{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "interactive-link",
   "metadata": {},
   "source": [
    "> **This is a saved, working copy.** Sliders here are frozen at their\n",
    "> starting value — there's no marimo runtime in plain Jupyter to drive them.\n",
    "> For the live, drag-the-sliders version of this lab, see\n",
    "> [Week 2 lab — interactive](https://math4120.pages.dev/wasm/week02_lab.html).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ipython-import",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:35.544651Z",
     "iopub.status.busy": "2026-11-13T23:25:35.544505Z",
     "iopub.status.idle": "2026-11-13T23:25:35.548284Z",
     "shell.execute_reply": "2026-11-13T23:25:35.547561Z"
    }
   },
   "outputs": [],
   "source": [
    "from IPython.display import Markdown, HTML\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "Hbol",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "# Week 2 lab — Nondimensionalisation\n",
    "\n",
    "**MATH4120 — Mathematical Modelling and Programming** Lancaster University, 2026–27\n",
    "\n",
    "---\n",
    "\n",
    "Work through the exercises below. Press **Ctrl+Enter** (or **Shift+Enter**) to run a cell and see its output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "MJUe",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:35.550148Z",
     "iopub.status.busy": "2026-11-13T23:25:35.549880Z",
     "iopub.status.idle": "2026-11-13T23:25:35.923432Z",
     "shell.execute_reply": "2026-11-13T23:25:35.922227Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "vblA",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## Parameters\n",
    "\n",
    "A cup of coffee cools in a room.  You can change these numbers at any point and everything below will update automatically."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "bkHC",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:35.925937Z",
     "iopub.status.busy": "2026-11-13T23:25:35.925649Z",
     "iopub.status.idle": "2026-11-13T23:25:35.929126Z",
     "shell.execute_reply": "2026-11-13T23:25:35.928313Z"
    }
   },
   "outputs": [],
   "source": [
    "k    = 0.05   # cooling rate (min⁻¹)\n",
    "T0   = 90.0   # initial temperature (°C)\n",
    "Tinf = 20.0   # ambient temperature (°C)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "lEQa",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## Exercise 1 — one time, three quantities\n",
    "\n",
    "Newton's law of cooling has analytic solution $$T(t) = T_\\infty + (T_0 - T_\\infty)\\,e^{-kt}.$$\n",
    "\n",
    "The nondimensional variables are $s = kt$ and $\\theta = (T - T_\\infty)/(T_0 - T_\\infty)$.\n",
    "\n",
    "**Task.** In the cell below, replace the three `0.0` placeholders with the correct formulas. Use `k`, `T0`, `Tinf`, `t`, and `np.exp(...)`. Run the cell.  You should get roughly $T \\approx 62$°C, $s = 0.5$, $\\theta \\approx 0.61$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "PKri",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:35.930708Z",
     "iopub.status.busy": "2026-11-13T23:25:35.930563Z",
     "iopub.status.idle": "2026-11-13T23:25:35.936220Z",
     "shell.execute_reply": "2026-11-13T23:25:35.935414Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 0.0, 0.0)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t     = 10.0\n",
    "T     = 0.0    # ← temperature at time t\n",
    "s     = 0.0    # ← dimensionless time\n",
    "theta = 0.0    # ← dimensionless temperature\n",
    "T, s, theta"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "Xref",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## Exercise 2 — over a range of times\n",
    "\n",
    "Now compute $T$, $s$, and $\\theta$ for every time in an array. The array `t_arr` is already defined.  Replace the three `np.zeros_like(t_arr)` placeholders with the same formulas as Exercise 1 — just using `t_arr` instead of `t`.\n",
    "\n",
    "When you run the cell, the plot below will update."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "SFPL",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:35.937760Z",
     "iopub.status.busy": "2026-11-13T23:25:35.937626Z",
     "iopub.status.idle": "2026-11-13T23:25:35.940756Z",
     "shell.execute_reply": "2026-11-13T23:25:35.939894Z"
    }
   },
   "outputs": [],
   "source": [
    "t_arr     = np.linspace(0, 30, 300)\n",
    "T_arr     = np.zeros_like(t_arr)    # ← same formula as Ex 1, but for t_arr\n",
    "s_arr     = np.zeros_like(t_arr)    # ← same formula as Ex 1, but for t_arr\n",
    "theta_arr = np.zeros_like(t_arr)    # ← same formula as Ex 1, but for t_arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "BYtC",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:35.942472Z",
     "iopub.status.busy": "2026-11-13T23:25:35.942259Z",
     "iopub.status.idle": "2026-11-13T23:25:36.352300Z",
     "shell.execute_reply": "2026-11-13T23:25:36.351484Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1100x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_s_ref = np.linspace(0, max(s_arr.max(), 0.1), 300)\n",
    "\n",
    "_fig, (_ax_dim, _ax_nd) = plt.subplots(1, 2, figsize=(11, 4))\n",
    "\n",
    "_ax_dim.plot(t_arr, T_arr, color=\"#1a5276\", linewidth=2)\n",
    "_ax_dim.axhline(Tinf, color=\"grey\", linestyle=\":\", linewidth=1.5,\n",
    "                label=f\"$T_\\\\infty = {Tinf:.0f}$°C\")\n",
    "_ax_dim.set_xlabel(\"Time $t$ (min)\", fontsize=12)\n",
    "_ax_dim.set_ylabel(\"Temperature $T$ (°C)\", fontsize=12)\n",
    "_ax_dim.set_title(f\"Dimensional   ($k = {k}$)\", fontsize=12)\n",
    "_ax_dim.legend(fontsize=10)\n",
    "_ax_dim.grid(True, alpha=0.3)\n",
    "\n",
    "_ax_nd.plot(s_arr, theta_arr, color=\"#1a5276\", linewidth=2, label=\"your solution\")\n",
    "_ax_nd.plot(_s_ref, np.exp(-_s_ref), \"k--\", linewidth=1.5, label=r\"$e^{-s}$\")\n",
    "_ax_nd.set_xlabel(\"Dimensionless time $s = kt$\", fontsize=12)\n",
    "_ax_nd.set_ylabel(r\"$\\theta(s)$\", fontsize=12)\n",
    "_ax_nd.set_title(\"Nondimensional\", fontsize=12)\n",
    "_ax_nd.legend(fontsize=10)\n",
    "_ax_nd.grid(True, alpha=0.3)\n",
    "\n",
    "_fig.tight_layout()\n",
    "_fig;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "RGSE",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## Exercise 3 — numerical verification\n",
    "\n",
    "If your formulas in Exercise 2 are correct, `theta_arr` should match $e^{-s}$ evaluated at every point in `s_arr`.\n",
    "\n",
    "**Task.** Run the cell below.  The number it prints is the largest pointwise difference between your solution and the exact answer.  How small is it?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "Kclp",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:36.354589Z",
     "iopub.status.busy": "2026-11-13T23:25:36.354390Z",
     "iopub.status.idle": "2026-11-13T23:25:36.358110Z",
     "shell.execute_reply": "2026-11-13T23:25:36.357293Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(1.0)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(np.abs(theta_arr - np.exp(-s_arr)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "emfo",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## Observation — solution collapse\n",
    "\n",
    "Once your formulas are correct, the right panel should show your curve sitting exactly on top of $e^{-s}$.\n",
    "\n",
    "**Now go back to the parameters cell at the top and change $k$.** Try $k = 0.1$, then $k = 2.0$.\n",
    "\n",
    "- What changes in the left panel?\n",
    "- What changes in the right panel?\n",
    "\n",
    "This is **solution collapse**: every Newton's cooling experiment, regardless of $k$, $T_0$, or $T_\\infty$, maps to the same nondimensional curve $\\theta(s) = e^{-s}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "Hstk",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## Extension — a new scenario\n",
    "\n",
    "A pan of water starts at $T_0 = 95$°C in a cold kitchen at $T_\\infty = 5$°C with cooling rate $k = 0.08$ s⁻¹.\n",
    "\n",
    "**Task.**\n",
    "1. Update the parameters cell at the top.\n",
    "2. Update $t$ in Exercise 1 to find the temperature after 20 s.\n",
    "3. Does $\\theta$ change compared to the coffee? Should it?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "nWHF",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## AI extension — feature normalisation\n",
    "\n",
    "In machine learning, before training a model you almost always *normalise* the input data.  The most common recipe is **standardisation**: subtract the mean, divide by the standard deviation, so every variable is centred at zero with spread one. Libraries like scikit-learn do this automatically with `StandardScaler`.\n",
    "\n",
    "Written in NumPy it is just two lines:\n",
    "```python\n",
    "theta_stat = (T_arr - T_arr.mean()) / T_arr.std()\n",
    "```\n",
    "\n",
    "This looks a lot like what you did in Exercise 2 — but the scales are *data-driven* (mean and std of your particular dataset) rather than *physics-motivated* ($T_0$ and $T_\\infty$).\n",
    "\n",
    "**Task.**\n",
    "1. Run the cell below.  The plot shows your physical $\\theta$ alongside the statistically standardised version.\n",
    "2. What does $\\theta_\\text{stat} = 0$ mean physically? What does $\\theta = 0$ mean physically?\n",
    "3. Which normalisation is more interpretable, and why?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "iLit",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:36.359767Z",
     "iopub.status.busy": "2026-11-13T23:25:36.359620Z",
     "iopub.status.idle": "2026-11-13T23:25:36.365352Z",
     "shell.execute_reply": "2026-11-13T23:25:36.364583Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_15307/3543410467.py:1: RuntimeWarning: invalid value encountered in divide\n",
      "  theta_stat = (T_arr - T_arr.mean()) / T_arr.std()\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n",
       "       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n",
       "       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n",
       "       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n",
       "       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n",
       "       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n",
       "       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n",
       "       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n",
       "       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n",
       "       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n",
       "       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n",
       "       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n",
       "       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n",
       "       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n",
       "       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n",
       "       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n",
       "       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n",
       "       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n",
       "       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n",
       "       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n",
       "       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n",
       "       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n",
       "       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n",
       "       nan])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_stat = (T_arr - T_arr.mean()) / T_arr.std()\n",
    "theta_stat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ZHCJ",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:36.367252Z",
     "iopub.status.busy": "2026-11-13T23:25:36.367106Z",
     "iopub.status.idle": "2026-11-13T23:25:36.548357Z",
     "shell.execute_reply": "2026-11-13T23:25:36.547454Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_fig, _ax = plt.subplots(figsize=(8, 4))\n",
    "_ax.plot(s_arr, theta_arr,  color=\"#1a5276\", linewidth=2,\n",
    "         label=r\"Physical: $\\theta = (T - T_\\infty)/(T_0 - T_\\infty)$\")\n",
    "_ax.plot(s_arr, theta_stat, color=\"tomato\",  linewidth=2, linestyle=\"--\",\n",
    "         label=r\"Statistical: $(T - \\bar T)/\\sigma_T$\")\n",
    "_ax.plot(np.linspace(0, s_arr.max(), 300),\n",
    "         np.exp(-np.linspace(0, s_arr.max(), 300)),\n",
    "         \"k:\", linewidth=1.5, label=r\"$e^{-s}$\")\n",
    "_ax.axhline(0, color=\"grey\", linewidth=0.8, alpha=0.5)\n",
    "_ax.set_xlabel(\"Dimensionless time $s = kt$\", fontsize=12)\n",
    "_ax.set_ylabel(\"Normalised temperature\", fontsize=12)\n",
    "_ax.set_title(\"Physical vs statistical normalisation\", fontsize=12)\n",
    "_ax.legend(fontsize=10)\n",
    "_ax.grid(True, alpha=0.3)\n",
    "_fig;"
   ]
  }
 ],
 "metadata": {
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.3"
  },
  "marimo": {
   "app_config": {
    "app_title": "Week 2 Lab — Nondimensionalisation",
    "width": "medium"
   },
   "marimo_version": "0.25.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}