2-Growth.ipynb

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   "source": [
    "# Day 2"
   ]
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   "source": [
    "Simple plant growth modeling with some mechanisms"
   ]
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    "<div class=\"alert alert-warning\">\n",
    "If figures/tables are not rendered correctly, make sure your notebook is `trusted` by choosing `Trust Notebook` command found in `View` - `Activate Command Palette` menu. Typing in the first letters (i.e. \"tr\") should give you the command.\n",
    "</div>"
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  {
   "cell_type": "code",
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   "source": [
    "using Cropbox"
   ]
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       "    WebIO Jupyter integration documentation\n",
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    "Cropbox.Interact.WebIO.setup(:ijulia)"
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   "source": [
    "## 1. Introduction"
   ]
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    "Previously, you built a model to simulate the growth of a whole-plant using the relative growth rate (RGR) along that showed an exponential growth pattern and later in combination with a known final size using the logistic equation. Here, you will modify and expand the model to represent some basic physiological mechanisms. In the logistic growth model, we assumed that the growth rate slows down as the plant reaches its potential biomass (this is analogous to running out of space or resources in a density dependent population). There could be other reasons for plants to slow down their growth rate. One possible mechanism is that the efficiency of growth may decline over time as the plant ages. For example, the efficiency of resource acquisition and use (*e.g.*, light) per carbon invested in foliage tissue will slow down as plants grow bigger with increasingly overlapping foliage that results in self-shading. In addition, the efficacy of a leaf, even if it's not shaded, for producing photosynthates would also decline over time as the leaf ages. At the lower level of organizations, a constant turn over of tissues, cells, proteins and metabolites takes place. That is, old tissue, cells, or molecules die or degrade while new tissue, cells, or molecules are synthesized. Here we will explore some of the simple but physiologically meaningful ways to model realistic plant growth patterns. As done in the previous examples, we will be simulating biomass accumulation of a whole-plant from seed to maturity for an annual crop."
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   "source": [
    "## 2. Growth efficiency decays over time"
   ]
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   "source": [
    "### 2.1. The Gompertz growth function"
   ]
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   "source": [
    "As discussed above, the growth of a plant will slow down if its efficiency of synthesising new tissue declines (or inefficiency increases) even if the resources are non-limiting. For example, a very tall tree may slow down its height growth because of the physical constraints (i.e. reduced transport efficiency) it is facing in getting the resources (e.g., water) to where they are needed - the meristems, even if it is physiologically young and active and the resources like water and nitrogen are abundant in the soil. This transport inefficiency increases over time as the tree gets taller. As a result of this constraint, the growth efficiency (RGR) declines correspondingly over time.  This case can be expressed as:"
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   "source": [
    "- Eq 2.1\n",
    "\n",
    "\\begin{align}\n",
    "  \\frac{dW}{dt} &= r W \\\\\n",
    "  \\frac{dr}{dt} &= -\\alpha r\n",
    "\\end{align}\n",
    "\n",
    "where $W$ represents biomass, $r$ is the relative growth rate (RGR), and $\\alpha$ is the decay rate of growth efficiency over time. This set of differential equations can be integrated into what is known as the Gompertz equation. The Gompertz growth model is a popular choice for modeling tumor growth in oncology by assuming that the growth rate declines as the cell mass multiplies"
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   "source": [
    "- Eq 2.2\n",
    "\n",
    "$$\n",
    "W = W_0 \\exp \\left[ \\frac{r_0}{\\alpha} (1 - e^{-\\alpha t}) \\right]\n",
    "$$\n",
    "\n",
    "This is the integrated form of Gompertz equation where $r_0$ is the intrinsic rate of growth without any decline in efficiency and $W_0$ represents initial biomass (g)."
   ]
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   "source": [
    "- Table 2.1\n",
    "\n",
    "| Symbol | Value | Units | Description |\n",
    "| :- | :- | :- | :- |\n",
    "| $t$ | - | $\\mathrm{d}$ | Time unit used in the model |\n",
    "| $r_0$ | 0.24 | $\\mathrm{g}$ $\\mathrm{g^{-1}}$ $\\mathrm{d^{-1}}$ | Maximum $r$, intrinsic growth rate |\n",
    "| $W_0$ | 0.15 | $\\mathrm{g}$ | Seed mass or initial biomass |\n",
    "| $\\alpha$ | 0.03 | $\\mathrm{d^{-1}}$ | Decay rate of the growth efficiency over time |\n",
    "| $r$ | - | $\\mathrm{g}$ $\\mathrm{g^{-1}}$ $\\mathrm{d^{-1}}$ | Relative growth rate |\n",
    "| $W$ | - | $\\mathrm{g}$ | Whole-plant biomass as dry matter |"
   ]
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   "cell_type": "markdown",
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   "source": [
    "#### Ex 2.1.\n",
    "\n",
    "Create a system that implements the differential form of the Gompertz equation."
   ]
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   "execution_count": 3,
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "G_diff"
      ]
     },
     "execution_count": 3,
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   "source": [
    "@system G_diff(Controller) begin\n",
    "    t(context.clock.time) ~ track(u\"d\")\n",
    "\n",
    "    r0: intrinsic_growth_rate => 0.24 ~ preserve(parameter, u\"g/g/d\")\n",
    "    W0: initial_biomass       => 0.15 ~ preserve(parameter, u\"g\")\n",
    "    α:  decay_rate            => 0.03 ~ preserve(parameter, u\"d^-1\")\n",
    "\n",
    "    r(α, r): actual_growth_rate => -α*r ~ accumulate(init = r0, u\"g/g/d\")\n",
    "    W(r, W): biomass            => r*W  ~ accumulate(init = W0, u\"g\")\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Ex 2.2.\n",
    "\n",
    "Create a system that implements the integrated form (*i.e.*, analytical solution) of the Gompertz equation."
   ]
  },
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   "cell_type": "code",
   "execution_count": 4,
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "G_anal"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "@system G_anal(Controller) begin\n",
    "    t(context.clock.time) ~ track(u\"d\")\n",
    "\n",
    "    r0: intrinsic_growth_rate => 0.24 ~ preserve(parameter, u\"g/g/d\")\n",
    "    W0: initial_biomass       => 0.15 ~ preserve(parameter, u\"g\")\n",
    "    α:  decay_rate            => 0.03 ~ preserve(parameter, u\"d^-1\")\n",
    "\n",
    "    W(t, W0, r0, α): biomass => begin\n",
    "        W0 * exp((r0 / α) * (1 - ℯ^(-α*t)))\n",
    "    end ~ track(u\"g\")\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "#### Ex 2.3.\n",
    "\n",
    "Simulate both forms of the Gompertz model for 300 days using daily steps. Plot and compare the results.\n",
    "\n",
    "* Before running simulations, predict if you expect the results from both models to be identifical? Why or why not?\n",
    "* Do your simulations support your predictions? Why or why not?"
   ]
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   "cell_type": "code",
   "execution_count": 5,
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      "\u001b[32mProgress: 100%[===========================] Time: 0:00:01 ( 6.12 ms/it)\u001b[39m\n"
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   "source": [
    "c0 = Clock => :step => 1u\"d\"\n",
    "stop = 300u\"d\"\n",
    "y0 = simulate(G_diff; stop, config = c0)\n",
    "y1 = simulate(G_anal; stop, config = c0)\n",
    "y2 = simulate(G_diff; stop, config = Clock => :step => 0.5u\"d\")\n",
    "y3 = simulate(G_diff; stop, config = Clock => :step => 1u\"hr\");"
   ]
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   "cell_type": "code",
   "execution_count": 6,
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       "\"<Cropbox.Plot{Gadfly.Plot}>\""
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     },
     "execution_count": 6,
     "metadata": {},
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   ],
   "source": [
    "p = visualize(y1, :t, :W; kind = :line, name = \"Analytical\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
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    "visualize!(p, y0, :t, :W; kind = :line, name = \"Numerical (1 d)\")\n",
    "visualize!(p, y2, :t, :W; kind = :line, name = \"Numerical (0.5 d)\")\n",
    "visualize!(p, y3, :t, :W; kind = :line, name = \"Numerical (1 hr)\")"
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   "source": [
    "## 3. Physiological processes governing plant growth"
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    "### 3.1. Photosynthesis and respiration\n",
    "\n",
    "Let's think about ways to talyor a simple growth function in the form of $\\frac{dW}{dt}=rW$ to account for the basic physiological mechanisms that are specific to plants. Three key physiological processes that determine the rate of plant growth are photosynthesis, respiration, and allocation of assimilates. Photosynthesis assimilates CO<sub>2</sub> to provide carbohydrates as the substrate for respiration. Respiration breaks down the photosynthates to supply energy needed for maintenance of existing biomass as well as C skeletons and energy needed for construction of new biomass (growth). In its simplest form to incorporate the relationship between photosynthesis and respiration, the rate of biomass accumulation can be written as:\n",
    "\n",
    "- Eq 2.3\n",
    "\n",
    "$$\n",
    "\\frac{dW}{dt} = rW = c \\cdot (P_g - R)\n",
    "$$\n",
    "  \n",
    "See Table 2.2 below for description of each term. \n",
    "\n",
    "[Thornley (1970)](https://doi.org/10.1038/227304b0) illustrated elegantly how the above relationship translates to RGR, photosynthesis, and two components of respiration (growth and maintenance) as follows. This is a simple but robust representation of the photosynthesis-respiration relationship commonly applicable to all plant taxa.\n",
    "\n",
    "- Eq 2.4\n",
    "\n",
    "$$\n",
    "c = Y_g \\cdot c_1\n",
    "$$\n",
    "\n",
    "$$\n",
    "R = k_m W\n",
    "$$\n",
    "\n",
    "\\begin{align}\n",
    "r &= c \\cdot \\frac{P_g - R}{W} \\\\\n",
    "  &= Y_g \\cdot c_1 \\cdot \\frac{P_g - k_m W}{W} \\\\\n",
    "  &= Y_g \\cdot c_1 \\cdot \\left( \\frac{P_g}{W} - k_m \\right) \\\\\n",
    "  &= Y_g \\cdot c_1 \\cdot \\left( P_{g_m} - k_m \\right)\n",
    "\\end{align}\n",
    "  \n",
    "As shown in section 4.1 with the Gompertz equation, the growth yield ($Y_g$) may decline over time as the plant ages."
   ]
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    "- Table 2.2\n",
    "\n",
    "| Symbol | Value | Units | Description |\n",
    "| :- | :- | :- | :- |\n",
    "| $t$ | - | $\\mathrm{d}$ | Time unit used in the model |\n",
    "| $\\alpha$ | 0.03 | $\\mathrm{d^{-1}}$ | Decay rate of the growth efficiency over time |\n",
    "| $Y_{g_0}$ | 0.75 | - | Potential growth yield of the biomass conversion process |\n",
    "| $Y_g$ | - | - | Actual growth yield of the biomass conversion process |\n",
    "| $c_1$ | 0.889 | - | Conversion factor from $\\mathrm{CH_2O}$ to biomass assuming 45% carbon in biomass |\n",
    "| $P_g$ | - | $\\mathrm{g}$ $\\mathrm{d^{-1}}$ | Substrate (as $\\mathrm{C}$, $\\mathrm{CO_2}$, $\\mathrm{CH_2O}$) production rate by a whole-plant per unit time |\n",
    "| $P_{g_m}$ | 0.4 | $\\mathrm{g}$ $\\mathrm{g^{-1}}$ $\\mathrm{d^{-1}}$ | Substrate (as $\\mathrm{CH_2O}$) production rate per whole-plant mass per unit time |\n",
    "| $k_m$ | 0.015 | $\\mathrm{g}$ $\\mathrm{g^{-1}}$ $\\mathrm{d^{-1}}$ | Coefficient of maintenance respiration |\n",
    "| $r$ | - | $\\mathrm{g}$ $\\mathrm{g^{-1}}$ $\\mathrm{d^{-1}}$ | Relative growth rate |\n",
    "| $W_0$ | 0.15 | $\\mathrm{g}$ | Seed mass or initial biomass |\n",
    "| $W$ | - | $\\mathrm{g}$ | Whole-plant biomass as dry matter |"
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   "source": [
    "#### Ex 2.4.\n",
    "\n",
    "Implement the growth model by [Thornley (1970)](https://doi.org/10.1038/227304b0) into a system in Cropbox and examine its behavior using the information provided in the Table 2.2. Assume the $Y_g$ declines over time at a rate that given by $\\alpha$. Mull over if this assumption is valid and if so, what plant or canopy process can make this decline over time.\n",
    "\n",
    "* Evaluate the dependency of your model using `dependency()` function of the Cropbhox framework.\n",
    "* List the parameters and their values using `parameters()` function of the Cropbox framework.\n",
    "* Run your simulation on daily step for 300 days.\n",
    "* Compare the results with those from Ex 2.3."
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    "@system Thornley1970(Controller) begin\n",
    "    t(context.clock.time) ~ track(u\"d\")\n",
    "\n",
    "    α:         decay_rate             => 0.03  ~ preserve(parameter, u\"d^-1\")\n",
    "    Yg0:       potential_growth_yield => 0.75  ~ preserve(parameter)\n",
    "    Yg(α, Yg): growth_efficiency      => -α*Yg ~ accumulate(init = Yg0)\n",
    "\n",
    "    c1:   conversion_factor        => 12/30/0.45 ~ preserve(parameter)\n",
    "    Pg_m: production_rate_per_mass => 0.4        ~ preserve(parameter, u\"g/g/d\")\n",
    "    km:   maintenance_coeff        => 0.015      ~ preserve(parameter, u\"g/g/d\")\n",
    "\n",
    "    r(Yg, c1, Pg_m, km): intrinsic_RGR => begin\n",
    "        Yg * c1 * (Pg_m - km)\n",
    "    end ~ track(u\"g/g/d\")\n",
    "\n",
    "    W0:      initial_biomass => 0.15 ~ preserve(parameter, u\"g\")\n",
    "    W(r, W): biomass         => r*W  ~ accumulate(init = W0, u\"g\")\n",
    "end"
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      "text/plain": [
       "\u001b[90m[\u001b[39m\u001b[94mconfig\u001b[39m\u001b[90m → \u001b[39m\u001b[94mW0\u001b[39m\u001b[90m → \u001b[39m\u001b[94mkm\u001b[39m\u001b[90m → \u001b[39m\u001b[94mPg_m\u001b[39m\u001b[90m → \u001b[39m\u001b[94mc1\u001b[39m\u001b[90m → \u001b[39m\u001b[94mYg0\u001b[39m\u001b[90m → \u001b[39m\u001b[94mα\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[94mYg\u001b[39m\u001b[90m → \u001b[39m\u001b[94mr\u001b[39m\u001b[90m → \u001b[39m\u001b[94m⋆W\u001b[39m\u001b[90m → \u001b[39m\u001b[94m⋆Yg\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": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Cropbox.dependency(Thornley1970)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-family: monospace\">Config for 1 system:</p>\n",
       "<table style=\"font-family: monospace\">\n",
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       "<td colspan=\"3\" style=\"text-align: left; padding: 2px; padding-left: 20px; color: rebeccapurple\">Thornley1970</th>\n",
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       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">α</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">0.03 d^-1</td></tr>\n",
       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">Yg0</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">0.75</td></tr>\n",
       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">c1</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">0.888889</td></tr>\n",
       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">Pg_m</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">0.4 d^-1</td></tr>\n",
       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">km</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">0.015 d^-1</td></tr>\n",
       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">W0</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">0.15 g</td></tr>\n",
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       "Config for 1 system:\n",
       "  \u001b[95mThornley1970\u001b[39m\n",
       "    \u001b[94mα   \u001b[39m\u001b[90m = \u001b[39m0.03 d^-1\n",
       "    \u001b[94mYg0 \u001b[39m\u001b[90m = \u001b[39m0.75\n",
       "    \u001b[94mc1  \u001b[39m\u001b[90m = \u001b[39m0.888889\n",
       "    \u001b[94mPg_m\u001b[39m\u001b[90m = \u001b[39m0.4 d^-1\n",
       "    \u001b[94mkm  \u001b[39m\u001b[90m = \u001b[39m0.015 d^-1\n",
       "    \u001b[94mW0  \u001b[39m\u001b[90m = \u001b[39m0.15 g"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "parameters(Thornley1970)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a configuration for running the model in daily time step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Clock => (:step => 1 d)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = Clock => :step => 1u\"d\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run model simulation on daily time step for 300 days."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>301×11 DataFrame</span></div><div style = \"float: right;\"><span style = \"font-style: italic;\">276 rows omitted</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">time</th><th style = \"text-align: left;\">t</th><th style = \"text-align: left;\">α</th><th style = \"text-align: left;\">Yg0</th><th style = \"text-align: left;\">Yg</th><th style = \"text-align: left;\">c1</th><th style = \"text-align: left;\">Pg_m</th><th style = \"text-align: left;\">km</th><th style = \"text-align: left;\">r</th><th style = \"text-align: left;\">W0</th><th style = \"text-align: left;\">W</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Unitful.Quantity{Float64, 𝐓, Unitful.FreeUnits{(hr,), 𝐓, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝐓, Unitful.FreeUnits{(d,), 𝐓, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝐓^-1, Unitful.FreeUnits{(d^-1,), 𝐓^-1, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Unitful.Quantity{Float64, 𝐓^-1, Unitful.FreeUnits{(d^-1,), 𝐓^-1, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝐓^-1, Unitful.FreeUnits{(d^-1,), 𝐓^-1, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝐓^-1, Unitful.FreeUnits{(d^-1,), 𝐓^-1, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝐌, Unitful.FreeUnits{(g,), 𝐌, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝐌, Unitful.FreeUnits{(g,), 𝐌, nothing}}\" style = \"text-align: left;\">Quantity…</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">0.0 hr</td><td style = \"text-align: right;\">0.0 d</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.75</td><td style = \"text-align: right;\">0.75</td><td style = \"text-align: right;\">0.888889</td><td style = \"text-align: right;\">0.4 d^-1</td><td style = \"text-align: right;\">0.015 d^-1</td><td style = \"text-align: right;\">0.256667 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">0.15 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">1.0 d</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.75</td><td style = \"text-align: right;\">0.7275</td><td style = \"text-align: right;\">0.888889</td><td style = \"text-align: right;\">0.4 d^-1</td><td style = \"text-align: right;\">0.015 d^-1</td><td style = \"text-align: right;\">0.248967 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">0.1885 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">48.0 hr</td><td style = \"text-align: right;\">2.0 d</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.75</td><td style = \"text-align: right;\">0.705675</td><td style = \"text-align: right;\">0.888889</td><td style = \"text-align: right;\">0.4 d^-1</td><td style = \"text-align: right;\">0.015 d^-1</td><td style = \"text-align: right;\">0.241498 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">0.23543 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">72.0 hr</td><td style = \"text-align: right;\">3.0 d</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.75</td><td style = \"text-align: right;\">0.684505</td><td style = \"text-align: right;\">0.888889</td><td style = \"text-align: right;\">0.4 d^-1</td><td style = \"text-align: right;\">0.015 d^-1</td><td style = \"text-align: right;\">0.234253 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">0.292286 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">96.0 hr</td><td style = \"text-align: right;\">4.0 d</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.75</td><td style = \"text-align: right;\">0.66397</td><td style = \"text-align: right;\">0.888889</td><td style = \"text-align: right;\">0.4 d^-1</td><td style = \"text-align: right;\">0.015 d^-1</td><td style = \"text-align: right;\">0.227225 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">0.360755 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">120.0 hr</td><td style = \"text-align: right;\">5.0 d</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.75</td><td style = \"text-align: right;\">0.644051</td><td style = \"text-align: right;\">0.888889</td><td style = \"text-align: right;\">0.4 d^-1</td><td style = \"text-align: right;\">0.015 d^-1</td><td style = \"text-align: right;\">0.220408 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">0.442727 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">144.0 hr</td><td style = \"text-align: right;\">6.0 d</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.75</td><td style = \"text-align: right;\">0.624729</td><td style = \"text-align: right;\">0.888889</td><td style = \"text-align: right;\">0.4 d^-1</td><td style = \"text-align: right;\">0.015 d^-1</td><td style = \"text-align: right;\">0.213796 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">0.540308 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">168.0 hr</td><td style = \"text-align: right;\">7.0 d</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.75</td><td style = \"text-align: right;\">0.605987</td><td style = \"text-align: right;\">0.888889</td><td style = \"text-align: right;\">0.4 d^-1</td><td style = \"text-align: right;\">0.015 d^-1</td><td style = \"text-align: right;\">0.207382 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">0.655824 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">192.0 hr</td><td style = \"text-align: right;\">8.0 d</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.75</td><td style = \"text-align: right;\">0.587808</td><td style = \"text-align: right;\">0.888889</td><td style = \"text-align: right;\">0.4 d^-1</td><td style = \"text-align: right;\">0.015 d^-1</td><td style = \"text-align: right;\">0.201161 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">0.79183 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: right;\">216.0 hr</td><td style = \"text-align: right;\">9.0 d</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.75</td><td style = \"text-align: right;\">0.570173</td><td style = \"text-align: right;\">0.888889</td><td style = \"text-align: right;\">0.4 d^-1</td><td style = \"text-align: right;\">0.015 d^-1</td><td style = \"text-align: right;\">0.195126 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">0.951116 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">11</td><td style = \"text-align: right;\">240.0 hr</td><td style = \"text-align: right;\">10.0 d</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.75</td><td style = \"text-align: right;\">0.553068</td><td style = \"text-align: right;\">0.888889</td><td style = \"text-align: right;\">0.4 d^-1</td><td style = \"text-align: right;\">0.015 d^-1</td><td style = \"text-align: right;\">0.189272 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">1.1367 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">12</td><td style = \"text-align: right;\">264.0 hr</td><td style = \"text-align: right;\">11.0 d</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.75</td><td style = \"text-align: right;\">0.536476</td><td style = \"text-align: right;\">0.888889</td><td style = \"text-align: right;\">0.4 d^-1</td><td style = \"text-align: right;\">0.015 d^-1</td><td style = \"text-align: right;\">0.183594 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">1.35185 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">13</td><td style = \"text-align: right;\">288.0 hr</td><td style = \"text-align: right;\">12.0 d</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.75</td><td style = \"text-align: right;\">0.520382</td><td style = \"text-align: right;\">0.888889</td><td style = \"text-align: right;\">0.4 d^-1</td><td style = \"text-align: right;\">0.015 d^-1</td><td style = \"text-align: right;\">0.178086 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">1.60004 g</td></tr><tr><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">290</td><td style = \"text-align: right;\">6936.0 hr</td><td style = \"text-align: right;\">289.0 d</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.75</td><td style = \"text-align: right;\">0.000112744</td><td style = \"text-align: right;\">0.888889</td><td style = \"text-align: right;\">0.4 d^-1</td><td style = \"text-align: right;\">0.015 d^-1</td><td style = \"text-align: right;\">3.85834e-5 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">471.646 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">291</td><td style = \"text-align: right;\">6960.0 hr</td><td style = \"text-align: right;\">290.0 d</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.75</td><td style = \"text-align: right;\">0.000109361</td><td style = \"text-align: right;\">0.888889</td><td style = \"text-align: right;\">0.4 d^-1</td><td style = \"text-align: right;\">0.015 d^-1</td><td style = \"text-align: right;\">3.74259e-5 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">471.664 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">292</td><td style = \"text-align: right;\">6984.0 hr</td><td style = \"text-align: right;\">291.0 d</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.75</td><td style = \"text-align: right;\">0.000106081</td><td style = \"text-align: right;\">0.888889</td><td style = \"text-align: right;\">0.4 d^-1</td><td style = \"text-align: right;\">0.015 d^-1</td><td style = \"text-align: right;\">3.63031e-5 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">471.682 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">293</td><td style = \"text-align: right;\">7008.0 hr</td><td style = \"text-align: right;\">292.0 d</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.75</td><td style = \"text-align: right;\">0.000102898</td><td style = \"text-align: right;\">0.888889</td><td style = \"text-align: right;\">0.4 d^-1</td><td style = \"text-align: right;\">0.015 d^-1</td><td style = \"text-align: right;\">3.5214e-5 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">471.699 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">294</td><td style = \"text-align: right;\">7032.0 hr</td><td style = \"text-align: right;\">293.0 d</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.75</td><td style = \"text-align: right;\">9.98112e-5</td><td style = \"text-align: right;\">0.888889</td><td style = \"text-align: right;\">0.4 d^-1</td><td style = \"text-align: right;\">0.015 d^-1</td><td style = \"text-align: right;\">3.41576e-5 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">471.715 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">295</td><td style = \"text-align: right;\">7056.0 hr</td><td style = \"text-align: right;\">294.0 d</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.75</td><td style = \"text-align: right;\">9.68169e-5</td><td style = \"text-align: right;\">0.888889</td><td style = \"text-align: right;\">0.4 d^-1</td><td style = \"text-align: right;\">0.015 d^-1</td><td style = \"text-align: right;\">3.31329e-5 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">471.731 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">296</td><td style = \"text-align: right;\">7080.0 hr</td><td style = \"text-align: right;\">295.0 d</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.75</td><td style = \"text-align: right;\">9.39124e-5</td><td style = \"text-align: right;\">0.888889</td><td style = \"text-align: right;\">0.4 d^-1</td><td style = \"text-align: right;\">0.015 d^-1</td><td style = \"text-align: right;\">3.21389e-5 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">471.747 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">297</td><td style = \"text-align: right;\">7104.0 hr</td><td style = \"text-align: right;\">296.0 d</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.75</td><td style = \"text-align: right;\">9.1095e-5</td><td style = \"text-align: right;\">0.888889</td><td style = \"text-align: right;\">0.4 d^-1</td><td style = \"text-align: right;\">0.015 d^-1</td><td style = \"text-align: right;\">3.11747e-5 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">471.762 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">298</td><td style = \"text-align: right;\">7128.0 hr</td><td style = \"text-align: right;\">297.0 d</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.75</td><td style = \"text-align: right;\">8.83622e-5</td><td style = \"text-align: right;\">0.888889</td><td style = \"text-align: right;\">0.4 d^-1</td><td style = \"text-align: right;\">0.015 d^-1</td><td style = \"text-align: right;\">3.02395e-5 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">471.777 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">299</td><td style = \"text-align: right;\">7152.0 hr</td><td style = \"text-align: right;\">298.0 d</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.75</td><td style = \"text-align: right;\">8.57113e-5</td><td style = \"text-align: right;\">0.888889</td><td style = \"text-align: right;\">0.4 d^-1</td><td style = \"text-align: right;\">0.015 d^-1</td><td style = \"text-align: right;\">2.93323e-5 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">471.791 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">300</td><td style = \"text-align: right;\">7176.0 hr</td><td style = \"text-align: right;\">299.0 d</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.75</td><td style = \"text-align: right;\">8.314e-5</td><td style = \"text-align: right;\">0.888889</td><td style = \"text-align: right;\">0.4 d^-1</td><td style = \"text-align: right;\">0.015 d^-1</td><td style = \"text-align: right;\">2.84523e-5 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">471.805 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">301</td><td style = \"text-align: right;\">7200.0 hr</td><td style = \"text-align: right;\">300.0 d</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.75</td><td style = \"text-align: right;\">8.06458e-5</td><td style = \"text-align: right;\">0.888889</td><td style = \"text-align: right;\">0.4 d^-1</td><td style = \"text-align: right;\">0.015 d^-1</td><td style = \"text-align: right;\">2.75988e-5 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">471.818 g</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccccccccc}\n",
       "\t& time & t & α & Yg0 & Yg & c1 & Pg\\_m & km & \\\\\n",
       "\t\\hline\n",
       "\t& Quantity… & Quantity… & Quantity… & Float64 & Float64 & Float64 & Quantity… & Quantity… & \\\\\n",
       "\t\\hline\n",
       "\t1 & 0.0 hr & 0.0 d & 0.03 d\\^-1 & 0.75 & 0.75 & 0.888889 & 0.4 d\\^-1 & 0.015 d\\^-1 & $\\dots$ \\\\\n",
       "\t2 & 24.0 hr & 1.0 d & 0.03 d\\^-1 & 0.75 & 0.7275 & 0.888889 & 0.4 d\\^-1 & 0.015 d\\^-1 & $\\dots$ \\\\\n",
       "\t3 & 48.0 hr & 2.0 d & 0.03 d\\^-1 & 0.75 & 0.705675 & 0.888889 & 0.4 d\\^-1 & 0.015 d\\^-1 & $\\dots$ \\\\\n",
       "\t4 & 72.0 hr & 3.0 d & 0.03 d\\^-1 & 0.75 & 0.684505 & 0.888889 & 0.4 d\\^-1 & 0.015 d\\^-1 & $\\dots$ \\\\\n",
       "\t5 & 96.0 hr & 4.0 d & 0.03 d\\^-1 & 0.75 & 0.66397 & 0.888889 & 0.4 d\\^-1 & 0.015 d\\^-1 & $\\dots$ \\\\\n",
       "\t6 & 120.0 hr & 5.0 d & 0.03 d\\^-1 & 0.75 & 0.644051 & 0.888889 & 0.4 d\\^-1 & 0.015 d\\^-1 & $\\dots$ \\\\\n",
       "\t7 & 144.0 hr & 6.0 d & 0.03 d\\^-1 & 0.75 & 0.624729 & 0.888889 & 0.4 d\\^-1 & 0.015 d\\^-1 & $\\dots$ \\\\\n",
       "\t8 & 168.0 hr & 7.0 d & 0.03 d\\^-1 & 0.75 & 0.605987 & 0.888889 & 0.4 d\\^-1 & 0.015 d\\^-1 & $\\dots$ \\\\\n",
       "\t9 & 192.0 hr & 8.0 d & 0.03 d\\^-1 & 0.75 & 0.587808 & 0.888889 & 0.4 d\\^-1 & 0.015 d\\^-1 & $\\dots$ \\\\\n",
       "\t10 & 216.0 hr & 9.0 d & 0.03 d\\^-1 & 0.75 & 0.570173 & 0.888889 & 0.4 d\\^-1 & 0.015 d\\^-1 & $\\dots$ \\\\\n",
       "\t11 & 240.0 hr & 10.0 d & 0.03 d\\^-1 & 0.75 & 0.553068 & 0.888889 & 0.4 d\\^-1 & 0.015 d\\^-1 & $\\dots$ \\\\\n",
       "\t12 & 264.0 hr & 11.0 d & 0.03 d\\^-1 & 0.75 & 0.536476 & 0.888889 & 0.4 d\\^-1 & 0.015 d\\^-1 & $\\dots$ \\\\\n",
       "\t13 & 288.0 hr & 12.0 d & 0.03 d\\^-1 & 0.75 & 0.520382 & 0.888889 & 0.4 d\\^-1 & 0.015 d\\^-1 & $\\dots$ \\\\\n",
       "\t14 & 312.0 hr & 13.0 d & 0.03 d\\^-1 & 0.75 & 0.50477 & 0.888889 & 0.4 d\\^-1 & 0.015 d\\^-1 & $\\dots$ \\\\\n",
       "\t15 & 336.0 hr & 14.0 d & 0.03 d\\^-1 & 0.75 & 0.489627 & 0.888889 & 0.4 d\\^-1 & 0.015 d\\^-1 & $\\dots$ \\\\\n",
       "\t16 & 360.0 hr & 15.0 d & 0.03 d\\^-1 & 0.75 & 0.474938 & 0.888889 & 0.4 d\\^-1 & 0.015 d\\^-1 & $\\dots$ \\\\\n",
       "\t17 & 384.0 hr & 16.0 d & 0.03 d\\^-1 & 0.75 & 0.46069 & 0.888889 & 0.4 d\\^-1 & 0.015 d\\^-1 & $\\dots$ \\\\\n",
       "\t18 & 408.0 hr & 17.0 d & 0.03 d\\^-1 & 0.75 & 0.44687 & 0.888889 & 0.4 d\\^-1 & 0.015 d\\^-1 & $\\dots$ \\\\\n",
       "\t19 & 432.0 hr & 18.0 d & 0.03 d\\^-1 & 0.75 & 0.433463 & 0.888889 & 0.4 d\\^-1 & 0.015 d\\^-1 & $\\dots$ \\\\\n",
       "\t20 & 456.0 hr & 19.0 d & 0.03 d\\^-1 & 0.75 & 0.42046 & 0.888889 & 0.4 d\\^-1 & 0.015 d\\^-1 & $\\dots$ \\\\\n",
       "\t21 & 480.0 hr & 20.0 d & 0.03 d\\^-1 & 0.75 & 0.407846 & 0.888889 & 0.4 d\\^-1 & 0.015 d\\^-1 & $\\dots$ \\\\\n",
       "\t22 & 504.0 hr & 21.0 d & 0.03 d\\^-1 & 0.75 & 0.39561 & 0.888889 & 0.4 d\\^-1 & 0.015 d\\^-1 & $\\dots$ \\\\\n",
       "\t23 & 528.0 hr & 22.0 d & 0.03 d\\^-1 & 0.75 & 0.383742 & 0.888889 & 0.4 d\\^-1 & 0.015 d\\^-1 & $\\dots$ \\\\\n",
       "\t24 & 552.0 hr & 23.0 d & 0.03 d\\^-1 & 0.75 & 0.37223 & 0.888889 & 0.4 d\\^-1 & 0.015 d\\^-1 & $\\dots$ \\\\\n",
       "\t25 & 576.0 hr & 24.0 d & 0.03 d\\^-1 & 0.75 & 0.361063 & 0.888889 & 0.4 d\\^-1 & 0.015 d\\^-1 & $\\dots$ \\\\\n",
       "\t26 & 600.0 hr & 25.0 d & 0.03 d\\^-1 & 0.75 & 0.350231 & 0.888889 & 0.4 d\\^-1 & 0.015 d\\^-1 & $\\dots$ \\\\\n",
       "\t27 & 624.0 hr & 26.0 d & 0.03 d\\^-1 & 0.75 & 0.339724 & 0.888889 & 0.4 d\\^-1 & 0.015 d\\^-1 & $\\dots$ \\\\\n",
       "\t28 & 648.0 hr & 27.0 d & 0.03 d\\^-1 & 0.75 & 0.329532 & 0.888889 & 0.4 d\\^-1 & 0.015 d\\^-1 & $\\dots$ \\\\\n",
       "\t29 & 672.0 hr & 28.0 d & 0.03 d\\^-1 & 0.75 & 0.319646 & 0.888889 & 0.4 d\\^-1 & 0.015 d\\^-1 & $\\dots$ \\\\\n",
       "\t30 & 696.0 hr & 29.0 d & 0.03 d\\^-1 & 0.75 & 0.310057 & 0.888889 & 0.4 d\\^-1 & 0.015 d\\^-1 & $\\dots$ \\\\\n",
       "\t$\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ &  \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m301×11 DataFrame\n",
       "\u001b[1m Row │\u001b[1m time      \u001b[1m t         \u001b[1m α         \u001b[1m Yg0     \u001b[1m Yg          \u001b[1m c1       \u001b[1m Pg_m   ⋯\n",
       "     │\u001b[90m Quantity… \u001b[90m Quantity… \u001b[90m Quantity… \u001b[90m Float64 \u001b[90m Float64     \u001b[90m Float64  \u001b[90m Quanti ⋯\n",
       "─────┼──────────────────────────────────────────────────────────────────────────\n",
       "   1 │    0.0 hr      0.0 d  0.03 d^-1     0.75  0.75         0.888889   0.4 d ⋯\n",
       "   2 │   24.0 hr      1.0 d  0.03 d^-1     0.75  0.7275       0.888889   0.4 d\n",
       "   3 │   48.0 hr      2.0 d  0.03 d^-1     0.75  0.705675     0.888889   0.4 d\n",
       "   4 │   72.0 hr      3.0 d  0.03 d^-1     0.75  0.684505     0.888889   0.4 d\n",
       "   5 │   96.0 hr      4.0 d  0.03 d^-1     0.75  0.66397      0.888889   0.4 d ⋯\n",
       "   6 │  120.0 hr      5.0 d  0.03 d^-1     0.75  0.644051     0.888889   0.4 d\n",
       "   7 │  144.0 hr      6.0 d  0.03 d^-1     0.75  0.624729     0.888889   0.4 d\n",
       "   8 │  168.0 hr      7.0 d  0.03 d^-1     0.75  0.605987     0.888889   0.4 d\n",
       "   9 │  192.0 hr      8.0 d  0.03 d^-1     0.75  0.587808     0.888889   0.4 d ⋯\n",
       "  10 │  216.0 hr      9.0 d  0.03 d^-1     0.75  0.570173     0.888889   0.4 d\n",
       "  11 │  240.0 hr     10.0 d  0.03 d^-1     0.75  0.553068     0.888889   0.4 d\n",
       "  ⋮  │     ⋮          ⋮          ⋮         ⋮          ⋮          ⋮          ⋮  ⋱\n",
       " 292 │ 6984.0 hr    291.0 d  0.03 d^-1     0.75  0.000106081  0.888889   0.4 d\n",
       " 293 │ 7008.0 hr    292.0 d  0.03 d^-1     0.75  0.000102898  0.888889   0.4 d ⋯\n",
       " 294 │ 7032.0 hr    293.0 d  0.03 d^-1     0.75  9.98112e-5   0.888889   0.4 d\n",
       " 295 │ 7056.0 hr    294.0 d  0.03 d^-1     0.75  9.68169e-5   0.888889   0.4 d\n",
       " 296 │ 7080.0 hr    295.0 d  0.03 d^-1     0.75  9.39124e-5   0.888889   0.4 d\n",
       " 297 │ 7104.0 hr    296.0 d  0.03 d^-1     0.75  9.1095e-5    0.888889   0.4 d ⋯\n",
       " 298 │ 7128.0 hr    297.0 d  0.03 d^-1     0.75  8.83622e-5   0.888889   0.4 d\n",
       " 299 │ 7152.0 hr    298.0 d  0.03 d^-1     0.75  8.57113e-5   0.888889   0.4 d\n",
       " 300 │ 7176.0 hr    299.0 d  0.03 d^-1     0.75  8.314e-5     0.888889   0.4 d\n",
       " 301 │ 7200.0 hr    300.0 d  0.03 d^-1     0.75  8.06458e-5   0.888889   0.4 d ⋯\n",
       "\u001b[36m                                                  5 columns and 280 rows omitted"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t70 = simulate(Thornley1970, config = c, stop = 300u\"d\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
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    "### 3.2. Carbon partitioning\n",
    "\n",
    "Allocation or partitioning of the photosynthates but not represented in the above model is a critical element to determine their destination and fate as to how and in what part they will be used. For example, some assimilates will be transported to roots to function as subsrates for providing ATPs to maintain the ion gradients while others can be invested back to build more new leaves. More investment in photosynthetic machinery (i.e. allocation to foliage) will yield greater return of biomass at a faster rate; this is similar to the growth of bank account balance with the compound interest rate. \n",
    "\n",
    "[Monsi (1960)](https://api.semanticscholar.org/CorpusID:82751532)'s model as summarized in [Kim et al. (2020)](https://doi.org/10.1201/9780429266591) intuitively demonstrates the importance of photosynthate allocation in plant growth.\n",
    "\n",
    "- Eq 2.5\n",
    "\n",
    "$$\n",
    "r = c_2 \\cdot (m A' - n R')\n",
    "$$\n",
    "  \n",
    "Both models are simple but robustly grounded in physiology to provide critical insights for understanding the intricate relationship between these three processes and their trade-offs determining plant growth. The trade-offs of allocating photosynthates between photosynthetic and non-photosynthetic parts can be particularly insightful and relevant for the growth of crops like lettuce and cabbage for which the foliage biomass accounts for the majority of harvested yield or crops with large underground storage organs like radish, potato, garlic, and onions. Carbon allocation to non-photosynthetic parts is also functionally important in  herbaceous perennials with storage organs such as rhizomes and woody plants for which dead parts (i.e. wood and bark) continue to be part of the whole-plant biomass."
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    "- Table 2.3\n",
    "\n",
    "| Symbol | Value | Units | Description |\n",
    "| :- | :- | :- | :- |\n",
    "| $t$ | - | $\\mathrm{d}$ | Time unit used in the model |\n",
    "| $c_2$ | 0.606 | - | Conversion factor from $\\mathrm{CO_2}$ to biomass assuming 45% carbon in biomass |\n",
    "| $m$ | 0.5 | - | Fraction of photosynthetic biomass |\n",
    "| $n$ | 0.5 | - | Fraction of non-photosynthetic biomass ($1 - m$) |\n",
    "| $A_{\\mathrm{max}}$ | 0.08 | $\\mathrm{g}$ $\\mathrm{g^{-1}}$ $\\mathrm{hr^{-1}}$ | Maximal net $\\mathrm{CO_2}$ assimilation rate |\n",
    "| $R_{\\mathrm{max}}$ | 0.006 | $\\mathrm{g}$ $\\mathrm{g^{-1}}$ $\\mathrm{hr^{-1}}$ | Maximal respiration rate |\n",
    "| $\\alpha$ | 0.03 | $\\mathrm{d^{-1}}$ | Decay rate of the growth efficiency over time |\n",
    "| $A'$ | - | $\\mathrm{g}$ $\\mathrm{g^{-1}}$ $\\mathrm{d^{-1}}$ | Actual net $\\mathrm{CO_2}$ assimilation rate per day during photoperiod |\n",
    "| $R'$ | - | $\\mathrm{g}$ $\\mathrm{g^{-1}}$ $\\mathrm{d^{-1}}$ | Actual respiration rate per day |\n",
    "| $D_L$ | 12 | $\\mathrm{hr}$ | Day length (i.e. photoperiod) |\n",
    "| $D$ | 24 | $\\mathrm{hr}$ | Total hours per day |\n",
    "| $r$ | - | $\\mathrm{g}$ $\\mathrm{g^{-1}}$ $\\mathrm{d^{-1}}$ | Relative growth rate |\n",
    "| $W_0$ | 0.15 | $\\mathrm{g}$ | Seed mass or initial biomass |\n",
    "| $W$ | - | $\\mathrm{g}$ | Whole-plant biomass as dry matter |"
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   "source": [
    "#### Ex 2.5\n",
    "\n",
    "Implement the growth model by [Monsi (1960)](https://api.semanticscholar.org/CorpusID:82751532) into a system in Cropbox and examine its behavior using the information provided in the Table 4.1. Assume both $A$ and $R$ declines over time at a rate given by $\\alpha$. Also note that 1) $A$ and $R$ are expressed in $g$ of CO<sub>2</sub> in hourly unit and 2) photosynthesis requires light.  \n",
    "\n",
    "* Evaluate the dependency of your model using `dependency()` function of the Cropbhox framework.\n",
    "* List the parameters and their values using `parameters()` function of the Cropbox framework.\n",
    "* Run your simulation on daily step for 300 days.\n",
    "* Compare the results with those from Ex 2.4."
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       "Monsi1960"
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    "@system Monsi1960(Controller) begin\n",
    "    t(context.clock.time) ~ track(u\"d\")\n",
    "\n",
    "    c2: conversion_factor => 12/44/0.45 ~ preserve(parameter)    \n",
    "\n",
    "    m:    leaf_mass_ratio   => 0.5 ~ preserve(parameter)\n",
    "    n(m): non_leaf_fraction => 1-m ~ track\n",
    "\n",
    "    Amax: maximal_assimilation => 0.08  ~ preserve(parameter, u\"g/g/hr\")\n",
    "    Rmax: maximal_respiration  => 0.005 ~ preserve(parameter, u\"g/g/hr\")\n",
    "    α:    decay_rate           => 0.03  ~ preserve(parameter, u\"d^-1\")\n",
    "\n",
    "    A(α, A): hourly_assimilation_per_mass => -α*A ~ accumulate(init = Amax, u\"g/g/hr\")\n",
    "    R(α, R): hourly_respiration_per_mass  => -α*R ~ accumulate(init = Rmax, u\"g/g/hr\")\n",
    "\n",
    "    DL: day_length  => 12 ~ preserve(parameter, u\"hr\")\n",
    "    D:  total_hours => 24 ~ preserve(parameter, u\"hr\")\n",
    "\n",
    "    A′(A, DL, D): assimilation_per_mass => A * (DL/D) ~ track(u\"g/g/d\")\n",
    "    R′(R):        respiration_per_mass                ~ track(u\"g/g/d\")\n",
    "\n",
    "    r(c2, m, n, A′, R′): RGR => c2 * (m*A′ - n*R′) ~ track(u\"g/g/d\")\n",
    "\n",
    "    W0:      initial_biomass => 0.15 ~ preserve(parameter, u\"g\")\n",
    "    W(r, W): biomass         => r*W  ~ accumulate(init = W0, u\"g\")\n",
    "end"
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       "<p style=\"font-family: monospace\">Config for 1 system:</p>\n",
       "<table style=\"font-family: monospace\">\n",
       "<tr style=\"background-color: transparent\">\n",
       "<td colspan=\"3\" style=\"text-align: left; padding: 2px; padding-left: 20px; color: rebeccapurple\">Monsi1960</th>\n",
       "</tr>\n",
       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">c2</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">0.606061</td></tr>\n",
       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">m</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">0.5</td></tr>\n",
       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">Amax</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">0.08 hr^-1</td></tr>\n",
       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">Rmax</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">0.005 hr^-1</td></tr>\n",
       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">α</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">0.03 d^-1</td></tr>\n",
       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">DL</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">12 hr</td></tr>\n",
       "<tr style=\"background-color: transparent\"><td style=\"text-align: left; padding: 2px; padding-left: 40px; color: royalblue\">D</td><td style=\"text-align: center; padding: 2px 10px 2px 10px; color: gray\">=</td><td style=\"text-align: left; padding: 2px;\">24 hr</td></tr>\n",
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       "Config for 1 system:\n",
       "  \u001b[95mMonsi1960\u001b[39m\n",
       "    \u001b[94mc2  \u001b[39m\u001b[90m = \u001b[39m0.606061\n",
       "    \u001b[94mm   \u001b[39m\u001b[90m = \u001b[39m0.5\n",
       "    \u001b[94mAmax\u001b[39m\u001b[90m = \u001b[39m0.08 hr^-1\n",
       "    \u001b[94mRmax\u001b[39m\u001b[90m = \u001b[39m0.005 hr^-1\n",
       "    \u001b[94mα   \u001b[39m\u001b[90m = \u001b[39m0.03 d^-1\n",
       "    \u001b[94mDL  \u001b[39m\u001b[90m = \u001b[39m12 hr\n",
       "    \u001b[94mD   \u001b[39m\u001b[90m = \u001b[39m24 hr\n",
       "    \u001b[94mW0  \u001b[39m\u001b[90m = \u001b[39m0.15 g"
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      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Cropbox.dependency(Monsi1960)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
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      "text/html": [
       "<div><div style = \"float: left;\"><span>301×17 DataFrame</span></div><div style = \"float: right;\"><span style = \"font-style: italic;\">276 rows omitted</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">time</th><th style = \"text-align: left;\">t</th><th style = \"text-align: left;\">c2</th><th style = \"text-align: left;\">m</th><th style = \"text-align: left;\">n</th><th style = \"text-align: left;\">Amax</th><th style = \"text-align: left;\">Rmax</th><th style = \"text-align: left;\">α</th><th style = \"text-align: left;\">A</th><th style = \"text-align: left;\">R</th><th style = \"text-align: left;\">DL</th><th style = \"text-align: left;\">D</th><th style = \"text-align: left;\">A′</th><th style = \"text-align: left;\">R′</th><th style = \"text-align: left;\">r</th><th style = \"text-align: left;\">W0</th><th style = \"text-align: left;\">W</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Unitful.Quantity{Float64, 𝐓, Unitful.FreeUnits{(hr,), 𝐓, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝐓, Unitful.FreeUnits{(d,), 𝐓, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Unitful.Quantity{Float64, 𝐓^-1, Unitful.FreeUnits{(hr^-1,), 𝐓^-1, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝐓^-1, Unitful.FreeUnits{(hr^-1,), 𝐓^-1, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝐓^-1, Unitful.FreeUnits{(d^-1,), 𝐓^-1, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝐓^-1, Unitful.FreeUnits{(hr^-1,), 𝐓^-1, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝐓^-1, Unitful.FreeUnits{(hr^-1,), 𝐓^-1, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝐓, Unitful.FreeUnits{(hr,), 𝐓, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝐓, Unitful.FreeUnits{(hr,), 𝐓, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝐓^-1, Unitful.FreeUnits{(d^-1,), 𝐓^-1, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝐓^-1, Unitful.FreeUnits{(d^-1,), 𝐓^-1, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝐓^-1, Unitful.FreeUnits{(d^-1,), 𝐓^-1, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝐌, Unitful.FreeUnits{(g,), 𝐌, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝐌, Unitful.FreeUnits{(g,), 𝐌, nothing}}\" style = \"text-align: left;\">Quantity…</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">0.0 hr</td><td style = \"text-align: right;\">0.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.005 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.005 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.96 d^-1</td><td style = \"text-align: right;\">0.12 d^-1</td><td style = \"text-align: right;\">0.254545 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">0.15 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">1.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.005 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.0776 hr^-1</td><td style = \"text-align: right;\">0.00485 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.9312 d^-1</td><td style = \"text-align: right;\">0.1164 d^-1</td><td style = \"text-align: right;\">0.246909 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">0.188182 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">48.0 hr</td><td style = \"text-align: right;\">2.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.005 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.075272 hr^-1</td><td style = \"text-align: right;\">0.0047045 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.903264 d^-1</td><td style = \"text-align: right;\">0.112908 d^-1</td><td style = \"text-align: right;\">0.239502 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">0.234646 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">72.0 hr</td><td style = \"text-align: right;\">3.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.005 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.0730138 hr^-1</td><td style = \"text-align: right;\">0.00456337 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.876166 d^-1</td><td style = \"text-align: right;\">0.109521 d^-1</td><td style = \"text-align: right;\">0.232317 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">0.290844 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">96.0 hr</td><td style = \"text-align: right;\">4.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.005 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.0708234 hr^-1</td><td style = \"text-align: right;\">0.00442646 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.849881 d^-1</td><td style = \"text-align: right;\">0.106235 d^-1</td><td style = \"text-align: right;\">0.225347 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">0.358412 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">120.0 hr</td><td style = \"text-align: right;\">5.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.005 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.0686987 hr^-1</td><td style = \"text-align: right;\">0.00429367 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.824385 d^-1</td><td style = \"text-align: right;\">0.103048 d^-1</td><td style = \"text-align: right;\">0.218587 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">0.439179 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">144.0 hr</td><td style = \"text-align: right;\">6.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.005 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.0666378 hr^-1</td><td style = \"text-align: right;\">0.00416486 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.799653 d^-1</td><td style = \"text-align: right;\">0.0999566 d^-1</td><td style = \"text-align: right;\">0.212029 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">0.535177 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">168.0 hr</td><td style = \"text-align: right;\">7.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.005 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.0646386 hr^-1</td><td style = \"text-align: right;\">0.00403991 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.775664 d^-1</td><td style = \"text-align: right;\">0.0969579 d^-1</td><td style = \"text-align: right;\">0.205668 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">0.64865 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">192.0 hr</td><td style = \"text-align: right;\">8.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.005 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.0626995 hr^-1</td><td style = \"text-align: right;\">0.00391872 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.752394 d^-1</td><td style = \"text-align: right;\">0.0940492 d^-1</td><td style = \"text-align: right;\">0.199498 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">0.782057 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: right;\">216.0 hr</td><td style = \"text-align: right;\">9.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.005 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.0608185 hr^-1</td><td style = \"text-align: right;\">0.00380116 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.729822 d^-1</td><td style = \"text-align: right;\">0.0912277 d^-1</td><td style = \"text-align: right;\">0.193513 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">0.938076 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">11</td><td style = \"text-align: right;\">240.0 hr</td><td style = \"text-align: right;\">10.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.005 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.0589939 hr^-1</td><td style = \"text-align: right;\">0.00368712 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.707927 d^-1</td><td style = \"text-align: right;\">0.0884909 d^-1</td><td style = \"text-align: right;\">0.187708 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">1.11961 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">12</td><td style = \"text-align: right;\">264.0 hr</td><td style = \"text-align: right;\">11.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.005 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.0572241 hr^-1</td><td style = \"text-align: right;\">0.00357651 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.686689 d^-1</td><td style = \"text-align: right;\">0.0858362 d^-1</td><td style = \"text-align: right;\">0.182077 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">1.32977 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">13</td><td style = \"text-align: right;\">288.0 hr</td><td style = \"text-align: right;\">12.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.005 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.0555074 hr^-1</td><td style = \"text-align: right;\">0.00346921 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.666089 d^-1</td><td style = \"text-align: right;\">0.0832611 d^-1</td><td style = \"text-align: right;\">0.176614 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">1.57189 g</td></tr><tr><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">290</td><td style = \"text-align: right;\">6936.0 hr</td><td style = \"text-align: right;\">289.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.005 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">1.2026e-5 hr^-1</td><td style = \"text-align: right;\">7.51625e-7 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.000144312 d^-1</td><td style = \"text-align: right;\">1.8039e-5 d^-1</td><td style = \"text-align: right;\">3.82645e-5 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">442.914 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">291</td><td style = \"text-align: right;\">6960.0 hr</td><td style = \"text-align: right;\">290.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.005 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">1.16652e-5 hr^-1</td><td style = \"text-align: right;\">7.29076e-7 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.000139983 d^-1</td><td style = \"text-align: right;\">1.74978e-5 d^-1</td><td style = \"text-align: right;\">3.71166e-5 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">442.931 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">292</td><td style = \"text-align: right;\">6984.0 hr</td><td style = \"text-align: right;\">291.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.005 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">1.13153e-5 hr^-1</td><td style = \"text-align: right;\">7.07204e-7 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.000135783 d^-1</td><td style = \"text-align: right;\">1.69729e-5 d^-1</td><td style = \"text-align: right;\">3.60031e-5 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">442.947 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">293</td><td style = \"text-align: right;\">7008.0 hr</td><td style = \"text-align: right;\">292.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.005 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">1.09758e-5 hr^-1</td><td style = \"text-align: right;\">6.85988e-7 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.00013171 d^-1</td><td style = \"text-align: right;\">1.64637e-5 d^-1</td><td style = \"text-align: right;\">3.4923e-5 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">442.963 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">294</td><td style = \"text-align: right;\">7032.0 hr</td><td style = \"text-align: right;\">293.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.005 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">1.06465e-5 hr^-1</td><td style = \"text-align: right;\">6.65408e-7 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.000127758 d^-1</td><td style = \"text-align: right;\">1.59698e-5 d^-1</td><td style = \"text-align: right;\">3.38753e-5 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">442.978 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">295</td><td style = \"text-align: right;\">7056.0 hr</td><td style = \"text-align: right;\">294.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.005 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">1.03271e-5 hr^-1</td><td style = \"text-align: right;\">6.45446e-7 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.000123926 d^-1</td><td style = \"text-align: right;\">1.54907e-5 d^-1</td><td style = \"text-align: right;\">3.28591e-5 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">442.993 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">296</td><td style = \"text-align: right;\">7080.0 hr</td><td style = \"text-align: right;\">295.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.005 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">1.00173e-5 hr^-1</td><td style = \"text-align: right;\">6.26083e-7 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.000120208 d^-1</td><td style = \"text-align: right;\">1.5026e-5 d^-1</td><td style = \"text-align: right;\">3.18733e-5 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">443.008 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">297</td><td style = \"text-align: right;\">7104.0 hr</td><td style = \"text-align: right;\">296.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.005 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">9.7168e-6 hr^-1</td><td style = \"text-align: right;\">6.073e-7 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.000116602 d^-1</td><td style = \"text-align: right;\">1.45752e-5 d^-1</td><td style = \"text-align: right;\">3.09171e-5 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">443.022 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">298</td><td style = \"text-align: right;\">7128.0 hr</td><td style = \"text-align: right;\">297.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.005 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">9.4253e-6 hr^-1</td><td style = \"text-align: right;\">5.89081e-7 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.000113104 d^-1</td><td style = \"text-align: right;\">1.41379e-5 d^-1</td><td style = \"text-align: right;\">2.99896e-5 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">443.036 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">299</td><td style = \"text-align: right;\">7152.0 hr</td><td style = \"text-align: right;\">298.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.005 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">9.14254e-6 hr^-1</td><td style = \"text-align: right;\">5.71409e-7 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.00010971 d^-1</td><td style = \"text-align: right;\">1.37138e-5 d^-1</td><td style = \"text-align: right;\">2.90899e-5 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">443.049 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">300</td><td style = \"text-align: right;\">7176.0 hr</td><td style = \"text-align: right;\">299.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.005 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">8.86826e-6 hr^-1</td><td style = \"text-align: right;\">5.54266e-7 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.000106419 d^-1</td><td style = \"text-align: right;\">1.33024e-5 d^-1</td><td style = \"text-align: right;\">2.82172e-5 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">443.062 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">301</td><td style = \"text-align: right;\">7200.0 hr</td><td style = \"text-align: right;\">300.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.005 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">8.60221e-6 hr^-1</td><td style = \"text-align: right;\">5.37638e-7 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.000103227 d^-1</td><td style = \"text-align: right;\">1.29033e-5 d^-1</td><td style = \"text-align: right;\">2.73707e-5 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">443.074 g</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccccccccc}\n",
       "\t& time & t & c2 & m & n & Amax & Rmax & α & \\\\\n",
       "\t\\hline\n",
       "\t& Quantity… & Quantity… & Float64 & Float64 & Float64 & Quantity… & Quantity… & Quantity… & \\\\\n",
       "\t\\hline\n",
       "\t1 & 0.0 hr & 0.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.005 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t2 & 24.0 hr & 1.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.005 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t3 & 48.0 hr & 2.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.005 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t4 & 72.0 hr & 3.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.005 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t5 & 96.0 hr & 4.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.005 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t6 & 120.0 hr & 5.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.005 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t7 & 144.0 hr & 6.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.005 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t8 & 168.0 hr & 7.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.005 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t9 & 192.0 hr & 8.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.005 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t10 & 216.0 hr & 9.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.005 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t11 & 240.0 hr & 10.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.005 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t12 & 264.0 hr & 11.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.005 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t13 & 288.0 hr & 12.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.005 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t14 & 312.0 hr & 13.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.005 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t15 & 336.0 hr & 14.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.005 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t16 & 360.0 hr & 15.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.005 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t17 & 384.0 hr & 16.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.005 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t18 & 408.0 hr & 17.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.005 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t19 & 432.0 hr & 18.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.005 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t20 & 456.0 hr & 19.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.005 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t21 & 480.0 hr & 20.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.005 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t22 & 504.0 hr & 21.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.005 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t23 & 528.0 hr & 22.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.005 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t24 & 552.0 hr & 23.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.005 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t25 & 576.0 hr & 24.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.005 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t26 & 600.0 hr & 25.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.005 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t27 & 624.0 hr & 26.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.005 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t28 & 648.0 hr & 27.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.005 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t29 & 672.0 hr & 28.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.005 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t30 & 696.0 hr & 29.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.005 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t$\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ &  \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m301×17 DataFrame\n",
       "\u001b[1m Row │\u001b[1m time      \u001b[1m t         \u001b[1m c2       \u001b[1m m       \u001b[1m n       \u001b[1m Amax       \u001b[1m Rmax      ⋯\n",
       "     │\u001b[90m Quantity… \u001b[90m Quantity… \u001b[90m Float64  \u001b[90m Float64 \u001b[90m Float64 \u001b[90m Quantity…  \u001b[90m Quantity… ⋯\n",
       "─────┼──────────────────────────────────────────────────────────────────────────\n",
       "   1 │    0.0 hr      0.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.005 hr^ ⋯\n",
       "   2 │   24.0 hr      1.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.005 hr^\n",
       "   3 │   48.0 hr      2.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.005 hr^\n",
       "   4 │   72.0 hr      3.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.005 hr^\n",
       "   5 │   96.0 hr      4.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.005 hr^ ⋯\n",
       "   6 │  120.0 hr      5.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.005 hr^\n",
       "   7 │  144.0 hr      6.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.005 hr^\n",
       "   8 │  168.0 hr      7.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.005 hr^\n",
       "   9 │  192.0 hr      8.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.005 hr^ ⋯\n",
       "  10 │  216.0 hr      9.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.005 hr^\n",
       "  11 │  240.0 hr     10.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.005 hr^\n",
       "  ⋮  │     ⋮          ⋮         ⋮         ⋮        ⋮         ⋮            ⋮    ⋱\n",
       " 292 │ 6984.0 hr    291.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.005 hr^\n",
       " 293 │ 7008.0 hr    292.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.005 hr^ ⋯\n",
       " 294 │ 7032.0 hr    293.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.005 hr^\n",
       " 295 │ 7056.0 hr    294.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.005 hr^\n",
       " 296 │ 7080.0 hr    295.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.005 hr^\n",
       " 297 │ 7104.0 hr    296.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.005 hr^ ⋯\n",
       " 298 │ 7128.0 hr    297.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.005 hr^\n",
       " 299 │ 7152.0 hr    298.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.005 hr^\n",
       " 300 │ 7176.0 hr    299.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.005 hr^\n",
       " 301 │ 7200.0 hr    300.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.005 hr^ ⋯\n",
       "\u001b[36m                                                 11 columns and 280 rows omitted"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m60 = simulate(Monsi1960, config = c, stop = 300u\"d\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n",
       "<svg xmlns=\"http://www.w3.org/2000/svg\"\n",
       "     xmlns:xlink=\"http://www.w3.org/1999/xlink\"\n",
       "     xmlns:gadfly=\"http://www.gadflyjl.org/ns\"\n",
       "     version=\"1.2\"\n",
       "     width=\"141.42mm\" height=\"100mm\" viewBox=\"0 0 141.42 100\"\n",
       "     stroke=\"none\"\n",
       "     fill=\"#000000\"\n",
       "     stroke-width=\"0.3\"\n",
       "     font-size=\"3.88\"\n",
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       "                '<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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       "  titles=Dict{Symbol, AbstractString}()\n",
       ")\n",
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      ]
     },
     "execution_count": 19,
     "metadata": {
      "@webio": {
       "kernelId": "773e1f5a-01c5-4b71-ae66-40e4fcf904ab"
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "manipulate(Monsi1960, :t, :W;\n",
    "    parameters = Monsi1960 => (;\n",
    "        :m => 0:0.01:1,\n",
    "        :α => 0:0.001:0.06,\n",
    "    ),\n",
    "    config = c,\n",
    "    stop = 300u\"d\",\n",
    "    ylim = (0, 500),\n",
    "    kind = :line,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "\"<Cropbox.Plot{Gadfly.Plot}>\""
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = visualize(t70, :t, :W, kind = :line, name = \"Thornley (1970)\")\n",
    "visualize!(p, m60, :t, :W, kind = :line, name = \"Monsi (1960)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Ex 2.6\n",
    "\n",
    "What are the physiological and micrometeorological mechanisms missing in Thornley and Monsi models you examined above? Why are they important? How would you incorporate them into the models?  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.3. Senescence and decline of biomass\n",
    "\n",
    "Plants, especially annuals, will lose their biomass. Cells, tissues, and organs will senesce, die, and disintegrate eventually, and are no longer part of the living \"biomass\". The models we've looked at so far do not account for this aspect of senescence and death. Think about how the processes and mechanisms associated with senescence and death of plant can be implemented in these models. Some useful information may be found in Table 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Ex 2.7\n",
    "\n",
    "This is an open exercise where you will build your own plant growth model that accounts for photosynthesis, respiration, allocation, and senescence based on the exercises above. Any part of this exercise can be reused, repurposed, and modified to do this exercise."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Table 4.1.\n",
    "\n",
    "| Symbol | Value | Units | Description |\n",
    "| :- | :- | :- | :- |\n",
    "| $\\alpha_{\\mathrm{sen}}$ | 100 | $\\mathrm{d}$ | Plant age (days) at which senescence begins |\n",
    "| $k_s$ | 0.01 | $\\mathrm{g}$ $\\mathrm{g^{-1}}$ $\\mathrm{d^{-1}}$ | Senescence rate of degradable biomass over time |\n",
    "| $f_d$ | 1.0 | - | Fraction of degradable biomass |\n",
    "| ... | - | - | ... |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MyPlantModel"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@system MyPlantModel(Controller) begin\n",
    "    t(context.clock.time) ~ track(u\"d\")\n",
    "\n",
    "    c2: conversion_factor => 12/44/0.45 ~ preserve(parameter)    \n",
    "\n",
    "    m:    leaf_mass_ratio   => 0.5 ~ preserve(parameter)\n",
    "    n(m): non_leaf_fraction => 1-m ~ track\n",
    "\n",
    "    Amax: maximal_assimilation => 0.08  ~ preserve(parameter, u\"g/g/hr\")\n",
    "    Rmax: maximal_respiration  => 0.006 ~ preserve(parameter, u\"g/g/hr\")\n",
    "\n",
    "    α:       decay_rate                   => 0.03 ~ preserve(parameter, u\"d^-1\")\n",
    "    A(α, A): hourly_assimilation_per_mass => -α*A ~ accumulate(init = Amax, u\"g/g/hr\")\n",
    "    R(α, R): hourly_respiration_per_mass  => -α*R ~ accumulate(init = Rmax, u\"g/g/hr\")\n",
    "\n",
    "    DL: day_length  => 12 ~ preserve(parameter, u\"hr\")\n",
    "    D:  total_hours => 24 ~ preserve(parameter, u\"hr\")\n",
    "\n",
    "    A′(A, DL, D): assimilation_per_mass => A * (DL/D) ~ track(u\"g/g/d\")\n",
    "    R′(R):        respiration_per_mass                ~ track(u\"g/g/d\")\n",
    "\n",
    "    r(c2, m, n, A′, R′): RGR => c2 * (m*A′ - n*R′) ~ track(u\"g/g/d\")\n",
    "\n",
    "    ks:          senescence_rate => 0.01       ~ preserve(parameter, u\"g/g/d\")\n",
    "    W0:          initial_biomass => 0.15       ~ preserve(parameter, u\"g\")\n",
    "    W(r, ks, W): biomass         => (r - ks)*W ~ accumulate(init = W0, u\"g\")\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>301×18 DataFrame</span></div><div style = \"float: right;\"><span style = \"font-style: italic;\">276 rows omitted</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">time</th><th style = \"text-align: left;\">t</th><th style = \"text-align: left;\">c2</th><th style = \"text-align: left;\">m</th><th style = \"text-align: left;\">n</th><th style = \"text-align: left;\">Amax</th><th style = \"text-align: left;\">Rmax</th><th style = \"text-align: left;\">α</th><th style = \"text-align: left;\">A</th><th style = \"text-align: left;\">R</th><th style = \"text-align: left;\">DL</th><th style = \"text-align: left;\">D</th><th style = \"text-align: left;\">A′</th><th style = \"text-align: left;\">R′</th><th style = \"text-align: left;\">r</th><th style = \"text-align: left;\">ks</th><th style = \"text-align: left;\">W0</th><th style = \"text-align: left;\">W</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Unitful.Quantity{Float64, 𝐓, Unitful.FreeUnits{(hr,), 𝐓, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝐓, Unitful.FreeUnits{(d,), 𝐓, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Unitful.Quantity{Float64, 𝐓^-1, Unitful.FreeUnits{(hr^-1,), 𝐓^-1, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝐓^-1, Unitful.FreeUnits{(hr^-1,), 𝐓^-1, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝐓^-1, Unitful.FreeUnits{(d^-1,), 𝐓^-1, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝐓^-1, Unitful.FreeUnits{(hr^-1,), 𝐓^-1, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝐓^-1, Unitful.FreeUnits{(hr^-1,), 𝐓^-1, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝐓, Unitful.FreeUnits{(hr,), 𝐓, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝐓, Unitful.FreeUnits{(hr,), 𝐓, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝐓^-1, Unitful.FreeUnits{(d^-1,), 𝐓^-1, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝐓^-1, Unitful.FreeUnits{(d^-1,), 𝐓^-1, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝐓^-1, Unitful.FreeUnits{(d^-1,), 𝐓^-1, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝐓^-1, Unitful.FreeUnits{(d^-1,), 𝐓^-1, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝐌, Unitful.FreeUnits{(g,), 𝐌, nothing}}\" style = \"text-align: left;\">Quantity…</th><th title = \"Unitful.Quantity{Float64, 𝐌, Unitful.FreeUnits{(g,), 𝐌, nothing}}\" style = \"text-align: left;\">Quantity…</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">0.0 hr</td><td style = \"text-align: right;\">0.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.006 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.006 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.96 d^-1</td><td style = \"text-align: right;\">0.144 d^-1</td><td style = \"text-align: right;\">0.247273 d^-1</td><td style = \"text-align: right;\">0.01 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">0.15 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">1.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.006 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.0776 hr^-1</td><td style = \"text-align: right;\">0.00582 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.9312 d^-1</td><td style = \"text-align: right;\">0.13968 d^-1</td><td style = \"text-align: right;\">0.239855 d^-1</td><td style = \"text-align: right;\">0.01 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">0.185591 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">48.0 hr</td><td style = \"text-align: right;\">2.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.006 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.075272 hr^-1</td><td style = \"text-align: right;\">0.0056454 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.903264 d^-1</td><td style = \"text-align: right;\">0.13549 d^-1</td><td style = \"text-align: right;\">0.232659 d^-1</td><td style = \"text-align: right;\">0.01 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">0.22825 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">72.0 hr</td><td style = \"text-align: right;\">3.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.006 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.0730138 hr^-1</td><td style = \"text-align: right;\">0.00547604 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.876166 d^-1</td><td style = \"text-align: right;\">0.131425 d^-1</td><td style = \"text-align: right;\">0.225679 d^-1</td><td style = \"text-align: right;\">0.01 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">0.279072 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">96.0 hr</td><td style = \"text-align: right;\">4.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.006 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.0708234 hr^-1</td><td style = \"text-align: right;\">0.00531176 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.849881 d^-1</td><td style = \"text-align: right;\">0.127482 d^-1</td><td style = \"text-align: right;\">0.218909 d^-1</td><td style = \"text-align: right;\">0.01 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">0.339262 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">120.0 hr</td><td style = \"text-align: right;\">5.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.006 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.0686987 hr^-1</td><td style = \"text-align: right;\">0.0051524 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.824385 d^-1</td><td style = \"text-align: right;\">0.123658 d^-1</td><td style = \"text-align: right;\">0.212342 d^-1</td><td style = \"text-align: right;\">0.01 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">0.410136 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">144.0 hr</td><td style = \"text-align: right;\">6.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.006 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.0666378 hr^-1</td><td style = \"text-align: right;\">0.00499783 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.799653 d^-1</td><td style = \"text-align: right;\">0.119948 d^-1</td><td style = \"text-align: right;\">0.205971 d^-1</td><td style = \"text-align: right;\">0.01 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">0.493124 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">168.0 hr</td><td style = \"text-align: right;\">7.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.006 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.0646386 hr^-1</td><td style = \"text-align: right;\">0.0048479 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.775664 d^-1</td><td style = \"text-align: right;\">0.11635 d^-1</td><td style = \"text-align: right;\">0.199792 d^-1</td><td style = \"text-align: right;\">0.01 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">0.589762 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">192.0 hr</td><td style = \"text-align: right;\">8.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.006 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.0626995 hr^-1</td><td style = \"text-align: right;\">0.00470246 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.752394 d^-1</td><td style = \"text-align: right;\">0.112859 d^-1</td><td style = \"text-align: right;\">0.193798 d^-1</td><td style = \"text-align: right;\">0.01 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">0.701694 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: right;\">216.0 hr</td><td style = \"text-align: right;\">9.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.006 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.0608185 hr^-1</td><td style = \"text-align: right;\">0.00456139 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.729822 d^-1</td><td style = \"text-align: right;\">0.109473 d^-1</td><td style = \"text-align: right;\">0.187984 d^-1</td><td style = \"text-align: right;\">0.01 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">0.830665 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">11</td><td style = \"text-align: right;\">240.0 hr</td><td style = \"text-align: right;\">10.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.006 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.0589939 hr^-1</td><td style = \"text-align: right;\">0.00442454 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.707927 d^-1</td><td style = \"text-align: right;\">0.106189 d^-1</td><td style = \"text-align: right;\">0.182345 d^-1</td><td style = \"text-align: right;\">0.01 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">0.97851 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">12</td><td style = \"text-align: right;\">264.0 hr</td><td style = \"text-align: right;\">11.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.006 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.0572241 hr^-1</td><td style = \"text-align: right;\">0.00429181 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.686689 d^-1</td><td style = \"text-align: right;\">0.103003 d^-1</td><td style = \"text-align: right;\">0.176875 d^-1</td><td style = \"text-align: right;\">0.01 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">1.14715 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">13</td><td style = \"text-align: right;\">288.0 hr</td><td style = \"text-align: right;\">12.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.006 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">0.0555074 hr^-1</td><td style = \"text-align: right;\">0.00416305 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.666089 d^-1</td><td style = \"text-align: right;\">0.0999133 d^-1</td><td style = \"text-align: right;\">0.171568 d^-1</td><td style = \"text-align: right;\">0.01 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">1.33858 g</td></tr><tr><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">290</td><td style = \"text-align: right;\">6936.0 hr</td><td style = \"text-align: right;\">289.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.006 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">1.2026e-5 hr^-1</td><td style = \"text-align: right;\">9.0195e-7 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.000144312 d^-1</td><td style = \"text-align: right;\">2.16468e-5 d^-1</td><td style = \"text-align: right;\">3.71713e-5 d^-1</td><td style = \"text-align: right;\">0.01 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">21.0549 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">291</td><td style = \"text-align: right;\">6960.0 hr</td><td style = \"text-align: right;\">290.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.006 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">1.16652e-5 hr^-1</td><td style = \"text-align: right;\">8.74891e-7 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.000139983 d^-1</td><td style = \"text-align: right;\">2.09974e-5 d^-1</td><td style = \"text-align: right;\">3.60561e-5 d^-1</td><td style = \"text-align: right;\">0.01 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">20.8452 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">292</td><td style = \"text-align: right;\">6984.0 hr</td><td style = \"text-align: right;\">291.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.006 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">1.13153e-5 hr^-1</td><td style = \"text-align: right;\">8.48645e-7 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.000135783 d^-1</td><td style = \"text-align: right;\">2.03675e-5 d^-1</td><td style = \"text-align: right;\">3.49744e-5 d^-1</td><td style = \"text-align: right;\">0.01 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">20.6375 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">293</td><td style = \"text-align: right;\">7008.0 hr</td><td style = \"text-align: right;\">292.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.006 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">1.09758e-5 hr^-1</td><td style = \"text-align: right;\">8.23185e-7 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.00013171 d^-1</td><td style = \"text-align: right;\">1.97564e-5 d^-1</td><td style = \"text-align: right;\">3.39252e-5 d^-1</td><td style = \"text-align: right;\">0.01 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">20.4318 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">294</td><td style = \"text-align: right;\">7032.0 hr</td><td style = \"text-align: right;\">293.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.006 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">1.06465e-5 hr^-1</td><td style = \"text-align: right;\">7.9849e-7 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.000127758 d^-1</td><td style = \"text-align: right;\">1.91638e-5 d^-1</td><td style = \"text-align: right;\">3.29075e-5 d^-1</td><td style = \"text-align: right;\">0.01 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">20.2282 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">295</td><td style = \"text-align: right;\">7056.0 hr</td><td style = \"text-align: right;\">294.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.006 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">1.03271e-5 hr^-1</td><td style = \"text-align: right;\">7.74535e-7 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.000123926 d^-1</td><td style = \"text-align: right;\">1.85888e-5 d^-1</td><td style = \"text-align: right;\">3.19202e-5 d^-1</td><td style = \"text-align: right;\">0.01 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">20.0266 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">296</td><td style = \"text-align: right;\">7080.0 hr</td><td style = \"text-align: right;\">295.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.006 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">1.00173e-5 hr^-1</td><td style = \"text-align: right;\">7.51299e-7 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.000120208 d^-1</td><td style = \"text-align: right;\">1.80312e-5 d^-1</td><td style = \"text-align: right;\">3.09626e-5 d^-1</td><td style = \"text-align: right;\">0.01 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">19.827 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">297</td><td style = \"text-align: right;\">7104.0 hr</td><td style = \"text-align: right;\">296.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.006 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">9.7168e-6 hr^-1</td><td style = \"text-align: right;\">7.2876e-7 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.000116602 d^-1</td><td style = \"text-align: right;\">1.74902e-5 d^-1</td><td style = \"text-align: right;\">3.00338e-5 d^-1</td><td style = \"text-align: right;\">0.01 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">19.6293 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">298</td><td style = \"text-align: right;\">7128.0 hr</td><td style = \"text-align: right;\">297.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.006 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">9.4253e-6 hr^-1</td><td style = \"text-align: right;\">7.06897e-7 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.000113104 d^-1</td><td style = \"text-align: right;\">1.69655e-5 d^-1</td><td style = \"text-align: right;\">2.91327e-5 d^-1</td><td style = \"text-align: right;\">0.01 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">19.4336 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">299</td><td style = \"text-align: right;\">7152.0 hr</td><td style = \"text-align: right;\">298.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.006 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">9.14254e-6 hr^-1</td><td style = \"text-align: right;\">6.8569e-7 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.00010971 d^-1</td><td style = \"text-align: right;\">1.64566e-5 d^-1</td><td style = \"text-align: right;\">2.82588e-5 d^-1</td><td style = \"text-align: right;\">0.01 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">19.2398 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">300</td><td style = \"text-align: right;\">7176.0 hr</td><td style = \"text-align: right;\">299.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.006 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">8.86826e-6 hr^-1</td><td style = \"text-align: right;\">6.6512e-7 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.000106419 d^-1</td><td style = \"text-align: right;\">1.59629e-5 d^-1</td><td style = \"text-align: right;\">2.7411e-5 d^-1</td><td style = \"text-align: right;\">0.01 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">19.048 g</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">301</td><td style = \"text-align: right;\">7200.0 hr</td><td style = \"text-align: right;\">300.0 d</td><td style = \"text-align: right;\">0.606061</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.5</td><td style = \"text-align: right;\">0.08 hr^-1</td><td style = \"text-align: right;\">0.006 hr^-1</td><td style = \"text-align: right;\">0.03 d^-1</td><td style = \"text-align: right;\">8.60221e-6 hr^-1</td><td style = \"text-align: right;\">6.45166e-7 hr^-1</td><td style = \"text-align: right;\">12.0 hr</td><td style = \"text-align: right;\">24.0 hr</td><td style = \"text-align: right;\">0.000103227 d^-1</td><td style = \"text-align: right;\">1.5484e-5 d^-1</td><td style = \"text-align: right;\">2.65887e-5 d^-1</td><td style = \"text-align: right;\">0.01 d^-1</td><td style = \"text-align: right;\">0.15 g</td><td style = \"text-align: right;\">18.858 g</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccccccccc}\n",
       "\t& time & t & c2 & m & n & Amax & Rmax & α & \\\\\n",
       "\t\\hline\n",
       "\t& Quantity… & Quantity… & Float64 & Float64 & Float64 & Quantity… & Quantity… & Quantity… & \\\\\n",
       "\t\\hline\n",
       "\t1 & 0.0 hr & 0.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.006 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t2 & 24.0 hr & 1.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.006 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t3 & 48.0 hr & 2.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.006 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t4 & 72.0 hr & 3.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.006 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t5 & 96.0 hr & 4.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.006 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t6 & 120.0 hr & 5.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.006 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t7 & 144.0 hr & 6.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.006 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t8 & 168.0 hr & 7.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.006 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t9 & 192.0 hr & 8.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.006 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t10 & 216.0 hr & 9.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.006 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t11 & 240.0 hr & 10.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.006 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t12 & 264.0 hr & 11.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.006 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t13 & 288.0 hr & 12.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.006 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t14 & 312.0 hr & 13.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.006 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t15 & 336.0 hr & 14.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.006 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t16 & 360.0 hr & 15.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.006 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t17 & 384.0 hr & 16.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.006 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t18 & 408.0 hr & 17.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.006 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t19 & 432.0 hr & 18.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.006 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t20 & 456.0 hr & 19.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.006 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t21 & 480.0 hr & 20.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.006 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t22 & 504.0 hr & 21.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.006 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t23 & 528.0 hr & 22.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.006 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t24 & 552.0 hr & 23.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.006 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t25 & 576.0 hr & 24.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.006 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t26 & 600.0 hr & 25.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.006 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t27 & 624.0 hr & 26.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.006 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t28 & 648.0 hr & 27.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.006 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t29 & 672.0 hr & 28.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.006 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t30 & 696.0 hr & 29.0 d & 0.606061 & 0.5 & 0.5 & 0.08 hr\\^-1 & 0.006 hr\\^-1 & 0.03 d\\^-1 & $\\dots$ \\\\\n",
       "\t$\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ &  \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m301×18 DataFrame\n",
       "\u001b[1m Row │\u001b[1m time      \u001b[1m t         \u001b[1m c2       \u001b[1m m       \u001b[1m n       \u001b[1m Amax       \u001b[1m Rmax      ⋯\n",
       "     │\u001b[90m Quantity… \u001b[90m Quantity… \u001b[90m Float64  \u001b[90m Float64 \u001b[90m Float64 \u001b[90m Quantity…  \u001b[90m Quantity… ⋯\n",
       "─────┼──────────────────────────────────────────────────────────────────────────\n",
       "   1 │    0.0 hr      0.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.006 hr^ ⋯\n",
       "   2 │   24.0 hr      1.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.006 hr^\n",
       "   3 │   48.0 hr      2.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.006 hr^\n",
       "   4 │   72.0 hr      3.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.006 hr^\n",
       "   5 │   96.0 hr      4.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.006 hr^ ⋯\n",
       "   6 │  120.0 hr      5.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.006 hr^\n",
       "   7 │  144.0 hr      6.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.006 hr^\n",
       "   8 │  168.0 hr      7.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.006 hr^\n",
       "   9 │  192.0 hr      8.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.006 hr^ ⋯\n",
       "  10 │  216.0 hr      9.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.006 hr^\n",
       "  11 │  240.0 hr     10.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.006 hr^\n",
       "  ⋮  │     ⋮          ⋮         ⋮         ⋮        ⋮         ⋮            ⋮    ⋱\n",
       " 292 │ 6984.0 hr    291.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.006 hr^\n",
       " 293 │ 7008.0 hr    292.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.006 hr^ ⋯\n",
       " 294 │ 7032.0 hr    293.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.006 hr^\n",
       " 295 │ 7056.0 hr    294.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.006 hr^\n",
       " 296 │ 7080.0 hr    295.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.006 hr^\n",
       " 297 │ 7104.0 hr    296.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.006 hr^ ⋯\n",
       " 298 │ 7128.0 hr    297.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.006 hr^\n",
       " 299 │ 7152.0 hr    298.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.006 hr^\n",
       " 300 │ 7176.0 hr    299.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.006 hr^\n",
       " 301 │ 7200.0 hr    300.0 d  0.606061      0.5      0.5  0.08 hr^-1  0.006 hr^ ⋯\n",
       "\u001b[36m                                                 12 columns and 280 rows omitted"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mp = simulate(MyPlantModel, config = Clock => :step => 1u\"d\", stop = 300u\"d\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
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     "execution_count": 23,
     "metadata": {},
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    "visualize(mp, :t, :W, kind = :line)"
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   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
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     "execution_count": 25,
     "metadata": {},
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    "visualize(mp, :t, :r, kind = :line)"
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   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
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      "text/plain": [
       "\"<Cropbox.Plot{Gadfly.Plot}>\""
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "visualize(mp, :t, :(r - ks), kind = :line, ylim = (-0.1, 0.3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You may construct the same system with much less code by reusing `Monsi1960` system as a mix-in."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MyPlantModel2"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@system MyPlantModel2(Monsi1960, Controller) begin\n",
    "    ks:          senescence_rate => 0.01       ~ preserve(parameter, u\"g/g/d\")\n",
    "    W(r, ks, W): biomass         => (r - ks)*W ~ accumulate(init = W0, u\"g\")\n",
    "end"
   ]
  }
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