.PhV Tutorium Gruppe 3.md

Jupyter-Notebooks zu den Tutorien in Physik V.

(PS: manchmal ist GitHub etwas überfordert mit der Vorschau der ganzen Notebooks — am Besten runterladen, oder im Binder anschauen!)

Tutorium 1.ipynb

Tutorium 10.ipynb

Tutorium 11.ipynb

Tutorium 12.ipynb

Tutorium 13.ipynb

Tutorium 3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Physik V Gruppe 3 — Tutorium #3\n",
    "\n",
    "> 19.11.2020         ralf@uni-bonn.de"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
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   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import astropy.units as u\n",
    "import astropy.constants as const\n",
    "\n",
    "import sympy as sy\n",
    "\n",
    "from uncertainties import ufloat, unumpy as unp\n",
    "\n",
    "u.c = u.def_unit('c', const.c)  # verwende 'c' als Einheit, statt als Konstante"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Magie zum hübschen Anzeigen von Ergebnissen:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
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     "iopub.status.busy": "2020-11-19T12:31:57.629198Z",
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     "shell.execute_reply": "2020-11-19T12:31:57.636098Z",
     "shell.execute_reply.started": "2020-11-19T12:31:57.629353Z"
    }
   },
   "outputs": [],
   "source": [
    "from IPython.display import display, Math, Latex, Markdown\n",
    "from IPython.core.magic import register_line_magic, needs_local_scope\n",
    "import re\n",
    "\n",
    "def _pretty(s):\n",
    "    \n",
    "    try:\n",
    "        # `import pint`\n",
    "        if isinstance(s, pint.quantity.Quantity):\n",
    "            return re.sub(r\"\\\\$\", \"\", f\"{s:.5~L}\")\n",
    "    except:\n",
    "        pass\n",
    "    try:\n",
    "        # `import sympy as sy`\n",
    "        if isinstance(s, sy.core.expr.Expr):\n",
    "            return sy.latex(s)\n",
    "    except:\n",
    "        pass\n",
    "    try:\n",
    "        # `import astropy.units as u`\n",
    "        if isinstance(s, (int, float)):\n",
    "            s = u.Quantity(s)\n",
    "        if isinstance(s, u.quantity.Quantity):\n",
    "            return s.to_string(format=\"latex\").lstrip(\"$\").rstrip(\"$\")\n",
    "    except Exception as e:\n",
    "        raise e\n",
    "        pass\n",
    "    \n",
    "    return str(s)\n",
    "\n",
    "def tex(*s, tag=\"align\"):\n",
    "    display(Latex(r\"\\begin{\"+tag+\"}\" + \"\\n\"+ ' '.join(_pretty(e) for e in s) + \"\\n\" + r\"\\end{\"+tag+\"}\"))\n",
    "\n",
    "@register_line_magic(\"tex\")\n",
    "@needs_local_scope\n",
    "def _tex(line, local_ns):\n",
    "    # TODO: handle single `<` and `>`\n",
    "    tex(re.sub(\"<(.*?)>\", lambda m: _pretty(eval(m.group(1))), line))\n",
    "\n",
    "del _tex  # prevent conflicts in interactive session"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# letztes Blatt: A2. Yukawa-Potential"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:57.638604Z",
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     "shell.execute_reply": "2020-11-19T12:31:57.640968Z",
     "shell.execute_reply.started": "2020-11-19T12:31:57.638584Z"
    }
   },
   "outputs": [],
   "source": [
    "m_pi = 140*u.MeV"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "R = \\frac\\hbar{M_X c} \\overset{\\text{nat}}=  \\frac1m\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:57.643482Z",
     "iopub.status.busy": "2020-11-19T12:31:57.643233Z",
     "iopub.status.idle": "2020-11-19T12:31:57.653298Z",
     "shell.execute_reply": "2020-11-19T12:31:57.652815Z",
     "shell.execute_reply.started": "2020-11-19T12:31:57.643454Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$0.0071428571 \\; \\mathrm{\\frac{1}{MeV}}$"
      ],
      "text/plain": [
       "<Quantity 0.00714286 1 / MeV>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_nat = 1/m_pi\n",
    "R_nat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Frage:** Welche Reichweite ergibt sich für den Austausch von Pionen (`m = m_pi`)?\n",
    "\n",
    "**Hausaufgabe:** Mit was muss ich `R_nat` multiplizieren, um auf *Meter* zu kommen?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:57.654206Z",
     "iopub.status.busy": "2020-11-19T12:31:57.654009Z",
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     "shell.execute_reply": "2020-11-19T12:31:57.656562Z",
     "shell.execute_reply.started": "2020-11-19T12:31:57.654175Z"
    }
   },
   "outputs": [],
   "source": [
    "# R_si = ...."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A1. Radiokarbonmethode"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:57.658011Z",
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     "shell.execute_reply": "2020-11-19T12:31:57.661026Z",
     "shell.execute_reply.started": "2020-11-19T12:31:57.657991Z"
    }
   },
   "outputs": [],
   "source": [
    "R0 = 1.5e-12\n",
    "T = 5730*u.a\n",
    "\n",
    "M = 50*u.mg\n",
    "alter = 2000*u.a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Aktivität:\n",
    "$$\n",
    "A(t) = - \\frac{\\mathrm d N(t)}{\\mathrm dt} = \\lambda N_0 e^{-\\lambda t} \\qquad \\lambda = \\frac{\\ln 2}{T_{1/2}}\n",
    "$$\n",
    "\n",
    "$$\n",
    "N_0 = N_A \\frac{M}{m_{\\text{mol}}}\\cdot R_0\n",
    "$$\n",
    "\n",
    "$$R(t) = R_0 e^{-\\lambda t}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:57.663255Z",
     "iopub.status.busy": "2020-11-19T12:31:57.663025Z",
     "iopub.status.idle": "2020-11-19T12:31:57.666489Z",
     "shell.execute_reply": "2020-11-19T12:31:57.665806Z",
     "shell.execute_reply.started": "2020-11-19T12:31:57.663230Z"
    }
   },
   "outputs": [],
   "source": [
    "m_mol = 12 * u.g/u.mol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:57.667500Z",
     "iopub.status.busy": "2020-11-19T12:31:57.667319Z",
     "iopub.status.idle": "2020-11-19T12:31:57.674307Z",
     "shell.execute_reply": "2020-11-19T12:31:57.673679Z",
     "shell.execute_reply.started": "2020-11-19T12:31:57.667479Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "N_0 = 3.763838 \\times 10^{9} \\; \\mathrm{}\n",
       "\\end{align}"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N0 = const.N_A * M / m_mol * R0\n",
    "%tex N_0 = <N0.decompose()>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
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    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "\\lambda = 0.00012096809 \\; \\mathrm{\\frac{1}{a}}\n",
       "\\end{align}"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lam = np.log(2)/T\n",
    "\n",
    "%tex \\lambda = <lam>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
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     "shell.execute_reply.started": "2020-11-19T12:31:57.683474Z"
    }
   },
   "outputs": [],
   "source": [
    "def A(t):\n",
    "    t = u.Quantity(t, u.a)  # <- cheat: t ohne angeben\n",
    "    return (lam*N0 * np.exp(-lam*t)).decompose()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:57.687658Z",
     "iopub.status.busy": "2020-11-19T12:31:57.687469Z",
     "iopub.status.idle": "2020-11-19T12:31:57.692558Z",
     "shell.execute_reply": "2020-11-19T12:31:57.691929Z",
     "shell.execute_reply.started": "2020-11-19T12:31:57.687636Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$0.014427723 \\; \\mathrm{\\frac{1}{s}}$"
      ],
      "text/plain": [
       "<Quantity 0.01442772 1 / s>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:57.693750Z",
     "iopub.status.busy": "2020-11-19T12:31:57.693553Z",
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     "shell.execute_reply.started": "2020-11-19T12:31:57.693728Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "A(0) &= 0.014427723 \\; \\mathrm{\\frac{1}{s}} \\\\ A(2000) &= 0.011327296 \\; \\mathrm{\\frac{1}{s}}\n",
       "\\end{align}"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%tex A(0) &= <A(0)> \\\\ A(2000) &= <A(2000)>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:57.700648Z",
     "iopub.status.busy": "2020-11-19T12:31:57.700487Z",
     "iopub.status.idle": "2020-11-19T12:31:57.703654Z",
     "shell.execute_reply": "2020-11-19T12:31:57.703021Z",
     "shell.execute_reply.started": "2020-11-19T12:31:57.700628Z"
    }
   },
   "outputs": [],
   "source": [
    "def R(t):\n",
    "    t = u.Quantity(t, u.a)  # <- cheat: t ohne angeben\n",
    "    return R0*np.exp(-lam*t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:57.704550Z",
     "iopub.status.busy": "2020-11-19T12:31:57.704394Z",
     "iopub.status.idle": "2020-11-19T12:31:57.708934Z",
     "shell.execute_reply": "2020-11-19T12:31:57.708388Z",
     "shell.execute_reply.started": "2020-11-19T12:31:57.704530Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$1.1776594 \\times 10^{-12} \\; \\mathrm{}$"
      ],
      "text/plain": [
       "<Quantity 1.17765941e-12>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R(2000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:57.709843Z",
     "iopub.status.busy": "2020-11-19T12:31:57.709678Z",
     "iopub.status.idle": "2020-11-19T12:31:57.714433Z",
     "shell.execute_reply": "2020-11-19T12:31:57.713775Z",
     "shell.execute_reply.started": "2020-11-19T12:31:57.709823Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "R_0 = 1.5 \\times 10^{-12} \\; \\mathrm{} \\qquad R(2000) = 1.1776594 \\times 10^{-12} \\; \\mathrm{}\n",
       "\\end{align}"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%tex R_0 = <R0> \\qquad R(2000) = <R(2000)>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### b) Turiner Grabtuch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:57.715415Z",
     "iopub.status.busy": "2020-11-19T12:31:57.715247Z",
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     "shell.execute_reply": "2020-11-19T12:31:57.717262Z",
     "shell.execute_reply.started": "2020-11-19T12:31:57.715394Z"
    }
   },
   "outputs": [],
   "source": [
    "R_turin = 1.373e-12"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\frac{R(t)}{R_0} = e^{-\\lambda t}\n",
    "\\quad\\Rightarrow\\quad t = \\frac{\\ln R_0 - \\ln R(t)}{\\lambda}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:57.719227Z",
     "iopub.status.busy": "2020-11-19T12:31:57.718992Z",
     "iopub.status.idle": "2020-11-19T12:31:57.724945Z",
     "shell.execute_reply": "2020-11-19T12:31:57.724059Z",
     "shell.execute_reply.started": "2020-11-19T12:31:57.719202Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$731.32492 \\; \\mathrm{a}$"
      ],
      "text/plain": [
       "<Quantity 731.3249151 a>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_turin = (np.log(R0) - np.log(R_turin))/lam\n",
    "t_turin"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mit `uncertanities`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:57.726297Z",
     "iopub.status.busy": "2020-11-19T12:31:57.725995Z",
     "iopub.status.idle": "2020-11-19T12:31:57.731500Z",
     "shell.execute_reply": "2020-11-19T12:31:57.730656Z",
     "shell.execute_reply.started": "2020-11-19T12:31:57.726266Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.373e-12+/-5e-15"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_turin = ufloat(1.373e-12, 0.005e-12)  # 1.373(5) * 10^-12\n",
    "R_turin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:57.732918Z",
     "iopub.status.busy": "2020-11-19T12:31:57.732533Z",
     "iopub.status.idle": "2020-11-19T12:31:57.738901Z",
     "shell.execute_reply": "2020-11-19T12:31:57.737757Z",
     "shell.execute_reply.started": "2020-11-19T12:31:57.732860Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.373e-12+/-5e-15"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_turin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:57.740583Z",
     "iopub.status.busy": "2020-11-19T12:31:57.740267Z",
     "iopub.status.idle": "2020-11-19T12:31:57.746453Z",
     "shell.execute_reply": "2020-11-19T12:31:57.745450Z",
     "shell.execute_reply.started": "2020-11-19T12:31:57.740547Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$731.3249151030976+/-30.104306570625496 \\; \\mathrm{a}$"
      ],
      "text/plain": [
       "<Quantity 731.3249151030976+/-30.104306570625496 a>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_turin = (unp.log(R0) - unp.log(R_turin))/lam\n",
    "t_turin"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "…oder per Hand mit Formel:\n",
    "\n",
    "$$\n",
    "\\Delta t = \\left| \\Delta R\\ \\frac{\\partial t}{\\partial R} \\right| = \\frac{\\Delta R}{\\lambda\\,R}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  A2. Tröpfchenmodell"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zahlenwerte (aus der Literatur)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:57.748131Z",
     "iopub.status.busy": "2020-11-19T12:31:57.747824Z",
     "iopub.status.idle": "2020-11-19T12:31:57.754512Z",
     "shell.execute_reply": "2020-11-19T12:31:57.753642Z",
     "shell.execute_reply.started": "2020-11-19T12:31:57.748091Z"
    }
   },
   "outputs": [],
   "source": [
    "# wenn ich sympy verwende, habe ich für die Zahlenwerte immer einen\n",
    "# Unterstrich am Ende, um sie von den \"Symbolen\" zu unterscheiden.\n",
    "\n",
    "a_v_ = 15.67 * u.MeV/u.c**2\n",
    "a_s_ = 17.23 * u.MeV/u.c**2\n",
    "a_c_ = 0.714 * u.MeV/u.c**2\n",
    "a_a_ = 93.15 * u.MeV/u.c**2\n",
    "delta_ = 11.2 * u.MeV/u.c**2   # gg:- uu:+ ug/gu:0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Symbole definieren, für die Verwendung mit sympy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:57.755471Z",
     "iopub.status.busy": "2020-11-19T12:31:57.755277Z",
     "iopub.status.idle": "2020-11-19T12:31:57.760668Z",
     "shell.execute_reply": "2020-11-19T12:31:57.759821Z",
     "shell.execute_reply.started": "2020-11-19T12:31:57.755447Z"
    }
   },
   "outputs": [],
   "source": [
    "a_v, a_s, a_c, a_a, a_p = sy.symbols(\"a_v a_s a_c a_a a_p\", real=True)\n",
    "m_p, m_e, m_n = sy.symbols(\"m_p, m_e m_n\", real=True, positive=True)\n",
    "A, Z = sy.symbols(\"A Z\", real=True, positive=True)\n",
    "\n",
    "# \"real\" und \"positive\" sind hier nicht notwendig,\n",
    "# helfen sympy aber ab und an beim Lösen von Gleichungen"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### kurze Einführung in Sympy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Achtung**, wenn man `numpy` verwendet, wird der Zahlenwert weiterverarbeitet, bevor sympy die Chance hat, etwas zu unternehmen! *nie* numpy verwenden!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:57.761879Z",
     "iopub.status.busy": "2020-11-19T12:31:57.761670Z",
     "iopub.status.idle": "2020-11-19T12:31:58.068407Z",
     "shell.execute_reply": "2020-11-19T12:31:58.067712Z",
     "shell.execute_reply.started": "2020-11-19T12:31:57.761854Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 1.4142135623731 a_{v}$"
      ],
      "text/plain": [
       "1.4142135623731*a_v"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a_v*np.sqrt(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "besser:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:58.069552Z",
     "iopub.status.busy": "2020-11-19T12:31:58.069341Z",
     "iopub.status.idle": "2020-11-19T12:31:58.074838Z",
     "shell.execute_reply": "2020-11-19T12:31:58.074216Z",
     "shell.execute_reply.started": "2020-11-19T12:31:58.069527Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\sqrt{2} a_{v}$"
      ],
      "text/plain": [
       "sqrt(2)*a_v"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res = a_v*sy.sqrt(2)\n",
    "res"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Um einen Wert \"einzusetzen\" kann man `.evalf` verwenden, und die Ersetzungen als `dict` übergeben:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:58.076222Z",
     "iopub.status.busy": "2020-11-19T12:31:58.075901Z",
     "iopub.status.idle": "2020-11-19T12:31:58.081383Z",
     "shell.execute_reply": "2020-11-19T12:31:58.080779Z",
     "shell.execute_reply.started": "2020-11-19T12:31:58.076180Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2.82842712474619$"
      ],
      "text/plain": [
       "2.82842712474619"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res.evalf(subs={a_v: 2})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Achtung** bei rationalen Zahlen! Schlecht:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:58.082417Z",
     "iopub.status.busy": "2020-11-19T12:31:58.082173Z",
     "iopub.status.idle": "2020-11-19T12:31:58.088376Z",
     "shell.execute_reply": "2020-11-19T12:31:58.087614Z",
     "shell.execute_reply.started": "2020-11-19T12:31:58.082384Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle A^{0.666666666666667}$"
      ],
      "text/plain": [
       "A**0.666666666666667"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A**(2/3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "besser: (`sympify` macht aus einem Zahlenwert ein \"Symbol\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:58.091889Z",
     "iopub.status.busy": "2020-11-19T12:31:58.091671Z",
     "iopub.status.idle": "2020-11-19T12:31:58.097837Z",
     "shell.execute_reply": "2020-11-19T12:31:58.097019Z",
     "shell.execute_reply.started": "2020-11-19T12:31:58.091866Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle A^{\\frac{2}{3}}$"
      ],
      "text/plain": [
       "A**(2/3)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A**(sy.sympify(2)/3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "oder:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:58.099298Z",
     "iopub.status.busy": "2020-11-19T12:31:58.099028Z",
     "iopub.status.idle": "2020-11-19T12:31:58.104191Z",
     "shell.execute_reply": "2020-11-19T12:31:58.103414Z",
     "shell.execute_reply.started": "2020-11-19T12:31:58.099274Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle A^{\\frac{2}{3}}$"
      ],
      "text/plain": [
       "A**(2/3)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A**sy.Rational(2, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Massenformel\n",
    "\n",
    "Definition aus der Literatur (ohne $\\delta$, und ohne $f(A)=\\text{const}$):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:58.105952Z",
     "iopub.status.busy": "2020-11-19T12:31:58.105635Z",
     "iopub.status.idle": "2020-11-19T12:31:58.116639Z",
     "shell.execute_reply": "2020-11-19T12:31:58.116028Z",
     "shell.execute_reply.started": "2020-11-19T12:31:58.105913Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Z \\left(- a_{a} + m_{e} - m_{n} + m_{p}\\right) + \\frac{Z^{2} \\left(A^{\\frac{2}{3}} a_{c} + a_{a}\\right)}{A}$"
      ],
      "text/plain": [
       "Z*(-a_a + m_e - m_n + m_p) + Z**2*(A**(2/3)*a_c + a_a)/A"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M = Z*(m_p + m_e - m_n - a_a) + Z**2/A * (a_a + a_c*A**(sy.sympify(2)/3))\n",
    "M"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ableitung nach $Z$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:58.117574Z",
     "iopub.status.busy": "2020-11-19T12:31:58.117408Z",
     "iopub.status.idle": "2020-11-19T12:31:58.131021Z",
     "shell.execute_reply": "2020-11-19T12:31:58.130164Z",
     "shell.execute_reply.started": "2020-11-19T12:31:58.117554Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - a_{a} + m_{e} - m_{n} + m_{p} + \\frac{2 Z \\left(A^{\\frac{2}{3}} a_{c} + a_{a}\\right)}{A}$"
      ],
      "text/plain": [
       "-a_a + m_e - m_n + m_p + 2*Z*(A**(2/3)*a_c + a_a)/A"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dM = sy.diff(M, Z)\n",
    "dM"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`sy.solve` setzt eine Gleichung `=0` und löst sie:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:58.132719Z",
     "iopub.status.busy": "2020-11-19T12:31:58.132378Z",
     "iopub.status.idle": "2020-11-19T12:31:58.243153Z",
     "shell.execute_reply": "2020-11-19T12:31:58.242228Z",
     "shell.execute_reply.started": "2020-11-19T12:31:58.132675Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{A \\left(a_{a} - m_{e} + m_{n} - m_{p}\\right)}{2 \\left(A^{\\frac{2}{3}} a_{c} + a_{a}\\right)}$"
      ],
      "text/plain": [
       "A*(a_a - m_e + m_n - m_p)/(2*(A**(2/3)*a_c + a_a))"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Zmin = sy.solve(dM, Z)[0]\n",
    "# es wird eine Liste möglicher Lösungen zurückgegeben, hier nehmen wir nur die erste (und einzige)\n",
    "Zmin"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(PS: `.evalf` klappt irgendwie nicht immer... wenn jemand weiß, warum, gerne Bescheid geben... )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:58.245025Z",
     "iopub.status.busy": "2020-11-19T12:31:58.244527Z",
     "iopub.status.idle": "2020-11-19T12:31:58.252954Z",
     "shell.execute_reply": "2020-11-19T12:31:58.252367Z",
     "shell.execute_reply.started": "2020-11-19T12:31:58.244967Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{0.5 A \\left(a_{a} - m_{e} + m_{n} - m_{p}\\right)}{A^{0.666666666666667} a_{c} + a_{a}}$"
      ],
      "text/plain": [
       "0.5*A*(a_a - m_e + m_n - m_p)/(A**0.666666666666667*a_c + a_a)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Zmin.evalf(subs={a_c: 3})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`subs().evalf()` geht aber:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:58.254029Z",
     "iopub.status.busy": "2020-11-19T12:31:58.253848Z",
     "iopub.status.idle": "2020-11-19T12:31:58.266343Z",
     "shell.execute_reply": "2020-11-19T12:31:58.265721Z",
     "shell.execute_reply.started": "2020-11-19T12:31:58.254006Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{0.5 A \\left(a_{a} - m_{e} + m_{n} - m_{p}\\right)}{3.0 A^{0.666666666666667} + a_{a}}$"
      ],
      "text/plain": [
       "0.5*A*(a_a - m_e + m_n - m_p)/(3.0*A**0.666666666666667 + a_a)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Zmin.subs({a_c: 3}).evalf()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Konstanten einsetzen:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:58.267766Z",
     "iopub.status.busy": "2020-11-19T12:31:58.267458Z",
     "iopub.status.idle": "2020-11-19T12:31:58.291238Z",
     "shell.execute_reply": "2020-11-19T12:31:58.290607Z",
     "shell.execute_reply.started": "2020-11-19T12:31:58.267728Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{46.575 A}{0.714 A^{0.666666666666667} + 93.15}$"
      ],
      "text/plain": [
       "46.575*A/(0.714*A**0.666666666666667 + 93.15)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Zmin_eingesetzt = Zmin.subs({\n",
    "    a_v: a_v_.value, a_s:a_s_.value, a_c:a_c_.value, a_a: a_a_.value,\n",
    "    m_e: const.m_e.value, m_p: const.m_p.value,\n",
    "    m_n: const.m_n.value\n",
    "    # `.value` nötig, weil sympy mit den Einheiten durcheinander kommt :(\n",
    "    # jemand eine bessere Idee?\n",
    "}).evalf()\n",
    "\n",
    "Zmin_eingesetzt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mit `lambdify` kann man aus einem sympy-Ausdruck eine normale Python-Funktion machen, die man aufrufen kann. Um `f(A)` zu definieren:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:58.292226Z",
     "iopub.status.busy": "2020-11-19T12:31:58.292029Z",
     "iopub.status.idle": "2020-11-19T12:31:58.392813Z",
     "shell.execute_reply": "2020-11-19T12:31:58.392258Z",
     "shell.execute_reply.started": "2020-11-19T12:31:58.292202Z"
    }
   },
   "outputs": [],
   "source": [
    "Zmin_fkt = sy.lambdify(A, Zmin_eingesetzt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bei zB. $A=20$ haben wir:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:58.393887Z",
     "iopub.status.busy": "2020-11-19T12:31:58.393721Z",
     "iopub.status.idle": "2020-11-19T12:31:58.399047Z",
     "shell.execute_reply": "2020-11-19T12:31:58.398269Z",
     "shell.execute_reply.started": "2020-11-19T12:31:58.393867Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "Z_{\\text{min}} = 9.4654248 \\; \\mathrm{} \\approx 9 \\; \\mathrm{}\n",
       "\\end{align}"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%tex Z_{\\text{min}} = <Zmin_fkt(20)> \\approx <round(Zmin_fkt(20))>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Das nächste ganzzahlige $Z$ wäre $Z=9$, damit ist $N=11$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:58.400166Z",
     "iopub.status.busy": "2020-11-19T12:31:58.399956Z",
     "iopub.status.idle": "2020-11-19T12:31:58.987172Z",
     "shell.execute_reply": "2020-11-19T12:31:58.985933Z",
     "shell.execute_reply.started": "2020-11-19T12:31:58.400141Z"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns  # hübschere Plots :)\n",
    "\n",
    "sns.set_style(\"whitegrid\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:58.988395Z",
     "iopub.status.busy": "2020-11-19T12:31:58.988208Z",
     "iopub.status.idle": "2020-11-19T12:31:59.745373Z",
     "shell.execute_reply": "2020-11-19T12:31:59.744802Z",
     "shell.execute_reply.started": "2020-11-19T12:31:58.988374Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 543,
       "width": 804
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A-Werte als Berechnungsgrundlage\n",
    "A_values = np.linspace(0, 300)\n",
    "\n",
    "\n",
    "plt.figure(dpi=150)  # größere Grafik\n",
    "\n",
    "plt.plot(A_values/2, A_values/2, label=r\"$N=Z$\")\n",
    "\n",
    "# N = A-Z\n",
    "Z_values = Zmin_fkt(A_values)  # eigentlich mit .round(), dann wird der Plot aber abgehackt...\n",
    "plt.plot(A_values - Z_values, Z_values, label=r\"$Z_{min}$\")\n",
    "\n",
    "plt.xlabel(\"N\")\n",
    "plt.ylabel(\"Z\")\n",
    "plt.legend();\n",
    "# ^ Semikolon verhindert, dass die Ausgabe des letzten Befehls von Jupyter angezeigt wird."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br><br><br><br><br><br><br><br><br><br><br>\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-19T12:31:59.746486Z",
     "iopub.status.busy": "2020-11-19T12:31:59.746302Z",
     "iopub.status.idle": "2020-11-19T12:31:59.775371Z",
     "shell.execute_reply": "2020-11-19T12:31:59.774727Z",
     "shell.execute_reply.started": "2020-11-19T12:31:59.746468Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "**conda `environment.yml`:**"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "name: phyv-py38\n",
      "channels:\n",
      "  - conda-forge\n",
      "  - defaults\n",
      "dependencies:\n",
      "  - python=3.8.5\n",
      "  - pip=20.2.4\n",
      "  - numpy=1.19.2\n",
      "  - pip:\n",
      "    - astropy==4.1\n",
      "    - matplotlib==3.3.2\n",
      "    - sympy==1.6.2\n",
      "    - scipy==1.5.2\n",
      "    - pint==0.16.1\n",
      "    - seaborn==0.11.0\n",
      "    - uncertainties==3.1.4\n"
     ]
    },
    {
     "data": {
      "text/markdown": [
       "&nbsp;\n",
       "\n",
       "**Binder badge:**"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/git/https%3A%2F%2Fgist.github.com%2FXXXXXXXXXXXXX.git/HEAD?filepath=Tutorium%203.ipynb&urlpath=lab)\n"
     ]
    }
   ],
   "source": [
    "from IPython.display import Markdown\n",
    "import sys, pip, numpy, astropy, matplotlib, sympy, scipy, pint, seaborn, uncertainties\n",
    "\n",
    "display(Markdown(\"**conda `environment.yml`:**\"))\n",
    "print(\"name: phyv-py38\\nchannels:\\n  - conda-forge\\n  - defaults\\ndependencies:\")\n",
    "print(f\"  - python={sys.version.split()[0]}\")\n",
    "print(f\"  - pip={pip.__version__}\")\n",
    "print(f\"  - numpy={numpy.__version__}\")\n",
    "print(f\"  - pip:\")  # use double == for pip\n",
    "print(f\"    - astropy=={astropy.__version__}\")\n",
    "print(f\"    - matplotlib=={matplotlib.__version__}\")\n",
    "print(f\"    - sympy=={sympy.__version__}\")\n",
    "print(f\"    - scipy=={scipy.__version__}\")\n",
    "print(f\"    - pint=={pint.__version__}\")\n",
    "print(f\"    - seaborn=={seaborn.__version__}\")\n",
    "print(f\"    - uncertainties=={uncertainties.__version__}\")\n",
    "\n",
    "\n",
    "display(Markdown(\"&nbsp;\\n\\n**Binder badge:**\"))\n",
    "id = \"XXXXXXXXXXXXX\"\n",
    "fn = \"Tutorium 3.ipynb\"\n",
    "print(f\"[![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/git/https%3A%2F%2Fgist.github.com%2F{id}.git/HEAD?filepath={fn.replace(' ', '%20')}&urlpath=lab)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "3.8.5 (Framework)",
   "language": "python",
   "name": "3.8.5-framework"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}

Tutorium 4.ipynb

Tutorium 5.ipynb

environment.yml

Tutorium 6.ipynb

Tutorium 8.ipynb