Create DP-Sea-Polarization-Model.ipynb

Author: tlabshier

dp-sea-polarization/DP-Sea-Polarization-Model.ipynb

@@ -0,0 +1,165 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# CPP-600-Cell Dream Model\n",
+    "## Velocity-Dependent DP Sea Polarization & Inertial Resistance\n",
+    "\n",
+    "Inspired by dream insight after 60-probe handedness paper.\n",
+    "\n",
+    "Goal: reproduce silly-putty behavior (transparent → viscous → solid) and converge to Lorentz γ(v)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from scipy.constants import c\n",
+    "\n",
+    "# Constants (tunable)\n",
+    "v0 = c          # characteristic velocity (m/s)\n",
+    "alpha = 1.8     # sharpness of transition\n",
+    "k_omega = 2.0   # frequency coupling\n",
+    "beta = 3.0      # closest-approach coupling\n",
+    "k_q = 1.5       # charge enhancement\n",
+    "k_f = 1.0       # force multiplier\n",
+    "omega0 = 1e20   # base ZBW frequency (rad/s)\n",
+    "d0 = 1e-15      # base closest approach (m)\n",
+    "\n",
+    "def P(v, r=None):\n",
+    "    \"\"\"Polarization of DP Sea (v in m/s)\"\"\"\n",
+    "    if r is None:\n",
+    "        return np.tanh(v / v0)\n",
+    "    else:\n",
+    "        v0_r = v0 * (r / 1e-10)**0.5  # example radial dependence\n",
+    "        return np.tanh(v / v0_r)\n",
+    "\n",
+    "# Example plot\n",
+    "v = np.linspace(0, 0.999*c, 1000)\n",
+    "plt.figure(figsize=(10,6))\n",
+    "plt.plot(v/c, P(v), label='P(v) (tanh)')\n",
+    "plt.xlabel('v / c')\n",
+    "plt.ylabel('Polarization P')\n",
+    "plt.title('DP Sea Polarization vs Velocity')\n",
+    "plt.grid(True)\n",
+    "plt.legend()\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Tranche 2 – Oscillation Parameters"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def omega(v):\n",
+    "    return omega0 * np.exp(k_omega * P(v))\n",
+    "\n",
+    "def d_min(v):\n",
+    "    return d0 * np.exp(-beta * P(v))\n",
+    "\n",
+    "plt.figure(figsize=(10,6))\n",
+    "plt.semilogy(v/c, omega(v)/omega0, label='ω(v)/ω₀')\n",
+    "plt.semilogy(v/c, d_min(v)/d0, label='d_min(v)/d₀')\n",
+    "plt.xlabel('v / c')\n",
+    "plt.ylabel('Relative value')\n",
+    "plt.title('Oscillation Parameters vs Velocity')\n",
+    "plt.grid(True)\n",
+    "plt.legend()\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Tranche 3 – Repulsive Force (at closest approach)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def F_rep(v):\n",
+    "    return (1 + k_q * P(v))**2 * (omega(v)/omega0) * (d0 / d_min(v))**2\n",
+    "\n",
+    "plt.figure(figsize=(10,6))\n",
+    "plt.semilogy(v/c, F_rep(v), label='F_rep(v) / F₀')\n",
+    "plt.xlabel('v / c')\n",
+    "plt.ylabel('Relative force amplification')\n",
+    "plt.title('Repulsive Force Amplification vs Velocity')\n",
+    "plt.grid(True)\n",
+    "plt.legend()\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Tranche 4 – Effective Mass & Lorentz Convergence"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def gamma(v):\n",
+    "    return 1 / np.sqrt(1 - (v/c)**2)\n",
+    "\n",
+    "def m_eff(v, k=0.04):\n",
+    "    # Simple linear + gamma term\n",
+    "    return 1 + k * (v/c) * gamma(v)\n",
+    "\n",
+    "plt.figure(figsize=(10,6))\n",
+    "plt.plot(v/c, gamma(v), 'k--', label='Lorentz γ(v)')\n",
+    "plt.plot(v/c, m_eff(v), label='m_eff(v) / m₀')\n",
+    "plt.xlabel('v / c')\n",
+    "plt.ylabel('Relative mass')\n",
+    "plt.title('Effective Mass vs Velocity')\n",
+    "plt.grid(True)\n",
+    "plt.legend()\n",
+    "plt.show()"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.10.12"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
+