8.04,5.27 8.06,5.27 8.07,5.27 8.09,5.28 8.11,5.28 8.12,5.28 8.14,5.28 8.15,5.29 8.17,5.29 8.18,5.29 8.2,5.3 8.21,5.3 8.23,5.3 8.25,5.3 8.26,5.31 8.28,5.31 8.29,5.31 8.31,5.32 8.32,5.32 8.34,5.32 8.36,5.32 8.37,5.33 8.39,5.33 8.4,5.33 8.42,5.34 8.43,5.34 8.45,5.34 8.46,5.34 8.48,5.35 8.5,5.35 8.51,5.35 8.53,5.36 8.54,5.36 8.56,5.36 8.57,5.36 8.59,5.37 8.61,5.37 8.62,5.37 8.64,5.38 8.65,5.38 8.67,5.38 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"11, nothing)), Set{String}(), nothing, WebIO.Asset[WebIO.Asset(\"js\", \"knockout\", \"/Users/tomyun/.julia/packages/Knockout/3gjS1/src/../assets/knockout.js\"), WebIO.Asset(\"js\", \"knockout_punches\", \"/Users/tomyun/.julia/packages/Knockout/3gjS1/src/../assets/knockout_punches.js\"), WebIO.Asset(\"js\", nothing, \"/Users/tomyun/.julia/packages/InteractBase/o1I6G/src/../assets/all.js\"), WebIO.Asset(\"css\", nothing, \"/Users/tomyun/.julia/packages/InteractBase/o1I6G/src/../assets/style.css\"), WebIO.Asset(\"css\", nothing, \"/Users/tomyun/.julia/packages/Interact/pVyN2/src/../assets/bulma_confined.min.css\")], Dict{Any, Any}(\"changes\" => Any[WebIO.JSString(\"(function (val){return (val!=this.model[\\\"changes\\\"]()) ? (this.valueFromJulia[\\\"changes\\\"]=true, this.model[\\\"changes\\\"](val)) : undefined})\")], \"index\" => Any[WebIO.JSString(\"(function (val){return (val!=this.model[\\\"index\\\"]()) ? (this.valueFromJulia[\\\"index\\\"]=true, this.model[\\\"index\\\"](val)) : undefined})\")]), WebIO.ConnectionPool(Channel{Any}(32), Set{WebIO.AbstractConnection}(), Condition(Base.InvasiveLinkedList{Task}(Task (runnable) @0x000000016a902210, Task (runnable) @0x000000016a902210), Base.AlwaysLockedST(1))), WebIO.JSString[WebIO.JSString(\"function () {\\n var handler = (function (ko, koPunches) {\\n ko.punches.enableAll();\\n ko.bindingHandlers.numericValue = {\\n init: function(element, valueAccessor, allBindings, data, context) {\\n var stringified = ko.observable(ko.unwrap(valueAccessor()));\\n stringified.subscribe(function(value) {\\n var val = parseFloat(value);\\n if (!isNaN(val)) {\\n valueAccessor()(val);\\n }\\n });\\n valueAccessor().subscribe(function(value) {\\n var str = JSON.stringify(value);\\n if ((str == \\\"0\\\") && ([\\\"-0\\\", \\\"-0.\\\"].indexOf(stringified()) >= 0))\\n return;\\n if ([\\\"null\\\", \\\"\\\"].indexOf(str) >= 0)\\n return;\\n stringified(str);\\n });\\n ko.applyBindingsToNode(\\n element,\\n {\\n value: stringified,\\n valueUpdate: allBindings.get('valueUpdate'),\\n },\\n context,\\n );\\n }\\n };\\n var json_data = {\\\"formatted_vals\\\":[\\\"0.0\\\",\\\"0.001\\\",\\\"0.002\\\",\\\"0.003\\\",\\\"0.004\\\",\\\"0.005\\\",\\\"0.006\\\",\\\"0.007\\\",\\\"0.008\\\",\\\"0.009\\\",\\\"0.01\\\",\\\"0.011\\\",\\\"0.012\\\",\\\"0.013\\\",\\\"0.014\\\",\\\"0.015\\\",\\\"0.016\\\",\\\"0.017\\\",\\\"0.018\\\",\\\"0.019\\\",\\\"0.02\\\"],\\\"changes\\\":WebIO.getval({\\\"name\\\":\\\"changes\\\",\\\"scope\\\":\\\"13712546257730639579\\\",\\\"id\\\":\\\"4445412567246842577\\\",\\\"type\\\":\\\"observable\\\"}),\\\"index\\\":WebIO.getval({\\\"name\\\":\\\"index\\\",\\\"scope\\\":\\\"13712546257730639579\\\",\\\"id\\\":\\\"11452243288313603969\\\",\\\"type\\\":\\\"observable\\\"})};\\n var self = this;\\n function AppViewModel() {\\n for (var key in json_data) {\\n var el = json_data[key];\\n this[key] = Array.isArray(el) ? ko.observableArray(el) : ko.observable(el);\\n }\\n \\n [this[\\\"formatted_val\\\"]=ko.computed( function(){\\n return this.formatted_vals()[parseInt(this.index())-(1)];\\n }\\n,this)]\\n [this[\\\"changes\\\"].subscribe((function (val){!(this.valueFromJulia[\\\"changes\\\"]) ? (WebIO.setval({\\\"name\\\":\\\"changes\\\",\\\"scope\\\":\\\"13712546257730639579\\\",\\\"id\\\":\\\"4445412567246842577\\\",\\\"type\\\":\\\"observable\\\"},val)) : undefined; return this.valueFromJulia[\\\"changes\\\"]=false}),self),this[\\\"index\\\"].subscribe((function (val){!(this.valueFromJulia[\\\"index\\\"]) ? (WebIO.setval({\\\"name\\\":\\\"index\\\",\\\"scope\\\":\\\"13712546257730639579\\\",\\\"id\\\":\\\"11452243288313603969\\\",\\\"type\\\":\\\"observable\\\"},val)) : undefined; return this.valueFromJulia[\\\"index\\\"]=false}),self)]\\n \\n }\\n self.model = new AppViewModel();\\n self.valueFromJulia = {};\\n for (var key in json_data) {\\n self.valueFromJulia[key] = false;\\n }\\n ko.applyBindings(self.model, self.dom);\\n}\\n);\\n (WebIO.importBlock({\\\"data\\\":[{\\\"name\\\":\\\"knockout\\\",\\\"type\\\":\\\"js\\\",\\\"url\\\":\\\"/assetserver/c853cad7a3e123085fa7960dd53fd3d4c05dc309-knockout.js\\\"},{\\\"name\\\":\\\"knockout_punches\\\",\\\"type\\\":\\\"js\\\",\\\"url\\\":\\\"/assetserver/fab584ebb4dc64eb3ddf5ca7c73b2e76fd533845-knockout_punches.js\\\"}],\\\"type\\\":\\\"async_block\\\"})).then((imports) => handler.apply(this, imports));\\n}\\n\")])], Dict{Symbol, Any}(:className => \"field interact-widget\")), WebIO.Node{WebIO.DOM}(WebIO.DOM(:html, :div), Any[WebIO.Scope(WebIO.Node{WebIO.DOM}(WebIO.DOM(:html, :div), Any[WebIO.Node{WebIO.DOM}(WebIO.DOM(:html, :div), Any[WebIO.Node{WebIO.DOM}(WebIO.DOM(:html, :label), Any[\"r0\"], Dict{Symbol, Any}(:className => \"interact \", :style => Dict{Any, Any}(:padding => \"5px 10px 0px 10px\", \"color\" => :royalblue)))], Dict{Symbol, Any}(:className => \"interact-flex-row-left\")), WebIO.Node{WebIO.DOM}(WebIO.DOM(:html, :div), Any[WebIO.Node{WebIO.DOM}(WebIO.DOM(:html, :input), Any[], Dict{Symbol, Any}(:max => 11, :min => 1, :attributes => Dict{Any, Any}(:type => \"range\", Symbol(\"data-bind\") => \"numericValue: index, valueUpdate: 'input', event: {change: function (){this.changes(this.changes()+1)}}\", \"orient\" => \"horizontal\"), :step => 1, :className => \"slider slider is-fullwidth\", :style => Dict{Any, Any}()))], Dict{Symbol, Any}(:className => \"interact-flex-row-center\")), WebIO.Node{WebIO.DOM}(WebIO.DOM(:html, :div), Any[WebIO.Node{WebIO.DOM}(WebIO.DOM(:html, :p), Any[], Dict{Symbol, Any}(:attributes => Dict(\"data-bind\" => \"text: formatted_val\")))], Dict{Symbol, Any}(:className => \"interact-flex-row-right\"))], Dict{Symbol, Any}(:className => \"interact-flex-row interact-widget\", :style => Dict(\"font-family\" => \"monospace\", \"width\" => \"25%\"))), Dict{String, Tuple{Observables.AbstractObservable, Union{Nothing, Bool}}}(\"changes\" => (Observable{Int64} with 2 listeners. Value:\n",
"0, nothing), \"index\" => (Observable{Any} with 2 listeners. Value:\n",
"6, nothing)), Set{String}(), nothing, WebIO.Asset[WebIO.Asset(\"js\", \"knockout\", \"/Users/tomyun/.julia/packages/Knockout/3gjS1/src/../assets/knockout.js\"), WebIO.Asset(\"js\", \"knockout_punches\", \"/Users/tomyun/.julia/packages/Knockout/3gjS1/src/../assets/knockout_punches.js\"), WebIO.Asset(\"js\", nothing, \"/Users/tomyun/.julia/packages/InteractBase/o1I6G/src/../assets/all.js\"), WebIO.Asset(\"css\", nothing, \"/Users/tomyun/.julia/packages/InteractBase/o1I6G/src/../assets/style.css\"), WebIO.Asset(\"css\", nothing, \"/Users/tomyun/.julia/packages/Interact/pVyN2/src/../assets/bulma_confined.min.css\")], Dict{Any, Any}(\"changes\" => Any[WebIO.JSString(\"(function (val){return (val!=this.model[\\\"changes\\\"]()) ? (this.valueFromJulia[\\\"changes\\\"]=true, this.model[\\\"changes\\\"](val)) : undefined})\")], \"index\" => Any[WebIO.JSString(\"(function (val){return (val!=this.model[\\\"index\\\"]()) ? (this.valueFromJulia[\\\"index\\\"]=true, this.model[\\\"index\\\"](val)) : undefined})\")]), WebIO.ConnectionPool(Channel{Any}(32), Set{WebIO.AbstractConnection}(), Condition(Base.InvasiveLinkedList{Task}(Task (runnable) @0x000000016a902760, Task (runnable) @0x000000016a902760), Base.AlwaysLockedST(1))), WebIO.JSString[WebIO.JSString(\"function () {\\n var handler = (function (ko, koPunches) {\\n ko.punches.enableAll();\\n ko.bindingHandlers.numericValue = {\\n init: function(element, valueAccessor, allBindings, data, context) {\\n var stringified = ko.observable(ko.unwrap(valueAccessor()));\\n stringified.subscribe(function(value) {\\n var val = parseFloat(value);\\n if (!isNaN(val)) {\\n valueAccessor()(val);\\n }\\n });\\n valueAccessor().subscribe(function(value) {\\n var str = JSON.stringify(value);\\n if ((str == \\\"0\\\") && ([\\\"-0\\\", \\\"-0.\\\"].indexOf(stringified()) >= 0))\\n return;\\n if ([\\\"null\\\", \\\"\\\"].indexOf(str) >= 0)\\n return;\\n stringified(str);\\n });\\n ko.applyBindingsToNode(\\n element,\\n {\\n value: stringified,\\n valueUpdate: allBindings.get('valueUpdate'),\\n },\\n context,\\n );\\n }\\n };\\n var json_data = {\\\"formatted_vals\\\":[\\\"0.0\\\",\\\"0.01\\\",\\\"0.02\\\",\\\"0.03\\\",\\\"0.04\\\",\\\"0.05\\\",\\\"0.06\\\",\\\"0.07\\\",\\\"0.08\\\",\\\"0.09\\\",\\\"0.1\\\"],\\\"changes\\\":WebIO.getval({\\\"name\\\":\\\"changes\\\",\\\"scope\\\":\\\"3240076548114206083\\\",\\\"id\\\":\\\"8192866228045257484\\\",\\\"type\\\":\\\"observable\\\"}),\\\"index\\\":WebIO.getval({\\\"name\\\":\\\"index\\\",\\\"scope\\\":\\\"3240076548114206083\\\",\\\"id\\\":\\\"5747002155652071212\\\",\\\"type\\\":\\\"observable\\\"})};\\n var self = this;\\n function AppViewModel() {\\n for (var key in json_data) {\\n var el = json_data[key];\\n this[key] = Array.isArray(el) ? ko.observableArray(el) : ko.observable(el);\\n }\\n \\n [this[\\\"formatted_val\\\"]=ko.computed( function(){\\n return this.formatted_vals()[parseInt(this.index())-(1)];\\n }\\n,this)]\\n [this[\\\"changes\\\"].subscribe((function (val){!(this.valueFromJulia[\\\"changes\\\"]) ? (WebIO.setval({\\\"name\\\":\\\"changes\\\",\\\"scope\\\":\\\"3240076548114206083\\\",\\\"id\\\":\\\"8192866228045257484\\\",\\\"type\\\":\\\"observable\\\"},val)) : undefined; return this.valueFromJulia[\\\"changes\\\"]=false}),self),this[\\\"index\\\"].subscribe((function (val){!(this.valueFromJulia[\\\"index\\\"]) ? (WebIO.setval({\\\"name\\\":\\\"index\\\",\\\"scope\\\":\\\"3240076548114206083\\\",\\\"id\\\":\\\"5747002155652071212\\\",\\\"type\\\":\\\"observable\\\"},val)) : undefined; return this.valueFromJulia[\\\"index\\\"]=false}),self)]\\n \\n }\\n self.model = new AppViewModel();\\n self.valueFromJulia = {};\\n for (var key in json_data) {\\n self.valueFromJulia[key] = false;\\n }\\n ko.applyBindings(self.model, self.dom);\\n}\\n);\\n (WebIO.importBlock({\\\"data\\\":[{\\\"name\\\":\\\"knockout\\\",\\\"type\\\":\\\"js\\\",\\\"url\\\":\\\"/assetserver/c853cad7a3e123085fa7960dd53fd3d4c05dc309-knockout.js\\\"},{\\\"name\\\":\\\"knockout_punches\\\",\\\"type\\\":\\\"js\\\",\\\"url\\\":\\\"/assetserver/fab584ebb4dc64eb3ddf5ca7c73b2e76fd533845-knockout_punches.js\\\"}],\\\"type\\\":\\\"async_block\\\"})).then((imports) => handler.apply(this, imports));\\n}\\n\")])], Dict{Symbol, Any}(:className => \"field interact-widget\")), Observable{Cropbox.Plot{Gadfly.Plot}} with 0 listeners. Value:\n",
"Gadfly.Plot(Gadfly.Layer[Gadfly.Layer(nothing, Dict{Symbol, Any}(:y => [0.05, 0.04997916666666667, 0.04995834201388889, 0.049937526038049775, 0.04991671873553392, 0.04989592010272745, 0.04987513013601798, 0.04985434883179464, 0.049833576186448056, 0.04981281219637037 … 0.002497146333312398, 0.002496105855673518, 0.002495065811566987, 0.0024940262008121676, 0.002492987023228496, 0.002491948278635484, 0.0024909099668527193, 0.002489872087699864, 0.0024888346409966556, 0.002487797626562907], :x => [0.0, 0.041666666666666664, 0.08333333333333333, 0.125, 0.16666666666666666, 0.20833333333333331, 0.25, 0.29166666666666663, 0.3333333333333333, 0.375 … 299.625, 299.66666666666663, 299.7083333333333, 299.75, 299.79166666666663, 299.8333333333333, 299.875, 299.91666666666663, 299.9583333333333, 300.0]), Gadfly.StatisticElement[], Gadfly.Geom.LineGeometry(Gadfly.Stat.Identity(), false, 2, Symbol(\"\")), Gadfly.Theme(LCHab{Float32}(70.0f0,60.0f0,240.0f0), 0.7mm, 0.45mm, 1.8mm, Gadfly.Scale.default_discrete_sizes, Gadfly.Scale.default_continuous_sizes, Gadfly.Scale.default_discrete_colors, Function[Compose.circle, Gadfly.Shape.square, Gadfly.Shape.diamond, Gadfly.Shape.cross, Gadfly.Shape.xcross, Gadfly.Shape.utriangle, Gadfly.Shape.dtriangle, Gadfly.Shape.star1, Gadfly.Shape.star2, Gadfly.Shape.hexagon, Gadfly.Shape.octagon, Gadfly.Shape.hline, Gadfly.Shape.vline, Gadfly.Shape.ltriangle, Gadfly.Shape.rtriangle], 0.3mm, [:solid, :dash, :dot, :dashdot, :dashdotdot, :ldash, :ldashdash, :ldashdot, :ldashdashdot], [1.0, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, 0.0], nothing, nothing, 0.3mm, 0.0, RGB{N0f8}(1.0,1.0,1.0), Measures.AbsoluteLength[5.0mm, 5.0mm, 5.0mm, 0.0mm], RGB{N0f8}(0.816,0.816,0.878), Measures.AbsoluteLength[0.5mm, 0.5mm], RGB{N0f8}(0.627,0.627,0.627), 0.2mm, 0, \"'PT Sans Caption','Helvetica Neue','Helvetica',sans-serif\", 2.822222222222222mm, RGB{N0f8}(0.424,0.376,0.42), \"'PT Sans','Helvetica Neue','Helvetica',sans-serif\", 3.5277777777777777mm, RGB{N0f8}(0.337,0.29,0.333), \"'PT Sans Caption','Helvetica Neue','Helvetica',sans-serif\", 2.822222222222222mm, RGB{N0f8}(0.298,0.251,0.294), \"'PT Sans','Helvetica Neue','Helvetica',sans-serif\", 3.175mm, RGB{N0f8}(0.212,0.165,0.208), \"'PT Sans','Helvetica Neue','Helvetica',sans-serif\", 2.822222222222222mm, RGB{N0f8}(0.298,0.251,0.294), 40, -0.05mm, 1.0mm, 3.0mm, Gadfly.default_stroke_color, 0.3mm, Cropbox.var\"#504#513\"(), Gadfly.default_continuous_highlight_color, Gadfly.default_lowlight_color, Gadfly.default_middle_color, 0.6mm, :left, :square, nothing, nothing, nothing, :right, nothing, 2.0mm, 1000, 10.0, 0.5, 0.2, 1.0mm, 4, Gadfly.Scale.DiscreteColorScale(Gadfly.Scale.default_discrete_colors, nothing, nothing, true), Gadfly.Scale.ContinuousColorScale(Gadfly.Scale.var\"#69#73\"{Int64, Int64, Int64, Int64, Float64, Int64}(100, 40, 260, 10, 1.5, 70), Gadfly.Scale.ContinuousScaleTransform(identity, identity, Gadfly.Scale.identity_formatter), nothing, nothing)), 0)], nothing, Data(\n",
" titles=Dict{Symbol, AbstractString}()\n",
")\n",
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]
},
"execution_count": 5,
"metadata": {
"application/vnd.webio.node+json": {
"kernelId": "cf1f84de-2548-4892-ac97-3dc4528bd326"
}
},
"output_type": "execute_result"
}
],
"source": [
"manipulate(Gompertz, :t, :r;\n",
" config = :Gompertz => (;\n",
" W0 = 0.25,\n",
" ),\n",
" parameters = :Gompertz => (;\n",
" α = 0:0.001:0.02,\n",
" r0 = 0:0.01:0.1,\n",
" ),\n",
" stop = 300u\"d\",\n",
" kind = :line,\n",
" ylim = (0, 0.1),\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 2.2. 성장률(`r`) 분해"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"식물 성장에 중요한 영향을 미치는 생리적 현상에는 먼저 광합성과 호흡을 생각해볼 수 있습니다. 광합성(photosynthesis)은 대기중의 이산화탄소($\\mathrm{CO_2}$)을 흡수하여 탄수화물(carbohydrate)를 만들어냅니다. 이렇게 만들어진 탄수화물은 호흡(respiration)을 통해 분해되어 식물체를 유지하기 위한 에너지로 쓰이거나, 새로운 생체량을 만들어내는데 사용됩니다. 이때 전자를 유지호흡(maintenance respiration), 후자를 성장호흡(growth respiration)이라고 구분하는데요. 지금까지 여러가지 성장 곡선으로 표현하고자 하였던 것이 바로 이 성장호흡 부분 되겠습니다."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 2.2.1. 광합성(`A`)과 호흡(`R`) 분리"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"식물이 성장하기 위해 필요한 기질(substrate)은 광합성을 통해 생성되고, 이중에서 현상유지를 위해 필요한 만큼 유지호흡으로 먼저 사용된다고 가정하면, 그 나머지가 실제 성장을 위해 사용될 것입니다. 이때 광합성 산물인 탄수화물이 100% 그대로 식물의 구조로 변환될 수는 없기 때문에 변환효율을 고려하도록 하겠습니다. 그 결과, 성장률(`r`)은 아래와 같이 광합성(`A`)과 호흡(`R`)의 차이, 그리고 그 변환효율(`c`)로 표현할 수 있습니다. 여기서는 수식을 많이 단순화하였지만 보다 자세한 내용이 궁금하시다면 [Thornley (1970)](https://doi.org/10.1038/227304b0)를 참고해보세요."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"r = c \\cdot (A - R)\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"| 이름 | 값 | 단위 | 설명 |\n",
"| :- | :- | :- | :- |\n",
"| $c$ | - | | 기질 변환효율 |\n",
"| $A$ | 0.4 | $$\\mathrm{g}\\ \\mathrm{g^{-1}}\\ \\mathrm{d^{-1}}$$ | 탄수화물 등 기질 생산률 |\n",
"| $R$ | 0.015 | $\\mathrm{g}\\ \\mathrm{g^{-1}}\\ \\mathrm{d^{-1}}$ | 유지호흡률 |"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"여기서 변환효율은 조금 더 자세히 표현해보도록 하겠습니다. 성장을 통해 새로 만들어지는 구조물을 만들기 위한 재료는 결국 광합성 산물인 탄수화물($\\mathrm{CH_2O}$)에서 유래하게 되는데요. 이 구조물의 상당 부분이 탄소($\\mathrm{C}$)로 구성되어 있다고 가정할 때 1만큼의 탄수화물이 얼마만큼의 생체량으로 변환되는지 그 비율($c_0$)을 생각해볼 수 있습니다. 또한 위에서 언급했던 것처럼 변환 과정 자체의 효율($Y$)을 고려하여 실제 변환비율($c$)은 아래와 같이 정의하겠습니다."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"c = Y c_0\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"| 이름 | 값 | 단위 | 설명 |\n",
"| :- | :- | :- | :- |\n",
"| $Y$ | 0.75 | - | 생체량 변환 과정의 효율 |\n",
"| $c_0$ | 0.889 | - | 생체량의 45%가 탄수화물($\\mathrm{CH_2O}$)의 탄소($\\mathrm{C}$)에서 유래한다고 가정할 때의 변환비율 ($\\frac{\\frac{12\\ \\mathrm{g}\\ \\mathrm{mol^{-1}}}{30\\ \\mathrm{g}\\ \\mathrm{mol^{-1}}}}{0.45}$) |"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"이제 위의 수식을 모형 명세로 표현해보겠습니다. 우선 생체량(`W`) 관련 변수들은 이전과 동일한 형태로 들어갑니다.\n",
"\n",
"$$\n",
"\\begin{align}\n",
"\\frac{dW}{dt} &= r W_t \\\\\n",
"W_{t = 0} &= W_0\n",
"\\end{align}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"| 이름 | 값 | 단위 | 설명 |\n",
"| :- | :- | :- | :- |\n",
"| $t$ | - | $\\mathrm{d}$ | 시간 |\n",
"| $r$ | - | $$\\mathrm{g}\\ \\mathrm{g^{-1}}\\ \\mathrm{d^{-1}}$$ | 상대성장률 |\n",
"| $$W_0$$ | 0.25 | $\\mathrm{g}$ | 최초 생체량 |\n",
"| $W$ | - | $\\mathrm{g}$ | 시간별 생체량 |"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"새로 추가되는 부분은 상대성장률(`r`)을 광합성(`A`)과 호흡(`R`), 그리고 변환효율(`c`) 관련 변수들입니다."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Growth0"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"@system Growth0(Controller) begin\n",
" t(context.clock.time) ~ track(u\"d\")\n",
"\n",
" W0: initial_biomass => 0.25 ~ preserve(parameter, u\"g\")\n",
" W(r, W): biomass => r * W ~ accumulate(init = W0, u\"g\")\n",
"\n",
" Y: growth_yield => 0.75 ~ preserve(parameter)\n",
" c0: potential_conversion_factor => 0.889 ~ preserve(parameter)\n",
" c(c0, Y): conversion_factor => c0 * Y ~ track\n",
"\n",
" A: assimilation_rate => 0.4 ~ preserve(parameter, u\"g/g/d\")\n",
" R: respiration_rate => 0.015 ~ preserve(parameter, u\"g/g/d\")\n",
"\n",
" r(c, A, R): growth_rate => c * (A - R) ~ track(u\"g/g/d\")\n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"변수들간의 관계도를 `Cropbox.dependency()` 함수를 이용해 그려보겠습니다. 이 관계도를 통해 각 변수들이 서로 어떻게 관련되어 있는지 확인해볼 수 있습니다. 예를 들어 생장률(`r`)은 광합성(`A`), 호흡(`R`), 변환비율(`c`)에 기반하여 계산된다는 것을 화살표의 연결 방향으로 알 수 있습니다."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
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"text/plain": [
"\u001b[90m[\u001b[39m\u001b[94mconfig\u001b[39m\u001b[90m → \u001b[39m\u001b[94mR\u001b[39m\u001b[90m → \u001b[39m\u001b[94mA\u001b[39m\u001b[90m → \u001b[39m\u001b[94mc0\u001b[39m\u001b[90m → \u001b[39m\u001b[94mY\u001b[39m\u001b[90m → \u001b[39m\u001b[94mc\u001b[39m\u001b[90m → \u001b[39m\u001b[94mr\u001b[39m\u001b[90m → \u001b[39m\u001b[94mW0\u001b[39m\u001b[90m → \u001b[39m\u001b[94m∘context\u001b[39m\u001b[90m → \u001b[39m\u001b[94mcontext\u001b[39m\u001b[90m → \u001b[39m\u001b[94mW\u001b[39m\u001b[90m → \u001b[39m\u001b[94m⋆W\u001b[39m\u001b[90m → \u001b[39m\u001b[94mt\u001b[39m\u001b[90m → \u001b[39m\u001b[94m⋆context\u001b[39m\u001b[90m]\u001b[39m"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Cropbox.dependency(Growth0)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"방금 만든 시스템에 정의되어 있는 모수들을 확인하기 위해 `parameters()` 함수를 호출하면 해당 값들이 담긴 설정(configuration)을 만들어낼 수 있습니다."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Config for 1 system:\n",
" \u001b[95mGrowth0\u001b[39m\n",
" \u001b[94mW0\u001b[39m\u001b[90m = \u001b[39m0.25 g\n",
" \u001b[94mY \u001b[39m\u001b[90m = \u001b[39m0.75\n",
" \u001b[94mc0\u001b[39m\u001b[90m = \u001b[39m0.889\n",
" \u001b[94mA \u001b[39m\u001b[90m = \u001b[39m0.4 d⁻¹\n",
" \u001b[94mR \u001b[39m\u001b[90m = \u001b[39m0.015 d⁻¹"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"parameters(Growth0)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"그럼 이제 모의를 수행해보겠습니다. `simulate()`로 모의를 따로 진행하지 않고, `visualize()` 함수를 이용하여 모의를 수행하여 그대로 그래프를 그려보았습니다. 300일간의 생체량(`W`) 변화입니다."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
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"지난 시간에 보았던 지수적(exponential) 성장곡선처럼 비현실적인 증가를 보이고 있습니다. 상대성장률(`r`)이 항상 같은 값으로 고정되어 있기 때문에 끝없이 성장을 하기 때문입니다. 그래프로 확인해보겠습니다."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
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"text/plain": [
"\"<Cropbox.Plot{Gadfly.Plot}>\""
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"visualize(Growth0, :t, :r;\n",
" stop = 300u\"d\",\n",
" kind = :line,\n",
" ylim = (0, 0.5),\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 2.2.2. 성장 저하 1안 - 변환효율 (`Y`)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"그럼 이제 모형을 조금씩 수정하며 보다 현실적으로 만들어보겠습니다. 시간에 따라 성장률(`r`)이 감소하도록 앞서 복습했던 Gompertz 모형의 효율 저하도(decay rate) 개념을 도입해보겠습니다.\n",
"\n",
"$$r = c \\cdot (A - R)$$\n",
"\n",
"성장률(`r`)은 좌측의 변환비율(`c`)과 우측의 광합성(`A`), 호흡(`R`) 차이의 두 부분으로 구성되는데요. 이중에서 먼저 변환비율(`c`)에 효율 저하도(`α`)를 적용해보겠습니다."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"\\begin{align}\n",
"\\frac{dY}{dt} &= -\\alpha Y_t \\\\\n",
"Y_{t = 0} &= Y_0\n",
"\\end{align}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"| 이름 | 값 | 단위 | 설명 |\n",
"| :- | :- | :- | :- |\n",
"| $\\alpha$ | 0.03 | $\\mathrm{d^{-1}}$ | 시간에 따른 성장 효율 저하도 |\n",
"| $Y_0$ | 0.75 | - | 효율 저하 이전의 최적 변환효율 |\n",
"| $Y$ | - | - | 시간에 따라 저하되는 실제 생체량 변환효율 |"
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{
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"Growth1"
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"source": [
"@system Growth1(Growth0, Controller) begin\n",
" α: decary_rate => 0.03 ~ preserve(parameter, u\"d^-1\")\n",
" Y0: potential_growth_yield => 0.75 ~ preserve(parameter)\n",
" Y(α, Y): growth_yield => -α*Y ~ accumulate(init = Y0)\n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"변환효율(`Y`)가 이제는 더 이상 고정된 모수가 아니라 매번 갱신되는 상태변수로 바뀌었습니다. 대신 효율 저하도(`α`)와 최적 변환효율(`Y0`)이 새로운 모수로 들어갔습니다."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
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]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Cropbox.dependency(Growth1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"이제 생체량(`W`) 변화가 앞선 보았던 Gompertz 성장곡선과 유사한 형태가 되었습니다."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
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"text/plain": [
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},
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}
],
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" stop = 300u\"d\",\n",
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")"
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{
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"source": [
"성장률(`r`)이 시간에 따라 아래와 같이 감소하기 때문입니다."
]
},
{
"cell_type": "code",
"execution_count": 14,
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},
"execution_count": 14,
"metadata": {},
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],
"source": [
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")"
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"source": [
"직접적으로는 변환효율(`Y`)이 감소하는 영향이 그대로 반영되고 있기 때문입니다."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
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"source": [
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" stop = 300u\"d\",\n",
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"대신 광합성(`A`)과 호흡(`R`)에는 아무런 변화가 없습니다. 과연 식물 성장에 따라 단위 생체량 기준 광합성과 호흡량에 아무런 변화가 없는 것은 괜찮을까요?"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
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"text/plain": [
"\"<Cropbox.Plot{Gadfly.Plot}>\""
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"visualize(Growth1, :t, [:A, :R];\n",
" stop = 300u\"d\",\n",
" kind = :line,\n",
" ylim = (0, 0.5),\n",
")"
]
},
{
"cell_type": "markdown",
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"source": [
"### 2.2.3. 성장 저하 2안 - 광합성(`A`)과 호흡(`R`)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"이번에는 변환효율(`Y`) 대신 광합성(`A`)과 호흡(`R`) 자체의 효율이 시간에 따라 감소한다고 가정해보겠습니다. 앞에서와 동일하게 효율 저하도(`α`)를 추가해보세요. 참고로 `α`(a가 아닌 알파)를 입력하려면 `\\alpha`라고 친 다음 탭(tab)키를 누르시면 됩니다."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
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"data": {
"text/plain": [
"Growth2"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
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"source": [
"@system Growth2(Growth0, Controller) begin\n",
" α: decary_rate => 0.03 ~ preserve(parameter, u\"d^-1\")\n",
"\n",
" Amax: maximum_assimilation_rate => 0.4 ~ preserve(parameter, u\"g/g/d\")\n",
" Rmax: maximum_respiration_rate => 0.015 ~ preserve(parameter, u\"g/g/d\")\n",
"\n",
" A(α, A): assimilation_rate => -α * A ~ accumulate(init = Amax, u\"g/g/d\")\n",
" R(α, R): respiration_rate => -α * R ~ accumulate(init = Rmax, u\"g/g/d\")\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
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]
},
"execution_count": 18,
"metadata": {},
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],
"source": [
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]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"이제 생체량(`W`) 변화를 확인해보겠습니다. 내부적으로는 다른 가정으로 접근하였지만 전반적인 변화의 양상은 동일하게 나오고 있습니다."
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
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"마찬가지로 성장률(`r`)의 감소 역시 확인해보겠습니다."
]
},
{
"cell_type": "code",
"execution_count": 20,
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],
"source": [
"visualize(Growth2, :t, :r;\n",
" stop = 300u\"d\",\n",
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{
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"source": [
"이러한 성장률의 감소는 변환효율(`Y`)에 의한 것이 아닙니다."
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
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"execution_count": 21,
"metadata": {},
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"source": [
"visualize(Growth2, :t, :Y;\n",
" stop = 300u\"d\",\n",
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")"
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{
"cell_type": "markdown",
"metadata": {},
"source": [
"단위 생체량 기준 광합성(`A`)과 호흡(`R`)량을 그려보면 이전과 달리 시간에 따라 감소하는 것을 확인할 수 있습니다."
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
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"text/plain": [
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]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"visualize(Growth2, :t, [:A, :R];\n",
" stop = 300u\"d\",\n",
" kind = :line,\n",
" ylim = (0, 0.5),\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"사실 위의 두가지 접근 방식은 수식에서 값을 어떤 위치에서 곱해주는지의 차이일뿐이며 그 결과 정리된 수식은 동일합니다. 하지만 각 변수가 어떤 의미를 가지고 어떤 기작에 의해 설명되는지 분명한 차이가 있을 수 있다는 점은 기억해주세요. 잘 정의된 모형은 이후 수정하거나 확장하기에도 수월합니다."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 2.2.4. 분배 (partitioning)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"위의 모형에서는 식물의 성장이 전체 생체량에 비례해서 이루어진다고 가정하였지만, 실제로는 잎에서 생성된 동화산물이 다른 부위에 얼마만큼씩 분배되어 사용되는지에 따라 실제 관측되는 성장의 형태는 크게 달라질 수 있습니다. 특히 동화산물은 잎의 광합성에 의해 생성되므로 잎이 전체 식물에서 차지하는 비중에 따라 그 생산량도 달라질 것입니다. 그리고 성장 단계에 따라 영양성장(vegetative growth) 시기에는 많은 부분이 잎으로 할당되다가 생식성장(reproductive growth) 단계에서는 그 비중이 열매 쪽으로 옮겨가는 등의 변화도 고려해볼 수 있습니다.\n",
"\n",
"여기에서는 [Monsi (1960)](https://www.cabdirect.org/cabdirect/abstract/19600600113)의 모형을 참고하여 식물의 전체 생체량을 광합성이 가능한 부위와 아닌 부위로 나누어 광합성과 호흡의 비중을 조정해보도록 하겠습니다."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"r = c \\cdot (m A - n R)\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"| 이름 | 값 | 단위 | 설명 |\n",
"| :- | :- | :- | :- |\n",
"| $m$ | 0.5 | - | 광합성을 하는 생체량의 비중 |\n",
"| $n$ | $$1 - m$$ | - | 광합성을 하지 않는 생체량의 비중 |"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"전체 생체량에서 광합성이 가능한(photosynthetic) 부분의 비중(`m`)과 그렇지 않은(non-photosynthetic) 부분의 비중(`n`)을 모수로 추가하고 각각 광합성(`A`)과 호흡(`R`)에 적용합니다."
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Growth3"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"@system Growth3(Growth2, Controller) begin\n",
" m: leaf_fraction => 0.5 ~ preserve(parameter)\n",
" n(m): non_leaf_fraction => 1 - m ~ track\n",
"\n",
" mA(m, A): actual_assimilation_rate => m * A ~ track(u\"g/g/d\")\n",
" nR(n, R): actual_respiration_rate => n * R ~ track(u\"g/g/d\")\n",
"\n",
" r(c, mA, nR): growth_rate => c * (mA - nR) ~ track(u\"g/g/d\")\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
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"<title>5</title>\n",
"<text text-anchor=\"middle\" x=\"259\" y=\"-39.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">t</text>\n",
"</g>\n",
"<!-- 2->5 -->\n",
"<g id=\"edge3\" class=\"edge\">\n",
"<title>2->5</title>\n",
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"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"261.08,-50.95 260.05,-49.1 259.71,-51.19 261.08,-50.95\"/>\n",
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"<g id=\"node7\" class=\"node\">\n",
"<title>7</title>\n",
"<text text-anchor=\"middle\" x=\"86\" y=\"-73.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">W</text>\n",
"</g>\n",
"<!-- 2->7 -->\n",
"<g id=\"edge4\" class=\"edge\">\n",
"<title>2->7</title>\n",
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"</g>\n",
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"<g id=\"node8\" class=\"node\">\n",
"<title>8</title>\n",
"<text text-anchor=\"middle\" x=\"152\" y=\"-39.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">⋆W</text>\n",
"</g>\n",
"<!-- 2->8 -->\n",
"<g id=\"edge5\" class=\"edge\">\n",
"<title>2->8</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M260.6,-170.37C235.37,-162.61 193.95,-146.15 171,-117 155.36,-97.13 152.48,-65.82 152.03,-51.13\"/>\n",
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"</g>\n",
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"<g id=\"node13\" class=\"node\">\n",
"<title>13</title>\n",
"<text text-anchor=\"middle\" x=\"393\" y=\"-141.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">A</text>\n",
"</g>\n",
"<!-- 2->13 -->\n",
"<g id=\"edge6\" class=\"edge\">\n",
"<title>2->13</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M303.26,-170.48C321.95,-165.57 349.86,-158.09 374,-151 377.78,-149.89 381.95,-148.58 385.42,-147.47\"/>\n",
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"</g>\n",
"<!-- 14 -->\n",
"<g id=\"node14\" class=\"node\">\n",
"<title>14</title>\n",
"<text text-anchor=\"middle\" x=\"464\" y=\"-107.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">⋆A</text>\n",
"</g>\n",
"<!-- 2->14 -->\n",
"<g id=\"edge7\" class=\"edge\">\n",
"<title>2->14</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M303.19,-171.77C338.83,-164.64 406.92,-151.03 407,-151 425.91,-142.9 444.86,-127.9 455.45,-118.74\"/>\n",
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"</g>\n",
"<!-- 17 -->\n",
"<g id=\"node17\" class=\"node\">\n",
"<title>17</title>\n",
"<text text-anchor=\"middle\" x=\"327\" y=\"-141.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">R</text>\n",
"</g>\n",
"<!-- 2->17 -->\n",
"<g id=\"edge8\" class=\"edge\">\n",
"<title>2->17</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M291.11,-169.73C299.63,-163.86 312.18,-155.21 319.96,-149.85\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"320.58,-150.27 321.83,-148.56 319.79,-149.12 320.58,-150.27\"/>\n",
"</g>\n",
"<!-- 18 -->\n",
"<g id=\"node18\" class=\"node\">\n",
"<title>18</title>\n",
"<text text-anchor=\"middle\" x=\"409\" y=\"-107.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">⋆R</text>\n",
"</g>\n",
"<!-- 2->18 -->\n",
"<g id=\"edge9\" class=\"edge\">\n",
"<title>2->18</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M297.78,-169.97C309.81,-165.21 326.69,-158.2 341,-151 362.46,-140.2 386.43,-125.43 399.4,-117.19\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"399.92,-117.69 401.23,-116.02 399.17,-116.51 399.92,-117.69\"/>\n",
"</g>\n",
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"<g id=\"node4\" class=\"node\">\n",
"<title>4</title>\n",
"<text text-anchor=\"middle\" x=\"191\" y=\"-242.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">config</text>\n",
"</g>\n",
"<!-- 4->1 -->\n",
"<g id=\"edge10\" class=\"edge\">\n",
"<title>4->1</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M202.47,-237.98C212.65,-232.64 227.54,-224.83 238.33,-219.17\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"238.72,-219.76 240.16,-218.21 238.07,-218.52 238.72,-219.76\"/>\n",
"</g>\n",
"<!-- 4->3 -->\n",
"<g id=\"edge11\" class=\"edge\">\n",
"<title>4->3</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M172.34,-241.61C124.28,-234.95 0,-214.22 0,-178 0,-178 0,-178 0,-75 0,-20.17 196.51,-10.88 268.76,-9.31\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"268.87,-10.01 270.86,-9.27 268.84,-8.61 268.87,-10.01\"/>\n",
"</g>\n",
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"<g id=\"node6\" class=\"node\">\n",
"<title>6</title>\n",
"<text text-anchor=\"middle\" x=\"40\" y=\"-107.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">W0</text>\n",
"</g>\n",
"<!-- 4->6 -->\n",
"<g id=\"edge12\" class=\"edge\">\n",
"<title>4->6</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M172.3,-241.65C154.73,-238.65 128.44,-232.05 110,-218 74.2,-190.72 51.2,-139.53 43.18,-119.42\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"43.66,-118.73 42.27,-117.13 42.36,-119.24 43.66,-118.73\"/>\n",
"</g>\n",
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"<g id=\"node10\" class=\"node\">\n",
"<title>10</title>\n",
"<text text-anchor=\"middle\" x=\"124\" y=\"-208.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Y</text>\n",
"</g>\n",
"<!-- 4->10 -->\n",
"<g id=\"edge13\" class=\"edge\">\n",
"<title>4->10</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M178.4,-237.98C164.35,-231.27 142.14,-220.67 130.94,-215.32\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"131.22,-214.67 129.12,-214.44 130.62,-215.94 131.22,-214.67\"/>\n",
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"<g id=\"node11\" class=\"node\">\n",
"<title>11</title>\n",
"<text text-anchor=\"middle\" x=\"155\" y=\"-208.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">c0</text>\n",
"</g>\n",
"<!-- 4->11 -->\n",
"<g id=\"edge14\" class=\"edge\">\n",
"<title>4->11</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M184.06,-237.83C178.18,-232.61 169.74,-225.1 163.46,-219.52\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"163.88,-218.96 161.92,-218.15 162.95,-220 163.88,-218.96\"/>\n",
"</g>\n",
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"<g id=\"node15\" class=\"node\">\n",
"<title>15</title>\n",
"<text text-anchor=\"middle\" x=\"393\" y=\"-174.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Amax</text>\n",
"</g>\n",
"<!-- 4->15 -->\n",
"<g id=\"edge15\" class=\"edge\">\n",
"<title>4->15</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M209.75,-241.22C233.34,-237.42 274.87,-229.71 309,-218 335.28,-208.98 364.17,-194.02 380.29,-185.18\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"380.78,-185.71 382.2,-184.13 380.11,-184.48 380.78,-185.71\"/>\n",
"</g>\n",
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"<g id=\"node16\" class=\"node\">\n",
"<title>16</title>\n",
"<text text-anchor=\"middle\" x=\"535\" y=\"-141.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">α</text>\n",
"</g>\n",
"<!-- 4->16 -->\n",
"<g id=\"edge16\" class=\"edge\">\n",
"<title>4->16</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M209.93,-241.8C238.32,-238.25 293.43,-230.38 339,-218 415.01,-197.36 502.92,-159.29 528,-148.14\"/>\n",
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"</g>\n",
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"<g id=\"node19\" class=\"node\">\n",
"<title>19</title>\n",
"<text text-anchor=\"middle\" x=\"334\" y=\"-174.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Rmax</text>\n",
"</g>\n",
"<!-- 4->19 -->\n",
"<g id=\"edge17\" class=\"edge\">\n",
"<title>4->19</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M209.86,-241.15C229.46,-237.66 260.63,-230.6 285,-218 301.46,-209.49 317.51,-194.82 326.54,-185.81\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"327.34,-186 328.25,-184.08 326.35,-185.01 327.34,-186\"/>\n",
"</g>\n",
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"<g id=\"node22\" class=\"node\">\n",
"<title>22</title>\n",
"<text text-anchor=\"middle\" x=\"180\" y=\"-174.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">m</text>\n",
"</g>\n",
"<!-- 4->22 -->\n",
"<g id=\"edge18\" class=\"edge\">\n",
"<title>4->22</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M189.98,-237.91C188.01,-226.08 183.67,-199.99 181.41,-186.48\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"182.06,-186.13 181.04,-184.27 180.68,-186.36 182.06,-186.13\"/>\n",
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"<!-- 5->3 -->\n",
"<g id=\"edge19\" class=\"edge\">\n",
"<title>5->3</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M264.01,-36.55C269.78,-31.42 279.36,-22.9 286.35,-16.69\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"287.03,-17.02 288.06,-15.17 286.1,-15.97 287.03,-17.02\"/>\n",
"</g>\n",
"<!-- 6->7 -->\n",
"<g id=\"edge20\" class=\"edge\">\n",
"<title>6->7</title>\n",
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"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"79.58,-82.32 80.82,-80.6 78.78,-81.17 79.58,-82.32\"/>\n",
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"<!-- 6->8 -->\n",
"<g id=\"edge21\" class=\"edge\">\n",
"<title>6->8</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M43.31,-102.92C48.36,-94.18 58.83,-78.11 72,-69 94.21,-53.64 126.07,-46.9 142.06,-44.35\"/>\n",
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"<g id=\"edge22\" class=\"edge\">\n",
"<title>7->3</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M91.08,-69.26C99.32,-60.33 116.57,-43.29 135,-35 178.98,-15.21 235.79,-10.26 268.53,-9.16\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"268.87,-9.85 270.85,-9.08 268.83,-8.45 268.87,-9.85\"/>\n",
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"<!-- 7->8 -->\n",
"<g id=\"edge23\" class=\"edge\">\n",
"<title>7->8</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M91.18,-72.49C102.19,-67.15 128.06,-54.61 142.25,-47.73\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"142.77,-48.26 144.26,-46.75 142.15,-47 142.77,-48.26\"/>\n",
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"<!-- 8->3 -->\n",
"<g id=\"edge24\" class=\"edge\">\n",
"<title>8->3</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M159.69,-39.28C179.99,-34.74 235.78,-22.25 269.04,-14.81\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"269.2,-15.49 271,-14.37 268.89,-14.12 269.2,-15.49\"/>\n",
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"<g id=\"node9\" class=\"node\">\n",
"<title>9</title>\n",
"<text text-anchor=\"middle\" x=\"187\" y=\"-73.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">r</text>\n",
"</g>\n",
"<!-- 9->8 -->\n",
"<g id=\"edge25\" class=\"edge\">\n",
"<title>9->8</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M181.84,-70.28C176.23,-65.15 167.18,-56.88 160.51,-50.78\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"160.82,-50.12 158.87,-49.28 159.88,-51.15 160.82,-50.12\"/>\n",
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"<g id=\"node12\" class=\"node\">\n",
"<title>12</title>\n",
"<text text-anchor=\"middle\" x=\"124\" y=\"-174.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">c</text>\n",
"</g>\n",
"<!-- 10->12 -->\n",
"<g id=\"edge26\" class=\"edge\">\n",
"<title>10->12</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M124,-203.83C124,-198.87 124,-191.86 124,-186.39\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"124.7,-186.15 124,-184.15 123.3,-186.15 124.7,-186.15\"/>\n",
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"<!-- 11->12 -->\n",
"<g id=\"edge27\" class=\"edge\">\n",
"<title>11->12</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M149.02,-203.83C143.79,-198.43 136.2,-190.6 130.75,-184.97\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"131.03,-184.25 129.14,-183.3 130.03,-185.23 131.03,-184.25\"/>\n",
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"<!-- 12->9 -->\n",
"<g id=\"edge28\" class=\"edge\">\n",
"<title>12->9</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M124.46,-169.86C125.27,-161.89 127.42,-147.73 133,-137 145.21,-113.54 168.76,-92.06 180.3,-82.39\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"180.82,-82.87 181.91,-81.05 179.93,-81.79 180.82,-82.87\"/>\n",
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"<!-- 13->3 -->\n",
"<g id=\"edge29\" class=\"edge\">\n",
"<title>13->3</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M389.79,-136.75C380.79,-119.52 353.96,-70.27 324,-35 318.29,-28.27 310.86,-21.65 304.96,-16.77\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"305.17,-16.04 303.18,-15.31 304.28,-17.12 305.17,-16.04\"/>\n",
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"<!-- 13->14 -->\n",
"<g id=\"edge30\" class=\"edge\">\n",
"<title>13->14</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M398.11,-140.7C409.86,-135.4 439.01,-122.26 454.3,-115.37\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"454.91,-115.86 456.45,-114.4 454.34,-114.59 454.91,-115.86\"/>\n",
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"<g id=\"node21\" class=\"node\">\n",
"<title>21</title>\n",
"<text text-anchor=\"middle\" x=\"221\" y=\"-107.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">mA</text>\n",
"</g>\n",
"<!-- 13->21 -->\n",
"<g id=\"edge31\" class=\"edge\">\n",
"<title>13->21</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M387.66,-142.01C363.41,-137.49 263.36,-118.88 231.09,-112.88\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"230.98,-112.14 228.88,-112.47 230.72,-113.52 230.98,-112.14\"/>\n",
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"<!-- 14->3 -->\n",
"<g id=\"edge32\" class=\"edge\">\n",
"<title>14->3</title>\n",
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"<g id=\"edge33\" class=\"edge\">\n",
"<title>15->13</title>\n",
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"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"393.7,-153.26 393,-151.26 392.3,-153.26 393.7,-153.26\"/>\n",
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"<!-- 15->14 -->\n",
"<g id=\"edge34\" class=\"edge\">\n",
"<title>15->14</title>\n",
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"<g id=\"edge35\" class=\"edge\">\n",
"<title>16->14</title>\n",
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"<!-- 16->18 -->\n",
"<g id=\"edge36\" class=\"edge\">\n",
"<title>16->18</title>\n",
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"<g id=\"edge37\" class=\"edge\">\n",
"<title>17->3</title>\n",
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"<!-- 17->18 -->\n",
"<g id=\"edge38\" class=\"edge\">\n",
"<title>17->18</title>\n",
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"<g id=\"node20\" class=\"node\">\n",
"<title>20</title>\n",
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"</g>\n",
"<!-- 17->20 -->\n",
"<g id=\"edge39\" class=\"edge\">\n",
"<title>17->20</title>\n",
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]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Cropbox.dependency(Growth3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"이제 실제 광합성이 가능한 부분만을 통해 동화산물이 생성되기 때문에 전체 생체량(`W`)도 그에 맞춰 감소하였습니다. 소폭의 비중 변화에 따라 생체량이 크게 변화하는 것을 확인할 수 있습니다."
]
},
{
"cell_type": "code",
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" .querySelector('[data-webio-mountpoint=\"1539599927433915543\"]')\n",
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" '<div style=\"padding: 1em; background-color: #f8d6da; border: 1px solid #f5c6cb; font-weight: bold;\">' +\n",
" '<p><strong>WebIO not detected.</strong></p>' +\n",
" '<p>Please read ' +\n",
" '<a href=\"https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/\" target=\"_blank\">the troubleshooting guide</a> ' +\n",
" 'for more information on how to resolve this issue.</p>' +\n",
" '<p><a href=\"https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/\" target=\"_blank\">https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/</a></p>' +\n",
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},
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"manipulate(Growth3, :t, :W;\n",
" parameters = :0 => (;\n",
" :m => 0:0.1:1,\n",
" ),\n",
" stop = 300u\"d\",\n",
" kind = :line,\n",
" ylim = (0, 300),\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"이러한 분배 비율의 변화가 성장률(`r`)에는 어떠한 영향을 미치는지 보도록 하겠습니다."
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
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{
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},
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},
"nodeType": "Scope",
"props": {},
"type": "node"
}
],
"instanceArgs": {
"namespace": "html",
"tag": "div"
},
"nodeType": "DOM",
"props": {
"style": {
"display": "flex",
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}
},
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"<div\n",
" class=\"webio-mountpoint\"\n",
" data-webio-mountpoint=\"9171853683960641538\"\n",
">\n",
" <script>\n",
" (function(){\n",
" // Some integrations (namely, IJulia/Jupyter) use an alternate render pathway than\n",
" // just putting the html on the page. If WebIO isn't defined, then it's pretty likely\n",
" // that we're in one of those situations and the integration just isn't installed\n",
" // correctly.\n",
" if (typeof window.WebIO === \"undefined\") {\n",
" document\n",
" .querySelector('[data-webio-mountpoint=\"9171853683960641538\"]')\n",
" .innerHTML = (\n",
" '<div style=\"padding: 1em; background-color: #f8d6da; border: 1px solid #f5c6cb; font-weight: bold;\">' +\n",
" '<p><strong>WebIO not detected.</strong></p>' +\n",
" '<p>Please read ' +\n",
" '<a href=\"https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/\" target=\"_blank\">the troubleshooting guide</a> ' +\n",
" 'for more information on how to resolve this issue.</p>' +\n",
" '<p><a href=\"https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/\" target=\"_blank\">https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/</a></p>' +\n",
" '</div>'\n",
" );\n",
" return;\n",
" }\n",
" WebIO.mount(\n",
" document.querySelector('[data-webio-mountpoint=\"9171853683960641538\"]'),\n",
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(this.valueFromJulia[\\\"changes\\\"]=true, this.model[\\\"changes\\\"](val)) : undefined})\"],\"index\":[\"(function (val){return (val!=this.model[\\\"index\\\"]()) ? (this.valueFromJulia[\\\"index\\\"]=true, this.model[\\\"index\\\"](val)) : undefined})\"]},\"systemjs_options\":null,\"mount_callbacks\":[\"function () {\\n var handler = (function (ko, koPunches) {\\n ko.punches.enableAll();\\n ko.bindingHandlers.numericValue = {\\n init: function(element, valueAccessor, allBindings, data, context) {\\n var stringified = ko.observable(ko.unwrap(valueAccessor()));\\n stringified.subscribe(function(value) {\\n var val = parseFloat(value);\\n if (!isNaN(val)) {\\n valueAccessor()(val);\\n }\\n });\\n valueAccessor().subscribe(function(value) {\\n var str = JSON.stringify(value);\\n if ((str == \\\"0\\\") && ([\\\"-0\\\", \\\"-0.\\\"].indexOf(stringified()) >= 0))\\n return;\\n if ([\\\"null\\\", \\\"\\\"].indexOf(str) >= 0)\\n return;\\n stringified(str);\\n });\\n ko.applyBindingsToNode(\\n element,\\n {\\n value: stringified,\\n valueUpdate: allBindings.get('valueUpdate'),\\n },\\n context,\\n );\\n }\\n };\\n var json_data = {\\\"formatted_vals\\\":[\\\"0.0\\\",\\\"0.1\\\",\\\"0.2\\\",\\\"0.3\\\",\\\"0.4\\\",\\\"0.5\\\",\\\"0.6\\\",\\\"0.7\\\",\\\"0.8\\\",\\\"0.9\\\",\\\"1.0\\\"],\\\"changes\\\":WebIO.getval({\\\"name\\\":\\\"changes\\\",\\\"scope\\\":\\\"10105620532934211232\\\",\\\"id\\\":\\\"4916152218009476045\\\",\\\"type\\\":\\\"observable\\\"}),\\\"index\\\":WebIO.getval({\\\"name\\\":\\\"index\\\",\\\"scope\\\":\\\"10105620532934211232\\\",\\\"id\\\":\\\"3602310455852054983\\\",\\\"type\\\":\\\"observable\\\"})};\\n var self = this;\\n function AppViewModel() {\\n for (var key in json_data) {\\n var el = json_data[key];\\n this[key] = Array.isArray(el) ? ko.observableArray(el) : ko.observable(el);\\n }\\n \\n [this[\\\"formatted_val\\\"]=ko.computed( function(){\\n return this.formatted_vals()[parseInt(this.index())-(1)];\\n }\\n,this)]\\n [this[\\\"changes\\\"].subscribe((function (val){!(this.valueFromJulia[\\\"changes\\\"]) ? (WebIO.setval({\\\"name\\\":\\\"changes\\\",\\\"scope\\\":\\\"10105620532934211232\\\",\\\"id\\\":\\\"4916152218009476045\\\",\\\"type\\\":\\\"observable\\\"},val)) : undefined; return this.valueFromJulia[\\\"changes\\\"]=false}),self),this[\\\"index\\\"].subscribe((function (val){!(this.valueFromJulia[\\\"index\\\"]) ? (WebIO.setval({\\\"name\\\":\\\"index\\\",\\\"scope\\\":\\\"10105620532934211232\\\",\\\"id\\\":\\\"3602310455852054983\\\",\\\"type\\\":\\\"observable\\\"},val)) : undefined; return this.valueFromJulia[\\\"index\\\"]=false}),self)]\\n \\n }\\n self.model = new AppViewModel();\\n self.valueFromJulia = {};\\n for (var key in json_data) {\\n self.valueFromJulia[key] = false;\\n }\\n ko.applyBindings(self.model, self.dom);\\n}\\n);\\n (WebIO.importBlock({\\\"data\\\":[{\\\"name\\\":\\\"knockout\\\",\\\"type\\\":\\\"js\\\",\\\"url\\\":\\\"\\/assetserver\\/c853cad7a3e123085fa7960dd53fd3d4c05dc309-knockout.js\\\"},{\\\"name\\\":\\\"knockout_punches\\\",\\\"type\\\":\\\"js\\\",\\\"url\\\":\\\"\\/assetserver\\/fab584ebb4dc64eb3ddf5ca7c73b2e76fd533845-knockout_punches.js\\\"}],\\\"type\\\":\\\"async_block\\\"})).then((imports) => handler.apply(this, 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" titles=Dict{Symbol, AbstractString}()\n",
")\n",
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]
},
"execution_count": 26,
"metadata": {
"application/vnd.webio.node+json": {
"kernelId": "cf1f84de-2548-4892-ac97-3dc4528bd326"
}
},
"output_type": "execute_result"
}
],
"source": [
"manipulate(Growth3, :t, [:mA, :nR, :r];\n",
" parameters = :0 => (;\n",
" :m => 0:0.1:1,\n",
" ),\n",
" stop = 300u\"d\",\n",
" kind = :line,\n",
" ylim = (0, 0.4),\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"단순해보이지만 실제 작물 모형에서는 좀 더 상세하게 구조를 나눈 다음, 각 구조별로 특화된 기작을 부여하여 서로 간의 상호작용을 만들어내는 등 다양하게 응용이 가능합니다. 예를 들어 잎은 광합성을, 줄기는 동화산물의 저장을, 뿌리는 토양수분 흡수를 담당하도록 되어 있으면 각 부위가 전체 식물에서 어떤 비중을 갖는지에 따라 전체적인 성장의 형태가 달라질 수 있는 것입니다."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 2.3. 광합성 (`A`) 분해"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"여기서는 성장률(`r`)을 분해해내가는 과정을 좀 더 진행해보겠습니다. 지금까지 만든 모형에서 광합성(`A`)은 효율 저하가 반영되기는 하였지만 그 외에는 항상 같은 값을 가지는 고정된 모수로 표현되어 있었습니다. 하지만 실제 광합성은 말그대로 빛이 있어야만 일어날 수 있는 생화학 반응이며, 이외에도 대기중 이산화탄소($\\mathrm{CO_2}$) 농도, 온도, 습도 등 환경 요인에 큰 영향을 받는 기작입니다. 내부적으로는 잎의 영양상태나 수분함량 등에 따라 그 효율이 변화하기도 합니다. 여기서는 우선 광량(irradiance)에 따라 변화하는 광합성율을 표현해보겠습니다."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"\\begin{align}\n",
"A_g &= \\frac{\\alpha I A_{\\mathrm{max}}}{\\alpha I + A_{\\mathrm{max}}} \\\\\n",
"A_n &= A_g - R_d\n",
"\\end{align}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"| 이름 | 값 | 단위 | 설명 |\n",
"|:-------|:------|:------|:------------|\n",
"| $\\alpha$ | 0.05 | $$\\mathrm{\\mu mol_{CO_2}}\\ \\mathrm{\\mu mol_{photon}^{-1}}$$ | 광화학적 효율 (양자 수율; quantum yield) |\n",
"| $$A_{\\mathrm{max}}$$ | 25.0 | $\\mathrm{\\mu mol}\\ \\mathrm{m^{-2}}\\ \\mathrm{s^{-1}}$ | 현재 대기 $\\mathrm{[CO_2]}$와 표준 기온(25 $\\mathrm{^{\\circ}C}$) 기준 광포화 총광합성율 ($A_g$) |\n",
"| $R_d$ | 1.0 | $\\mathrm{\\mu mol_{CO_2}}\\ \\mathrm{m^{-2}}\\ \\mathrm{s^{-1}}$ | 표준 온도(25 $\\mathrm{^{\\circ}C}$) 기준 엽 세포호흡율 (dark respiration) |\n",
"| $I$ | - | $\\mathrm{\\mu mol_{photon}}\\ \\mathrm{m^{-2}}$ | 엽 표면에 도달하는 PAR (photosynthetically active radiation) |\n",
"| $A_g$ | - | $\\mathrm{\\mu mol_{CO_2}}\\ \\mathrm{m^{-2}}\\ \\mathrm{s^{-1}}$ | 엽 $\\mathrm{CO_2}$ 총동화율 (총광합성율; gross photosynthesis rate) |\n",
"| $A_n$ | - | $\\mathrm{\\mu mol_{CO_2}}\\ \\mathrm{m^{-2}}\\ \\mathrm{s^{-1}}$ | 엽 $\\mathrm{CO_2}$ 순동화율 (순광합성율; net photosynthesis rate) |"
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"총광합성율($A_g$)은 광량($I$)이 증가함에 따라 함께 증가하는 직각쌍곡선(rectangular hyperbola)의 형태로 정의합니다. 광량이 많아질수록 그 증가량은 줄어들고 광포화 상태가 되어 최대값($A_max$)에 근접하게 됩니다. 순광합성율($A_n$)은 총광합성율($A_g$)에서 세포호흡율($R_d$) 제외한 값입니다. 실제 광합성은 광량 외에도 다른 요인에 영향을 받고, 세포호흡 역시 엽온에 따라 변할 수 있지만 여기서는 편의상 다른 요인들은 고정되어 있다고 가정하겠습니다."
]
},
{
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"Photosynthesis"
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"source": [
"@system Photosynthesis(Controller) begin\n",
" α: photochemical_efficiency => 0.05 ~ preserve(parameter)\n",
" Amax: maximum_photosynthetic_rate => 25 ~ preserve(parameter, u\"μmol/m^2/s\")\n",
" Rd: dark_respiration => 1.0 ~ preserve(parameter, u\"μmol/m^2/s\")\n",
"\n",
" I: irradiance => 0 ~ preserve(parameter, u\"μmol/m^2/s\")\n",
"\n",
" Ag(α, I, Amax): gross_photosynthesis => α*I * Amax / (α*I + Amax) ~ track(u\"μmol/m^2/s\")\n",
" An(Ag, Rd): net_photosynthesis => Ag - Rd ~ track(u\"μmol/m^2/s\")\n",
"end"
]
},
{
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"일단 특정 광량(`I`)에 대한 순광합성율(`An`)이 제대로 계산되는지 확인해보겠습니다."
]
},
{
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"execution_count": 28,
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")"
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"그럼 이제는 한 점이 아니라 일정 범위 내의 광량(`I`)에 대해 다수의 모의를 진행하여 그 결과를 한꺼번에 표출해보도록 하겠습니다. `visualize()` 함수의 `xstep` 옵션을 사용하면 내부적으로 여러 개의 설정(configuration)을 만들어 모의를 진행한 후 결과를 합쳐서 볼 수 있습니다."
]
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{
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"text/plain": [
"\"<Cropbox.Plot{Gadfly.Plot}>\""
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"visualize(Photosynthesis, :I, :An;\n",
" xstep = :0 => :I => 0:1000,\n",
" kind = :line,\n",
" ylim = (0, 20),\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"일단 결과적으로는 실제 광합성 측정 기기로 얻을 수 있는 광반응 곡선과 유사한 형태를 보여주고 있습니다. 하지만 앞에서 언급되었던 것처럼 다른 환경 요인에 대한 고려 없이 대략적인 곡선의 형태를 맞추어 본 것에 그치고 있다는 한계가 있습니다."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 2.4. 기체교환 모형 (coupled gas-exchange model)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"목적에 따라 다르겠지만, 기후 변화와 같이 기존에 알려지지 않은 환경에 대한 실험을 진행해야 한다면 다양한 요인의 상호작용에 대한 응답을 줄 수 있는 모형을 선택하는 것이 타당할 것입니다. 이런 측면에서 광합성의 주요 기작들을 생화학적으로 설명하고, 기공전도도(stomatal conductance)와의 연계를 통한 증산(transpiration), 이러한 과정에서 이루어지는 엽온(leaf temperature)의 에너지 균형(energy balance)까지 표현하는 기체교환 모형(gas-exchange model)은 작물모형을 비롯한 여러 분야에서 응용이 가능합니다."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Cropbox로 구현한 기체교환 모형은 지난 시간에 보았던 [마늘 모형](https://github.com/cropbox/Garlic.jl)에서 내부적으로 활용중이며, [LeafGasExchange.jl](https://github.com/cropbox/LeafGasExchange.jl)이라는 이름의 별도 Julia 패키지로 배포되고 있기도 합니다. 여기서는 후자의 패키지를 통해 모형을 사용해보는 실습을 진행하도록 하겠습니다."
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [],
"source": [
"using LeafGasExchange"
]
},
{
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"metadata": {},
"source": [
"LeafGasExchange 모듈은 광합성의 종류에 따라 C3, C4, 그리고 기공전도도 모형의 종류에 따라 Ball-Berry, Medlyn, 각 두가지씩 구현이 되어 있으며 이를 합쳐서 `ModelC3BB`, `ModelC3MD`, `ModelC4BB`, `ModelC4MD`와 같이 바로 사용할 수 있는 4개의 시스템을 제공하고 있습니다. 실습에서는 C3 광합성에 Ball-Berry 모형이 결합된 `ModelC3BB`를 사용하겠습니다."
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"scrolled": false
},
"outputs": [
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"<!-- 4->28 -->\n",
"<g id=\"edge24\" class=\"edge\">\n",
"<title>4->28</title>\n",
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"<!-- 33 -->\n",
"<g id=\"node33\" class=\"node\">\n",
"<title>33</title>\n",
"<text text-anchor=\"middle\" x=\"1643.9\" y=\"-1015.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">v</text>\n",
"</g>\n",
"<!-- 4->33 -->\n",
"<g id=\"edge25\" class=\"edge\">\n",
"<title>4->33</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1269.49,-1142.79C1337.13,-1141.67 1568.98,-1134.44 1622.9,-1088 1640.98,-1072.42 1643.78,-1041.78 1644.03,-1027.15\"/>\n",
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"<g id=\"node34\" class=\"node\">\n",
"<title>34</title>\n",
"<text text-anchor=\"middle\" x=\"1519.9\" y=\"-1015.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">κ</text>\n",
"</g>\n",
"<!-- 4->34 -->\n",
"<g id=\"edge26\" class=\"edge\">\n",
"<title>4->34</title>\n",
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"<g id=\"node42\" class=\"node\">\n",
"<title>42</title>\n",
"<text text-anchor=\"middle\" x=\"1053.9\" y=\"-389.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">g0</text>\n",
"</g>\n",
"<!-- 4->42 -->\n",
"<g id=\"edge27\" class=\"edge\">\n",
"<title>4->42</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1269.82,-1142.59C1406.96,-1139.56 2244.61,-1119.79 2286.9,-1088 2312.85,-1068.49 2310.9,-1051.47 2310.9,-1019 2310.9,-1019 2310.9,-1019 2310.9,-579 2310.9,-505.4 2279.54,-473.57 2210.9,-447 2097.76,-403.2 1169.67,-393.99 1063.74,-393.08\"/>\n",
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"<g id=\"node45\" class=\"node\">\n",
"<title>45</title>\n",
"<text text-anchor=\"middle\" x=\"1018.9\" y=\"-389.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">g1</text>\n",
"</g>\n",
"<!-- 4->45 -->\n",
"<g id=\"edge28\" class=\"edge\">\n",
"<title>4->45</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1269.53,-1142.54C1393.11,-1139.43 2092.34,-1120.45 2180.9,-1088 2228.89,-1070.41 2272.9,-1070.11 2272.9,-1019 2272.9,-1019 2272.9,-1019 2272.9,-579 2272.9,-301.66 1308.23,-460.96 1037.9,-399 1034.83,-398.3 1031.54,-397.34 1028.58,-396.39\"/>\n",
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"</g>\n",
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"<g id=\"node52\" class=\"node\">\n",
"<title>52</title>\n",
"<text text-anchor=\"middle\" x=\"55.9\" y=\"-1015.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">drb</text>\n",
"</g>\n",
"<!-- 4->52 -->\n",
"<g id=\"edge29\" class=\"edge\">\n",
"<title>4->52</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1232.27,-1142.75C1085.58,-1140.74 120.88,-1126.08 73.9,-1088 55.57,-1073.14 54.56,-1042.15 55.23,-1027.29\"/>\n",
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"</g>\n",
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"<g id=\"node53\" class=\"node\">\n",
"<title>53</title>\n",
"<text text-anchor=\"middle\" x=\"94.9\" y=\"-1015.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">dra</text>\n",
"</g>\n",
"<!-- 4->53 -->\n",
"<g id=\"edge30\" class=\"edge\">\n",
"<title>4->53</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1232.26,-1143.03C1095.17,-1143.1 245.47,-1141.36 145.9,-1088 120.62,-1074.45 104.52,-1042.25 98.09,-1027.12\"/>\n",
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"</g>\n",
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"<g id=\"node67\" class=\"node\">\n",
"<title>67</title>\n",
"<text text-anchor=\"middle\" x=\"949.9\" y=\"-1015.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">δ</text>\n",
"</g>\n",
"<!-- 4->67 -->\n",
"<g id=\"edge31\" class=\"edge\">\n",
"<title>4->67</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1232.19,-1142.45C1143.78,-1139.64 770.72,-1125.63 736.9,-1088 732.74,-1083.37 733.06,-1078.9 736.9,-1074 793.08,-1002.31 849.53,-1053.93 935.9,-1025 938.16,-1024.24 940.56,-1023.28 942.72,-1022.34\"/>\n",
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"<g id=\"node68\" class=\"node\">\n",
"<title>68</title>\n",
"<text text-anchor=\"middle\" x=\"802.9\" y=\"-953.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">f</text>\n",
"</g>\n",
"<!-- 4->68 -->\n",
"<g id=\"edge32\" class=\"edge\">\n",
"<title>4->68</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1232.22,-1142.91C1129.32,-1142.26 634.59,-1136.56 589.9,-1088 560.64,-1056.21 550.51,-1074.94 647.9,-1011 661.04,-1002.37 766.73,-968.48 795.62,-959.3\"/>\n",
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"<g id=\"node71\" class=\"node\">\n",
"<title>71</title>\n",
"<text text-anchor=\"middle\" x=\"2225.9\" y=\"-827.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">ϵ</text>\n",
"</g>\n",
"<!-- 4->71 -->\n",
"<g id=\"edge33\" class=\"edge\">\n",
"<title>4->71</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1269.65,-1142.53C1391.03,-1139.36 2063.12,-1120.48 2147.9,-1088 2193.98,-1070.34 2234.9,-1068.35 2234.9,-1019 2234.9,-1019 2234.9,-1019 2234.9,-955 2234.9,-911.44 2229.31,-859.51 2226.94,-839.46\"/>\n",
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"</g>\n",
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"<g id=\"node73\" class=\"node\">\n",
"<title>73</title>\n",
"<text text-anchor=\"middle\" x=\"2345.9\" y=\"-514.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">λ</text>\n",
"</g>\n",
"<!-- 4->73 -->\n",
"<g id=\"edge34\" class=\"edge\">\n",
"<title>4->73</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1269.61,-1142.63C1408.98,-1139.83 2280.93,-1120.98 2324.9,-1088 2350.87,-1068.52 2348.9,-1051.47 2348.9,-1019 2348.9,-1019 2348.9,-1019 2348.9,-641 2348.9,-597.9 2347.04,-546.32 2346.25,-526.41\"/>\n",
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"</g>\n",
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"<g id=\"node74\" class=\"node\">\n",
"<title>74</title>\n",
"<text text-anchor=\"middle\" x=\"1808.9\" y=\"-827.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Cp</text>\n",
"</g>\n",
"<!-- 4->74 -->\n",
"<g id=\"edge35\" class=\"edge\">\n",
"<title>4->74</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1269.76,-1142.51C1388.92,-1139.35 2034.91,-1120.78 2115.9,-1088 2159.74,-1070.26 2196.9,-1066.29 2196.9,-1019 2196.9,-1019 2196.9,-1019 2196.9,-955 2196.9,-917.39 2179.92,-905.73 2147.9,-886 2024.65,-810.07 1966.33,-872.13 1825.9,-837 1823.43,-836.38 1820.82,-835.55 1818.4,-834.71\"/>\n",
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"<g id=\"node77\" class=\"node\">\n",
"<title>77</title>\n",
"<text text-anchor=\"middle\" x=\"2157.9\" y=\"-953.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">α_s</text>\n",
"</g>\n",
"<!-- 4->77 -->\n",
"<g id=\"edge36\" class=\"edge\">\n",
"<title>4->77</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1269.43,-1142.8C1386.51,-1141.4 2020.89,-1131.84 2093.9,-1088 2139.52,-1060.6 2153.37,-989.87 2156.87,-965.44\"/>\n",
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"<g id=\"node89\" class=\"node\">\n",
"<title>89</title>\n",
"<text text-anchor=\"middle\" x=\"1394.9\" y=\"-1078.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">WP_leaf</text>\n",
"</g>\n",
"<!-- 4->89 -->\n",
"<g id=\"edge37\" class=\"edge\">\n",
"<title>4->89</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1265.23,-1136.93C1292.19,-1125.51 1350.26,-1100.91 1378.63,-1088.89\"/>\n",
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"<title>91</title>\n",
"<text text-anchor=\"middle\" x=\"1437.9\" y=\"-1015.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Ψf</text>\n",
"</g>\n",
"<!-- 4->91 -->\n",
"<g id=\"edge38\" class=\"edge\">\n",
"<title>4->91</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1269.68,-1142.97C1305.63,-1141.82 1384.23,-1133.87 1424.9,-1088 1440.04,-1070.93 1439.99,-1041.94 1438.87,-1027.58\"/>\n",
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"<g id=\"node92\" class=\"node\">\n",
"<title>92</title>\n",
"<text text-anchor=\"middle\" x=\"1355.9\" y=\"-1015.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">sf</text>\n",
"</g>\n",
"<!-- 4->92 -->\n",
"<g id=\"edge39\" class=\"edge\">\n",
"<title>4->92</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1261.51,-1136.93C1276.57,-1127.89 1304.25,-1109.62 1321.9,-1088 1337.68,-1068.68 1348.53,-1040.81 1353.25,-1027.16\"/>\n",
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"<title>94</title>\n",
"<text text-anchor=\"middle\" x=\"1328.9\" y=\"-890.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Tb</text>\n",
"</g>\n",
"<!-- 4->94 -->\n",
"<g id=\"edge40\" class=\"edge\">\n",
"<title>4->94</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1255.44,-1136.9C1262.53,-1127.1 1276.22,-1107 1283.9,-1088 1311.63,-1019.41 1324.44,-929.94 1327.9,-902.42\"/>\n",
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"<title>98</title>\n",
"<text text-anchor=\"middle\" x=\"1459.9\" y=\"-953.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Q10</text>\n",
"</g>\n",
"<!-- 4->98 -->\n",
"<g id=\"edge41\" class=\"edge\">\n",
"<title>4->98</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1269.59,-1143.53C1307.95,-1143.53 1395.83,-1137.75 1441.9,-1088 1474.39,-1052.92 1465.93,-988.21 1461.64,-965.3\"/>\n",
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"<title>100</title>\n",
"<text text-anchor=\"middle\" x=\"1193.9\" y=\"-1015.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">s</text>\n",
"</g>\n",
"<!-- 4->100 -->\n",
"<g id=\"edge42\" class=\"edge\">\n",
"<title>4->100</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1246.6,-1136.8C1239.83,-1126.85 1226.58,-1106.56 1217.9,-1088 1208.04,-1066.93 1199.99,-1040.64 1196.22,-1027.42\"/>\n",
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"<title>101</title>\n",
"<text text-anchor=\"middle\" x=\"1155.9\" y=\"-1015.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">N0</text>\n",
"</g>\n",
"<!-- 4->101 -->\n",
"<g id=\"edge43\" class=\"edge\">\n",
"<title>4->101</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1246.09,-1136.92C1238.11,-1126.81 1221.63,-1105.88 1207.9,-1088 1191.01,-1066 1171.39,-1039.78 1161.8,-1026.92\"/>\n",
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"<title>103</title>\n",
"<text text-anchor=\"middle\" x=\"1765.9\" y=\"-890.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Kc25</text>\n",
"</g>\n",
"<!-- 4->103 -->\n",
"<g id=\"edge44\" class=\"edge\">\n",
"<title>4->103</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1269.57,-1142.38C1356.97,-1139.29 1722.82,-1124.26 1756.9,-1088 1807.19,-1034.5 1778.43,-931.63 1768.72,-902.11\"/>\n",
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"<title>104</title>\n",
"<text text-anchor=\"middle\" x=\"1527.9\" y=\"-765.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Eac</text>\n",
"</g>\n",
"<!-- 4->104 -->\n",
"<g id=\"edge45\" class=\"edge\">\n",
"<title>4->104</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1269.46,-1142.22C1358.06,-1138.36 1735.35,-1120.1 1775.9,-1088 1846.42,-1032.18 1840.83,-958.71 1787.9,-886 1725.22,-799.9 1584.25,-775.88 1540.86,-770.41\"/>\n",
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"<title>106</title>\n",
"<text text-anchor=\"middle\" x=\"1821.9\" y=\"-765.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Ko25</text>\n",
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"<g id=\"edge46\" class=\"edge\">\n",
"<title>4->106</title>\n",
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"<title>107</title>\n",
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"</g>\n",
"<!-- 4->107 -->\n",
"<g id=\"edge47\" class=\"edge\">\n",
"<title>4->107</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1269.59,-1142.63C1364.27,-1140.55 1788.06,-1129.01 1827.9,-1088 1897.24,-1016.62 1858.86,-875.1 1847.65,-839.35\"/>\n",
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"<g id=\"edge48\" class=\"edge\">\n",
"<title>4->109</title>\n",
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"<title>111</title>\n",
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"<g id=\"edge49\" class=\"edge\">\n",
"<title>4->111</title>\n",
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"</g>\n",
"<!-- 112 -->\n",
"<g id=\"node112\" class=\"node\">\n",
"<title>112</title>\n",
"<text text-anchor=\"middle\" x=\"1209.9\" y=\"-765.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">EaVc</text>\n",
"</g>\n",
"<!-- 4->112 -->\n",
"<g id=\"edge50\" class=\"edge\">\n",
"<title>4->112</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1251.19,-1136.93C1252.23,-1112.95 1255.28,-1022.53 1245.9,-949 1239.43,-898.31 1229.4,-887.21 1219.9,-837 1215.83,-815.5 1212.46,-789.91 1210.87,-777.12\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1211.56,-776.93 1210.62,-775.03 1210.17,-777.1 1211.56,-776.93\"/>\n",
"</g>\n",
"<!-- 114 -->\n",
"<g id=\"node114\" class=\"node\">\n",
"<title>114</title>\n",
"<text text-anchor=\"middle\" x=\"885.9\" y=\"-765.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Jm25</text>\n",
"</g>\n",
"<!-- 4->114 -->\n",
"<g id=\"edge51\" class=\"edge\">\n",
"<title>4->114</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1232.08,-1142.96C1127.31,-1142.52 618.83,-1137.81 572.9,-1088 512.24,-1022.22 715.48,-973.45 728.9,-963 803.02,-905.3 864.2,-806.2 881.2,-777.2\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"881.94,-777.31 882.34,-775.23 880.73,-776.61 881.94,-777.31\"/>\n",
"</g>\n",
"<!-- 115 -->\n",
"<g id=\"node115\" class=\"node\">\n",
"<title>115</title>\n",
"<text text-anchor=\"middle\" x=\"883.9\" y=\"-827.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Haj</text>\n",
"</g>\n",
"<!-- 4->115 -->\n",
"<g id=\"edge52\" class=\"edge\">\n",
"<title>4->115</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1232.33,-1142.82C1133.24,-1141.65 669.79,-1133.75 627.9,-1088 623.7,-1083.41 624.81,-1079.4 627.9,-1074 676.29,-989.46 745.36,-1029.12 816.9,-963 841.98,-939.82 845.56,-930.52 860.9,-900 871.3,-879.31 878.6,-852.85 881.91,-839.51\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"882.65,-839.44 882.44,-837.33 881.29,-839.11 882.65,-839.44\"/>\n",
"</g>\n",
"<!-- 116 -->\n",
"<g id=\"node116\" class=\"node\">\n",
"<title>116</title>\n",
"<text text-anchor=\"middle\" x=\"730.9\" y=\"-765.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Hdj</text>\n",
"</g>\n",
"<!-- 4->116 -->\n",
"<g id=\"edge53\" class=\"edge\">\n",
"<title>4->116</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1232.12,-1142.88C1121.5,-1142 557.83,-1135.22 498.9,-1088 471.39,-1065.96 460.22,-1040.25 479.9,-1011 511.5,-964.02 553.81,-998.52 597.9,-963 666.84,-907.47 714.4,-806.86 727.35,-777.35\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"728.06,-777.46 728.22,-775.35 726.78,-776.9 728.06,-777.46\"/>\n",
"</g>\n",
"<!-- 117 -->\n",
"<g id=\"node117\" class=\"node\">\n",
"<title>117</title>\n",
"<text text-anchor=\"middle\" x=\"749.9\" y=\"-827.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Toj</text>\n",
"</g>\n",
"<!-- 4->117 -->\n",
"<g id=\"edge54\" class=\"edge\">\n",
"<title>4->117</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1232.27,-1143.08C1122.62,-1143.39 564.25,-1142.25 513.9,-1088 394.11,-958.93 639.35,-1027.68 707.9,-963 744.5,-928.47 749.33,-862.2 749.87,-839.14\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"750.57,-839.06 749.91,-837.05 749.17,-839.04 750.57,-839.06\"/>\n",
"</g>\n",
"<!-- 119 -->\n",
"<g id=\"node119\" class=\"node\">\n",
"<title>119</title>\n",
"<text text-anchor=\"middle\" x=\"973.9\" y=\"-639.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">θ</text>\n",
"</g>\n",
"<!-- 4->119 -->\n",
"<g id=\"edge55\" class=\"edge\">\n",
"<title>4->119</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1232.28,-1142.5C1142.57,-1139.93 757.76,-1126.68 722.9,-1088 718.73,-1083.38 720.48,-1079.73 722.9,-1074 750.4,-1008.85 792.31,-1017.89 836.9,-963 922.45,-857.68 963.32,-690.95 972.08,-651.55\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"972.81,-651.45 972.56,-649.34 971.45,-651.15 972.81,-651.45\"/>\n",
"</g>\n",
"<!-- 121 -->\n",
"<g id=\"node121\" class=\"node\">\n",
"<title>121</title>\n",
"<text text-anchor=\"middle\" x=\"1962.9\" y=\"-827.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Tp25</text>\n",
"</g>\n",
"<!-- 4->121 -->\n",
"<g id=\"edge56\" class=\"edge\">\n",
"<title>4->121</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1269.66,-1142.92C1375.31,-1142.31 1892.97,-1136.83 1941.9,-1088 2012.43,-1017.62 1976.19,-875.36 1965.53,-839.4\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1966.17,-839.1 1964.92,-837.38 1964.83,-839.5 1966.17,-839.1\"/>\n",
"</g>\n",
"<!-- 122 -->\n",
"<g id=\"node122\" class=\"node\">\n",
"<title>122</title>\n",
"<text text-anchor=\"middle\" x=\"2003.9\" y=\"-890.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">EaTp</text>\n",
"</g>\n",
"<!-- 4->122 -->\n",
"<g id=\"edge57\" class=\"edge\">\n",
"<title>4->122</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1269.58,-1142.97C1378.35,-1142.64 1926.96,-1138.47 1979.9,-1088 2033.39,-1037 2013.24,-932.38 2006.03,-902.27\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"2006.69,-902.01 2005.54,-900.24 2005.33,-902.35 2006.69,-902.01\"/>\n",
"</g>\n",
"<!-- 124 -->\n",
"<g id=\"node124\" class=\"node\">\n",
"<title>124</title>\n",
"<text text-anchor=\"middle\" x=\"2082.9\" y=\"-765.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Rd25</text>\n",
"</g>\n",
"<!-- 4->124 -->\n",
"<g id=\"edge58\" class=\"edge\">\n",
"<title>4->124</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1269.6,-1142.71C1380.98,-1140.82 1954.47,-1129.16 2019.9,-1088 2128.81,-1019.49 2093.73,-820.11 2084.72,-777.2\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"2085.37,-776.86 2084.27,-775.05 2084,-777.15 2085.37,-776.86\"/>\n",
"</g>\n",
"<!-- 125 -->\n",
"<g id=\"node125\" class=\"node\">\n",
"<title>125</title>\n",
"<text text-anchor=\"middle\" x=\"2045.9\" y=\"-890.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Ear</text>\n",
"</g>\n",
"<!-- 4->125 -->\n",
"<g id=\"edge59\" class=\"edge\">\n",
"<title>4->125</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1269.5,-1142.76C1379.06,-1141.21 1937.46,-1131.22 1998.9,-1088 2060.91,-1044.39 2051.26,-933.66 2047.14,-902.36\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"2047.82,-902.13 2046.86,-900.24 2046.43,-902.32 2047.82,-902.13\"/>\n",
"</g>\n",
"<!-- 127 -->\n",
"<g id=\"node127\" class=\"node\">\n",
"<title>127</title>\n",
"<text text-anchor=\"middle\" x=\"1003.9\" y=\"-765.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Γ25</text>\n",
"</g>\n",
"<!-- 4->127 -->\n",
"<g id=\"edge60\" class=\"edge\">\n",
"<title>4->127</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1232.23,-1142.48C1143.16,-1139.79 764.24,-1126.16 729.9,-1088 725.74,-1083.38 727.03,-1079.52 729.9,-1074 739.79,-1054.96 871.37,-976.67 887.9,-963 918.9,-937.36 930.65,-933.52 952.9,-900 980.76,-858.05 996.84,-798.62 1002.03,-777.14\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1002.72,-777.29 1002.5,-775.18 1001.35,-776.96 1002.72,-777.29\"/>\n",
"</g>\n",
"<!-- 128 -->\n",
"<g id=\"node128\" class=\"node\">\n",
"<title>128</title>\n",
"<text text-anchor=\"middle\" x=\"1080.9\" y=\"-827.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Eag</text>\n",
"</g>\n",
"<!-- 4->128 -->\n",
"<g id=\"edge61\" class=\"edge\">\n",
"<title>4->128</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1242.71,-1136.85C1222.04,-1120.86 1167.41,-1075.67 1139.9,-1025 1103.8,-958.49 1086.73,-866.89 1082.18,-839.23\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1082.84,-838.91 1081.82,-837.05 1081.45,-839.14 1082.84,-838.91\"/>\n",
"</g>\n",
"<!-- 5->3 -->\n",
"<g id=\"edge62\" class=\"edge\">\n",
"<title>5->3</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M196.36,-951.89C173.49,-942.46 104.53,-914.04 72.54,-900.86\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"72.79,-900.2 70.67,-900.09 72.25,-901.5 72.79,-900.2\"/>\n",
"</g>\n",
"<!-- 13 -->\n",
"<g id=\"node13\" class=\"node\">\n",
"<title>13</title>\n",
"<text text-anchor=\"middle\" x=\"424.9\" y=\"-890.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">VPD</text>\n",
"</g>\n",
"<!-- 5->13 -->\n",
"<g id=\"edge63\" class=\"edge\">\n",
"<title>5->13</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M211.51,-952.9C243.95,-943.94 370.98,-908.88 412.03,-897.55\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"412.64,-898.11 414.38,-896.9 412.26,-896.76 412.64,-898.11\"/>\n",
"</g>\n",
"<!-- 14 -->\n",
"<g id=\"node14\" class=\"node\">\n",
"<title>14</title>\n",
"<text text-anchor=\"middle\" x=\"227.9\" y=\"-890.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">VPD_Δ</text>\n",
"</g>\n",
"<!-- 5->14 -->\n",
"<g id=\"edge64\" class=\"edge\">\n",
"<title>5->14</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M206.29,-948.93C210.64,-937.88 219.85,-914.47 224.72,-902.08\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"225.44,-902.16 225.52,-900.05 224.14,-901.65 225.44,-902.16\"/>\n",
"</g>\n",
"<!-- 15 -->\n",
"<g id=\"node15\" class=\"node\">\n",
"<title>15</title>\n",
"<text text-anchor=\"middle\" x=\"469.9\" y=\"-890.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">VPD_s</text>\n",
"</g>\n",
"<!-- 5->15 -->\n",
"<g id=\"edge65\" class=\"edge\">\n",
"<title>5->15</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M211.77,-953.2C241.89,-946.32 352.67,-920.98 443.9,-900 446.37,-899.43 448.97,-898.83 451.53,-898.24\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"451.88,-898.88 453.67,-897.75 451.57,-897.52 451.88,-898.88\"/>\n",
"</g>\n",
"<!-- 84 -->\n",
"<g id=\"node84\" class=\"node\">\n",
"<title>84</title>\n",
"<text text-anchor=\"middle\" x=\"502.9\" y=\"-827.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Δw</text>\n",
"</g>\n",
"<!-- 5->84 -->\n",
"<g id=\"edge66\" class=\"edge\">\n",
"<title>5->84</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M201.43,-948.79C196.62,-935.53 187.71,-904.22 202.9,-886 222.13,-862.93 442.94,-837.55 492.9,-832.08\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"493.23,-832.74 495.14,-831.83 493.08,-831.35 493.23,-832.74\"/>\n",
"</g>\n",
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"<g id=\"node93\" class=\"node\">\n",
"<title>93</title>\n",
"<text text-anchor=\"middle\" x=\"572.9\" y=\"-263.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Ds</text>\n",
"</g>\n",
"<!-- 5->93 -->\n",
"<g id=\"edge67\" class=\"edge\">\n",
"<title>5->93</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M201.45,-948.88C196.94,-936.79 188.2,-909.06 192.9,-886 211.04,-797.03 228.95,-777.46 272.9,-698 373.45,-516.2 532.71,-316.54 566.48,-274.88\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"567.27,-275.01 567.99,-273.01 566.19,-274.12 567.27,-275.01\"/>\n",
"</g>\n",
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"<g id=\"node66\" class=\"node\">\n",
"<title>66</title>\n",
"<text text-anchor=\"middle\" x=\"1558.9\" y=\"-1015.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">PPFD</text>\n",
"</g>\n",
"<!-- 6->66 -->\n",
"<g id=\"edge68\" class=\"edge\">\n",
"<title>6->66</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1558.9,-1073.93C1558.9,-1062.88 1558.9,-1039.47 1558.9,-1027.08\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1559.6,-1027.05 1558.9,-1025.05 1558.2,-1027.05 1559.6,-1027.05\"/>\n",
"</g>\n",
"<!-- 54 -->\n",
"<g id=\"node54\" class=\"node\">\n",
"<title>54</title>\n",
"<text text-anchor=\"middle\" x=\"401.9\" y=\"-765.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Ca</text>\n",
"</g>\n",
"<!-- 7->54 -->\n",
"<g id=\"edge69\" class=\"edge\">\n",
"<title>7->54</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M191.38,-1073.7C160.12,-1047.3 41.21,-944.92 22.9,-900 20.55,-894.24 19.21,-891.01 22.9,-886 69.78,-822.47 336.79,-778.87 391.94,-770.48\"/>\n",
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"</g>\n",
"<!-- 8->13 -->\n",
"<g id=\"edge70\" class=\"edge\">\n",
"<title>8->13</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M372.67,-948.93C383.27,-937.78 405.8,-914.08 417.5,-901.78\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"418.28,-901.98 419.15,-900.05 417.26,-901.01 418.28,-901.98\"/>\n",
"</g>\n",
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"<g id=\"node46\" class=\"node\">\n",
"<title>46</title>\n",
"<text text-anchor=\"middle\" x=\"770.9\" y=\"-326.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">hs</text>\n",
"</g>\n",
"<!-- 8->46 -->\n",
"<g id=\"edge71\" class=\"edge\">\n",
"<title>8->46</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M366.71,-948.92C365.75,-906.73 365.17,-655.06 482.9,-510 564.87,-409 719.43,-348.4 760.61,-333.58\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"761.28,-334.08 762.93,-332.75 760.81,-332.76 761.28,-334.08\"/>\n",
"</g>\n",
"<!-- 8->84 -->\n",
"<g id=\"edge72\" class=\"edge\">\n",
"<title>8->84</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M368.93,-948.94C373.53,-935.99 385.83,-905.22 404.9,-886 431.57,-859.11 474.14,-841.38 493.16,-834.38\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"493.72,-834.92 495.36,-833.57 493.24,-833.6 493.72,-834.92\"/>\n",
"</g>\n",
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"<g id=\"node10\" class=\"node\">\n",
"<title>10</title>\n",
"<text text-anchor=\"middle\" x=\"1521.9\" y=\"-890.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Tk_air</text>\n",
"</g>\n",
"<!-- 9->10 -->\n",
"<g id=\"edge73\" class=\"edge\">\n",
"<title>9->10</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M486.34,-953.05C497.72,-951.76 513.21,-950.1 526.9,-949 917.83,-917.64 1396.62,-898.69 1501.13,-894.76\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1501.26,-895.46 1503.24,-894.69 1501.21,-894.06 1501.26,-895.46\"/>\n",
"</g>\n",
"<!-- 9->13 -->\n",
"<g id=\"edge74\" class=\"edge\">\n",
"<title>9->13</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M465.42,-948.93C457.2,-937.78 439.71,-914.08 430.64,-901.78\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"431.11,-901.24 429.36,-900.05 429.98,-902.07 431.11,-901.24\"/>\n",
"</g>\n",
"<!-- 9->14 -->\n",
"<g id=\"edge75\" class=\"edge\">\n",
"<title>9->14</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M453.65,-950.9C410.25,-939.96 291.86,-910.12 246.2,-898.61\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"246.19,-897.89 244.08,-898.08 245.85,-899.25 246.19,-897.89\"/>\n",
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"<!-- 9->15 -->\n",
"<g id=\"edge76\" class=\"edge\">\n",
"<title>9->15</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M469.9,-948.93C469.9,-937.88 469.9,-914.47 469.9,-902.08\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"470.6,-902.05 469.9,-900.05 469.2,-902.05 470.6,-902.05\"/>\n",
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"<g id=\"node50\" class=\"node\">\n",
"<title>50</title>\n",
"<text text-anchor=\"middle\" x=\"584.9\" y=\"-890.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">T</text>\n",
"</g>\n",
"<!-- 9->50 -->\n",
"<g id=\"edge77\" class=\"edge\">\n",
"<title>9->50</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M481.35,-948.93C504.82,-936.48 557.85,-908.35 577.44,-897.96\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"578.22,-898.33 579.66,-896.78 577.57,-897.1 578.22,-898.33\"/>\n",
"</g>\n",
"<!-- 9->84 -->\n",
"<g id=\"edge78\" class=\"edge\">\n",
"<title>9->84</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M473.49,-948.81C479.08,-938.87 489.73,-918.59 494.9,-900 500.82,-878.69 502.36,-852.5 502.76,-839.36\"/>\n",
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"<g id=\"node37\" class=\"node\">\n",
"<title>37</title>\n",
"<text text-anchor=\"middle\" x=\"1552.9\" y=\"-827.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">gh</text>\n",
"</g>\n",
"<!-- 10->37 -->\n",
"<g id=\"edge79\" class=\"edge\">\n",
"<title>10->37</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1524.99,-885.93C1530.6,-874.88 1542.5,-851.47 1548.79,-839.08\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1549.54,-839.15 1549.83,-837.05 1548.3,-838.51 1549.54,-839.15\"/>\n",
"</g>\n",
"<!-- 79 -->\n",
"<g id=\"node79\" class=\"node\">\n",
"<title>79</title>\n",
"<text text-anchor=\"middle\" x=\"2225.9\" y=\"-765.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">R_wall</text>\n",
"</g>\n",
"<!-- 10->79 -->\n",
"<g id=\"edge80\" class=\"edge\">\n",
"<title>10->79</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1521.08,-885.85C1519.64,-872.14 1518.38,-839.07 1536.9,-823 1592.61,-774.67 2125.93,-785.69 2198.9,-775 2200.97,-774.7 2203.11,-774.32 2205.25,-773.91\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"2205.55,-774.57 2207.37,-773.49 2205.28,-773.19 2205.55,-774.57\"/>\n",
"</g>\n",
"<!-- 31 -->\n",
"<g id=\"node31\" class=\"node\">\n",
"<title>31</title>\n",
"<text text-anchor=\"middle\" x=\"1608.9\" y=\"-1015.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">u</text>\n",
"</g>\n",
"<!-- 11->31 -->\n",
"<g id=\"edge81\" class=\"edge\">\n",
"<title>11->31</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1601.7,-1073.93C1603.15,-1062.88 1606.21,-1039.47 1607.84,-1027.08\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1608.54,-1027.12 1608.11,-1025.05 1607.15,-1026.94 1608.54,-1027.12\"/>\n",
"</g>\n",
"<!-- 12->15 -->\n",
"<g id=\"edge82\" class=\"edge\">\n",
"<title>12->15</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M543.74,-948.93C528.63,-937.69 496.37,-913.69 479.95,-901.48\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"480.05,-900.68 478.03,-900.05 479.22,-901.8 480.05,-900.68\"/>\n",
"</g>\n",
"<!-- 12->37 -->\n",
"<g id=\"edge83\" class=\"edge\">\n",
"<title>12->37</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M568.19,-949.9C610.52,-936.86 727.7,-902.21 827.9,-886 975.05,-862.2 1467.73,-835.5 1543.17,-831.51\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1543.32,-832.2 1545.28,-831.4 1543.25,-830.81 1543.32,-832.2\"/>\n",
"</g>\n",
"<!-- 39 -->\n",
"<g id=\"node39\" class=\"node\">\n",
"<title>39</title>\n",
"<text text-anchor=\"middle\" x=\"653.9\" y=\"-765.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">gb</text>\n",
"</g>\n",
"<!-- 12->39 -->\n",
"<g id=\"edge84\" class=\"edge\">\n",
"<title>12->39</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M558.4,-948.75C568.21,-939.05 586.91,-919.46 598.9,-900 625.6,-856.67 644.99,-798.08 651.51,-776.98\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"652.18,-777.18 652.1,-775.06 650.84,-776.77 652.18,-777.18\"/>\n",
"</g>\n",
"<!-- 12->54 -->\n",
"<g id=\"edge85\" class=\"edge\">\n",
"<title>12->54</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M552.12,-948.94C552.55,-928.63 551.29,-862.11 518.9,-823 490.15,-788.28 434.17,-774.76 411.64,-770.58\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"411.66,-769.87 409.57,-770.2 411.41,-771.25 411.66,-769.87\"/>\n",
"</g>\n",
"<!-- 16->20 -->\n",
"<g id=\"edge86\" class=\"edge\">\n",
"<title>16->20</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M771.96,-1076.55C815.66,-1065 954.52,-1028.25 963.9,-1025 966.15,-1024.22 968.55,-1023.25 970.71,-1022.31\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"971.23,-1022.85 972.78,-1021.4 970.67,-1021.57 971.23,-1022.85\"/>\n",
"</g>\n",
"<!-- 17->20 -->\n",
"<g id=\"edge87\" class=\"edge\">\n",
"<title>17->20</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M843.03,-1074C868.19,-1063.99 920.17,-1043.21 963.9,-1025 966.1,-1024.09 968.48,-1023.07 970.65,-1022.14\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"971.16,-1022.68 972.72,-1021.25 970.61,-1021.4 971.16,-1022.68\"/>\n",
"</g>\n",
"<!-- 18->20 -->\n",
"<g id=\"edge88\" class=\"edge\">\n",
"<title>18->20</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M926.57,-1073.93C937.09,-1062.67 959.59,-1038.59 970.98,-1026.4\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"971.73,-1026.63 972.58,-1024.69 970.7,-1025.67 971.73,-1026.63\"/>\n",
"</g>\n",
"<!-- 19->20 -->\n",
"<g id=\"edge89\" class=\"edge\">\n",
"<title>19->20</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1010.32,-1073.93C1003.74,-1062.78 989.75,-1039.08 982.49,-1026.78\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"983.09,-1026.41 981.47,-1025.05 981.88,-1027.13 983.09,-1026.41\"/>\n",
"</g>\n",
"<!-- 21 -->\n",
"<g id=\"node21\" class=\"node\">\n",
"<title>21</title>\n",
"<text text-anchor=\"middle\" x=\"947.9\" y=\"-953.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Np</text>\n",
"</g>\n",
"<!-- 20->21 -->\n",
"<g id=\"edge90\" class=\"edge\">\n",
"<title>20->21</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M974.69,-1010.58C969.2,-999.61 958.03,-977.26 951.99,-965.18\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"952.52,-964.67 951,-963.2 951.27,-965.3 952.52,-964.67\"/>\n",
"</g>\n",
"<!-- 102 -->\n",
"<g id=\"node102\" class=\"node\">\n",
"<title>102</title>\n",
"<text text-anchor=\"middle\" x=\"1137.9\" y=\"-890.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">kN</text>\n",
"</g>\n",
"<!-- 20->102 -->\n",
"<g id=\"edge91\" class=\"edge\">\n",
"<title>20->102</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M983.22,-1012.91C1006.4,-995.09 1098.7,-924.13 1128.54,-901.19\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1129.09,-901.65 1130.25,-899.88 1128.24,-900.54 1129.09,-901.65\"/>\n",
"</g>\n",
"<!-- 22 -->\n",
"<g id=\"node22\" class=\"node\">\n",
"<title>22</title>\n",
"<text text-anchor=\"middle\" x=\"915.9\" y=\"-1015.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">SLA</text>\n",
"</g>\n",
"<!-- 22->21 -->\n",
"<g id=\"edge92\" class=\"edge\">\n",
"<title>22->21</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M919.32,-1010.58C925.18,-999.61 937.09,-977.26 943.53,-965.18\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"944.27,-965.29 944.6,-963.2 943.04,-964.63 944.27,-965.29\"/>\n",
"</g>\n",
"<!-- 38 -->\n",
"<g id=\"node38\" class=\"node\">\n",
"<title>38</title>\n",
"<text text-anchor=\"middle\" x=\"418.9\" y=\"-1015.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">rhw</text>\n",
"</g>\n",
"<!-- 23->38 -->\n",
"<g id=\"edge93\" class=\"edge\">\n",
"<title>23->38</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M170.64,-1076.86C173.24,-1075.87 176.17,-1074.82 178.9,-1074 264.39,-1048.3 370.12,-1027.93 406.17,-1021.3\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"406.4,-1021.96 408.24,-1020.92 406.15,-1020.59 406.4,-1021.96\"/>\n",
"</g>\n",
"<!-- 23->52 -->\n",
"<g id=\"edge94\" class=\"edge\">\n",
"<title>23->52</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M155.2,-1075.61C136.93,-1065.2 90.8,-1038.9 68.44,-1026.15\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"68.7,-1025.49 66.61,-1025.11 68,-1026.71 68.7,-1025.49\"/>\n",
"</g>\n",
"<!-- 23->53 -->\n",
"<g id=\"edge95\" class=\"edge\">\n",
"<title>23->53</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M156.13,-1073.93C143.61,-1062.69 116.85,-1038.69 103.23,-1026.48\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"103.6,-1025.86 101.64,-1025.05 102.66,-1026.9 103.6,-1025.86\"/>\n",
"</g>\n",
"<!-- 24->52 -->\n",
"<g id=\"edge96\" class=\"edge\">\n",
"<title>24->52</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M87.42,-1073.93C81.07,-1062.88 67.64,-1039.47 60.54,-1027.08\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"60.97,-1026.43 59.37,-1025.05 59.76,-1027.13 60.97,-1026.43\"/>\n",
"</g>\n",
"<!-- 24->53 -->\n",
"<g id=\"edge97\" class=\"edge\">\n",
"<title>24->53</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M91.3,-1073.93C92.02,-1062.88 93.56,-1039.47 94.37,-1027.08\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"95.07,-1027.09 94.5,-1025.05 93.67,-1027 95.07,-1027.09\"/>\n",
"</g>\n",
"<!-- 25->34 -->\n",
"<g id=\"edge98\" class=\"edge\">\n",
"<title>25->34</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M423.78,-1079.7C494.35,-1077 1025.22,-1056.19 1454.9,-1025 1475.88,-1023.48 1500.61,-1021.01 1512.62,-1019.77\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1512.93,-1020.44 1514.85,-1019.53 1512.79,-1019.04 1512.93,-1020.44\"/>\n",
"</g>\n",
"<!-- 25->38 -->\n",
"<g id=\"edge99\" class=\"edge\">\n",
"<title>25->38</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M416.2,-1073.93C416.74,-1062.88 417.89,-1039.47 418.5,-1027.08\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"419.2,-1027.08 418.6,-1025.05 417.8,-1027.01 419.2,-1027.08\"/>\n",
"</g>\n",
"<!-- 26->33 -->\n",
"<g id=\"edge100\" class=\"edge\">\n",
"<title>26->33</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1674.52,-1073.93C1668.35,-1062.88 1655.31,-1039.47 1648.4,-1027.08\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1648.86,-1026.45 1647.27,-1025.05 1647.63,-1027.14 1648.86,-1026.45\"/>\n",
"</g>\n",
"<!-- 32 -->\n",
"<g id=\"node32\" class=\"node\">\n",
"<title>32</title>\n",
"<text text-anchor=\"middle\" x=\"1679.9\" y=\"-1015.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">d</text>\n",
"</g>\n",
"<!-- 27->32 -->\n",
"<g id=\"edge101\" class=\"edge\">\n",
"<title>27->32</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1706.01,-1073.93C1700.76,-1062.88 1689.63,-1039.47 1683.74,-1027.08\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1684.27,-1026.55 1682.77,-1025.05 1683,-1027.15 1684.27,-1026.55\"/>\n",
"</g>\n",
"<!-- 29 -->\n",
"<g id=\"node29\" class=\"node\">\n",
"<title>29</title>\n",
"<text text-anchor=\"middle\" x=\"1732.9\" y=\"-953.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">scr</text>\n",
"</g>\n",
"<!-- 28->29 -->\n",
"<g id=\"edge102\" class=\"edge\">\n",
"<title>28->29</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1739.54,-1073.73C1738.38,-1053.24 1734.68,-988.26 1733.37,-965.21\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1734.06,-965.07 1733.25,-963.11 1732.66,-965.15 1734.06,-965.07\"/>\n",
"</g>\n",
"<!-- 29->37 -->\n",
"<g id=\"edge103\" class=\"edge\">\n",
"<title>29->37</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1730.97,-948.73C1726.56,-935.36 1714.49,-903.84 1693.9,-886 1672.96,-867.85 1590.8,-842.27 1562.52,-833.83\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1562.7,-833.15 1560.58,-833.25 1562.3,-834.49 1562.7,-833.15\"/>\n",
"</g>\n",
"<!-- 30 -->\n",
"<g id=\"node30\" class=\"node\">\n",
"<title>30</title>\n",
"<text text-anchor=\"middle\" x=\"1568.9\" y=\"-890.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">ocr</text>\n",
"</g>\n",
"<!-- 30->37 -->\n",
"<g id=\"edge104\" class=\"edge\">\n",
"<title>30->37</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1567.31,-885.93C1564.41,-874.88 1558.27,-851.47 1555.02,-839.08\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1555.67,-838.8 1554.49,-837.05 1554.32,-839.16 1555.67,-838.8\"/>\n",
"</g>\n",
"<!-- 35 -->\n",
"<g id=\"node35\" class=\"node\">\n",
"<title>35</title>\n",
"<text text-anchor=\"middle\" x=\"1643.9\" y=\"-953.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Re</text>\n",
"</g>\n",
"<!-- 31->35 -->\n",
"<g id=\"edge105\" class=\"edge\">\n",
"<title>31->35</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1612.64,-1010.58C1619.05,-999.61 1632.08,-977.26 1639.13,-965.18\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1639.88,-965.28 1640.29,-963.2 1638.67,-964.57 1639.88,-965.28\"/>\n",
"</g>\n",
"<!-- 32->35 -->\n",
"<g id=\"edge106\" class=\"edge\">\n",
"<title>32->35</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1676.05,-1010.58C1669.46,-999.61 1656.06,-977.26 1648.81,-965.18\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1649.25,-964.55 1647.62,-963.2 1648.05,-965.27 1649.25,-964.55\"/>\n",
"</g>\n",
"<!-- 32->37 -->\n",
"<g id=\"edge107\" class=\"edge\">\n",
"<title>32->37</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1680.85,-1010.81C1683.58,-990.66 1689.55,-925.97 1660.9,-886 1648.32,-868.45 1586.5,-843.69 1562.47,-834.56\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1562.66,-833.88 1560.54,-833.83 1562.16,-835.19 1562.66,-833.88\"/>\n",
"</g>\n",
"<!-- 33->35 -->\n",
"<g id=\"edge108\" class=\"edge\">\n",
"<title>33->35</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1643.9,-1010.58C1643.9,-999.7 1643.9,-977.63 1643.9,-965.49\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1644.6,-965.2 1643.9,-963.2 1643.2,-965.2 1644.6,-965.2\"/>\n",
"</g>\n",
"<!-- 34->37 -->\n",
"<g id=\"edge109\" class=\"edge\">\n",
"<title>34->37</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1524.91,-1011.19C1538.51,-994.98 1575.99,-947.32 1588.9,-900 1595.46,-875.95 1573.87,-850.73 1561.29,-838.51\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1561.73,-837.97 1559.81,-837.09 1560.76,-838.98 1561.73,-837.97\"/>\n",
"</g>\n",
"<!-- 36 -->\n",
"<g id=\"node36\" class=\"node\">\n",
"<title>36</title>\n",
"<text text-anchor=\"middle\" x=\"1643.9\" y=\"-890.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Nu</text>\n",
"</g>\n",
"<!-- 35->36 -->\n",
"<g id=\"edge110\" class=\"edge\">\n",
"<title>35->36</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1643.9,-948.93C1643.9,-937.88 1643.9,-914.47 1643.9,-902.08\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1644.6,-902.05 1643.9,-900.05 1643.2,-902.05 1644.6,-902.05\"/>\n",
"</g>\n",
"<!-- 36->37 -->\n",
"<g id=\"edge111\" class=\"edge\">\n",
"<title>36->37</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1636.14,-886.8C1619.49,-875.63 1580.36,-849.41 1562.32,-837.31\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1562.69,-836.72 1560.64,-836.19 1561.91,-837.88 1562.69,-836.72\"/>\n",
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"<!-- 37->39 -->\n",
"<g id=\"edge112\" class=\"edge\">\n",
"<title>37->39</title>\n",
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"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"663.7,-769.45 661.63,-769.92 663.54,-770.84 663.7,-769.45\"/>\n",
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"<!-- 86 -->\n",
"<g id=\"node86\" class=\"node\">\n",
"<title>86</title>\n",
"<text text-anchor=\"middle\" x=\"1453.9\" y=\"-765.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">H</text>\n",
"</g>\n",
"<!-- 37->86 -->\n",
"<g id=\"edge113\" class=\"edge\">\n",
"<title>37->86</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1545.13,-824.29C1526.56,-813.04 1479.77,-784.68 1461.44,-773.57\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1461.42,-772.74 1459.35,-772.3 1460.69,-773.94 1461.42,-772.74\"/>\n",
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"<!-- 38->39 -->\n",
"<g id=\"edge114\" class=\"edge\">\n",
"<title>38->39</title>\n",
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"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"654.11,-777.39 653.56,-775.35 652.72,-777.29 654.11,-777.39\"/>\n",
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"<!-- 39->46 -->\n",
"<g id=\"edge115\" class=\"edge\">\n",
"<title>39->46</title>\n",
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"<g id=\"node56\" class=\"node\">\n",
"<title>56</title>\n",
"<text text-anchor=\"middle\" x=\"790.9\" y=\"-201.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">gv</text>\n",
"</g>\n",
"<!-- 39->56 -->\n",
"<g id=\"edge116\" class=\"edge\">\n",
"<title>39->56</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M652.36,-760.66C648.19,-743.07 636.71,-692.11 632.9,-649 622.46,-530.72 631.02,-495.73 673.9,-385 702.42,-311.35 763.9,-236.29 784.22,-212.62\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"784.84,-212.98 785.61,-211.01 783.78,-212.07 784.84,-212.98\"/>\n",
"</g>\n",
"<!-- 57 -->\n",
"<g id=\"node57\" class=\"node\">\n",
"<title>57</title>\n",
"<text text-anchor=\"middle\" x=\"292.9\" y=\"-702.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">rbc</text>\n",
"</g>\n",
"<!-- 39->57 -->\n",
"<g id=\"edge117\" class=\"edge\">\n",
"<title>39->57</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M646.36,-765.73C600.93,-758.05 363.68,-717.96 305.7,-708.16\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"305.8,-707.47 303.71,-707.83 305.56,-708.85 305.8,-707.47\"/>\n",
"</g>\n",
"<!-- 40 -->\n",
"<g id=\"node40\" class=\"node\">\n",
"<title>40</title>\n",
"<text text-anchor=\"middle\" x=\"827.9\" y=\"-263.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">gs</text>\n",
"</g>\n",
"<!-- 40->56 -->\n",
"<g id=\"edge118\" class=\"edge\">\n",
"<title>40->56</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M823.94,-258.58C817.17,-247.61 803.39,-225.26 795.95,-213.18\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"796.37,-212.53 794.72,-211.2 795.17,-213.26 796.37,-212.53\"/>\n",
"</g>\n",
"<!-- 58 -->\n",
"<g id=\"node58\" class=\"node\">\n",
"<title>58</title>\n",
"<text text-anchor=\"middle\" x=\"305.9\" y=\"-201.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">rsc</text>\n",
"</g>\n",
"<!-- 40->58 -->\n",
"<g id=\"edge119\" class=\"edge\">\n",
"<title>40->58</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M820.12,-264.11C761.72,-257.39 392.46,-214.95 318.71,-206.47\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"318.68,-205.76 316.61,-206.23 318.52,-207.16 318.68,-205.76\"/>\n",
"</g>\n",
"<!-- 41 -->\n",
"<g id=\"node41\" class=\"node\">\n",
"<title>41</title>\n",
"<text text-anchor=\"middle\" x=\"889.9\" y=\"-451.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">A_net</text>\n",
"</g>\n",
"<!-- 41->40 -->\n",
"<g id=\"edge120\" class=\"edge\">\n",
"<title>41->40</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M887.84,-446.81C878.6,-419.11 841.06,-306.5 830.61,-275.14\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"831.2,-274.7 829.91,-273.02 829.88,-275.14 831.2,-274.7\"/>\n",
"</g>\n",
"<!-- 43 -->\n",
"<g id=\"node43\" class=\"node\">\n",
"<title>43</title>\n",
"<text text-anchor=\"middle\" x=\"690.9\" y=\"-389.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Cs</text>\n",
"</g>\n",
"<!-- 41->43 -->\n",
"<g id=\"edge121\" class=\"edge\">\n",
"<title>41->43</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M873.61,-448.09C833.91,-436.12 733.02,-405.7 700.89,-396.01\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"700.82,-395.26 698.7,-395.35 700.41,-396.6 700.82,-395.26\"/>\n",
"</g>\n",
"<!-- 41->46 -->\n",
"<g id=\"edge122\" class=\"edge\">\n",
"<title>41->46</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M883.06,-446.85C872.19,-437 850.4,-416.97 832.9,-399 812.12,-377.67 789.01,-351.15 777.78,-338.07\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"778.05,-337.31 776.21,-336.24 776.98,-338.22 778.05,-337.31\"/>\n",
"</g>\n",
"<!-- 65 -->\n",
"<g id=\"node65\" class=\"node\">\n",
"<title>65</title>\n",
"<text text-anchor=\"middle\" x=\"382.9\" y=\"-13.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Ci</text>\n",
"</g>\n",
"<!-- 41->65 -->\n",
"<g id=\"edge123\" class=\"edge\">\n",
"<title>41->65</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M885.28,-446.95C870.97,-428.25 826.05,-369.73 787.9,-322 745.9,-269.46 691.9,-272.26 691.9,-205 691.9,-205 691.9,-205 691.9,-140 691.9,-73.94 445.01,-27.7 392.6,-18.63\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"392.63,-17.92 390.54,-18.27 392.39,-19.3 392.63,-17.92\"/>\n",
"</g>\n",
"<!-- 130 -->\n",
"<g id=\"node130\" class=\"node\">\n",
"<title>130</title>\n",
"<text text-anchor=\"middle\" x=\"933.9\" y=\"-389.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">A_gross</text>\n",
"</g>\n",
"<!-- 41->130 -->\n",
"<g id=\"edge124\" class=\"edge\">\n",
"<title>41->130</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M894.61,-446.58C902.72,-435.51 919.31,-412.89 928.12,-400.89\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"928.74,-401.22 929.36,-399.2 927.61,-400.39 928.74,-401.22\"/>\n",
"</g>\n",
"<!-- 42->40 -->\n",
"<g id=\"edge125\" class=\"edge\">\n",
"<title>42->40</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1051.6,-384.6C1046.38,-370.97 1032.32,-338.99 1009.9,-322 954.62,-280.12 867.49,-269.94 838.03,-267.63\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"837.73,-266.91 835.68,-267.46 837.62,-268.3 837.73,-266.91\"/>\n",
"</g>\n",
"<!-- 42->46 -->\n",
"<g id=\"edge126\" class=\"edge\">\n",
"<title>42->46</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1046.25,-388.23C1043.07,-387.14 1039.33,-385.93 1035.9,-385 937.59,-358.51 815.85,-337.46 780.77,-331.62\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"780.87,-330.93 778.78,-331.29 780.64,-332.31 780.87,-330.93\"/>\n",
"</g>\n",
"<!-- 43->40 -->\n",
"<g id=\"edge127\" class=\"edge\">\n",
"<title>43->40</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M695.88,-384.94C706.24,-372.51 731.13,-343.46 754.9,-322 776.4,-302.59 804.37,-282.89 818.64,-273.19\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"819.04,-273.76 820.31,-272.05 818.26,-272.6 819.04,-273.76\"/>\n",
"</g>\n",
"<!-- 43->46 -->\n",
"<g id=\"edge128\" class=\"edge\">\n",
"<title>43->46</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M698.57,-385.15C713.3,-373.92 745.51,-349.36 761.5,-337.17\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"762.2,-337.51 763.37,-335.74 761.35,-336.4 762.2,-337.51\"/>\n",
"</g>\n",
"<!-- 44 -->\n",
"<g id=\"node44\" class=\"node\">\n",
"<title>44</title>\n",
"<text text-anchor=\"middle\" x=\"1398.9\" y=\"-953.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">fΨv</text>\n",
"</g>\n",
"<!-- 44->40 -->\n",
"<g id=\"edge129\" class=\"edge\">\n",
"<title>44->40</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1404.54,-948.83C1412.88,-939.23 1428.14,-919.78 1433.9,-900 1466.43,-788.28 1383.9,-759.36 1383.9,-643 1383.9,-643 1383.9,-643 1383.9,-579 1383.9,-391.72 1163.16,-495.9 1002.9,-399 934.84,-357.85 861.28,-295.92 836.55,-274.56\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"836.83,-273.87 834.86,-273.09 835.91,-274.93 836.83,-273.87\"/>\n",
"</g>\n",
"<!-- 44->46 -->\n",
"<g id=\"edge130\" class=\"edge\">\n",
"<title>44->46</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1401.89,-948.95C1410.93,-929.75 1436.31,-868.75 1417.9,-823 1389.16,-751.55 1359.05,-744.81 1297.9,-698 1123.69,-564.65 1032.5,-602.57 864.9,-461 820.36,-423.38 786.07,-360.26 774.84,-338.04\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"775.35,-337.49 773.82,-336.02 774.09,-338.12 775.35,-337.49\"/>\n",
"</g>\n",
"<!-- 45->40 -->\n",
"<g id=\"edge131\" class=\"edge\">\n",
"<title>45->40</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1018.21,-384.68C1016.41,-371.23 1010.35,-339.56 991.9,-322 946.41,-278.7 865.8,-269.44 837.81,-267.5\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"837.61,-266.79 835.57,-267.36 837.52,-268.18 837.61,-266.79\"/>\n",
"</g>\n",
"<!-- 45->46 -->\n",
"<g id=\"edge132\" class=\"edge\">\n",
"<title>45->46</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1011.21,-389.11C974.97,-380.2 821.42,-342.43 780.8,-332.43\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"780.61,-331.67 778.5,-331.87 780.28,-333.03 780.61,-331.67\"/>\n",
"</g>\n",
"<!-- 46->40 -->\n",
"<g id=\"edge133\" class=\"edge\">\n",
"<title>46->40</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M776.57,-321.93C786.99,-310.78 809.13,-287.08 820.63,-274.78\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"821.39,-274.99 822.25,-273.05 820.37,-274.03 821.39,-274.99\"/>\n",
"</g>\n",
"<!-- 46->93 -->\n",
"<g id=\"edge134\" class=\"edge\">\n",
"<title>46->93</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M763.38,-325.68C732.63,-316.21 616.47,-280.42 582.37,-269.92\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"582.54,-269.24 580.43,-269.32 582.13,-270.58 582.54,-269.24\"/>\n",
"</g>\n",
"<!-- 47 -->\n",
"<g id=\"node47\" class=\"node\">\n",
"<title>47</title>\n",
"<text text-anchor=\"middle\" x=\"910.9\" y=\"-514.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Aj</text>\n",
"</g>\n",
"<!-- 47->41 -->\n",
"<g id=\"edge135\" class=\"edge\">\n",
"<title>47->41</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M908.81,-509.93C905,-498.88 896.95,-475.47 892.68,-463.08\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"893.29,-462.71 891.98,-461.05 891.97,-463.17 893.29,-462.71\"/>\n",
"</g>\n",
"<!-- 48 -->\n",
"<g id=\"node48\" class=\"node\">\n",
"<title>48</title>\n",
"<text text-anchor=\"middle\" x=\"1120.9\" y=\"-577.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Ac</text>\n",
"</g>\n",
"<!-- 48->41 -->\n",
"<g id=\"edge136\" class=\"edge\">\n",
"<title>48->41</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1113.21,-574.87C1079.69,-556.88 946.04,-485.14 903.19,-462.14\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"903.32,-461.41 901.22,-461.08 902.65,-462.64 903.32,-461.41\"/>\n",
"</g>\n",
"<!-- 49 -->\n",
"<g id=\"node49\" class=\"node\">\n",
"<title>49</title>\n",
"<text text-anchor=\"middle\" x=\"1567.9\" y=\"-639.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Ap</text>\n",
"</g>\n",
"<!-- 49->41 -->\n",
"<g id=\"edge137\" class=\"edge\">\n",
"<title>49->41</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1560.03,-638.2C1532.62,-628.52 1438.74,-595.76 1359.9,-573 1185.75,-522.74 971.84,-473.5 908.44,-459.16\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"908.35,-458.42 906.24,-458.67 908.04,-459.79 908.35,-458.42\"/>\n",
"</g>\n",
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"<g id=\"node81\" class=\"node\">\n",
"<title>81</title>\n",
"<text text-anchor=\"middle\" x=\"1274.9\" y=\"-827.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Tk</text>\n",
"</g>\n",
"<!-- 50->81 -->\n",
"<g id=\"edge138\" class=\"edge\">\n",
"<title>50->81</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M590.15,-891.77C645.39,-889.36 1120.84,-867.89 1258.9,-837 1260.98,-836.53 1263.16,-835.86 1265.21,-835.12\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1265.59,-835.73 1267.22,-834.37 1265.1,-834.42 1265.59,-835.73\"/>\n",
"</g>\n",
"<!-- 50->84 -->\n",
"<g id=\"edge139\" class=\"edge\">\n",
"<title>50->84</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M579.52,-888C565.89,-877.86 529.87,-851.06 512.52,-838.15\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"512.52,-837.28 510.49,-836.65 511.68,-838.41 512.52,-837.28\"/>\n",
"</g>\n",
"<!-- 50->93 -->\n",
"<g id=\"edge140\" class=\"edge\">\n",
"<title>50->93</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M584.38,-885.85C582.09,-857.88 572.9,-739.95 572.9,-643 572.9,-643 572.9,-643 572.9,-391 572.9,-347.56 572.9,-295.55 572.9,-275.48\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"573.6,-275.19 572.9,-273.19 572.2,-275.19 573.6,-275.19\"/>\n",
"</g>\n",
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"<g id=\"node96\" class=\"node\">\n",
"<title>96</title>\n",
"<text text-anchor=\"middle\" x=\"1324.9\" y=\"-765.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">kT</text>\n",
"</g>\n",
"<!-- 50->96 -->\n",
"<g id=\"edge141\" class=\"edge\">\n",
"<title>50->96</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M590.02,-891.15C650.72,-881.06 1232.05,-784.43 1315.06,-770.64\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1315.51,-771.27 1317.36,-770.25 1315.28,-769.89 1315.51,-771.27\"/>\n",
"</g>\n",
"<!-- 99 -->\n",
"<g id=\"node99\" class=\"node\">\n",
"<title>99</title>\n",
"<text text-anchor=\"middle\" x=\"1392.9\" y=\"-827.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">kTQ10</text>\n",
"</g>\n",
"<!-- 50->99 -->\n",
"<g id=\"edge142\" class=\"edge\">\n",
"<title>50->99</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M590.06,-891.61C652.4,-886.9 1260.61,-840.99 1374.56,-832.38\"/>\n",
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"</g>\n",
"<!-- 51->50 -->\n",
"<g id=\"edge143\" class=\"edge\">\n",
"<title>51->50</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M301.71,-952.76C349.04,-942.94 537.41,-903.85 577.41,-895.55\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"577.81,-896.19 579.62,-895.1 577.52,-894.82 577.81,-896.19\"/>\n",
"</g>\n",
"<!-- 51->86 -->\n",
"<g id=\"edge144\" class=\"edge\">\n",
"<title>51->86</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M296.92,-948.99C319.38,-927.06 401.32,-851.09 485.9,-823 491.96,-820.99 1357.61,-774.2 1446.54,-769.4\"/>\n",
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"<!-- 88 -->\n",
"<g id=\"node88\" class=\"node\">\n",
"<title>88</title>\n",
"<text text-anchor=\"middle\" x=\"1402.9\" y=\"-13.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">ΔT</text>\n",
"</g>\n",
"<!-- 51->88 -->\n",
"<g id=\"edge145\" class=\"edge\">\n",
"<title>51->88</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M288.21,-948.98C282.55,-936.62 268.63,-907.7 252.9,-886 188.68,-797.39 84.9,-815.43 84.9,-706 84.9,-706 84.9,-706 84.9,-140 84.9,-53.49 182.2,-88.6 266.9,-71 498.98,-22.76 1295.06,-17.51 1392.99,-17.04\"/>\n",
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"<!-- 52->57 -->\n",
"<g id=\"edge146\" class=\"edge\">\n",
"<title>52->57</title>\n",
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"<!-- 53->58 -->\n",
"<g id=\"edge147\" class=\"edge\">\n",
"<title>53->58</title>\n",
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"<g id=\"edge148\" class=\"edge\">\n",
"<title>54->43</title>\n",
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"<title>62</title>\n",
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"</g>\n",
"<!-- 54->62 -->\n",
"<g id=\"edge149\" class=\"edge\">\n",
"<title>54->62</title>\n",
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"<!-- 54->65 -->\n",
"<g id=\"edge150\" class=\"edge\">\n",
"<title>54->65</title>\n",
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"<g id=\"edge155\" class=\"edge\">\n",
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"</g>\n",
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"<title>58->60</title>\n",
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"<g id=\"edge158\" class=\"edge\">\n",
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"<g id=\"edge160\" class=\"edge\">\n",
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"<title>63</title>\n",
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"<title>63->64</title>\n",
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"<title>64->47</title>\n",
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"<g id=\"edge164\" class=\"edge\">\n",
"<title>64->48</title>\n",
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"<title>64->65</title>\n",
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"<title>66->69</title>\n",
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"<g id=\"edge167\" class=\"edge\">\n",
"<title>66->76</title>\n",
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"<g id=\"edge168\" class=\"edge\">\n",
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"<title>68->70</title>\n",
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"<g id=\"edge170\" class=\"edge\">\n",
"<title>69->70</title>\n",
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"<title>120</title>\n",
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"<title>70->120</title>\n",
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"<g id=\"edge172\" class=\"edge\">\n",
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"<title>71->80</title>\n",
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"<title>72->79</title>\n",
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"<g id=\"edge175\" class=\"edge\">\n",
"<title>72->80</title>\n",
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"<g id=\"edge177\" class=\"edge\">\n",
"<title>74->86</title>\n",
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"<title>75</title>\n",
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"<g id=\"edge178\" class=\"edge\">\n",
"<title>75->76</title>\n",
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"<g id=\"edge179\" class=\"edge\">\n",
"<title>76->78</title>\n",
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"<g id=\"edge180\" class=\"edge\">\n",
"<title>77->78</title>\n",
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"<g id=\"edge181\" class=\"edge\">\n",
"<title>78->83</title>\n",
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"<g id=\"edge183\" class=\"edge\">\n",
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"<g id=\"edge184\" class=\"edge\">\n",
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"<g id=\"edge185\" class=\"edge\">\n",
"<title>81->96</title>\n",
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"<title>81->97</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1274.64,-822.73C1273.81,-802.24 1271.17,-737.26 1270.23,-714.21\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1270.93,-714.08 1270.15,-712.11 1269.53,-714.14 1270.93,-714.08\"/>\n",
"</g>\n",
"<!-- 82->83 -->\n",
"<g id=\"edge187\" class=\"edge\">\n",
"<title>82->83</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M2198.9,-697.93C2198.9,-686.88 2198.9,-663.47 2198.9,-651.08\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"2199.6,-651.05 2198.9,-649.05 2198.2,-651.05 2199.6,-651.05\"/>\n",
"</g>\n",
"<!-- 83->88 -->\n",
"<g id=\"edge188\" class=\"edge\">\n",
"<title>83->88</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M2202.22,-634.53C2211.13,-616.55 2234.9,-564.28 2234.9,-518 2234.9,-518 2234.9,-518 2234.9,-140 2234.9,-52.53 1506,-21.04 1412.69,-17.37\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1412.63,-16.67 1410.6,-17.29 1412.58,-18.07 1412.63,-16.67\"/>\n",
"</g>\n",
"<!-- 84->85 -->\n",
"<g id=\"edge189\" class=\"edge\">\n",
"<title>84->85</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M502.9,-822.86C502.9,-804.88 502.9,-750.84 502.9,-706 502.9,-706 502.9,-706 502.9,-641 502.9,-558.29 496.9,-537.71 496.9,-455 496.9,-455 496.9,-455 496.9,-265 496.9,-136.72 738.05,-139.91 783.54,-141.65\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"783.77,-142.36 785.8,-141.74 783.83,-140.96 783.77,-142.36\"/>\n",
"</g>\n",
"<!-- 85->87 -->\n",
"<g id=\"edge190\" class=\"edge\">\n",
"<title>85->87</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M796.03,-139.47C849.38,-133.98 1302.73,-87.35 1374.38,-79.98\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1374.47,-80.67 1376.39,-79.77 1374.33,-79.28 1374.47,-80.67\"/>\n",
"</g>\n",
"<!-- 86->88 -->\n",
"<g id=\"edge191\" class=\"edge\">\n",
"<title>86->88</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1451.17,-760.95C1443.43,-743.22 1421.9,-689.69 1421.9,-643 1421.9,-643 1421.9,-643 1421.9,-140 1421.9,-96.4 1410.09,-45.11 1405.09,-25.34\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1405.69,-24.86 1404.52,-23.09 1404.34,-25.2 1405.69,-24.86\"/>\n",
"</g>\n",
"<!-- 87->88 -->\n",
"<g id=\"edge192\" class=\"edge\">\n",
"<title>87->88</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1385.93,-70.58C1389.41,-59.61 1396.48,-37.26 1400.31,-25.18\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1401,-25.31 1400.94,-23.2 1399.67,-24.89 1401,-25.31\"/>\n",
"</g>\n",
"<!-- 90 -->\n",
"<g id=\"node90\" class=\"node\">\n",
"<title>90</title>\n",
"<text text-anchor=\"middle\" x=\"1396.9\" y=\"-1015.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Ψv</text>\n",
"</g>\n",
"<!-- 89->90 -->\n",
"<g id=\"edge193\" class=\"edge\">\n",
"<title>89->90</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1395.1,-1073.93C1395.46,-1062.88 1396.23,-1039.47 1396.63,-1027.08\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1397.34,-1027.07 1396.7,-1025.05 1395.94,-1027.02 1397.34,-1027.07\"/>\n",
"</g>\n",
"<!-- 90->44 -->\n",
"<g id=\"edge194\" class=\"edge\">\n",
"<title>90->44</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1397.11,-1010.58C1397.48,-999.7 1398.21,-977.63 1398.62,-965.49\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1399.33,-965.22 1398.69,-963.2 1397.93,-965.17 1399.33,-965.22\"/>\n",
"</g>\n",
"<!-- 91->44 -->\n",
"<g id=\"edge195\" class=\"edge\">\n",
"<title>91->44</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1433.73,-1010.58C1426.53,-999.51 1411.83,-976.89 1404.03,-964.89\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1404.6,-964.49 1402.93,-963.2 1403.43,-965.25 1404.6,-964.49\"/>\n",
"</g>\n",
"<!-- 92->44 -->\n",
"<g id=\"edge196\" class=\"edge\">\n",
"<title>92->44</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1360.5,-1010.58C1368.43,-999.51 1384.65,-976.89 1393.25,-964.89\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1393.86,-965.23 1394.46,-963.2 1392.73,-964.41 1393.86,-965.23\"/>\n",
"</g>\n",
"<!-- 95 -->\n",
"<g id=\"node95\" class=\"node\">\n",
"<title>95</title>\n",
"<text text-anchor=\"middle\" x=\"1238.9\" y=\"-827.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Tbk</text>\n",
"</g>\n",
"<!-- 94->95 -->\n",
"<g id=\"edge197\" class=\"edge\">\n",
"<title>94->95</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1321.23,-886.8C1305.17,-875.91 1267.98,-850.71 1249.59,-838.25\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1249.92,-837.62 1247.87,-837.08 1249.13,-838.78 1249.92,-837.62\"/>\n",
"</g>\n",
"<!-- 94->96 -->\n",
"<g id=\"edge198\" class=\"edge\">\n",
"<title>94->96</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1328.7,-885.73C1328.03,-865.24 1325.92,-800.26 1325.17,-777.21\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1325.86,-777.09 1325.1,-775.11 1324.46,-777.13 1325.86,-777.09\"/>\n",
"</g>\n",
"<!-- 94->99 -->\n",
"<g id=\"edge199\" class=\"edge\">\n",
"<title>94->99</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1335.27,-885.93C1347.06,-874.69 1372.24,-850.69 1385.05,-838.48\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1385.59,-838.93 1386.55,-837.05 1384.62,-837.92 1385.59,-838.93\"/>\n",
"</g>\n",
"<!-- 95->96 -->\n",
"<g id=\"edge200\" class=\"edge\">\n",
"<title>95->96</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1247.78,-822.8C1263.94,-811.53 1298.07,-787.72 1314.97,-775.92\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1315.71,-776.27 1316.95,-774.55 1314.91,-775.12 1315.71,-776.27\"/>\n",
"</g>\n",
"<!-- 95->97 -->\n",
"<g id=\"edge201\" class=\"edge\">\n",
"<title>95->97</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1240.48,-822.73C1245.64,-802.24 1262.02,-737.26 1267.83,-714.21\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1268.55,-714.22 1268.36,-712.11 1267.19,-713.88 1268.55,-714.22\"/>\n",
"</g>\n",
"<!-- 96->97 -->\n",
"<g id=\"edge202\" class=\"edge\">\n",
"<title>96->97</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1319.42,-760.93C1309.38,-749.78 1288.01,-726.08 1276.91,-713.78\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1277.21,-713.06 1275.35,-712.05 1276.17,-714 1277.21,-713.06\"/>\n",
"</g>\n",
"<!-- 105 -->\n",
"<g id=\"node105\" class=\"node\">\n",
"<title>105</title>\n",
"<text text-anchor=\"middle\" x=\"1462.9\" y=\"-702.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Kc</text>\n",
"</g>\n",
"<!-- 96->105 -->\n",
"<g id=\"edge203\" class=\"edge\">\n",
"<title>96->105</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1332.71,-763.55C1356.34,-753.1 1426.99,-721.87 1453.08,-710.34\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1453.62,-710.87 1455.17,-709.42 1453.06,-709.58 1453.62,-710.87\"/>\n",
"</g>\n",
"<!-- 108 -->\n",
"<g id=\"node108\" class=\"node\">\n",
"<title>108</title>\n",
"<text text-anchor=\"middle\" x=\"1496.9\" y=\"-702.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Ko</text>\n",
"</g>\n",
"<!-- 96->108 -->\n",
"<g id=\"edge204\" class=\"edge\">\n",
"<title>96->108</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1332.74,-764.22C1360.72,-754.3 1455.69,-720.61 1486.88,-709.55\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1487.36,-710.12 1489.02,-708.8 1486.9,-708.8 1487.36,-710.12\"/>\n",
"</g>\n",
"<!-- 113 -->\n",
"<g id=\"node113\" class=\"node\">\n",
"<title>113</title>\n",
"<text text-anchor=\"middle\" x=\"1162.9\" y=\"-702.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Vcmax</text>\n",
"</g>\n",
"<!-- 96->113 -->\n",
"<g id=\"edge205\" class=\"edge\">\n",
"<title>96->113</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1317.09,-764.06C1292.48,-754.79 1216.17,-726.06 1181,-712.81\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1181.06,-712.09 1178.94,-712.04 1180.57,-713.4 1181.06,-712.09\"/>\n",
"</g>\n",
"<!-- 123 -->\n",
"<g id=\"node123\" class=\"node\">\n",
"<title>123</title>\n",
"<text text-anchor=\"middle\" x=\"1566.9\" y=\"-702.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Tp</text>\n",
"</g>\n",
"<!-- 96->123 -->\n",
"<g id=\"edge206\" class=\"edge\">\n",
"<title>96->123</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1332.75,-765.38C1361.8,-759.31 1465.88,-737.03 1549.9,-712 1552.34,-711.27 1554.94,-710.4 1557.36,-709.56\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1557.69,-710.18 1559.34,-708.85 1557.22,-708.86 1557.69,-710.18\"/>\n",
"</g>\n",
"<!-- 126 -->\n",
"<g id=\"node126\" class=\"node\">\n",
"<title>126</title>\n",
"<text text-anchor=\"middle\" x=\"1599.9\" y=\"-702.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Rd</text>\n",
"</g>\n",
"<!-- 96->126 -->\n",
"<g id=\"edge207\" class=\"edge\">\n",
"<title>96->126</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1332.63,-765.79C1364.21,-760.77 1486.38,-740.47 1583.9,-712 1585.95,-711.4 1588.11,-710.67 1590.16,-709.92\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1590.54,-710.52 1592.17,-709.17 1590.05,-709.21 1590.54,-710.52\"/>\n",
"</g>\n",
"<!-- 129 -->\n",
"<g id=\"node129\" class=\"node\">\n",
"<title>129</title>\n",
"<text text-anchor=\"middle\" x=\"1080.9\" y=\"-702.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Γ</text>\n",
"</g>\n",
"<!-- 96->129 -->\n",
"<g id=\"edge208\" class=\"edge\">\n",
"<title>96->129</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1317.33,-765.11C1280.89,-756 1123.87,-716.74 1088.15,-707.81\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1088.27,-707.12 1086.16,-707.32 1087.93,-708.48 1088.27,-707.12\"/>\n",
"</g>\n",
"<!-- 118 -->\n",
"<g id=\"node118\" class=\"node\">\n",
"<title>118</title>\n",
"<text text-anchor=\"middle\" x=\"910.9\" y=\"-639.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Jmax</text>\n",
"</g>\n",
"<!-- 97->118 -->\n",
"<g id=\"edge209\" class=\"edge\">\n",
"<title>97->118</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1251.1,-700.81C1187.8,-690.05 983.12,-655.27 925.89,-645.55\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"926.01,-644.86 923.92,-645.21 925.77,-646.24 926.01,-644.86\"/>\n",
"</g>\n",
"<!-- 98->99 -->\n",
"<g id=\"edge210\" class=\"edge\">\n",
"<title>98->99</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1456.48,-948.68C1445.28,-927.94 1409.64,-861.98 1397.22,-838.99\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1397.79,-838.59 1396.23,-837.16 1396.56,-839.25 1397.79,-838.59\"/>\n",
"</g>\n",
"<!-- 100->102 -->\n",
"<g id=\"edge211\" class=\"edge\">\n",
"<title>100->102</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1191.05,-1010.73C1181.72,-990.24 1152.13,-925.26 1141.64,-902.21\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1142.15,-901.64 1140.68,-900.11 1140.87,-902.22 1142.15,-901.64\"/>\n",
"</g>\n",
"<!-- 101->102 -->\n",
"<g id=\"edge212\" class=\"edge\">\n",
"<title>101->102</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1154.98,-1010.73C1151.98,-990.24 1142.47,-925.26 1139.1,-902.21\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1139.78,-901.99 1138.79,-900.11 1138.39,-902.19 1139.78,-901.99\"/>\n",
"</g>\n",
"<!-- 102->113 -->\n",
"<g id=\"edge213\" class=\"edge\">\n",
"<title>102->113</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1136.99,-885.9C1134.39,-867.04 1127.69,-808.12 1137.9,-761 1141.73,-743.32 1151.75,-724.49 1157.88,-714.09\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1158.63,-714.2 1159.05,-712.13 1157.42,-713.49 1158.63,-714.2\"/>\n",
"</g>\n",
"<!-- 102->118 -->\n",
"<g id=\"edge214\" class=\"edge\">\n",
"<title>102->118</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1130.28,-888.12C1115.45,-880.25 1082.35,-861.09 1061.9,-837 1037.46,-808.21 1045.65,-791.87 1023.9,-761 991.14,-714.5 940.37,-668.44 919.9,-650.67\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"919.99,-649.82 918.02,-649.04 919.07,-650.88 919.99,-649.82\"/>\n",
"</g>\n",
"<!-- 102->123 -->\n",
"<g id=\"edge215\" class=\"edge\">\n",
"<title>102->123</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1145.42,-889.65C1174.19,-880.69 1280.06,-847.88 1367.9,-823 1447.56,-800.44 1489.12,-833.31 1547.9,-775 1564.55,-758.49 1566.98,-728.82 1567.1,-714.37\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1567.8,-714.35 1567.11,-712.35 1566.4,-714.35 1567.8,-714.35\"/>\n",
"</g>\n",
"<!-- 103->105 -->\n",
"<g id=\"edge216\" class=\"edge\">\n",
"<title>103->105</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1752.75,-888.79C1712.36,-878.39 1588.05,-842.35 1508.9,-775 1488.21,-757.39 1473.02,-728.25 1466.47,-714.14\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1467.04,-713.7 1465.57,-712.18 1465.77,-714.29 1467.04,-713.7\"/>\n",
"</g>\n",
"<!-- 104->105 -->\n",
"<g id=\"edge217\" class=\"edge\">\n",
"<title>104->105</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1521.43,-760.93C1509.46,-749.69 1483.88,-725.69 1470.87,-713.48\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1471.28,-712.91 1469.34,-712.05 1470.32,-713.93 1471.28,-712.91\"/>\n",
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"<!-- 110 -->\n",
"<g id=\"node110\" class=\"node\">\n",
"<title>110</title>\n",
"<text text-anchor=\"middle\" x=\"1457.9\" y=\"-639.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Km</text>\n",
"</g>\n",
"<!-- 105->110 -->\n",
"<g id=\"edge218\" class=\"edge\">\n",
"<title>105->110</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1462.4,-697.93C1461.5,-686.88 1459.58,-663.47 1458.56,-651.08\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1459.26,-650.98 1458.4,-649.05 1457.86,-651.1 1459.26,-650.98\"/>\n",
"</g>\n",
"<!-- 106->108 -->\n",
"<g id=\"edge219\" class=\"edge\">\n",
"<title>106->108</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1808.71,-765.17C1766.13,-759.13 1628.62,-738.74 1516.9,-712 1513.58,-711.2 1509.99,-710.18 1506.78,-709.21\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1506.75,-708.46 1504.63,-708.54 1506.34,-709.8 1506.75,-708.46\"/>\n",
"</g>\n",
"<!-- 107->108 -->\n",
"<g id=\"edge220\" class=\"edge\">\n",
"<title>107->108</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1834.1,-825.18C1781.83,-806.71 1555.5,-726.71 1506.34,-709.34\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1506.52,-708.66 1504.4,-708.65 1506.05,-709.98 1506.52,-708.66\"/>\n",
"</g>\n",
"<!-- 108->110 -->\n",
"<g id=\"edge221\" class=\"edge\">\n",
"<title>108->110</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1493.02,-697.93C1485.89,-686.78 1470.74,-663.08 1462.87,-650.78\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1463.43,-650.36 1461.77,-649.05 1462.25,-651.11 1463.43,-650.36\"/>\n",
"</g>\n",
"<!-- 109->110 -->\n",
"<g id=\"edge222\" class=\"edge\">\n",
"<title>109->110</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1525.43,-697.93C1511.62,-686.69 1482.11,-662.69 1467.09,-650.48\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1467.33,-649.77 1465.33,-649.05 1466.44,-650.85 1467.33,-649.77\"/>\n",
"</g>\n",
"<!-- 110->48 -->\n",
"<g id=\"edge223\" class=\"edge\">\n",
"<title>110->48</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1450.23,-639.63C1405.67,-631.7 1180.44,-591.6 1130.65,-582.74\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1130.5,-582 1128.41,-582.34 1130.26,-583.38 1130.5,-582\"/>\n",
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"<!-- 111->113 -->\n",
"<g id=\"edge224\" class=\"edge\">\n",
"<title>111->113</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M1162.9,-760.93C1162.9,-749.88 1162.9,-726.47 1162.9,-714.08\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1163.6,-714.05 1162.9,-712.05 1162.2,-714.05 1163.6,-714.05\"/>\n",
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"<!-- 112->113 -->\n",
"<g id=\"edge225\" class=\"edge\">\n",
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"text/plain": [
"\u001b[90m[\u001b[39m\u001b[94mk\u001b[39m\u001b[90m → \u001b[39m\u001b[94mσ\u001b[39m\u001b[90m → \u001b[39m\u001b[94mCimin\u001b[39m\u001b[90m → \u001b[39m\u001b[94mocr\u001b[39m\u001b[90m → \u001b[39m\u001b[94mSLA\u001b[39m\u001b[90m → \u001b[39m\u001b[94mconfig\u001b[39m\u001b[90m → \u001b[39m\u001b[94mEag\u001b[39m\u001b[90m → \u001b[39m\u001b[94mΓ25\u001b[39m\u001b[90m → \u001b[39m\u001b[94mEar\u001b[39m\u001b[90m → \u001b[39m\u001b[94mRd25\u001b[39m\u001b[90m → \u001b[39m\u001b[94mEaTp\u001b[39m\u001b[90m → \u001b[39m\u001b[94mTp25\u001b[39m\u001b[90m → \u001b[39m\u001b[94mθ\u001b[39m\u001b[90m → \u001b[39m\u001b[94mToj\u001b[39m\u001b[90m → \u001b[39m\u001b[94mHdj\u001b[39m\u001b[90m → \u001b[39m\u001b[94mHaj\u001b[39m\u001b[90m → \u001b[39m\u001b[94mJm25\u001b[39m\u001b[90m → \u001b[39m\u001b[94mEaVc\u001b[39m\u001b[90m → \u001b[39m\u001b[94mVcm25\u001b[39m\u001b[90m → \u001b[39m\u001b[94mOm\u001b[39m\u001b[90m → \u001b[39m\u001b[94mEao\u001b[39m\u001b[90m → \u001b[39m\u001b[94mKo25\u001b[39m\u001b[90m → \u001b[39m\u001b[94mEac\u001b[39m\u001b[90m → \u001b[39m\u001b[94mKc25\u001b[39m\u001b[90m → \u001b[39m\u001b[94mN0\u001b[39m\u001b[90m → \u001b[39m\u001b[94ms\u001b[39m\u001b[90m → \u001b[39m\u001b[94mQ10\u001b[39m\u001b[90m → \u001b[39m\u001b[94mTb\u001b[39m\u001b[90m → \u001b[39m\u001b[94mTbk\u001b[39m\u001b[90m → \u001b[39m\u001b[94msf\u001b[39m\u001b[90m → \u001b[39m\u001b[94mΨf\u001b[39m\u001b[90m → \u001b[39m\u001b[94mWP_leaf\u001b[39m\u001b[90m → \u001b[39m\u001b[94mΨv\u001b[39m\u001b[90m → \u001b[39m\u001b[94mfΨv\u001b[39m\u001b[90m → \u001b[39m\u001b[94mα_s\u001b[39m\u001b[90m → \u001b[39m\u001b[94mCp\u001b[39m\u001b[90m → \u001b[39m\u001b[94mλ\u001b[39m\u001b[90m → \u001b[39m\u001b[94mϵ\u001b[39m\u001b[90m → \u001b[39m\u001b[94mf\u001b[39m\u001b[90m → \u001b[39m\u001b[94mδ\u001b[39m\u001b[90m → \u001b[39m\u001b[94mg1\u001b[39m\u001b[90m → \u001b[39m\u001b[94mg0\u001b[39m\u001b[90m → \u001b[39m\u001b[94msr\u001b[39m\u001b[90m → \u001b[39m\u001b[94mscr\u001b[39m\u001b[90m → \u001b[39m\u001b[94mw\u001b[39m\u001b[90m → \u001b[39m\u001b[94md\u001b[39m\u001b[90m → \u001b[39m\u001b[94mDm\u001b[39m\u001b[90m → \u001b[39m\u001b[94mv\u001b[39m\u001b[90m → \u001b[39m\u001b[94mDh\u001b[39m\u001b[90m → \u001b[39m\u001b[94mκ\u001b[39m\u001b[90m → \u001b[39m\u001b[94mDc\u001b[39m\u001b[90m → \u001b[39m\u001b[94mDw\u001b[39m\u001b[90m → \u001b[39m\u001b[94mdra\u001b[39m\u001b[90m → \u001b[39m\u001b[94mdrb\u001b[39m\u001b[90m → \u001b[39m\u001b[94mrhw\u001b[39m\u001b[90m → \u001b[39m\u001b[94m__Nitrogen__c\u001b[39m\u001b[90m → \u001b[39m\u001b[94m__Nitrogen__b\u001b[39m\u001b[90m → \u001b[39m\u001b[94m__Nitrogen__a\u001b[39m\u001b[90m → \u001b[39m\u001b[94mSPAD\u001b[39m\u001b[90m → \u001b[39m\u001b[94mN\u001b[39m\u001b[90m → \u001b[39m\u001b[94mkN\u001b[39m\u001b[90m → \u001b[39m\u001b[94mNp\u001b[39m\u001b[90m → \u001b[39m\u001b[94mP_air\u001b[39m\u001b[90m → \u001b[39m\u001b[94mwind\u001b[39m\u001b[90m → \u001b[39m\u001b[94mu\u001b[39m\u001b[90m → \u001b[39m\u001b[94mRe\u001b[39m\u001b[90m → \u001b[39m\u001b[94mNu\u001b[39m\u001b[90m → \u001b[39m\u001b[94mT_air\u001b[39m\u001b[90m → \u001b[39m\u001b[94mTk_air\u001b[39m\u001b[90m → \u001b[39m\u001b[94mR_wall\u001b[39m\u001b[90m → \u001b[39m\u001b[94mgh\u001b[39m\u001b[90m → \u001b[39m\u001b[94mgb\u001b[39m\u001b[90m → \u001b[39m\u001b[94mrbc\u001b[39m\u001b[90m → \u001b[39m\u001b[94mgbc\u001b[39m\u001b[90m → \u001b[39m\u001b[94mRH\u001b[39m\u001b[90m → \u001b[39m\u001b[94mCO2\u001b[39m\u001b[90m → \u001b[39m\u001b[94mCa\u001b[39m\u001b[90m → \u001b[39m\u001b[94mCimax\u001b[39m\u001b[90m → \u001b[39m\u001b[94mPFD\u001b[39m\u001b[90m → \u001b[39m\u001b[94mPPFD\u001b[39m\u001b[90m → \u001b[39m\u001b[94mPAR\u001b[39m\u001b[90m → \u001b[39m\u001b[94mR_sw\u001b[39m\u001b[90m → \u001b[39m\u001b[94mIa\u001b[39m\u001b[90m → \u001b[39m\u001b[94mI2\u001b[39m\u001b[90m → \u001b[39m\u001b[94m∘context\u001b[39m\u001b[90m → \u001b[39m\u001b[94mcontext\u001b[39m\u001b[90m → \u001b[39m\u001b[94m∘Ci\u001b[39m\u001b[90m → \u001b[39m\u001b[94m∘ΔT\u001b[39m\u001b[90m → \u001b[39m\u001b[94mH\u001b[39m\u001b[90m → \u001b[39m\u001b[94mT\u001b[39m\u001b[90m → \u001b[39m\u001b[94mkTQ10\u001b[39m\u001b[90m → \u001b[39m\u001b[94mTk\u001b[39m\u001b[90m → \u001b[39m\u001b[94mkT\u001b[39m\u001b[90m → \u001b[39m\u001b[94mΓ\u001b[39m\u001b[90m → \u001b[39m\u001b[94mRd\u001b[39m\u001b[90m → \u001b[39m\u001b[94mTp\u001b[39m\u001b[90m → \u001b[39m\u001b[94mAp\u001b[39m\u001b[90m → \u001b[39m\u001b[94mVcmax\u001b[39m\u001b[90m → \u001b[39m\u001b[94mKo\u001b[39m\u001b[90m → \u001b[39m\u001b[94mKc\u001b[39m\u001b[90m → \u001b[39m\u001b[94mKm\u001b[39m\u001b[90m → \u001b[39m\u001b[94mAc\u001b[39m\u001b[90m → \u001b[39m\u001b[94mkTpeak\u001b[39m\u001b[90m → \u001b[39m\u001b[94mJmax\u001b[39m\u001b[90m → \u001b[39m\u001b[94mJ\u001b[39m\u001b[90m → \u001b[39m\u001b[94mAj\u001b[39m\u001b[90m → \u001b[39m\u001b[94mA_net\u001b[39m\u001b[90m → \u001b[39m\u001b[94mA_gross\u001b[39m\u001b[90m → \u001b[39m\u001b[94mCs\u001b[39m\u001b[90m → \u001b[39m\u001b[94mhs\u001b[39m\u001b[90m → \u001b[39m\u001b[94mgs\u001b[39m\u001b[90m → \u001b[39m\u001b[94mrsc\u001b[39m\u001b[90m → \u001b[39m\u001b[94mgsc\u001b[39m\u001b[90m → \u001b[39m\u001b[94mrvc\u001b[39m\u001b[90m → \u001b[39m\u001b[94mgvc\u001b[39m\u001b[90m → \u001b[39m\u001b[94mCi\u001b[39m\u001b[90m → \u001b[39m\u001b[94mgv\u001b[39m\u001b[90m → \u001b[39m\u001b[94mR_leaf\u001b[39m\u001b[90m → \u001b[39m\u001b[94mR_thermal\u001b[39m\u001b[90m → \u001b[39m\u001b[94mR_net\u001b[39m\u001b[90m → \u001b[39m\u001b[94mvp\u001b[39m\u001b[90m → \u001b[39m\u001b[94mDs\u001b[39m\u001b[90m → \u001b[39m\u001b[94mΔw\u001b[39m\u001b[90m → \u001b[39m\u001b[94mE\u001b[39m\u001b[90m → \u001b[39m\u001b[94mλE\u001b[39m\u001b[90m → \u001b[39m\u001b[94mΔT\u001b[39m\u001b[90m → \u001b[39m\u001b[94mVPD_s\u001b[39m\u001b[90m → \u001b[39m\u001b[94mVPD_Δ\u001b[39m\u001b[90m → \u001b[39m\u001b[94mVPD\u001b[39m\u001b[90m → \u001b[39m\u001b[94m⋆context\u001b[39m\u001b[90m]\u001b[39m"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Cropbox.dependency(LeafGasExchange.ModelC3BB)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"의존관계도(dependency graph)를 살펴보면 지금까지 다루었던 모형과는 달리 굉장히 많은 변수들이 포함되어 있는 것을 알 수 있습니다. 하지만 결국 확인하고 싶은 것은 앞의 간단한 광합성 모형과 마찬가지로 총광합성율($A_g$) 혹은 순광합성율($A_n$)과 같은 값일 것입니다. 여기서 순광합성율(`A_n`)은 아래와 같이 구현되어 있습니다."
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\u001b[90m[doc]\u001b[39m\n",
"\n",
"\u001b[90m[code]\u001b[39m\n",
"\u001b[22;23;24m \u001b[38;2;66;102;213;22;23;24mA_net\u001b[39m\u001b[22;23;24m(\u001b[22;23;24mAc\u001b[22;23;24m,\u001b[22;23;24m \u001b[22;23;24mAj\u001b[22;23;24m,\u001b[22;23;24m \u001b[22;23;24mAp\u001b[22;23;24m)\u001b[38;2;102;102;102;1;23;24m:\u001b[39;22m\u001b[22;23;24mnet_photosynthesis\u001b[22;23;24m \u001b[38;2;102;102;102;1;23;24m=>\u001b[39;22m\u001b[22;23;24m \u001b[38;2;148;91;176;1;23;24mbegin\u001b[39;22m\u001b[22;23;24m\n",
" \u001b[38;2;153;153;119;22;3;24m#= /Users/tomyun/.julia/packages/LeafGasExchange/I1nMc/src/c3.jl:92 =#\u001b[39;23m\u001b[22;23;24m\n",
" \u001b[38;2;66;102;213;22;23;24mmin\u001b[39m\u001b[22;23;24m(\u001b[22;23;24mAc\u001b[22;23;24m,\u001b[22;23;24m \u001b[22;23;24mAj\u001b[22;23;24m,\u001b[22;23;24m \u001b[22;23;24mAp\u001b[22;23;24m)\u001b[22;23;24m\n",
" \u001b[38;2;148;91;176;1;23;24mend\u001b[39;22m\u001b[22;23;24m \u001b[38;2;102;102;102;1;23;24m~\u001b[39;22m\u001b[22;23;24m \u001b[38;2;66;102;213;22;23;24mtrack\u001b[39m\u001b[22;23;24m(\u001b[38;2;201;61;57;22;23;24mu\"μmol/m^2/s\"\u001b[39m\u001b[22;23;24m)"
]
}
],
"source": [
"@look LeafGasExchange.ModelC3BB.A_net"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"C3 광합성의 주요한 제한 요인들, 즉 이산화탄소($\\mathrm{CO_2}$ 혹은 RuBisCo 효소와 같은 기질의 부족(carboxylation-limited)인지, 아니면 전자전달계의 부하로 인한 제한(RuBP-renegeration limited)인지, 혹은 최종 산물의 수송이 저하되어 발생하는 제한(triose phosphate utilization-limited)인지에 따라 각각의 잠재 광합성율(`Ac`, `Aj`, `Ap`)이 계산되고 그중에서 가장 제한이 많이 걸리는 쪽, 다시 말해 최소값이 최종 광합성율로 채택됩니다.\n",
"\n",
"기질 부족으로 인한 광합성율(`Ac`)은 대개 이산화탄소 분압이 낮은 단계에서 발생하는데, 이러한 생화학적 기작은 앞서 보았던 광량에 따른 광합성율 수식과 유사한 쌍곡선의 형태로 구현되고 있습니다."
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\u001b[90m[doc]\u001b[39m\n",
"\n",
"\u001b[90m[code]\u001b[39m\n",
"\u001b[22;23;24m \u001b[38;2;66;102;213;22;23;24mAc\u001b[39m\u001b[22;23;24m(\u001b[22;23;24mVcmax\u001b[22;23;24m,\u001b[22;23;24m \u001b[22;23;24mCi\u001b[22;23;24m,\u001b[22;23;24m \u001b[22;23;24mΓ\u001b[22;23;24m,\u001b[22;23;24m \u001b[22;23;24mKm\u001b[22;23;24m,\u001b[22;23;24m \u001b[22;23;24mRd\u001b[22;23;24m)\u001b[38;2;102;102;102;1;23;24m:\u001b[39;22m\u001b[22;23;24menzyme_limited_photosynthesis_rate\u001b[22;23;24m \u001b[38;2;102;102;102;1;23;24m=>\u001b[39;22m\u001b[22;23;24m \u001b[38;2;148;91;176;1;23;24mbegin\u001b[39;22m\u001b[22;23;24m\n",
" \u001b[38;2;153;153;119;22;3;24m#= /Users/tomyun/.julia/packages/LeafGasExchange/I1nMc/src/c3.jl:79 =#\u001b[39;23m\u001b[22;23;24m\n",
" \u001b[22;23;24m(\u001b[22;23;24mVcmax\u001b[22;23;24m \u001b[38;2;102;102;102;1;23;24m*\u001b[39;22m\u001b[22;23;24m \u001b[22;23;24m(\u001b[22;23;24mCi\u001b[22;23;24m \u001b[38;2;102;102;102;1;23;24m-\u001b[39;22m\u001b[22;23;24m \u001b[22;23;24mΓ\u001b[22;23;24m))\u001b[22;23;24m \u001b[38;2;102;102;102;1;23;24m/\u001b[39;22m\u001b[22;23;24m \u001b[22;23;24m(\u001b[22;23;24mCi\u001b[22;23;24m \u001b[38;2;102;102;102;1;23;24m+\u001b[39;22m\u001b[22;23;24m \u001b[22;23;24mKm\u001b[22;23;24m)\u001b[22;23;24m \u001b[38;2;102;102;102;1;23;24m-\u001b[39;22m\u001b[22;23;24m \u001b[22;23;24mRd\u001b[22;23;24m\n",
" \u001b[38;2;148;91;176;1;23;24mend\u001b[39;22m\u001b[22;23;24m \u001b[38;2;102;102;102;1;23;24m~\u001b[39;22m\u001b[22;23;24m \u001b[38;2;66;102;213;22;23;24mtrack\u001b[39m\u001b[22;23;24m(\u001b[38;2;201;61;57;22;23;24mu\"μmol/m^2/s\"\u001b[39m\u001b[22;23;24m)"
]
}
],
"source": [
"@look LeafGasExchange.ModelC3BB.Ac"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"단, 각각의 모수 혹은 모수처럼 보이지만 사실은 또 다른 수식으로 표현되는 변수들이 워낙 많기 때문에 한눈에 모든 것을 파악하기는 쉽지 않습니다. 예를 들어 위에서 쓰인 `Vcmax`는 이산화탄소를 기질로 하는 RuBisCo 효소의 최대 반응속도이며, 앞의 `Amax`처럼 고정된 상수를 도입할 수도 있는 부분입니다. 하지만 온도에 따른 생화학 반응의 차이를 반영하기 위해 내부적으로는 [아레니우스 방정식(Arrhenius equation)](https://en.wikipedia.org/wiki/Arrhenius_equation)에 대입하여 계산하도록 되어 있습니다."
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\u001b[90m[doc]\u001b[39m\n",
"\n",
"\u001b[90m[code]\u001b[39m\n",
"\u001b[22;23;24m \u001b[38;2;66;102;213;22;23;24mVcmax\u001b[39m\u001b[22;23;24m(\u001b[22;23;24mVcm25\u001b[22;23;24m,\u001b[22;23;24m \u001b[22;23;24mkT\u001b[22;23;24m,\u001b[22;23;24m \u001b[22;23;24mEaVc\u001b[22;23;24m,\u001b[22;23;24m \u001b[22;23;24mkN\u001b[22;23;24m)\u001b[38;2;102;102;102;1;23;24m:\u001b[39;22m\u001b[22;23;24mmaximum_carboxylation_rate\u001b[22;23;24m \u001b[38;2;102;102;102;1;23;24m=>\u001b[39;22m\u001b[22;23;24m \u001b[38;2;148;91;176;1;23;24mbegin\u001b[39;22m\u001b[22;23;24m\n",
" \u001b[38;2;153;153;119;22;3;24m#= /Users/tomyun/.julia/packages/LeafGasExchange/I1nMc/src/c3.jl:30 =#\u001b[39;23m\u001b[22;23;24m\n",
" \u001b[22;23;24mVcm25\u001b[22;23;24m \u001b[38;2;102;102;102;1;23;24m*\u001b[39;22m\u001b[22;23;24m \u001b[38;2;66;102;213;22;23;24mkT\u001b[39m\u001b[22;23;24m(\u001b[22;23;24mEaVc\u001b[22;23;24m)\u001b[22;23;24m \u001b[38;2;102;102;102;1;23;24m*\u001b[39;22m\u001b[22;23;24m \u001b[22;23;24mkN\u001b[22;23;24m\n",
" \u001b[38;2;148;91;176;1;23;24mend\u001b[39;22m\u001b[22;23;24m \u001b[38;2;102;102;102;1;23;24m~\u001b[39;22m\u001b[22;23;24m \u001b[38;2;66;102;213;22;23;24mtrack\u001b[39m\u001b[22;23;24m(\u001b[38;2;201;61;57;22;23;24mu\"μmol/m^2/s\"\u001b[39m\u001b[22;23;24m)"
]
}
],
"source": [
"@look LeafGasExchange.ModelC3BB.Vcmax"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"이처럼 많은 변수들을 한곳에서 모두 정리하기에는 너무 복잡하기 때문에 실제 모형 명세는 관련된 변수들끼리 묶인 시스템 단위로 잘개 쪼개져 있습니다. 이러한 시스템간의 구조도는 `Cropbox.hierarchy()` 함수를 이용해 확인할 수 있습니다."
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
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"<g id=\"edge14\" class=\"edge\">\n",
"<title>4->10</title>\n",
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"<g id=\"edge15\" class=\"edge\">\n",
"<title>4->11</title>\n",
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"<g id=\"node12\" class=\"node\">\n",
"<title>12</title>\n",
"<text text-anchor=\"middle\" x=\"137.61\" y=\"-416.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Irradiance</text>\n",
"</g>\n",
"<!-- 4->12 -->\n",
"<g id=\"edge16\" class=\"edge\">\n",
"<title>4->12</title>\n",
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"</g>\n",
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"<g id=\"edge17\" class=\"edge\">\n",
"<title>4->13</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M743.15,-575.91C672.02,-568.68 444.94,-543.14 382.61,-506 343.26,-482.55 336.41,-467.78 317.61,-426 305.8,-399.74 303.84,-364.9 303.59,-349.24\"/>\n",
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"<title>14</title>\n",
"<text text-anchor=\"middle\" x=\"669.61\" y=\"-257.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">StomataBallBerry</text>\n",
"</g>\n",
"<!-- 4->14 -->\n",
"<g id=\"edge18\" class=\"edge\">\n",
"<title>4->14</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M762.82,-571.93C754.69,-544.37 720.34,-428.18 691.61,-333 684.69,-310.05 676.4,-283.03 672.25,-269.55\"/>\n",
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"<g id=\"node15\" class=\"node\">\n",
"<title>15</title>\n",
"<text text-anchor=\"middle\" x=\"808.61\" y=\"-416.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">StomataTuzet</text>\n",
"</g>\n",
"<!-- 4->15 -->\n",
"<g id=\"edge19\" class=\"edge\">\n",
"<title>4->15</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M766.29,-572C773.06,-547.66 798.52,-456.24 806.33,-428.22\"/>\n",
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"</g>\n",
"<!-- 16 -->\n",
"<g id=\"node16\" class=\"node\">\n",
"<title>16</title>\n",
"<text text-anchor=\"middle\" x=\"1073.61\" y=\"-97.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">C3</text>\n",
"</g>\n",
"<!-- 4->16 -->\n",
"<g id=\"edge20\" class=\"edge\">\n",
"<title>4->16</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M785.88,-576.35C867.3,-569.82 1158.8,-544.18 1242.61,-506 1296.27,-481.56 1343.61,-478.96 1343.61,-420 1343.61,-420 1343.61,-420 1343.61,-259 1343.61,-228.13 1130.67,-127.48 1083,-105.33\"/>\n",
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"</g>\n",
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"<g id=\"node17\" class=\"node\">\n",
"<title>17</title>\n",
"<text text-anchor=\"middle\" x=\"1073.61\" y=\"-177.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">C3Rate</text>\n",
"</g>\n",
"<!-- 4->17 -->\n",
"<g id=\"edge21\" class=\"edge\">\n",
"<title>4->17</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M767.76,-571.97C782.68,-543.62 848.58,-421.2 919.61,-333 968.63,-272.14 1039.66,-209.83 1064.57,-188.61\"/>\n",
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"</g>\n",
"<!-- 18 -->\n",
"<g id=\"node18\" class=\"node\">\n",
"<title>18</title>\n",
"<text text-anchor=\"middle\" x=\"1034.61\" y=\"-257.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">C3c</text>\n",
"</g>\n",
"<!-- 4->18 -->\n",
"<g id=\"edge22\" class=\"edge\">\n",
"<title>4->18</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M771.79,-571.71C785.23,-559.73 814.72,-532.45 835.61,-506 861.6,-473.1 864.87,-462.44 885.61,-426 908.63,-385.58 903.16,-368.15 933.61,-333 959.84,-302.73 1001.28,-278.44 1021.97,-267.42\"/>\n",
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"</g>\n",
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"<g id=\"node19\" class=\"node\">\n",
"<title>19</title>\n",
"<text text-anchor=\"middle\" x=\"1112.61\" y=\"-337.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">C3Base</text>\n",
"</g>\n",
"<!-- 4->19 -->\n",
"<g id=\"edge23\" class=\"edge\">\n",
"<title>4->19</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M785.86,-577.83C864.32,-576.71 1135.98,-568.32 1188.61,-506 1232.31,-454.26 1149.24,-373.23 1121.31,-348.45\"/>\n",
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"<g id=\"node20\" class=\"node\">\n",
"<title>20</title>\n",
"<text text-anchor=\"middle\" x=\"1112.61\" y=\"-416.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">CBase</text>\n",
"</g>\n",
"<!-- 4->20 -->\n",
"<g id=\"edge24\" class=\"edge\">\n",
"<title>4->20</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M785.85,-577.68C862.39,-576.02 1122.28,-565.99 1172.61,-506 1195.6,-478.6 1147.96,-442.6 1124.57,-427.34\"/>\n",
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"<g id=\"node21\" class=\"node\">\n",
"<title>21</title>\n",
"<text text-anchor=\"middle\" x=\"984.61\" y=\"-496.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">TemperatureDependence</text>\n",
"</g>\n",
"<!-- 4->21 -->\n",
"<g id=\"edge25\" class=\"edge\">\n",
"<title>4->21</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M781.88,-571.88C822.36,-557.53 923.17,-521.78 965.46,-506.79\"/>\n",
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"</g>\n",
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"<g id=\"node22\" class=\"node\">\n",
"<title>22</title>\n",
"<text text-anchor=\"middle\" x=\"1112.61\" y=\"-496.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">NitrogenDependence</text>\n",
"</g>\n",
"<!-- 4->22 -->\n",
"<g id=\"edge26\" class=\"edge\">\n",
"<title>4->22</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M785.86,-573.24C845.63,-559.84 1015.3,-521.81 1083.6,-506.5\"/>\n",
"<polygon fill=\"black\" stroke=\"black\" stroke-width=\"0.2\" points=\"1083.79,-507.18 1085.59,-506.06 1083.49,-505.81 1083.79,-507.18\"/>\n",
"</g>\n",
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"<g id=\"node23\" class=\"node\">\n",
"<title>23</title>\n",
"<text text-anchor=\"middle\" x=\"1073.61\" y=\"-257.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">C3j</text>\n",
"</g>\n",
"<!-- 4->23 -->\n",
"<g id=\"edge27\" class=\"edge\">\n",
"<title>4->23</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M773.3,-571.91C789.98,-560.06 827.34,-532.69 855.61,-506 946.96,-419.79 1042.76,-300.22 1067.5,-268.81\"/>\n",
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"<g id=\"node24\" class=\"node\">\n",
"<title>24</title>\n",
"<text text-anchor=\"middle\" x=\"1112.61\" y=\"-257.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">C3p</text>\n",
"</g>\n",
"<!-- 4->24 -->\n",
"<g id=\"edge28\" class=\"edge\">\n",
"<title>4->24</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M785.64,-577.99C865.91,-577.47 1151.34,-571.01 1206.61,-506 1272.27,-428.79 1152.83,-300.75 1120.41,-268.53\"/>\n",
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"<title>25</title>\n",
"<text text-anchor=\"middle\" x=\"1151.61\" y=\"-257.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">C3r</text>\n",
"</g>\n",
"<!-- 4->25 -->\n",
"<g id=\"edge29\" class=\"edge\">\n",
"<title>4->25</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M785.67,-577.92C867.49,-577.13 1162.72,-569.84 1224.61,-506 1293.35,-435.11 1187.49,-302.41 1158.58,-268.86\"/>\n",
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"<title>26</title>\n",
"<text text-anchor=\"middle\" x=\"1401.61\" y=\"-177.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Controller</text>\n",
"</g>\n",
"<!-- 4->26 -->\n",
"<g id=\"edge30\" class=\"edge\">\n",
"<title>4->26</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M785.79,-578.23C880.62,-578.87 1265.68,-576.99 1357.61,-506 1390.15,-480.88 1391.61,-461.1 1391.61,-420 1391.61,-420 1391.61,-420 1391.61,-339 1391.61,-281.49 1398.3,-212.43 1400.74,-189.13\"/>\n",
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"<title>5</title>\n",
"<text text-anchor=\"middle\" x=\"764.61\" y=\"-656.8\" font-family=\"Courier,monospace\" font-size=\"9.00\">Clock</text>\n",
"</g>\n",
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"<g id=\"edge31\" class=\"edge\">\n",
"<title>5->4</title>\n",
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"</g>\n",
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"<g id=\"edge32\" class=\"edge\">\n",
"<title>6->1</title>\n",
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"</g>\n",
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"<g id=\"edge33\" class=\"edge\">\n",
"<title>6->2</title>\n",
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"<g id=\"edge34\" class=\"edge\">\n",
"<title>6->3</title>\n",
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"</g>\n",
"<!-- 6->8 -->\n",
"<g id=\"edge35\" class=\"edge\">\n",
"<title>6->8</title>\n",
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"<!-- 6->10 -->\n",
"<g id=\"edge36\" class=\"edge\">\n",
"<title>6->10</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M452.04,-491.65C477.22,-466.79 569.08,-376.08 596.71,-348.81\"/>\n",
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"<g id=\"edge37\" class=\"edge\">\n",
"<title>6->11</title>\n",
"<path fill=\"none\" stroke=\"black\" stroke-width=\"0.2\" d=\"M433.74,-491.83C410.86,-479.84 359.24,-452.24 317.61,-426 275.11,-399.21 226.89,-363.71 206.52,-348.47\"/>\n",
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"<!-- 6->13 -->\n",
"<g id=\"edge38\" class=\"edge\">\n",
"<title>6->13</title>\n",
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"<g id=\"edge39\" class=\"edge\">\n",
"<title>6->14</title>\n",
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"<g id=\"edge40\" class=\"edge\">\n",
"<title>7->2</title>\n",
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"<g id=\"edge41\" class=\"edge\">\n",
"<title>8->2</title>\n",
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"<g id=\"edge42\" class=\"edge\">\n",
"<title>9->8</title>\n",
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"<g id=\"edge43\" class=\"edge\">\n",
"<title>9->10</title>\n",
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"<!-- 10->2 -->\n",
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"<title>10->2</title>\n",
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"<g id=\"edge45\" class=\"edge\">\n",
"<title>10->14</title>\n",
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"<g id=\"edge46\" class=\"edge\">\n",
"<title>11->2</title>\n",
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"<!-- 12->2 -->\n",
"<g id=\"edge47\" class=\"edge\">\n",
"<title>12->2</title>\n",
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"<g id=\"edge48\" class=\"edge\">\n",
"<title>13->2</title>\n",
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"<g id=\"edge49\" class=\"edge\">\n",
"<title>14->1</title>\n",
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"text/plain": [
"\u001b[90m{\u001b[39m\u001b[95mModelC3BB\u001b[39m\u001b[90m, \u001b[39m\u001b[95mModelBase\u001b[39m\u001b[90m, \u001b[39m\u001b[95mWeather\u001b[39m\u001b[90m, \u001b[39m\u001b[95mContext\u001b[39m\u001b[90m, \u001b[39m\u001b[95mClock\u001b[39m\u001b[90m, \u001b[39m\u001b[95mVaporPressure\u001b[39m\u001b[90m, \u001b[39m\u001b[95mNitrogen\u001b[39m\u001b[90m, \u001b[39m\u001b[95mBoundaryLayer\u001b[39m\u001b[90m, \u001b[39m\u001b[95mDiffusion\u001b[39m\u001b[90m, \u001b[39m\u001b[95mStomataBase\u001b[39m\u001b[90m, \u001b[39m\u001b[95mIntercellularSpace\u001b[39m\u001b[90m, \u001b[39m\u001b[95mIrradiance\u001b[39m\u001b[90m, \u001b[39m\u001b[95mEnergyBalance\u001b[39m\u001b[90m, \u001b[39m\u001b[95mStomataBallBerry\u001b[39m\u001b[90m, \u001b[39m\u001b[95mStomataTuzet\u001b[39m\u001b[90m, \u001b[39m\u001b[95mC3\u001b[39m\u001b[90m, \u001b[39m\u001b[95mC3Rate\u001b[39m\u001b[90m, \u001b[39m\u001b[95mC3c\u001b[39m\u001b[90m, \u001b[39m\u001b[95mC3Base\u001b[39m\u001b[90m, \u001b[39m\u001b[95mCBase\u001b[39m\u001b[90m, \u001b[39m\u001b[95mTemperatureDependence\u001b[39m\u001b[90m, \u001b[39m\u001b[95mNitrogenDependence\u001b[39m\u001b[90m, \u001b[39m\u001b[95mC3j\u001b[39m\u001b[90m, \u001b[39m\u001b[95mC3p\u001b[39m\u001b[90m, \u001b[39m\u001b[95mC3r\u001b[39m\u001b[90m, \u001b[39m\u001b[95mController\u001b[39m\u001b[90m}\u001b[39m"
]
},
"execution_count": 35,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Cropbox.hierarchy(LeafGasExchange.ModelC3BB)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"우측에는 방금 살펴보았던 C3 광합성 관련 시스템들이 보입니다. 제한 요인의 종류에 따라 `C3c`, `C3j`, `C3p`와 같이 서로 다른 시스템이 정의되어 있는 것을 알 수 있습니다. 좌측에는 기공전도도(`StomataBallBerry`) 및 에너지 균형(`EnergyBalance`) 관련 시스템들이 보입니다. 이러한 시스템들은 몇몇 공통되는 변수들을 이용해 정의되어 있으며, 최종적으로는 이러한 시스템들이 모두 묶여 해당 변수들이 서로 공유되는 형태로 통합(coupling)이 이루어지게 됩니다. 참고로, 지난 시간 강의자료의 마지막에 나오는 내부구조 안내에서 설명하는 믹스인(mix-in)을 통한 확장의 예라고 보시면 되겠습니다."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"하지만 이렇게 모형이 어떻게 만들어져 있는지에 대한 기술적인 부분은 모형을 불러서 사용하는 입장에서는 크게 중요하지 않은 부분일 수도 있습니다. 위에서 굉장히 복잡한 모형의 일면을 보여드렸지만, 실제 사용하는 방법은 앞서 다루었던 간단한 모형들과 크게 다를 바 없기 때문입니다."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"먼저 필요한 모수들을 살펴보겠습니다."
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Config for 1 system:\n",
" \u001b[95mModelC3BB\u001b[39m\n",
" \u001b[94mPFD \u001b[39m\u001b[90m = \u001b[39mnothing\n",
" \u001b[94mCO2 \u001b[39m\u001b[90m = \u001b[39mnothing\n",
" \u001b[94mRH \u001b[39m\u001b[90m = \u001b[39mnothing\n",
" \u001b[94mT_air \u001b[39m\u001b[90m = \u001b[39mnothing\n",
" \u001b[94mwind \u001b[39m\u001b[90m = \u001b[39mnothing\n",
" \u001b[94mP_air \u001b[39m\u001b[90m = \u001b[39m100 kPa\n",
" \u001b[94mSPAD \u001b[39m\u001b[90m = \u001b[39m60\n",
" \u001b[94m(Nitrogen) _a\u001b[39m\u001b[90m = \u001b[39m0.0004 g m⁻²\n",
" \u001b[94m(Nitrogen) _b\u001b[39m\u001b[90m = \u001b[39m0.012 g m⁻²\n",
" \u001b[94m(Nitrogen) _c\u001b[39m\u001b[90m = \u001b[39m0 g m⁻²\n",
" \u001b[94mN \u001b[39m\u001b[90m = \u001b[39mmissing\n",
" \u001b[94mDw \u001b[39m\u001b[90m = \u001b[39m24.2 mm² s⁻¹\n",
" \u001b[94mDc \u001b[39m\u001b[90m = \u001b[39m14.7 mm² s⁻¹\n",
" \u001b[94mDh \u001b[39m\u001b[90m = \u001b[39m21.5 mm² s⁻¹\n",
" \u001b[94mDm \u001b[39m\u001b[90m = \u001b[39m15.1 mm² s⁻¹\n",
" \u001b[94mw \u001b[39m\u001b[90m = \u001b[39m10 cm\n",
" \u001b[94msr \u001b[39m\u001b[90m = \u001b[39m1.0\n",
" \u001b[94mv \u001b[39m\u001b[90m = \u001b[39mmissing\n",
" \u001b[94mκ \u001b[39m\u001b[90m = \u001b[39mmissing\n",
" \u001b[94mg0 \u001b[39m\u001b[90m = \u001b[39m0.017 mol bar⁻¹ m⁻² s⁻¹\n",
" \u001b[94mg1 \u001b[39m\u001b[90m = \u001b[39m4.53\n",
" \u001b[94mdrb \u001b[39m\u001b[90m = \u001b[39mmissing\n",
" \u001b[94mdra \u001b[39m\u001b[90m = \u001b[39mmissing\n",
" \u001b[94mδ \u001b[39m\u001b[90m = \u001b[39m0.15\n",
" \u001b[94mf \u001b[39m\u001b[90m = \u001b[39m0.15\n",
" \u001b[94mϵ \u001b[39m\u001b[90m = \u001b[39m0.97\n",
" \u001b[94mλ \u001b[39m\u001b[90m = \u001b[39m44 kJ mol⁻¹\n",
" \u001b[94mCp \u001b[39m\u001b[90m = \u001b[39m29.3 J K⁻¹ mol⁻¹\n",
" \u001b[94mα_s \u001b[39m\u001b[90m = \u001b[39m0.5\n",
" \u001b[94mWP_leaf \u001b[39m\u001b[90m = \u001b[39m0 MPa\n",
" \u001b[94mΨf \u001b[39m\u001b[90m = \u001b[39m-2.0 MPa\n",
" \u001b[94msf \u001b[39m\u001b[90m = \u001b[39m2.3 MPa⁻¹\n",
" \u001b[94mTb \u001b[39m\u001b[90m = \u001b[39m25 °C\n",
" \u001b[94mQ10 \u001b[39m\u001b[90m = \u001b[39m2\n",
" \u001b[94ms \u001b[39m\u001b[90m = \u001b[39m2.9 m² g⁻¹\n",
" \u001b[94mN0 \u001b[39m\u001b[90m = \u001b[39m0.25 g m⁻²\n",
" \u001b[94mKc25 \u001b[39m\u001b[90m = \u001b[39m404.9 μbar\n",
" \u001b[94mEac \u001b[39m\u001b[90m = \u001b[39m79.43 kJ mol⁻¹\n",
" \u001b[94mKo25 \u001b[39m\u001b[90m = \u001b[39m278.4 mbar\n",
" \u001b[94mEao \u001b[39m\u001b[90m = \u001b[39m36.38 kJ mol⁻¹\n",
" \u001b[94mOm \u001b[39m\u001b[90m = \u001b[39m210 mbar\n",
" \u001b[94mVcm25 \u001b[39m\u001b[90m = \u001b[39m108.4 μmol m⁻² s⁻¹\n",
" \u001b[94mEaVc \u001b[39m\u001b[90m = \u001b[39m52.1573 kJ mol⁻¹\n",
" \u001b[94mJm25 \u001b[39m\u001b[90m = \u001b[39m169.0 μmol m⁻² s⁻¹\n",
" \u001b[94mHaj \u001b[39m\u001b[90m = \u001b[39m23.9976 kJ mol⁻¹\n",
" \u001b[94mHdj \u001b[39m\u001b[90m = \u001b[39m200 kJ mol⁻¹\n",
" \u001b[94mToj \u001b[39m\u001b[90m = \u001b[39m42.8 °C\n",
" \u001b[94mθ \u001b[39m\u001b[90m = \u001b[39m0.7\n",
" \u001b[94mTp25 \u001b[39m\u001b[90m = \u001b[39m16.03 μmol m⁻² s⁻¹\n",
" \u001b[94mEaTp \u001b[39m\u001b[90m = \u001b[39m47.1 kJ mol⁻¹\n",
" \u001b[94mRd25 \u001b[39m\u001b[90m = \u001b[39m1.08 μmol m⁻² s⁻¹\n",
" \u001b[94mEar \u001b[39m\u001b[90m = \u001b[39m49.39 kJ mol⁻¹\n",
" \u001b[94mΓ25 \u001b[39m\u001b[90m = \u001b[39m42.75 μbar\n",
" \u001b[94mEag \u001b[39m\u001b[90m = \u001b[39m37.83 kJ mol⁻¹"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"parameters(LeafGasExchange.ModelC3BB)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"광량(`PFD`)이나 기온(`T_air`) 등 환경 조건에 대한 모수들은 기본값이 없으므로 별도의 설정을 만들어서 넣어주도록 하겠습니다."
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Config for 1 system:\n",
" \u001b[95mWeather\u001b[39m\n",
" \u001b[94mPFD \u001b[39m\u001b[90m = \u001b[39m1500\n",
" \u001b[94mCO2 \u001b[39m\u001b[90m = \u001b[39m400\n",
" \u001b[94mRH \u001b[39m\u001b[90m = \u001b[39m60\n",
" \u001b[94mT_air\u001b[39m\u001b[90m = \u001b[39m30\n",
" \u001b[94mwind \u001b[39m\u001b[90m = \u001b[39m2.0"
]
},
"execution_count": 37,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ge_config = @config :Weather => (\n",
" PFD = 1500,\n",
" CO2 = 400,\n",
" RH = 60,\n",
" T_air = 30,\n",
" wind = 2.0,\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"이제 다른 모형과 동일한 방식으로 `visualize()` 함수를 이용하여 그래프를 그릴 수 있습니다. 예를 들어 세포내 이산화탄소 분압(intercellular $[\\mathrm{CO_2}]$; $C_i$)에 따른 순광합성율(`A_net`)을 각 제한 요인에 따른 잠재 광합성율(`Ac`, `Aj`, `Ap`)과 함께 확인해보겠습니다. 보통 A-Ci 곡선이라고 부르기도 합니다."
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {},
"outputs": [
{
"data": {
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"visualize(LeafGasExchange.ModelC3BB, :Ci, [:A_net, :Ac, :Aj, :Ap];\n",
" config = ge_config,\n",
" xstep = :Weather => :CO2 => 10:10:1500,\n",
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")"
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"아래에는 다양한 환경 요인들을 직접 조정하여 광합성 곡선을 그려볼 수 있도록 준비해보았습니다."
]
},
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]
},
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" '<div style=\"padding: 1em; background-color: #f8d6da; border: 1px solid #f5c6cb; font-weight: bold;\">' +\n",
" '<p><strong>WebIO not detected.</strong></p>' +\n",
" '<p>Please read ' +\n",
" '<a href=\"https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/\" target=\"_blank\">the troubleshooting guide</a> ' +\n",
" 'for more information on how to resolve this issue.</p>' +\n",
" '<p><a href=\"https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/\" target=\"_blank\">https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/</a></p>' +\n",
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" );\n",
" return;\n",
" }\n",
" WebIO.mount(\n",
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" titles=Dict{Symbol, AbstractString}()\n",
")\n",
", Gadfly.ScaleElement[], Gadfly.StatisticElement[], Gadfly.Coord.Cartesian([:x, :xmin, :xmax, :xintercept], [:y, :ymin, :ymax, :yintercept, :middle, :lower_hinge, :upper_hinge, :lower_fence, :upper_fence, :outliers], 0, 800, 0, 60, false, false, false, nothing, false), Gadfly.GuideElement[Gadfly.Guide.Title(\"\"), Gadfly.Guide.XLabel(\"Ci (μbar)\", :auto), Gadfly.Guide.YLabel(\" (μmol m⁻² s⁻¹)\", :auto), Gadfly.Guide.ManualDiscreteKey(\"\", [\"A_net\", \"Ac\", \"Aj\", \"Ap\"], Any[], ColorTypes.Colorant[LCHab{Float32}(70.0f0,60.0f0,240.0f0), LCHab{Float32}(80.0f0,70.000015f0,100.43479f0), LCHab{Float32}(65.89944f0,62.21457f0,353.99814f0), LCHab{Float32}(66.303474f0,50.090958f0,168.24765f0)], Function[], Measures.Measure[], true)], Gadfly.Theme(LCHab{Float32}(70.0f0,60.0f0,240.0f0), 0.7mm, 0.45mm, 1.8mm, Gadfly.Scale.default_discrete_sizes, Gadfly.Scale.default_continuous_sizes, Gadfly.Scale.default_discrete_colors, Function[Compose.circle, Gadfly.Shape.square, Gadfly.Shape.diamond, Gadfly.Shape.cross, Gadfly.Shape.xcross, Gadfly.Shape.utriangle, Gadfly.Shape.dtriangle, Gadfly.Shape.star1, Gadfly.Shape.star2, Gadfly.Shape.hexagon, Gadfly.Shape.octagon, Gadfly.Shape.hline, Gadfly.Shape.vline, Gadfly.Shape.ltriangle, Gadfly.Shape.rtriangle], 0.3mm, [:solid, :dash, :dot, :dashdot, :dashdotdot, :ldash, :ldashdash, :ldashdot, :ldashdashdot], [1.0, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, 0.0], nothing, nothing, 0.3mm, 0.0, RGB{N0f8}(1.0,1.0,1.0), Measures.AbsoluteLength[5.0mm, 5.0mm, 5.0mm, 0.0mm], RGB{N0f8}(0.816,0.816,0.878), Measures.AbsoluteLength[0.5mm, 0.5mm], RGB{N0f8}(0.627,0.627,0.627), 0.2mm, 0, \"'PT Sans Caption','Helvetica Neue','Helvetica',sans-serif\", 2.822222222222222mm, RGB{N0f8}(0.424,0.376,0.42), \"'PT Sans','Helvetica Neue','Helvetica',sans-serif\", 3.5277777777777777mm, RGB{N0f8}(0.337,0.29,0.333), \"'PT Sans Caption','Helvetica Neue','Helvetica',sans-serif\", 2.822222222222222mm, RGB{N0f8}(0.298,0.251,0.294), \"'PT Sans','Helvetica Neue','Helvetica',sans-serif\", 3.175mm, RGB{N0f8}(0.212,0.165,0.208), \"'PT Sans','Helvetica Neue','Helvetica',sans-serif\", 2.822222222222222mm, RGB{N0f8}(0.298,0.251,0.294), 40, -0.05mm, 1.0mm, 3.0mm, Gadfly.default_stroke_color, 0.3mm, Cropbox.var\"#504#513\"(), Gadfly.default_continuous_highlight_color, Gadfly.default_lowlight_color, Gadfly.default_middle_color, 0.6mm, :left, :square, nothing, nothing, nothing, :right, nothing, 2.0mm, 1000, 10.0, 0.5, 0.2, 1.0mm, 4, Gadfly.Scale.DiscreteColorScale(Gadfly.Scale.default_discrete_colors, nothing, nothing, true), Gadfly.Scale.ContinuousColorScale(Gadfly.Scale.var\"#69#73\"{Int64, Int64, Int64, Int64, Float64, Int64}(100, 40, 260, 10, 1.5, 70), Gadfly.Scale.ContinuousScaleTransform(identity, identity, Gadfly.Scale.identity_formatter), nothing, nothing)), Dict{Symbol, Any}())], Dict{Symbol, Any}(:style => Dict(\"display\" => \"flex\", \"flex-direction\" => \"column\")))"
]
},
"execution_count": 39,
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"source": [
"manipulate(LeafGasExchange.ModelC3BB, :Ci, [:A_net, :Ac, :Aj, :Ap],\n",
" config = ge_config,\n",
" parameters = :Weather => (;\n",
" PFD = 0:20:2000,\n",
" T_air = -10:1:50,\n",
" ),\n",
" xstep = :Weather => :CO2 => 10:10:1500,\n",
" xlim = (0, 800),\n",
" ylim = (0, 60),\n",
" kind = :line,\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### A-Q"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"광량(`PFD`)은 전자전달계의 제한으로 인한 잠재 광합성율(`Aj`)과 직접적인 연관을 가집니다. 어떤 상황에서 이러한 제한이 두드러지게 되는지 다양한 조건들을 실험해보세요."
]
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" // Some integrations (namely, IJulia/Jupyter) use an alternate render pathway than\n",
" // just putting the html on the page. If WebIO isn't defined, then it's pretty likely\n",
" // that we're in one of those situations and the integration just isn't installed\n",
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" '<div style=\"padding: 1em; background-color: #f8d6da; border: 1px solid #f5c6cb; font-weight: bold;\">' +\n",
" '<p><strong>WebIO not detected.</strong></p>' +\n",
" '<p>Please read ' +\n",
" '<a href=\"https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/\" target=\"_blank\">the troubleshooting guide</a> ' +\n",
" 'for more information on how to resolve this issue.</p>' +\n",
" '<p><a href=\"https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/\" target=\"_blank\">https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/</a></p>' +\n",
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" );\n",
" return;\n",
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" WebIO.mount(\n",
" document.querySelector('[data-webio-mountpoint=\"4089329378207958985\"]'),\n",
" {\"props\":{\"style\":{\"display\":\"flex\",\"flex-direction\":\"column\"}},\"nodeType\":\"DOM\",\"type\":\"node\",\"instanceArgs\":{\"namespace\":\"html\",\"tag\":\"div\"},\"children\":[{\"props\":{\"style\":{\"color\":\"darkorchid\",\"font-family\":\"monospace\"}},\"nodeType\":\"DOM\",\"type\":\"node\",\"instanceArgs\":{\"namespace\":\"html\",\"tag\":\"div\"},\"children\":[\"Weather\"]},{\"props\":{\"className\":\"field interact-widget\"},\"nodeType\":\"DOM\",\"type\":\"node\",\"instanceArgs\":{\"namespace\":\"html\",\"tag\":\"div\"},\"children\":[{\"props\":{},\"nodeType\":\"Scope\",\"type\":\"node\",\"instanceArgs\":{\"imports\":{\"data\":[{\"name\":\"knockout\",\"type\":\"js\",\"url\":\"\\/assetserver\\/c853cad7a3e123085fa7960dd53fd3d4c05dc309-knockout.js\"},{\"name\":\"knockout_punches\",\"type\":\"js\",\"url\":\"\\/assetserver\\/fab584ebb4dc64eb3ddf5ca7c73b2e76fd533845-knockout_punches.js\"},{\"name\":null,\"type\":\"js\",\"url\":\"\\/assetserver\\/f2016dce9a0d470782f38e7aa4873f823db566c0-all.js\"},{\"name\":null,\"type\":\"css\",\"url\":\"\\/assetserver\\/805f638970bef13ab5dd6d32d993673e39af56c0-style.css\"},{\"name\":null,\"type\":\"css\",\"url\":\"\\/assetserver\\/a99a2e54e5d65dd4545013d46edee359c5b0afdb-bulma_confined.min.css\"}],\"type\":\"async_block\"},\"id\":\"5750456328989607007\",\"handlers\":{\"changes\":[\"(function (val){return (val!=this.model[\\\"changes\\\"]()) ? (this.valueFromJulia[\\\"changes\\\"]=true, this.model[\\\"changes\\\"](val)) : undefined})\"],\"index\":[\"(function (val){return (val!=this.model[\\\"index\\\"]()) ? (this.valueFromJulia[\\\"index\\\"]=true, this.model[\\\"index\\\"](val)) : undefined})\"]},\"systemjs_options\":null,\"mount_callbacks\":[\"function () {\\n var handler = (function (ko, koPunches) {\\n ko.punches.enableAll();\\n ko.bindingHandlers.numericValue = {\\n init: function(element, valueAccessor, allBindings, data, context) {\\n var stringified = ko.observable(ko.unwrap(valueAccessor()));\\n stringified.subscribe(function(value) {\\n var val = parseFloat(value);\\n if (!isNaN(val)) {\\n valueAccessor()(val);\\n }\\n });\\n valueAccessor().subscribe(function(value) {\\n var str = JSON.stringify(value);\\n if ((str == \\\"0\\\") && ([\\\"-0\\\", \\\"-0.\\\"].indexOf(stringified()) >= 0))\\n return;\\n if ([\\\"null\\\", \\\"\\\"].indexOf(str) >= 0)\\n return;\\n stringified(str);\\n });\\n ko.applyBindingsToNode(\\n element,\\n {\\n value: stringified,\\n valueUpdate: allBindings.get('valueUpdate'),\\n },\\n context,\\n );\\n }\\n };\\n var json_data = {\\\"formatted_vals\\\":[\\\"10\\\",\\\"20\\\",\\\"30\\\",\\\"40\\\",\\\"50\\\",\\\"60\\\",\\\"70\\\",\\\"80\\\",\\\"90\\\",\\\"100\\\",\\\"110\\\",\\\"120\\\",\\\"130\\\",\\\"140\\\",\\\"150\\\",\\\"160\\\",\\\"170\\\",\\\"180\\\",\\\"190\\\",\\\"200\\\",\\\"210\\\",\\\"220\\\",\\\"230\\\",\\\"240\\\",\\\"250\\\",\\\"260\\\",\\\"270\\\",\\\"280\\\",\\\"290\\\",\\\"300\\\",\\\"310\\\",\\\"320\\\",\\\"330\\\",\\\"340\\\",\\\"350\\\",\\\"360\\\",\\\"370\\\",\\\"380\\\",\\\"390\\\",\\\"400\\\",\\\"410\\\",\\\"420\\\",\\\"430\\\",\\\"440\\\",\\\"450\\\",\\\"460\\\",\\\"470\\\",\\\"480\\\",\\\"490\\\",\\\"500\\\",\\\"510\\\",\\\"520\\\",\\\"530\\\",\\\"540\\\",\\\"550\\\",\\\"560\\\",\\\"570\\\",\\\"580\\\",\\\"590\\\",\\\"600\\\",\\\"610\\\",\\\"620\\\",\\\"630\\\",\\\"640\\\",\\\"650\\\",\\\"660\\\",\\\"670\\\",\\\"680\\\",\\\"690\\\",\\\"700\\\",\\\"710\\\",\\\"720\\\",\\\"730\\\",\\\"740\\\",\\\"750\\\",\\\"760\\\",\\\"770\\\",\\\"780\\\",\\\"790\\\",\\\"800\\\",\\\"810\\\",\\\"820\\\",\\\"830\\\",\\\"840\\\",\\\"850\\\",\\\"860\\\",\\\"870\\\",\\\"880\\\",\\\"890\\\",\\\"900\\\",\\\"910\\\",\\\"920\\\",\\\"930\\\",\\\"940\\\",\\\"950\\\",\\\"960\\\",\\\"970\\\",\\\"980\\\",\\\"990\\\",\\\"1000\\\",\\\"1010\\\",\\\"1020\\\",\\\"1030\\\",\\\"1040\\\",\\\"1050\\\",\\\"1060\\\",\\\"1070\\\",\\\"1080\\\",\\\"1090\\\",\\\"1100\\\",\\\"1110\\\",\\\"1120\\\",\\\"1130\\\",\\\"1140\\\",\\\"1150\\\",\\\"1160\\\",\\\"1170\\\",\\\"1180\\\",\\\"1190\\\",\\\"1200\\\",\\\"1210\\\",\\\"1220\\\",\\\"1230\\\",\\\"1240\\\",\\\"1250\\\",\\\"1260\\\",\\\"1270\\\",\\\"1280\\\",\\\"1290\\\",\\\"1300\\\",\\\"1310\\\",\\\"1320\\\",\\\"1330\\\",\\\"1340\\\",\\\"1350\\\",\\\"1360\\\",\\\"1370\\\",\\\"1380\\\",\\\"1390\\\",\\\"1400\\\",\\\"1410\\\",\\\"1420\\\",\\\"1430\\\",\\\"1440\\\",\\\"1450\\\",\\\"1460\\\",\\\"1470\\\",\\\"1480\\\",\\\"1490\\\",\\\"1500\\\"],\\\"changes\\\":WebIO.getval({\\\"name\\\":\\\"changes\\\",\\\"scope\\\":\\\"5750456328989607007\\\",\\\"id\\\":\\\"12471372383889254924\\\",\\\"type\\\":\\\"observable\\\"}),\\\"index\\\":WebIO.getval({\\\"name\\\":\\\"index\\\",\\\"scope\\\":\\\"5750456328989607007\\\",\\\"id\\\":\\\"16650279224431794842\\\",\\\"type\\\":\\\"observable\\\"})};\\n var self = this;\\n function AppViewModel() {\\n for (var key in json_data) {\\n var el = json_data[key];\\n this[key] = Array.isArray(el) ? ko.observableArray(el) : ko.observable(el);\\n }\\n \\n [this[\\\"formatted_val\\\"]=ko.computed( function(){\\n return this.formatted_vals()[parseInt(this.index())-(1)];\\n }\\n,this)]\\n [this[\\\"changes\\\"].subscribe((function (val){!(this.valueFromJulia[\\\"changes\\\"]) ? (WebIO.setval({\\\"name\\\":\\\"changes\\\",\\\"scope\\\":\\\"5750456328989607007\\\",\\\"id\\\":\\\"12471372383889254924\\\",\\\"type\\\":\\\"observable\\\"},val)) : undefined; return this.valueFromJulia[\\\"changes\\\"]=false}),self),this[\\\"index\\\"].subscribe((function (val){!(this.valueFromJulia[\\\"index\\\"]) ? (WebIO.setval({\\\"name\\\":\\\"index\\\",\\\"scope\\\":\\\"5750456328989607007\\\",\\\"id\\\":\\\"16650279224431794842\\\",\\\"type\\\":\\\"observable\\\"},val)) : undefined; return this.valueFromJulia[\\\"index\\\"]=false}),self)]\\n \\n }\\n self.model = new AppViewModel();\\n self.valueFromJulia = {};\\n for (var key in json_data) {\\n self.valueFromJulia[key] = false;\\n }\\n ko.applyBindings(self.model, self.dom);\\n}\\n);\\n (WebIO.importBlock({\\\"data\\\":[{\\\"name\\\":\\\"knockout\\\",\\\"type\\\":\\\"js\\\",\\\"url\\\":\\\"\\/assetserver\\/c853cad7a3e123085fa7960dd53fd3d4c05dc309-knockout.js\\\"},{\\\"name\\\":\\\"knockout_punches\\\",\\\"type\\\":\\\"js\\\",\\\"url\\\":\\\"\\/assetserver\\/fab584ebb4dc64eb3ddf5ca7c73b2e76fd533845-knockout_punches.js\\\"}],\\\"type\\\":\\\"async_block\\\"})).then((imports) => handler.apply(this, imports));\\n}\\n\"],\"observables\":{\"changes\":{\"sync\":true,\"id\":\"12471372383889254924\",\"value\":0},\"index\":{\"sync\":true,\"id\":\"16650279224431794842\",\"value\":40}}},\"children\":[{\"props\":{\"className\":\"interact-flex-row interact-widget\",\"style\":{\"font-family\":\"monospace\",\"width\":\"25%\"}},\"nodeType\":\"DOM\",\"type\":\"node\",\"instanceArgs\":{\"namespace\":\"html\",\"tag\":\"div\"},\"children\":[{\"props\":{\"className\":\"interact-flex-row-left\"},\"nodeType\":\"DOM\",\"type\":\"node\",\"instanceArgs\":{\"namespace\":\"html\",\"tag\":\"div\"},\"children\":[{\"props\":{\"className\":\"interact \",\"style\":{\"padding\":\"5px 10px 0px 10px\",\"color\":\"royalblue\"}},\"nodeType\":\"DOM\",\"type\":\"node\",\"instanceArgs\":{\"namespace\":\"html\",\"tag\":\"label\"},\"children\":[\"CO2\"]}]},{\"props\":{\"className\":\"interact-flex-row-center\"},\"nodeType\":\"DOM\",\"type\":\"node\",\"instanceArgs\":{\"namespace\":\"html\",\"tag\":\"div\"},\"children\":[{\"props\":{\"max\":150,\"min\":1,\"attributes\":{\"type\":\"range\",\"data-bind\":\"numericValue: index, valueUpdate: 'input', event: {change: function (){this.changes(this.changes()+1)}}\",\"orient\":\"horizontal\"},\"step\":1,\"className\":\"slider slider is-fullwidth\",\"style\":{}},\"nodeType\":\"DOM\",\"type\":\"node\",\"instanceArgs\":{\"namespace\":\"html\",\"tag\":\"input\"},\"children\":[]}]},{\"props\":{\"className\":\"interact-flex-row-right\"},\"nodeType\":\"DOM\",\"type\":\"node\",\"instanceArgs\":{\"namespace\":\"html\",\"tag\":\"div\"},\"children\":[{\"props\":{\"attributes\":{\"data-bind\":\"text: formatted_val\"}},\"nodeType\":\"DOM\",\"type\":\"node\",\"instanceArgs\":{\"namespace\":\"html\",\"tag\":\"p\"},\"children\":[]}]}]}]}]},{\"props\":{\"className\":\"field interact-widget\"},\"nodeType\":\"DOM\",\"type\":\"node\",\"instanceArgs\":{\"namespace\":\"html\",\"tag\":\"div\"},\"children\":[{\"props\":{},\"nodeType\":\"Scope\",\"type\":\"node\",\"instanceArgs\":{\"imports\":{\"data\":[{\"name\":\"knockout\",\"type\":\"js\",\"url\":\"\\/assetserver\\/c853cad7a3e123085fa7960dd53fd3d4c05dc309-knockout.js\"},{\"name\":\"knockout_punches\",\"type\":\"js\",\"url\":\"\\/assetserver\\/fab584ebb4dc64eb3ddf5ca7c73b2e76fd533845-knockout_punches.js\"},{\"name\":null,\"type\":\"js\",\"url\":\"\\/assetserver\\/f2016dce9a0d470782f38e7aa4873f823db566c0-all.js\"},{\"name\":null,\"type\":\"css\",\"url\":\"\\/assetserver\\/805f638970bef13ab5dd6d32d993673e39af56c0-style.css\"},{\"name\":null,\"type\":\"css\",\"url\":\"\\/assetserver\\/a99a2e54e5d65dd4545013d46edee359c5b0afdb-bulma_confined.min.css\"}],\"type\":\"async_block\"},\"id\":\"15774691736578578409\",\"handlers\":{\"changes\":[\"(function (val){return (val!=this.model[\\\"changes\\\"]()) ? (this.valueFromJulia[\\\"changes\\\"]=true, this.model[\\\"changes\\\"](val)) : undefined})\"],\"index\":[\"(function (val){return (val!=this.model[\\\"index\\\"]()) ? (this.valueFromJulia[\\\"index\\\"]=true, this.model[\\\"index\\\"](val)) : undefined})\"]},\"systemjs_options\":null,\"mount_callbacks\":[\"function () {\\n var handler = (function (ko, koPunches) {\\n ko.punches.enableAll();\\n ko.bindingHandlers.numericValue = {\\n init: function(element, valueAccessor, allBindings, data, context) {\\n var stringified = ko.observable(ko.unwrap(valueAccessor()));\\n stringified.subscribe(function(value) {\\n var val = parseFloat(value);\\n if (!isNaN(val)) {\\n valueAccessor()(val);\\n }\\n });\\n valueAccessor().subscribe(function(value) {\\n var str = JSON.stringify(value);\\n if ((str == \\\"0\\\") && ([\\\"-0\\\", \\\"-0.\\\"].indexOf(stringified()) >= 0))\\n return;\\n if ([\\\"null\\\", \\\"\\\"].indexOf(str) >= 0)\\n return;\\n stringified(str);\\n });\\n ko.applyBindingsToNode(\\n element,\\n {\\n value: stringified,\\n valueUpdate: allBindings.get('valueUpdate'),\\n },\\n context,\\n );\\n }\\n };\\n var json_data = {\\\"formatted_vals\\\":[\\\"-10\\\",\\\"-9\\\",\\\"-8\\\",\\\"-7\\\",\\\"-6\\\",\\\"-5\\\",\\\"-4\\\",\\\"-3\\\",\\\"-2\\\",\\\"-1\\\",\\\"0\\\",\\\"1\\\",\\\"2\\\",\\\"3\\\",\\\"4\\\",\\\"5\\\",\\\"6\\\",\\\"7\\\",\\\"8\\\",\\\"9\\\",\\\"10\\\",\\\"11\\\",\\\"12\\\",\\\"13\\\",\\\"14\\\",\\\"15\\\",\\\"16\\\",\\\"17\\\",\\\"18\\\",\\\"19\\\",\\\"20\\\",\\\"21\\\",\\\"22\\\",\\\"23\\\",\\\"24\\\",\\\"25\\\",\\\"26\\\",\\\"27\\\",\\\"28\\\",\\\"29\\\",\\\"30\\\",\\\"31\\\",\\\"32\\\",\\\"33\\\",\\\"34\\\",\\\"35\\\",\\\"36\\\",\\\"37\\\",\\\"38\\\",\\\"39\\\",\\\"40\\\",\\\"41\\\",\\\"42\\\",\\\"43\\\",\\\"44\\\",\\\"45\\\",\\\"46\\\",\\\"47\\\",\\\"48\\\",\\\"49\\\",\\\"50\\\"],\\\"changes\\\":WebIO.getval({\\\"name\\\":\\\"changes\\\",\\\"scope\\\":\\\"15774691736578578409\\\",\\\"id\\\":\\\"7517364805952464211\\\",\\\"type\\\":\\\"observable\\\"}),\\\"index\\\":WebIO.getval({\\\"name\\\":\\\"index\\\",\\\"scope\\\":\\\"15774691736578578409\\\",\\\"id\\\":\\\"16589659139012014219\\\",\\\"type\\\":\\\"observable\\\"})};\\n var self = this;\\n function AppViewModel() {\\n for (var key in json_data) {\\n var el = json_data[key];\\n this[key] = Array.isArray(el) ? ko.observableArray(el) : ko.observable(el);\\n }\\n \\n [this[\\\"formatted_val\\\"]=ko.computed( function(){\\n return this.formatted_vals()[parseInt(this.index())-(1)];\\n }\\n,this)]\\n [this[\\\"changes\\\"].subscribe((function (val){!(this.valueFromJulia[\\\"changes\\\"]) ? (WebIO.setval({\\\"name\\\":\\\"changes\\\",\\\"scope\\\":\\\"15774691736578578409\\\",\\\"id\\\":\\\"7517364805952464211\\\",\\\"type\\\":\\\"observable\\\"},val)) : undefined; return this.valueFromJulia[\\\"changes\\\"]=false}),self),this[\\\"index\\\"].subscribe((function (val){!(this.valueFromJulia[\\\"index\\\"]) ? (WebIO.setval({\\\"name\\\":\\\"index\\\",\\\"scope\\\":\\\"15774691736578578409\\\",\\\"id\\\":\\\"16589659139012014219\\\",\\\"type\\\":\\\"observable\\\"},val)) : undefined; return this.valueFromJulia[\\\"index\\\"]=false}),self)]\\n \\n }\\n self.model = new AppViewModel();\\n self.valueFromJulia = {};\\n for (var key in json_data) {\\n self.valueFromJulia[key] = false;\\n }\\n ko.applyBindings(self.model, self.dom);\\n}\\n);\\n (WebIO.importBlock({\\\"data\\\":[{\\\"name\\\":\\\"knockout\\\",\\\"type\\\":\\\"js\\\",\\\"url\\\":\\\"\\/assetserver\\/c853cad7a3e123085fa7960dd53fd3d4c05dc309-knockout.js\\\"},{\\\"name\\\":\\\"knockout_punches\\\",\\\"type\\\":\\\"js\\\",\\\"url\\\":\\\"\\/assetserver\\/fab584ebb4dc64eb3ddf5ca7c73b2e76fd533845-knockout_punches.js\\\"}],\\\"type\\\":\\\"async_block\\\"})).then((imports) => handler.apply(this, imports));\\n}\\n\"],\"observables\":{\"changes\":{\"sync\":true,\"id\":\"7517364805952464211\",\"value\":0},\"index\":{\"sync\":true,\"id\":\"16589659139012014219\",\"value\":41}}},\"children\":[{\"props\":{\"className\":\"interact-flex-row interact-widget\",\"style\":{\"font-family\":\"monospace\",\"width\":\"25%\"}},\"nodeType\":\"DOM\",\"type\":\"node\",\"instanceArgs\":{\"namespace\":\"html\",\"tag\":\"div\"},\"children\":[{\"props\":{\"className\":\"interact-flex-row-left\"},\"nodeType\":\"DOM\",\"type\":\"node\",\"instanceArgs\":{\"namespace\":\"html\",\"tag\":\"div\"},\"children\":[{\"props\":{\"className\":\"interact \",\"style\":{\"padding\":\"5px 10px 0px 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" titles=Dict{Symbol, AbstractString}()\n",
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]
},
"execution_count": 40,
"metadata": {
"application/vnd.webio.node+json": {
"kernelId": "cf1f84de-2548-4892-ac97-3dc4528bd326"
}
},
"output_type": "execute_result"
}
],
"source": [
"manipulate(LeafGasExchange.ModelC3BB, :PFD, [:A_net, :Ac, :Aj, :Ap],\n",
" config = ge_config,\n",
" parameters = :Weather => (;\n",
" CO2 = 10:10:1500,\n",
" T_air = -10:1:50,\n",
" ),\n",
" xstep = :Weather => :PFD => 0:20:2000,\n",
" ylim = (0, 60),\n",
" kind = :line,\n",
")"
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"### A-T"
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"엽온(`T`)은 기온(`T_air`)을 바탕으로 에너지 균형을 고려하여 계산됩니다. 이에 따라 광량(`PFD`)이 많아지면 복사열에 의한 엽온 상승 효과로 인해 전체적인 곡선이 옆으로 조금씩 이동하는 것을 볼 수 있습니다."
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" '<p>Please read ' +\n",
" '<a href=\"https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/\" target=\"_blank\">the troubleshooting guide</a> ' +\n",
" 'for more information on how to resolve this issue.</p>' +\n",
" '<p><a href=\"https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/\" target=\"_blank\">https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/</a></p>' +\n",
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" );\n",
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]
},
"execution_count": 41,
"metadata": {
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"kernelId": "cf1f84de-2548-4892-ac97-3dc4528bd326"
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"output_type": "execute_result"
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],
"source": [
"manipulate(LeafGasExchange.ModelC3BB, :T, [:A_net, :Ac, :Aj, :Ap],\n",
" config = ge_config,\n",
" parameters = :Weather => (;\n",
" CO2 = 10:10:1500,\n",
" PFD = 0:20:2000,\n",
" ),\n",
" xstep = :Weather => :T_air => -10:1:50,\n",
" xlim = (-10, 50),\n",
" ylim = (0, 60),\n",
" kind = :line,\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### N vs. Ψv"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"엽내 질소(`N`) 및 수분(`Ψv`) 함량 간의 상호작용을 고려하며 환경 요인의 변화에 따른 광합성을 살펴볼 수 있는 등고선(contour) 그래프입니다. 환경 조건에 따라 질소 및 수분 함량의 영향력이 상대적으로 바뀔 수 있다는 것을 확인할 수 있습니다."
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {},
"outputs": [
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"type": "range"
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"id": "1215184465447660770",
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"props": {},
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}
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" '<p>Please read ' +\n",
" '<a href=\"https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/\" target=\"_blank\">the troubleshooting guide</a> ' +\n",
" 'for more information on how to resolve this issue.</p>' +\n",
" '<p><a href=\"https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/\" target=\"_blank\">https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/</a></p>' +\n",
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"Gadfly.Plot(Gadfly.Layer[Gadfly.Layer(nothing, Dict{Any, Any}(), Gadfly.StatisticElement[], Gadfly.Geom.LineGeometry(Gadfly.Stat.ContourStatistic([0, 1, 2, 3, 4, 5, 6, 7, 8, 9 … 21, 22, 23, 24, 25, 26, 27, 28, 29, 30], 150), true, 2, Symbol(\"\")), nothing, 0)], nothing, Data(\n",
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" y=[-2.0, -1.8, -1.6, -1.4, -1.2, -1.0, -0.8, -0.6, -0.4, -0.2 … -1.8, -1.6, -1.4, -1.2, -1.0, -0.8, -0.6, -0.4, -0.2, 0.0]\n",
" z=[2.5683747289553147, 2.7168844549880555, 2.850863731289638, 2.959852914438665, 3.0417927024194515, 3.0997867627868247, 3.1392500358139097, 3.165308340707603, 3.1823441288671024, 3.1932504793922956 … 7.998074940273561, 9.631450071848118, 11.091621093905509, 12.222202423656354, 13.023551529545285, 13.564018279369272, 13.918067495343735, 14.147332020578354, 14.293689816048364, 14.387170982423015]\n",
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")\n",
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"source": [
"manipulate(LeafGasExchange.ModelC3BB, :N, :Ψv, :A_net;\n",
" config = ge_config,\n",
" parameters = :Weather => (;\n",
" CO2 = 10:10:1500,\n",
" PFD = 0:20:2000,\n",
" T_air = -10:1:50,\n",
" ),\n",
" xstep = :Nitrogen => :N => 0.4:0.2:2,\n",
" ystep = :StomataTuzet => :WP_leaf => -2:0.2:0,\n",
" xlim = (0.4, 2),\n",
" zlim = (0, 30),\n",
" zgap = 1,\n",
" kind = :contour,\n",
")"
]
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{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 2.5. 차회예고"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"지난 주 첫시간부터 간단한 성장곡선에서 시작하여 모형을 조금씩 분해해가며 기작을 추가해본 끝에 기체교환 모형까지 살펴보았습니다. 상대적으로 훨씬 복잡한 모형이지만 결국은 성장률(`r`)을 결정하는 주요 요인인 광합성율(`A`)을 계산하는 여러가지 방법 중의 하나라는 관점에서 보면 모두 같은 선상에 놓여있다고 생각합니다. 모형을 만드는 목적에 따라 필요한 기작을 더 넣어보거나, 바꾸거나 혹은 없애는 과정을 점진적으로 반복하는 것, 그것이 모형개발(modeling)의 핵심이라고 볼 수 있겠습니다. 비록 지금까지 2회에 걸쳐 작물모형의 일부만을 다루었지만 전체적으로는 유사한 과정의 확장이라는 점 기억해주세요. 다음 시간에는 작물모형의 중추라고 볼 수 있는 생물계절(phenology)에 대해 살펴보겠습니다. GDD(growing degree days)와 같은 열시간(thermal time) 개념을 구현하면서 실제 자료를 적용해보는 실습을 진행할 예정입니다."
]
},
{
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"execution_count": null,
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"outputs": [],
"source": []
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