{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Example 2.3: PO-ESF-RSM\n",
    "Pull-out of a short fiber from short matrix "
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Idealization of the pull-out problem\n",
    "This notebook explains the derivation of the pullout model and provides also its executable form.\n",
    "The one-dimensional idealization of the pull-out is introduced in the figure\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "**Remark**: The origin of the coordinate system is placed at the transition between the bond zone and free zone of the fiber. The domain in the bond zone is defined as $x \\in (-L_\\mathrm{b},0)$. As a result, in the bond domain $x < 0$. The fiber is assumed to have an infinite length for $x < -L_\\mathrm{b}$. This means that the length of the bond zone $L_\\mathrm{b}$ remains constant - this fiber will never be pulled out."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The meaning of the variables defining the idealization is summarized in the table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib widget\n",
    "import sympy as sp # symbolic algebra package\n",
    "import numpy as np # numerical package\n",
    "import matplotlib.pyplot as plt # plotting package\n",
    "sp.init_printing() # enable nice formating of the derived expressions"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Here we tell `sympy` to remember these variables for further use. The parameter of the `symbols( str )` is a string that contains comma-separated printable symbol definition. One can use latex commands in this string to introduce e.g. Greek symbols like `\\gamma, \\beta`, etc. The number of symbols in `str` must be equal to the number of variables assigned on the left hand side of the `=` sign"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "E_f, A_f = sp.symbols(r'E_\\mathrm{f}, A_\\mathrm{f}', nonnegative = True )\n",
    "E_m, A_m = sp.symbols(r'E_\\mathrm{m}, A_\\mathrm{m}', nonnegative = True )\n",
    "tau, p = sp.symbols(r'\\bar{\\tau}, p', nonnegative = True)\n",
    "P, w = sp.symbols('P, w')\n",
    "x, a, L_b = sp.symbols('x, a, L_b')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left( w, \\  \\bar{\\tau}, \\  p, \\  L_{b}, \\  A_\\mathrm{f}, \\  A_\\mathrm{m}, \\  E_\\mathrm{f}, \\  E_\\mathrm{m}\\right)$"
      ],
      "text/plain": [
       "(w, \\bar{\\tau}, p, L_b, A_\\mathrm{f}, A_\\mathrm{m}, E_\\mathrm{f}, E_\\mathrm{m}\n",
       ")"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "py_vars = ('w', 'tau', 'p', 'L_b', 'A_f', 'A_m', 'E_f', 'E_m')\n",
    "map_py2sp = {py_var : globals()[py_var] for py_var in py_vars}\n",
    "sp_vars = tuple(map_py2sp[py_var] for py_var in py_vars)\n",
    "sp_vars"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Reuse the pullout equation\n",
    "As long as the debonding did not reach the end of the fiber, everything remains the sam"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{w}$"
      ],
      "text/plain": [
       "     ______________   ______________   ____________      \n",
       "√2⋅╲╱ A_\\mathrm{f} ⋅╲╱ E_\\mathrm{f} ⋅╲╱ \\bar{\\tau} ⋅√p⋅√w"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Pw_pull = sp.sqrt(2*w*tau*E_f*A_f*p)\n",
    "Pw_pull"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Introduce finite embedded length\n",
    "What happens if the debonded  length $a$ reaches the end of the bond zone $x = -L_\\mathrm{b}$?\n",
    "With reference to the blue subplot above, we see that this point corresponds to a maximum possible shear flow area over the bond zone. Thus, the maximum force that can be transfered through the bond is \n",
    "\\begin{align}\n",
    " P_\\max = \\int_{x = -L_\\mathrm{b}}^{x=} p \\tau(x) \\; \\mathrm{d}x = p \\bar{\\tau} L_\\mathrm{b}\n",
    "\\end{align}\n",
    "The corresponding pullout displacement can be obtained by solving the equation\n",
    "\\begin{align}\n",
    "P_\\max = p \\bar{\\tau} L_\\mathrm{b} = P_\\mathrm{pull}(w) \\implies w\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{L_{b}^{2} \\bar{\\tau} p}{2 A_\\mathrm{f} E_\\mathrm{f}}$"
      ],
      "text/plain": [
       "        2                  \n",
       "     L_b ⋅\\bar{\\tau}⋅p     \n",
       "───────────────────────────\n",
       "2⋅A_\\mathrm{f}⋅E_\\mathrm{f}"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P_max = p * tau * L_b\n",
    "w_argmax = sp.solve(P_max - Pw_pull, w)[0]\n",
    "w_argmax"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Introduce finite fiber length\n",
    "What happens when the fiber has a length $L_\\mathrm{f} < L_\\mathrm{b}$? The debonding phase with ascending pull-out curve remains the same as in the previous example. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "Pw_up_pull = Pw_pull"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "Once $a = L_\\mathrm{b}$ the bond zone starts to shorten. \n",
    "The amount of shortening is equal to the slip at the unloaded end. Let us denote the diminishing effective length of the bond zone in the second phase  \n",
    "\\begin{align}\n",
    "  b = -L_\\mathrm{b} + u_\\mathrm{f}(-L_b)\n",
    "\\end{align}\n",
    "\\begin{align}\n",
    " P_{\\mathrm{down}} = p \\bar{\\tau} b\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "b, P_down = sp.symbols(r'b, P_\\mathrm{down}')"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![image.png](attachment:image.png)\n",
    "\n",
    "The strain at $x = b$ must be zero and the displacement must be equal to $L_\\mathrm{b} - b$. The strain profile of the pulled out fiber with the instantaneous length $b$ is linear with $\\varepsilon(b) = 0$. Thus the elongation of of the fibuer equals\n",
    "\\begin{align}\n",
    "\\frac{1}{2} \\varepsilon_\\mathrm{f}(0) b\n",
    "\\end{align}\n",
    "The current pull-out displacement is thus a sum of the slip \n",
    "at the free end and the fiber elongation of the zone $b$\n",
    "\\begin{align}\n",
    " w = u_\\mathrm{f}(-L_\\mathrm{b}) - \\frac{1}{2} \\varepsilon_\\mathrm{f}(0) b   \n",
    "\\end{align}\n",
    "After substituting\n",
    "\\begin{align}\n",
    "w = L_\\mathrm{b} + b - \\frac{1}{2} \\varepsilon_\\mathrm{f}(0) b\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{P_\\mathrm{down}}{A_\\mathrm{f} E_\\mathrm{f}}$"
      ],
      "text/plain": [
       "     P_\\mathrm{down}     \n",
       "─────────────────────────\n",
       "A_\\mathrm{f}⋅E_\\mathrm{f}"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sig_0_down = P_down / A_f\n",
    "eps_0_down = 1 / E_f * sig_0_down\n",
    "eps_0_down"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle L_{b} + b - \\frac{P_\\mathrm{down} b}{2 A_\\mathrm{f} E_\\mathrm{f}}$"
      ],
      "text/plain": [
       "               P_\\mathrm{down}⋅b     \n",
       "L_b + b - ───────────────────────────\n",
       "          2⋅A_\\mathrm{f}⋅E_\\mathrm{f}"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w_down =  (L_b + b) - sp.Rational(1,2) * eps_0_down * b\n",
    "w_down"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle - \\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{A_\\mathrm{f} E_\\mathrm{f} - 2 L_{b} \\bar{\\tau} p + 2 \\bar{\\tau} p w} + A_\\mathrm{f} E_\\mathrm{f}$"
      ],
      "text/plain": [
       "    ______________   ______________   ________________________________________\n",
       "- ╲╱ A_\\mathrm{f} ⋅╲╱ E_\\mathrm{f} ⋅╲╱ A_\\mathrm{f}⋅E_\\mathrm{f} - 2⋅L_b⋅\\bar{\n",
       "\n",
       "___________________________                            \n",
       "\\tau}⋅p + 2⋅\\bar{\\tau}⋅p⋅w  + A_\\mathrm{f}⋅E_\\mathrm{f}"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Pw_down_pull, Pw_down_push = sp.solve(w_down.subs(b, -P_down / p / tau) -w, P_down)\n",
    "Pw_down_pull"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\begin{cases} 0 & \\text{for}\\: w \\leq 0 \\\\\\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{w} & \\text{for}\\: w \\leq \\frac{L_{b}^{2} \\bar{\\tau} p}{2 A_\\mathrm{f} E_\\mathrm{f}} \\\\- \\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{A_\\mathrm{f} E_\\mathrm{f} - 2 L_{b} \\bar{\\tau} p + 2 \\bar{\\tau} p w} + A_\\mathrm{f} E_\\mathrm{f} & \\text{for}\\: L_{b} > w \\\\0 & \\text{otherwise} \\end{cases}$"
      ],
      "text/plain": [
       "⎧                                                                  0          \n",
       "⎪                                                                             \n",
       "⎪                                                                             \n",
       "⎪                                           ______________   ______________   \n",
       "⎪                                      √2⋅╲╱ A_\\mathrm{f} ⋅╲╱ E_\\mathrm{f} ⋅╲╱\n",
       "⎨                                                                             \n",
       "⎪                                                                             \n",
       "⎪    ______________   ______________   _______________________________________\n",
       "⎪- ╲╱ A_\\mathrm{f} ⋅╲╱ E_\\mathrm{f} ⋅╲╱ A_\\mathrm{f}⋅E_\\mathrm{f} - 2⋅L_b⋅\\bar\n",
       "⎪                                                                             \n",
       "⎩                                                                  0          \n",
       "\n",
       "                                                                       for w ≤\n",
       "                                                                              \n",
       "                                                                          2   \n",
       "____________                                                           L_b ⋅\\b\n",
       " \\bar{\\tau} ⋅√p⋅√w                                        for w ≤ ────────────\n",
       "                                                                  2⋅A_\\mathrm{\n",
       "                                                                              \n",
       "____________________________                                                  \n",
       "{\\tau}⋅p + 2⋅\\bar{\\tau}⋅p⋅w  + A_\\mathrm{f}⋅E_\\mathrm{f}              for L_b \n",
       "                                                                              \n",
       "                                                                       otherwi\n",
       "\n",
       " 0             \n",
       "               \n",
       "               \n",
       "ar{\\tau}⋅p     \n",
       "───────────────\n",
       "f}⋅E_\\mathrm{f}\n",
       "               \n",
       "               \n",
       "> w            \n",
       "               \n",
       "se             "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Pw_short = sp.Piecewise((0, w <= 0),\n",
    "                        (Pw_up_pull, w <= w_argmax),\n",
    "                        (Pw_down_pull, w < L_b),\n",
    "                        (0, True)\n",
    "                       )\n",
    "Pw_short"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle A_\\mathrm{f} E_\\mathrm{f} - 2 L_{b} \\bar{\\tau} p + \\frac{L_{b}^{2} \\bar{\\tau}^{2} p^{2}}{A_\\mathrm{f} E_\\mathrm{f}}$"
      ],
      "text/plain": [
       "                                                       2           2  2   \n",
       "                                                    L_b ⋅\\bar{\\tau} ⋅p    \n",
       "A_\\mathrm{f}⋅E_\\mathrm{f} - 2⋅L_b⋅\\bar{\\tau}⋅p + ─────────────────────────\n",
       "                                                 A_\\mathrm{f}⋅E_\\mathrm{f}"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.simplify(Pw_down_pull.args[1].args[3].args[0].subs(w,w_argmax))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "get_Pw_short = sp.lambdify(sp_vars, Pw_short)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "daaf80a467424a8c9b6103dd43387dd4",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f154c095340>]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w_range = np.linspace(0,2,5000)\n",
    "params = {w: w_range, A_f:1.8, E_f:2, A_m:1, E_m:4, tau:1, p:1, L_b:1}\n",
    "param_vals = tuple(params[map_py2sp[py_var]] for py_var in py_vars)\n",
    "fix, ax = plt.subplots(1,1, figsize=(8,2))\n",
    "ax.plot(w_range, get_Pw_short(*param_vals))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Postprocessing "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\begin{cases} 0 & \\text{for}\\: w \\leq \\frac{L_{b}^{2} \\bar{\\tau} p}{2 A_\\mathrm{f} E_\\mathrm{f}} \\\\L_{b} - \\frac{- \\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{A_\\mathrm{f} E_\\mathrm{f} - 2 L_{b} \\bar{\\tau} p + 2 \\bar{\\tau} p w} + A_\\mathrm{f} E_\\mathrm{f}}{\\bar{\\tau} p} & \\text{for}\\: L_{b} \\geq w \\\\w & \\text{otherwise} \\end{cases}$"
      ],
      "text/plain": [
       "⎧                                                                             \n",
       "⎪                                                                             \n",
       "⎪                                                                     0       \n",
       "⎪                                                                             \n",
       "⎪                                                                             \n",
       "⎨          ______________   ______________   _________________________________\n",
       "⎪      - ╲╱ A_\\mathrm{f} ⋅╲╱ E_\\mathrm{f} ⋅╲╱ A_\\mathrm{f}⋅E_\\mathrm{f} - 2⋅L_\n",
       "⎪L_b - ───────────────────────────────────────────────────────────────────────\n",
       "⎪                                                                   \\bar{\\tau}\n",
       "⎪                                                                             \n",
       "⎩                                                                     w       \n",
       "\n",
       "                                                                              \n",
       "                                                                             L\n",
       "                                                                for w ≤ ──────\n",
       "                                                                        2⋅A_\\m\n",
       "                                                                              \n",
       "__________________________________                                            \n",
       "b⋅\\bar{\\tau}⋅p + 2⋅\\bar{\\tau}⋅p⋅w  + A_\\mathrm{f}⋅E_\\mathrm{f}                \n",
       "──────────────────────────────────────────────────────────────              fo\n",
       "⋅p                                                                            \n",
       "                                                                              \n",
       "                                                                             o\n",
       "\n",
       "  2                  \n",
       "_b ⋅\\bar{\\tau}⋅p     \n",
       "─────────────────────\n",
       "athrm{f}⋅E_\\mathrm{f}\n",
       "                     \n",
       "                     \n",
       "                     \n",
       "r L_b ≥ w            \n",
       "                     \n",
       "                     \n",
       "therwise             "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w_L_b_a = L_b - Pw_down_pull / p / tau\n",
    "w_L_b = sp.Piecewise((0, w <= w_argmax),\n",
    "                     (w_L_b_a, (w > w_argmax) & (w <= L_b)),\n",
    "                     (w, True)) \n",
    "w_L_b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle - \\frac{\\begin{cases} 0 & \\text{for}\\: w \\leq 0 \\\\\\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{w} & \\text{for}\\: w \\leq \\frac{L_{b}^{2} \\bar{\\tau} p}{2 A_\\mathrm{f} E_\\mathrm{f}} \\\\- \\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{A_\\mathrm{f} E_\\mathrm{f} - 2 L_{b} \\bar{\\tau} p + 2 \\bar{\\tau} p w} + A_\\mathrm{f} E_\\mathrm{f} & \\text{for}\\: L_{b} > w \\\\0 & \\text{otherwise} \\end{cases}}{\\bar{\\tau} p}$"
      ],
      "text/plain": [
       " ⎛⎧                                                                  0        \n",
       " ⎜⎪                                                                           \n",
       " ⎜⎪                                                                           \n",
       " ⎜⎪                                           ______________   ______________ \n",
       " ⎜⎪                                      √2⋅╲╱ A_\\mathrm{f} ⋅╲╱ E_\\mathrm{f} ⋅\n",
       "-⎜⎨                                                                           \n",
       " ⎜⎪                                                                           \n",
       " ⎜⎪    ______________   ______________   _____________________________________\n",
       " ⎜⎪- ╲╱ A_\\mathrm{f} ⋅╲╱ E_\\mathrm{f} ⋅╲╱ A_\\mathrm{f}⋅E_\\mathrm{f} - 2⋅L_b⋅\\b\n",
       " ⎜⎪                                                                           \n",
       " ⎝⎩                                                                  0        \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "\n",
       "                                                                         for w\n",
       "                                                                              \n",
       "                                                                            2 \n",
       "  ____________                                                           L_b ⋅\n",
       "╲╱ \\bar{\\tau} ⋅√p⋅√w                                        for w ≤ ──────────\n",
       "                                                                    2⋅A_\\mathr\n",
       "                                                                              \n",
       "______________________________                                                \n",
       "ar{\\tau}⋅p + 2⋅\\bar{\\tau}⋅p⋅w  + A_\\mathrm{f}⋅E_\\mathrm{f}              for L_\n",
       "                                                                              \n",
       "                                                                         other\n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "    \\bar{\\tau}⋅p                                                              \n",
       "\n",
       " ≤ 0             ⎞ \n",
       "                 ⎟ \n",
       "                 ⎟ \n",
       "\\bar{\\tau}⋅p     ⎟ \n",
       "─────────────────⎟ \n",
       "m{f}⋅E_\\mathrm{f}⎟ \n",
       "                 ⎟ \n",
       "                 ⎟ \n",
       "b > w            ⎟ \n",
       "                 ⎟ \n",
       "wise             ⎠ \n",
       "───────────────────\n",
       "                   "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aw_pull_elastic = - (Pw_short / p / tau)\n",
    "aw_pull_elastic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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1YKbnQuBhJuN/zIRHMLsiTC7P5fJiO+7iFSylMRkBI2AErhYBjYEouyjMrLZzvAjlgk+4YnSwW8JYWe4moFTznI5YyUXZRFHG/0s9Y1S8kTu4oq6whhQHPhg8KMS/6GIs/p0u/h07/Fr/YaKwzUh5IOOsnJ0Mv1K65n9aFIaBht+Ysn5QGBi9IZ6uxuDS/RLqHWsrEmMwgN9agverisTspFCWIaOE9oChQDhl5n0eVuapR4w2DJqlWMNqkjLPzflOZnplgcKIz1BTD7uQ+HsXZhdkzfQaEHjYQkh1Igbw3orTFrzNwwgYASNwLQhoLETBHD3SoXCO34yOlQpHGU0GypoyK/0Q71F51uSxcRrkfbeQZ/ynC1iyALaGUPYbXIQbiia7Pcxlr9cwjDTi0fANvyFX8WgrQwbJIcvRqkv5YSzYYBgC87R+/M9Qa5dEzxgSvd09+U8d4RuTetddmLFM7W8ELgGBTYySSyiIZTACRsAIGIHrQkBKG7sBJaGIl584LsMOiv9HXfHVKowZdqRaRJzs8YnuW4o9/vJjNwtCucSoearrM90nvnKbXRLdT/KCiel+EMjtobdLIv9uO14Fyhj/VcycyAhcIQI2Sq6w0iyyETACRuAUCEhJQmHnuNAS6v0XRU1i5YWxwDn6wc/MKpzdjXIXiS9/famroczjuVxkIP4Q4c9L48lgyWkaQyQSZP85XhH9Yl2V42R1eLEgbCBYxnFol4QjhBzTDGO3zI34ZZstw4buW/yVlh0Y+kPZB9ml4Wt3g7tsQ0ztZwSuBYE5o6Tm61vXUlbLaQSMgBEwAgsQkOKDst47lrKARVVU5YNix/skfPWqZyBkJhyLwph4mZ9Jw3s7XJGGd3DSF6rkN6YMotSVYcTnHZUDvOS8kMsxqRpeJLtoUllOUocXDUKlcMKKNkX9D+18fK0w2mhDikd74YgW79DSNnmnq7c71ySYuFE6duWaXRg9wxvC4OHjFOz8sYvIDiF+u/dL5WEyAidFYM4oqX3R/aRCOzMjYASMgBG4DQSkZKEI8pJ+Oqefnw9yk3FBKXXPsa2Wsqdn0rGzgstHBHAxXDiKVR7zkleL2ClpeCkuSnusOqN4sgpdy6vF2A/Xi4DqnHZBG6TtfJvbRSqQ7jEQeJep946I/Jq2pDgYsosp82/tkogJvPhkNbsl3ylO9AfaK+3TZARuDoEnN1ciF8gIGAEjYASuAgEpWihXrA6zwozS96nuUfze60okP5RFFLEWyT+UtKSg5WdWkN/pPt476aaBP1TulCSPnA//ws6KN7wneaVE/rkZBFTnfCqatoeBinFaEjskQwZJ0y6VlnYabbJMm+4VTtvCwBgi8uvuwsRX4DCU3haJaMNNvoW/b43A1SPwcPUlcAGMgBEwAkbgWhHgrPxTXeWZ+YOUt7T6LBeDhfdGMCKaIzXyJ00ocV/rGUOiZ2goTkMK53jMy+zBJ3YjDF4YNiiVg++zRES7d4HAa5WSz1SzY0a7Su1DbuymjYHALt3gfwApLW1r8S5MzoiPOZQGEW2YHRSTEbg5BGyU3FyVukBGwAgYgetAQMrax1OSKhzjpDwek6LL/5fs3wsb46c07J4M7qCMpbH//SGgdhJHpdi9wBgY3CUZQAbDIwzlVrB4YjCzE0Oc4BtxRvkrPsYyRhHt/ZCf2Smx8QwgpptD4MnNlcgFMgJGwAgYgbtDQAobyhtGCi8q867JatqS12ohnPCcCGCMfKV2gAHwTO7cLkmSVfFGj2/lwryWyzsrtNVDdjnWNcYfI4awLxSHnT7kmvoYhIJNRuB6EfBOyfXWnSU3AkbACBiBjICUNlaTOUJzNG3J62hhzODkCKj+2S1hB+MHXVW7Eoo/+zWszBfDJXZLRndJcqHJmx0W7/BlQOzcNgJjOyX/o2Jz8ek5kxEwAkbACBgBI2AE7gkBdiUwCOZ2P5ZismQXhp2S8iX3pXk5vhG4KgTGjJJ/Uym4eMHKZASMgBEwAkbACBiBu0Eg72pssvNWggZfPb/XxS4MBsogKR67KL/XxaeCnw5GsqcRuDEEfHzrxirUxTECRsAIGAEjYAQuGgGMkZcyNkZ3YRRGnFGj5aJLZ+GMwEoEbJSsBM7JjIARMAJGwAgYASOwFAEZHOyWcJmMgBEoEDirUaKOyZ9TzX4lRfE+KmT2bQUCwuxDRbSDsa1ByXGMgBG4NAQ0dnHenmMtHHHhJWP+W2Lyv0oUx2QEjIARMAIXisDZjBJNHvyz6fdy9zizWaWQ19SJ5FtsEClNlbFVkz9xlsqg+GDLn4M1fzZWm9c540neVbgtxeecZXTeRsAIbIYARkj6nxO5GCf/1LV4vN5MGjM6GQKq79k53vPCyarDGRmBzRCYM0p+u1lOfUZ/0KDBP5xuSuI5q5ArzlNdv2yacWaW89/F2Fog7y7YLsh/cdQLwW2x3E5gBIzA2RAoP9XKbskuY/rZSueMBxHIc8Xmi27iu2pRbFBIeYrfYgP5EmQYK4/9jcApEJgzSv6xhxDqePwJ0F+Ct55Z5eK73RCTC/RK/msmmUmFPOf1s9zPdY39YdGjBOt+e/krH44Z8MIaXzP7VldZLv6cCX/+EGn0pTeFV5F4tLCtSrQwkvLYY5Wqh9tCsRzdCBiBG0Egj5n8ESLHezl7/1Z+rf9q0HM5XvKlos133cXTdHkIbD5XqC1VndxQvJte0FT5VhlmSrfYALu8ZmWJLgGBOaNkLxn5xF25S/InPTMBJdI9BsuPumb/jOgxxeOv0tUo5Bg/GEEYP5saJWP5y59vnSfjQ25Tzkep04oKAwGfCNyCWtgqPwbbHo7yX/VVj8xv01Uq8aypt0XYiOdfdPWwLpnksmyGTcnb90bACKxHQH0zxswXup80NhTOfPEfcgfHc/lvOgauL5VTHouA6rKZK3R/ssVM5M753fKCZpVhdmwdOr0RmELg5EZJOagUgn0l//IlRVa98PtU1+BEU6Qtb1sKeRnAvXixY/FGF50vdmR0uxlN5Y8RNvYS5t8lW7l7skog8WgG7GAgv63fK9l8lUqyTuEWRVnqztbvDtgsldHxjYARGEdgasxMqdSHmSswSH7R9Uddrd0UIslv6zEw5e2fsyBQzhWnXMyksLe+oLnH3H6WRuJMrxeBkxolmhxY2SgHlUCOFe138bDGFe+eQj7AByPnz7rY9n8+EL7aqyJ/DKJmxS/H/6tcjJHXqzPOCcWnh638UMzZhWGXpkvUw5iR1I2bnhW/wVj3GHac6WZHKwgl4rXCqg3JkmcwkR9YIfNz3SfM5FK+NAnl+5/1vPrIm3jMYqM4VWVUPHCB2HVBSeLISbpXWHnERN4mI2AEKhFgHBjd7VTfYuxhnMAYkXOgr7WMEvlv1s/JwHQ+BFSXzfyTpTjJYiZ5KW/a4l0taGaM7RiBkyLwsHVueRJ4IXdodYqVBpS2Fg3EZSJi96BKuVW8nkLeykAPilOuomEA8R5Hi4iTPT7R/ehk2EqkB8WdzF/hYRRgCGAMEf8z3acJVO4vwVP3ozIojAm2ClvFJQ+OaPHuDKuIs8eZQoYJNxmUmTfRMHi+1wVe1Be44tc7EiW/HmU+LSM1+4Xx+IFnXeDzpS7Kf+BZFwoIz4uVfqWdxSbHIbvJMioe9fUd8ugiLjhTplCYFstHpiYjcM8IqP/EmDm6cKI45YvuPbgUvlk/7zG3x0kRyHXZmiskAHP0KRYzKWvMSYznN7WgSeFELWyFN0bYrguDKVf/GIEOAnNGyaKvb+WGzGo5BsC3ulAmE+meCYKOPfkug8LpCKw0tyYc+Vcr5CnD4kdp6WDl5PaTnlFyG8r5ppX5HL8J40Z+q/NXcvJHkU6GjlzK2GCj+0TZf1AGhcFjEbaRX2b/LLurHPFC+ebsNgSvb3Wxk5AUcrkQZUqGQ3rSj9ItxQ3e7CDRBspjbZQdAyiIVavVCr/4l0bnEDa1ZQwDCblo4yHjK+VRZVST0GQEjEALgRgzV/dxuG3Yz1vC+WF7BFRXi+YKxe8ufDKmb7qYSSmVz9UvaE7VFuVTeMztlDd0NU6V7LIwOCWPw+4bgYeZ4i/6+pYaMIo/LygyobArUhog7JCUz3psk9IxKBGPYzmN0p75LVLI25zTsSmUx5fZn3ye6pkr8kEJTROg/EoD5qDnxQZBJ39kL3mSD0o1vBkAXsj9Tu6UDIuwFb8oF3kg/+rJXemRsVlJ0XPg1DUUPlW8br6L6q3gTV2BSRBlaAZOPIu4+FOnJbETFQZC+PPeUhyZS356HsSm4D1XxnJihFcYnjZIAvU7dtWOMNzpP3/TfTkG3DEqVUXvjpkpkTAES/p2zDP0fc7C9/qb/LpjUW8MVJyqsaxKYkdajYDqgbFz0VxRZqb0zD2bLmbCP8tV9turW9Ascereq3z0p2Zuz+HoIbsvDHZl8bMRAIGHnWB4Lb4ogLxfgDFAw/+93N7EEfkrDKWSFxYZmA75GZeVj0UKefDMfFjlKFfF4UleDGC4KAu4vLvAZFeuisgrybI6/8TgcaekkUF5MFkGFhhv4DQpQ+aDsxhbpaFsXQUdXg3l/F/ILZXsCEdGjMUufSaP0tDEkGAHJZF4HYMbkwwKx0F8aD8YkOXkAIaJ5N9gW/jxXzGpLYXfiDuHzWQZg6fySgaZ3FByaO89JSji2719BFT/HOGjv3LE5Ec9M/mXbfj2QVhfwsbA77BI4yV+YKnrma4YSztRW4+b9PMWRz9shgB1KWZhaFLH5bwyuaCptMydeyxmUj7aDToMcxtEXsxFXDEHocTHuN/q34pzlLElvl3jnHyWLmgic/XcLpmjLJS5amFQ8UxGYBMEnmzCpcNEjZqGTMNmcIFqBhUUUM7jc8QLBY9B6b2ukpjgMRpQUg/ZHTV2FM6AEAMHSRLJP3U6PdBZ4cMz7wO8033rRUnCC1qUP+nEj7JArcEKD4UhH/Iz6FXJoHiLsCUfEfmMTtxZDhR78E/YkgjKz9RJS349gx1xE775OeqNpCUtxk2J4Rv1j2HQkPJi9bklTxO4/GYUm7kyEq6Lf5GGGMCjXfFM+zXdKQK5jaK40F9py7jvbhkOlfULXRhfaVxdW1alHxwz4S+eabyEd86n7HNTWa7u51NMa8MkKx/pQH7TNAKL5orcBtJipu6ZR2kfMa9j5DAOM/eFLhK5T+okRFLatKAJj7jkHeN65IGL4fKC+HJbJL+jZBAz2m2zoCh+lDHmcsoE/1EZFEb6RXO74gfRD1Pe4sNcz3hWzrtp7o/Ido3AFgg8bMFkhAed9xs1Yqz6udUsVhRp9LgNKS2dqSE9x/sLdEb4jw4siouRw3sjdKJm9V/+5EM66Gs908nLjvYYMvCreNX5k1zxGaReZlb8t0e+TWVlIGHAaL07ExFm3CXYJlbKe3TyVhjlX7pKhewMjigictLL7a1jd3hCCl+E22OqVL/Uz1s9M/iBH/XG9jm7Z6PlUfgimuA1WUbS6eLdKeo5Bu+YmKgj0/0iwApnUh5y+0JxuUlS+VgkoL0zjqQPa6wtaO5L3TGTMZuFCZSkcvczGS85zW8U9kb3obDpsU0KGxszJvt5m8vyJ+WL/Bgk5INxahpBQFhVzxWKyxzKPI/REIYsOkN37MXQWXpyg7pi3mmR8mHMx4+8OWXBMwuaB7lzC5pLZYgy9fQT5YV8YaCjwwzKIP81czvFgSj/+3T32P/ybSrrlguDDV/fGIGHvSBQZ2BwQYn8Qdek4q14Hy+QgwFn1tgRTwanllFDHvKnow2GEV5BVfnDR3kxSE0NVBXZ9aOIbzW2pFb8qq9hKeqSwZs6xZCpLV81blnmNJhyvyfNYDNbRqUv21hv8thTdvO+eARiQr94QdcIqLaPAU77R9EeXJBYyjePJ7VjCgYKu7ucfw8FtTRamuwVPjUGzvbzhtG6GxQ45kKO773QddJxQvlhFDEPJ6zkXjrVzhWbL2YCjPC6xQXNJXN7tA/q4SQLg5GhXSMwZ5Qs+vrWAJw06pfq5GMrVANJpr3Ea5FCPs3tMb5FsXMAACAASURBVFQ8GbSZXDmmxMr/6GrWHvkjhfhWy0B80V7YUlezO1GKw0oNMlTRXrhNZL5Fm1tUxglZHGQEbgKBPE4xPrDyj5I7pezvXWZ2T2IMwihZS3v3c3Z5+Ww6x/cwTk5tlLCS/rnyRcFkp5l6qzX8FP20JNmq5njF23wxk5KKL7oAV4vkf7ULmpIdTGvn9lRuxT/JwmALZD/cPQIfffjwoQeCGmN4Mpg2R596Ec/kIZmYEDF2znIk4tz57wl7Lts3yiMmsR7GisPEyiopbYOtcwbrWbom3NaWcRYER7hpBNRuOHKB0o6iCyUFVP6pH8ll8YH+g3IIodRzrCPikY5wlGxWN1EknuvCn69MDRrbmS8r8r/R9ZOem3Fb98jEWJ4ULbmMn+RRvbuhNCF3kk/PDX/xOQtJBt5fYZfjIJfjKyjbixR+xV81ltUWWPzBms+8J+NJLqv7o/XY5av44E69QrSDV7poGy91QW8VZ3QR7TFK+1fxyx2u13quGr/bXPZ9kkybz/HiSZ97pot2P9iPlpZKfKgf5kv6GHPhZF2cUwblDaaTc7vCTUbgrAhcpVFyVsTuIPM9Bs47gM1FNAINAupDcca7Merlh+KCP8d4GqVI97yPxNfimtVr3fMBhW/x18V7EihUo4tEis+L1ChFSfGQ26wi6548eUk1HW2Si2EB39mvgSluKF3JSNLzpNIlniejXA4whTjbfzGyPYqUjKWWESIZqR9w763ER5rSVTwMrTAmMSYwTDBE+A8Jjhm9kLtqt0rpMHYwljDkqheXFPcqSeXd3NBZCsS5ZVD+mxtmSzFwfCMwhcDDVKDD7hYBJqqXGsAaxelukXDBjcB2CGAcxDGKkiv9jVV/3tGKF7V5HwWFMxTSj3U/uKItfxTzt5khhkf3XRaMkNc5/KD4kc9s/yZPXZH0olzKIYEW7YycsgCSj3rBWGpw1n06miQXI3GwPkNGhce7KOFFfBRrdkugZ7rY6VlF4s9uV/wfxQ96fqdnjNtG3lWMLzSRyoXRelbD9QJk8Nx+oe3TYj0isJlRos4WR76M7Y0g4DrdpiKF40fbcDKXa0VAbQAFld2GMB6aoiiMr/jw/FJXGCUooI1yqPApBRbFN9J9qXSlAUK+T3V1lfd3StPwV/goKR7HjZCd1XSUYBTXo49vicdVzhmSu7Y/c4yvqYsCYHY4MDianbEirLzt1hFH1WgrqS3IbXbhykRL78UnKetyMV45Ski7eCV3qs0dFE67+kEXbi3RlqKtpjR6vsp2UFvgS4y3NebiV9snLhEOy3RBCGxplLhRXlDFWhQjYAQuCgGUemhK0cOAKKm741GGNfdSCBJPuayioyCWBgOKJrsdLUVQfhzjqCalR1Hl+Bj8N3lhWrxuds7IOPHJ1i7uYE79cKxr0igZSNsyOGG0E1HHsyT5aHfpnZ7ZyBMRxOdm28FEsR1kBIzAAAKbGSUDvO11YgQ0uM8eCTixSM7OCBiBRwRiV2JK4Ys4gRlK3xLi6Fazkp4T4tfaJdE4gfEzpCznJONOVkQ5AsKuCX8uh3HDSvvJX5hW3pc83o3tkhwkN0YiR+gmv/RY1oLiYlzSdprjR/JLbUnu0nZSsj4oPcYs8tL+ql/CbzG5wwfhxnFMsJslxbXhNYuSIxiBw8FGyY20Ag16TFA/y+XPy1YpHDcChYthBC4OAfqkLpRHjIRGsURQ+aNwQig5xxC7MV3DBr9WfnrmfTEMi6NIPFjp54VrjiKld2LkYqxUK8mKy7iFQgzFblLt0aFV453yBG/K/5kuPiZQyovBhv+xX2jC4JjCmGNw1He3buSV2gS4EM5ROYxK3i3CmCnrlx2rqTyUZJyUtnzR3cbIOFS9kIwdH6fY5AhdLwN7GIE7RcBGye1UPBM7ExkTu42S26lXl+Q6EaAvdonPbPNCMV9UKvsoCirKfbmjQfohHl2e5TM8myNg4ofy/UxXKPuH7MeXtzYj8ey+MI1RUZZvKi+UbhTuRLr/i2442jT3RanV453yYJciGR9l3o8SJIMAY+B9PC91xRNln3KMkuLwHtB7Xfw31hBW1F0ynhROO2jJIz/C3o5mMBGgtOUngas/Cz3B8h6DMOJYYDAZASOwIQIPG/IyqzMhkCeoN8qeybBRQM4kjrM1AneLgPoiyi4KM6vtHC9CwY1PuLJbwhn8cjeB/spzMkjkomyipOP/pZ4xKt7IHVxRV1hDigMfDB4U4l90/Z+u3+n6pvBr/YeJwjYj5YGMs3J2MvxK6Xi5OgwyDDT8xpT1g8LA6NjxrnesrZALgwH81hK8X1UkZpeDsgwZJeCBsUc4ZeZ9HlbmqVuMNgyaaqwVF8OG+YG2RRuZM/oUzTSEgLDDqJs0OofSLfFTHowbs0fDFM/HwpYA67gXj8BDV0I1cgavoNbqTHjavTgEmMBZaWVrn+/Ym4yAETgDAuqDKJijRzpyH212BroiKhxlNBT0bvDss9IP8R6VZ5bh/hGQ993CbLYY71D2G1yEG4omn8fFGHm9UJ5WdPFo+LYCOg+KR1sZMkgOWY5WXcpvjdEHL+Z0DBl2pWyMdOphxSP/M9PaJdEzBl8PW/kvPl6Xeflo2IqKcZLrR6BnlKhI5Up7eX71+kt7gyXQAMbLpvEVFyZ3VmhbRJzs8YnuWxNdK6IfjIARMAInREDjUfmlMHJmfCo/cdyShrFM11HjndKzmwWhXD6Xi9L+WfCVi2GSSPdXP3bm8vQU5iij3XoEcnvo7ZLIv9uO65n2Y/poWB8T+9wJAkNGSaPUqqMNruLcCTYXX0zVD6t95aoqX8L5shRccZiAn8tloCO+yQgYASNQhYDGjFhlr4qfIzHWLJ47lIaxiiMrg5+ZzePXFuMd4yAvjacFmpxvY4jkMhyyv8fOAOTOXbUH+sLQLgkLuRy3CmO3RIr4ZZstw3r3iosR3Bg9emYHhv7ATlcQuzR87W5xHwsGdo3ApSIwZJTEtmT1edVLLdwdyMUxASbXl7msDI6cY+eKSfaZ/NKOl/yqB8fMz44RMAJ3jEAeR3ZfZVc+jF28TzL14vVW4x1zXDkWMj7yjspBcqB4vpDL/OexE1DuiHI7pP6Hdj6+FhS00YZye+GIFl+9ZC7mfZ1jTiM0Rk/mTV4YPHycgpMO7CJyIgK/3ful8jAZgZMi0DJKcieIl6saa/2kEjmzKgRUVxxjaA1+emZip/5weakWl4mcownlsQd5mYyAETAC50cgj1O8pJ8WxPLzQW5zfFj3W4537JQ0Y6d4s4ATq84onqxCe+w8f9M4qQSqc9oFbZC29m1uF0kG3WOs8i5T7x0R+TVtSXEwZFeR+LR2ScQEXnyymt2S7xQe/YH2Svs0GYGbQ+BJp0QMyBAdoFxJevT170UgoLph8GRgalExaKUBKz+zovJO93EOu5XGD0bACBiBcyGgcYmxigUwVphR+j7VPYrfe12J5LfZeJf5w7c3v+V8+Bd2VrxRAD12phq4jx/VOZ+Kpu1hoIYuFIVnh2TIIGnmYaWlnYbhEOmqXKXF6GGXpDmhovv4ChyG0tuCEX2kybfw960RuHoEHqIE6gBMDljqNPZX4W/3shBQPTGB894Ik2qzxSx/BrXYWv5az0ysvYlXcUxGwAgYgUtBgLPyjF3lmfmDxq60+ix3s/FOvJjfXuaC84ndfJvyZ/5DqRx8nyUi2r0LBF6rlHymmh0z5lHaJ8Zq7KaNgcCphNH/AFL61MbkNvN2wQgjKObvwjvd8p5vaRDRhtlBMRmBm0MgGSW509GZMEimzvTeHADXViDVFZN1uV2ciiB/6m4w7NrKaHmNgBG4DwQ0bn08VdItxzvxYrfYO8ZTgDvsoHYSR6UwFDAGBndJBqDCqB00LMSTsDVHwzBkMIqY35GNZ3ZKbDwDiOnmEHiiRk6DZ5WKbcff6XnV9uPNIXMDBcp1i6HCi3vxrtANlMxFMAJGwAi0EdhyvNuSV1tKP10JAhgjX6kdYAA8kzu3S5KKpXiD+pP8Fx8NyzhhzJD3F+LBTh9yeeFYIJhuE4GP/vM//5OXqNgip6FXdbzbhMKlMgJGwAgYASNgBIxA2pXgE/vPdKEbDRobS3ESHxYHeVfpY93H0TCOirGL0iP5o5sRD2PEZARuHgF2SjjfyJb2j7rHQDEZASNgBIyAETACRuCeEcAQYIdjE4MEIMWLF9nhx9EwaO5oGDsl5UvuKZF/jMCtIvDRhw8fUtnUWbDIMUp4AXDoRaxbxcDlMgJGwAgYASNgBIzA7ghIv2K35Btdn+viozS8IN8j+WOwcGQLfYxPZqf3SnoR7WEEbgiBxiihTGr0bFfyItWifyElrckIGAEjYASMgBEwAkZgGoGsa216NGw6R4cagetA4KEjJi9F8xWudOaxE+ZHI2AEjIARMAJGwAgYgeMQ4GjYSxknmx0NO04cpzYCbQTUNjk6yIew2Kj4RBfvPu3+NxOtnRJlelCm/5SDID7GBSAmI2AEjIARMAJGwAgYASNwJwhgC+hKn2yXi03A80d7F//JQAbxpzy9/8IYiGsvI2AEjIARMAJGwAgYASNgBG4HgfK/cNgtOck7Td3jW8DJ0S1eeP8U60jXSQQhY5MRMAJGwAgYgUBA8w/z0Wb/sbRmpe/cMmydf2Br934RWNMP7het+yy52kh5tJCPLgx+kGFrdIaMkvdFJp/pfvczZEV+vjUCRsAIGAEjcNCkyOLY93InJ0OF77Z4VivDXtVVm/+eGOxVNvO9HQTc/q6rLlVfvC/CaSgWfPhM9Vv58dcgPZI/X+bl628n+R/DIaOktI7YsjEZASNgBIyAETg1An/QRDj4p3IhiMI56/yz3M93mjR7MigfJnReVGbRjuPO5WkC/gEc/63+cK+Xv3i36BgMTlyWRu4sc/xXR+gZr+RfYnnI8lUpTw3zC7qpLecFibxYlFzGVX0w1++p+tList1qAuHO/+8wVr2QO7roo7D0Pzpy+QPPP+rqGS7yY/GIF+FbJH/qdTH1jBIxIvPFjJzACBgBI2AEjMAWCGgO4v8ZWKGbIxRbDBMU201X8sZkkH9M6J/pvvfupfw4claeONDjchrLf4DTagxOVZYBmf9UYqd76vpHXS3lppBvUnka4N/yEp9NFadgjty6em0gwuXOlnMv2QoZ9r69xva3NybXwJ8Fn9GTUGqX9EcMF4wROelPP4eMkk3/17BnlJCzyQgYASNgBIzAGRHgv7LmdkleSL43ulA4Y7V9S5GnZJia0P8u2Vsr/iuFmso/sVQ+W2BwirJ0IfhKspefGGVFFj/eZe0al1PydfkOPovnpopTkclcu5st546yFWLucyvZr7X97QPIdXGl7kYNatVt+aL7YMkUh/bPIgzGS5cYv1jAYXyGF0ZOEH36tcK6ff3wEDHsGgEjYASMgBE4NwKaqGp3SVBg/6yLI8fPt5S7QgYm9ObYQ47/V7kYI6+PlaUi/8hiCwx2LUsI2nFRht51/MYeJ5WnsUThLyw3V5yCd4U7Wc6tZBMfMEIxfK771C7lsoOYdmry/c963upYoVglutb2F/Lfpav2EEbE6E7JHDC5TXFEi6OznLDq7RrmOLDCcOE/ED+RH4s29H38WjujerZRAggmI2AEjMAeCGjwZZUI5eBvul89Aewh2yXyFEZgVbNDUJ5vZoLjPY4WiRfGDcREOLoi+Bjl1985GRQeEzpyYgwhM0e50tEGub8EN90vlkFpToaB8tq1LIFD11W+3Z0L6gdlpbVyWsg32ncUB4Wc41+8f9NND5abK07iWUWSZ7ScCttEtswnjIMPPOuiDX6pK+3k8KwL453n8r1hPa4j8Tu6D4rHWdrfuhLfVCr6TLSJ1QVT/ZXj6rMBRvjx3h3z4He5DRKN9pnaJg8lPSkfjrlXZljkXDRULKbBDI/Jw2mNgBEwAteCgMZAtqvf60Kh4itSTAR3T8wNupikhojz6RzlGaWMY6mk/qTIrflGcVB2WDXGUGBFrkXyP0aGmND5g2EUXhTiUp6U15QMR+Z/UHpkKPNcjEESUi+6ykU5WV2WzGe1o7ypK74CNHRcJOQbVaSVHhyeyW0ZJCFQLhtKEDSlOCFHleKUOC38GSrnRrJRJnbpwLA8OsgRGVangzjqOIpjRKpxldfNtL+a8t5gnMEjkapXDFrq9oCr6ydd9IseyT/61EH3pOm1LflHeyS/twUTeDbpC/9tdkqUMZMv58P4tNhB7lM5P8plJaknKHFMRsAIGIFbRUDjXtohkYuSg8LM2MiK/s2QyoUShBHBCnXVOK94TF5MUCxefaurmZh0z7zBiu/cV1s4noIi/VIuBL5MplzBD0UtySS/Unk/6PlYGboTOvmg8MGbMjCZU9+DMmyQP1kdhQEMMh1VFnioPCgYk4ZkzgvDp9VO9EzdkZZjRVF3OXpyuvIlT8UFZ3anOLMOjxbfFEk/Cmt46n5UcSK+wsmrVOJbipPCMT7JqyRkKNMQxrsyrR0SPffKKb9NZBOfaOf0h6SDZQEpLzI3VMRdXWeZ2cW0v6ZwlTfCgPbGJ3BLrCpT30w02ka5yxEFYzx/zYPwoW+NGvuRILu0h24/KKOwk12O67RVdlB69NDzWeghoZvJN5LKjwmDCqdD0NFNRsAIGIF7QoBxL63caixEaWDQvgnKYz4TDMp+Ok9cWzClJQ2THZMiE2A5UaEslM96bJPSYcy0JlM9o/BhIOFyTA4XvFEYyyMm8nqcbOWslkFpWxO68kC5jFX6NKlPyaCws2MgeYOOKgtMVB7Kvniezxjx/wcpbX4+yC0NjJZ8IbTcRnnSPQo26Tgq9xtdb3Qf9UFQ0FGKk3i22h1M5ccO6GTZFU57nCvnUbLlAoIDOhdyYbRhpJcGeWkEraqzzPvoPgifTK36lbyL+lIwqXUzLowV5HuXRokwSP1F5S/bxkH+aQyVm9qJXNpt2Rf1OErgObgwkfnQHku+yDC0M3p4MppFfQCdaWgAYKvmhQRCGJMRMAJG4N4QeH9LBdZYjjLCMSFeTmRlm5XvNNGsKCercfBL80N2OVI1NJck9gpj4uvlJ/+YOJlED/mZI1vvdJ/e88B/gNbIMDihw1t5IR9lYFEOmeZkWJP/ZhhIxi3LAgTVpLypKxRojnqzO4YsGKRNnxmTT/4t5UlpMArgQ13Dc1A5kj/YDbYvpUUe2mJqX/k5ZJL3Osp8JsuZOW8hG7IHfp+VEksOFo9bSmgZXnsvPtfe/sCB9sGxIspyNlL+GI2cKEKmk5DywnD/JmfG+M0rF/QdTjsxXiWjNoen8YE0OV6MFzm47ShOjMPtgF/73RfwUiD9fGxn9PDQTb3imYptbVVmHiEg4Xdpka7A0kmMgBEwAheDgCYRFLWvdaEIMnn1vpayRljxibP78GaSmtwlUXwmS17cRbFq5pssXyihX+sZg6BK+VK8pTIwob7UBTGhpxv9gBFKLXPd4Oqf/Hu0Iv/NMFDem5alV7h5D5QgcMNtSHKl3YgR+YiPso1yVO5O4EcbgpJh+njb/xXf0Eu6gdQdBguKE2FheP/CwxE0Wc6S7waygQF9gAVh5E5Kp1wWElDCx8qu4HlS+ltof2DChy/eqcSMG1VjxTw6y2NIBsaqz5WSOqOOGF+nFlGWZ9JJkfnX5hHGPu8rxSJC2e8a7gqfmhcYE9mZrsr3oeHavvmf/EjFjZIyYZCYo2dzERxuBIyAEbgFBDQmojChaKPkHPScxj+57CjzzJjJZMgkBDGYN//XoHDSEc4kwEo6isRzXfhPvruReceqG2le6YJPKNLV56gLOZM8ep6adJTFKkKJ+ka838idPLusOCirSWEtc5J/Ur6Gwsp4E/dLZGBSrZpYJ/LrBi3JfzMMhNseZemWbfRZ+X88GqiApfIpPu0AAiP6T48UZ6oNL1KcesxHPJTnZDkj2RayiQcK9m5KtvhfdfuT/CyspAVy3XPMkzGHnc1ZY01xGLcZW3+ji5e/y4URxnyMnTQ+ySUf2uDoboDCEiku7ZYxgON9sRONjK9zWIp3pp9qY39GPuYQylhFT0Zi/Zv8uRBqisLgANgxejoWYH8jYASMwC0hoImEyQ4DJCkI3Ofng1wmL1ZO2TLn/zW4mMjShCT3oGdWlGK1PZQoVihJy+A+RQ1fRWK1lG36F+LHhMA4PKisyb8hxeVIAdv4P+jivDyris0E3ETc4EZ8mXw5bkJe1ZPWXNbiS1nBlbKjIIzSuWU4d/6jwBQBS/Askp3yNhQ6dn94n2SNYk7fos8spVmFdinDgfhrZRtgdRqvLdvMhrxYLGIsDXqtm9pxh90MDHnaSHcchS+LP0HowzzP6c8RP7nw18WYz4IVx7rYOTmr/qz8KQvEeNotdwqY+lF60oAFH72qKsvDFMONwrAsTUbACBiBe0cAZT+ODJVYMDEyCWGQxJl3lHWUaiaDg9yPdcUEgVeLFBZnpcOfuCjk7JZALCDNTirkoYv4pyLK/lJ5bqbcUQbxTDtTlYU4twznzn8SphV4TvLbOlDyHbVDoPSl4kQfHO1nXdkVN/XPrv9Wz8fItpUMa/hkDJf0wdFstuAlHizqtI6wyY+xmIUcFmJG61xhpA2DleNLjM0lYTRi4CRS/BjHV41pSs8iUHzi+Qc9c2IJOVfxe5Rq1W+zWKbUq4x9yczYxlVNxxol3copM2YShP7v0fGvETACRuA+EdDgzMTGilFMbg0QCmN3heeXusIoYZJsJiGFj06aJBS9U5wmvp7ZbYFvSie3WkEgri5kZVJCYWNCPHq3RDw+iNcgTYUNJtjB89wynDv/HSC9NpYY9l+pHi5R7kuW7Wx4qa4+qsyc3YzGcCjSsHMCtlPHMjFmYlzmvbaGj/wZ15/q6u7OdcdjRVlG4s1OMoYTRg9HfBnfX8mdmwtSRoo3Ot6mCAt/xG9hinXRH9Yle0wFOFlQKqVL4VdOlN04fjYCRsAI3AMCKPnQ1ITCBFfS1KJPGe+gcTgmzfBvTZ7hWeuKH+M256QZxzd5EVO8ahWIWjEdzwgYASMwiUAew8a+7MdiC0dqR40SpU9jtlx2nhkPywUaDAb04O74G+8MKngzIu9qkkxXOd4eZZRkdLAQY8ItAYudkq4FWcbxvREwAkbgHhCIxZmpiSXiBB5pMoyHWleTERMl+bDSlkh+KV+5i3jm+GkLXveX9iJmFM+uETACRmAMgbFdkgPjmy6OW/HVtWa8HGHE0a1m9znHwa+l44oPi0tdIyVHr3eQSbGRnXlh8iMn9VzrYyr/yWNt9ZyWxZwzSn5bwY5z0kNnlVvHByr4OIoRMAJG4CYR0AAfkxmTWGvyUxhGBMRYupiYPJQojcO6Z4LknDuTbWnksNux6GxvVxClT19skstxh/QOjFyOeC0ydLp8/WwEjIAR2BEBDI6psQ/9lfGzNS4PyMPiezmmEgW/bjrekZvKj3SjlMdX0jOWH2WMiBdzA4YNFJsHs0fAcrqf5fLnuIsMLMVnPkN+XvT/Vlc5P2Cw4c+XybpYyvtwmDNK/pFiTfyIMS/kMDE1lqbuAYLjA59PJHWQETACRuBWEWAM7BLjIS8u8lWVcqBnUuTLK+WKG+mHeHR58swkkCaCPPa+LyPJj7C3pd8x9+LXfRGTSa4szzHsnfZOEFCbwbiNL8w1pZb/aoWuYeIbIyAEchvjvZFRUhzeGXmviz/xnBrHCGuO2Cou4yongkLZP2S/70czmwhQWr4ex4ISRs7s54QnWJVBvA8Iz0S6BwuOq/X63WOM5hdDhvmHsk1h0iSIG+XBzlMyPsq8i3AMwPfx3HUfuh4rn9kVofDP5fJiO+5iC0tpTEbACBiBq0UgD8YM6KwGsf3NAMz/g2B0sFvCWFnuLjDo85wMErlMdEwi+H+pZyY9vnzSXY2Td0OkxVAg7UFxeReEz/nGBMSEO5WeZIsp89yc72JBnOAqEVD7Kc/mX2UZLPTFI8DO9KsKKTGEGT9HFXC1V8ZpFpQYV3/Rha77O13811L4tf7DRGGTpHQo/hjnjPnwnjMWJvkNBH4lns3/YCmcBTD8Rg0whYHDG+Lpagwu3S+h3rG2IjFGIPgN0sOg70LPnEFjjS1M7uhGwAgYgZtAQGMhk9rol64Uzpb16FipcAyMcsdkFpeh8Vd+GAs2GGbRc4RzIKD2ibKDwd6sPBdy8J8GrLaiFGHEs7IbhLLDH8uNKo8R0a4RUDsZHYtLdHJ7mm1Tijc0dlflUebHvXhhkNC2WdDf2hghCwh536W7+h8MFhbRmKvYYFhDGDYNLuLFLhCnqjBGXk8x3MQomcrAYUbACBgBI2AEjIARAAEpJihjrExzmoJ3n1ghbil7OQ7RMVw4DsOfeLLCioKF315KnFibjMD+CKgto6Dv2o6VR3c3kn5WfuK4VVDF52Mm8SUy+ho7/otI6WOhgcUFjBr6+2fBVy7lHiUbJaPQOMAIGAEjcF8IaMJgAilXpmsA4GXM2VXGGkaOcx8IqL2URghHFLuEHy/JslvCfzXES7EoNGuPlCipyQjcJwLqQxgLX+hi97FHCmd3o9yl57PGvBveIsVj1wNioaDsx4++j8fgWGxIYXLJd9AQGeI1Z5TUfH0rBLFrBIyAETACV4yAJgkmj11X764YHou+AQK5jSVOukcRCoOj4S7/5CeX41rli8OjCk6T2DdGwAi0EFA/wpDnfZKpF+g5boUx8TInJg3vRXIlo0Iu/e+5XBai6LtD1H2fhL7MOyoHpXkq54VcFhoGec0ZJbNf3yIjkxEwAkbACBgBI2AEFiKAIlQaHd3kHB8pv8aFwsQOiskIGIEKBKT8Y1zwkj7GwiE/4zaLAbrn2FZr10PPpGNnBTd2wp/pPhYMyl0VeTeEsdLwEh8MmkjPR2Be55iDvJ7kQDtGwAgYASNgBIyAETglAigwobC08s1KESursUqLcsTqammktNL4wQgYgV8RyH2IL4Px3hYvsEf/eR+xGcdD4AAAGspJREFU5EcfTH0s/HDlH0YL/Y5nXBYR2OmII1wENSR/+EM9g0Vh5PN7uezGjPJ6SMn9YwSMgBEwAkbACBiBEyMgBSWUn27OYbDwH2iEcaxw6vgJcUxGwAj8igDvB2LYt94TVH+K9z0wWHhvBCOieSle4aThuBf0tZ4xJPgiHh+ZOMiNl+F5TCQ/DJU4+sVn6R8DHvPHCKE/p/dZFMbL9oO8HiKVXSNgBIyAETACRsAInAoBKSZT7y+hwKAI9RSgU8nnfIzANSOgvvPxlPwKxzhpjlpFXPmzczIYFnG6bu6nR/fVJ13GfjYCRsAIGAEjYASMwJkRYGX17ZllcPZGwAicEIE5o8Rf3zphZTgrI2AEjIARMAL3joBWXTk6wpEP/uuAoyQmI2AEzohA7ofsnvBOCS/Ar6YpXh99+PChx1gJwpNzYc05s15EexgBI2AEjIAROAMCmptYSUdhRXnlGNB/y6/3gqX8TUbACBgBI3AFCPidkiuoJItoBIyAETACPQQwQtKZabkYJ//U9VEvlj2MgBEwAkbgKhCwUXIV1XReITXhx87Z0YKI12KlQWn4SsNR24VHC24GN4XAmnZ4UwDcRmHKfyZmt4SXM00XjsDW4/mavnxuGbbO/8Kr3OKdAIE1/eAEYi3OwkbJYsjuK4Ea+lcq8dmO8eX8v5fL97FHSeHNv46ORnKAETACV4GA+jNHszi/zGLEd7reyq/1ZRc9l5+S5R2EyTFC4aYzI6A6Yz4563heK8NeUNXmr3ie0/aqBPOdReBc7c9GyWzV3H2EP6hxpn8CBQndoyzw51Wf6fpWV7k6yR/n4M+35EuFQV6rqZX/EBflxdGNn+V+rmvwj7iG0uGn+KcuD3kiL/9sCrHCC72Sf4kl8WYVs8ekl/tbW9bLLYElOwcCajd8CpbxhJcqJ40NhfOtff6xeLDvyx9FuPfpWfn7T/hOX7m7jueVxenJoLZwynmgl39XbslzVXMa8meZb35eqy1nt06v6fmc7e/hmoA6hayqDE9gGWhhwZ/hMOE3JL9QFj7T/dD3rTlq1fxbaJNwxc1Q/iNsGAgZxFHwBxWTkXSHU5ankOFPJXa6B2P+3KilOBWyzSpmBe/erfjs1qaRXVevHRRCTJZ1T9kKGXx7nQiwGDL54rraDzskGCT8udcfdbV2Uyi2/PyxFoA4M1E/EqE1n4yItHo8H+HXeI/JIP+TzGtj+TcC/nqzGoNTleVXUZu7ybE+YhXyXeS8JvmOmtMop3jsNucGjju7Z2t/Y0bJ/+QCv9u54BfHXo3JE9ivtcLnGJtdkl+9D1PKAv/U2VrxL9ItvR3Lv+GjvFjheqOLQSB2HZrwyptTlSfE+Upyl18KQrHC71NdXaNqSrbgN+mK555teg7zybLuLNskLg68eATo26MGr9oOhjy7KRgjcg7szraMEvnTPlkoIV6XGF9QRhk7eD+l/Ndj+t1rhXX7Y5eHn+sRONV4PiXRlAxTY+1W89pU/klutblrnNOQfXKs71TKFNadqMOPwmmvee2oOQ1pd5RtGIwNfc/d/h5GyvJv2f//yb2bQVmVsdkEJl6sCkGsfqN0cjY63Stsq6NNYrkPZfnHVrUYNJsjFTnuX+VijLzeQqKZ/MssUOT/rAtMn5cBC+53L09HFhStWoMf2UYVsw7f3qNwmW3TJFK8vRSzybLWyFcjm+KAE4rnc92ntin3qZ7T6l2+/1nPWx4tFDvTHgiovsKIGN0pUZzyRfeeGLnOOaLFsU52UnoroDkOaTFcvtf1ifxQQOmf+LV2L/VsWoGA8KzdJdliPB+UsEKGXeeBivxD7i0w2LUsIWjHnRzrO3F3n9eEt+e0DuiVj2dtfw+VQt58NDVgFJhNJrA8+Hwnl8mNiY3JkBWSWNm7aKNEcoLF4IqOwkJZIBwjgLgc5UorlHJ/0fNRJB6j+ZeMFa88roESwfssi0g8di9PVyDl2V3hYTCnrbQWAArZRhWzLu/yWenBcbJNEz/H43ZzxUy8R8taI1+NbDlODKQfeNZFO/xSV1r14lkX/Y7ni+5/ks+kd0kEQtTZajxU56VB/2yAEX68G4cCk8bsHIf2k9pOfrazEgHVwcnG8zER52RQ+K7zwFz+IbfiXeWchvySfXSsj/LleIH1bvNaxpvsPKeV4M/cX0L7s1FSVJIqZKsJrJxMGZBZgYNeKY+W4vnoffpfycGE+0JudyBBGM4TsrszRKEsJKyUngGGCbxHCmt2i3RfYnvQ89r8Uz5KjxzloPaTnlFCW6R4ozLkiJuUp5XpggfJB37sog2t+oZso0p0xoEdLV6e7LUt+ZW4PxsRDf/dFbOhslbIVyMbcdipA8fymAVHBKLv6TYd8xvFkghbk2RC2WUM+Jvuy/a6dVa3xm/weIcwBEsWQTh2Rf+YavvNuJTj9upe/slPbretfCreTfpbA3fr8gi/s4/nR8oQY+3qee3I/A9KjwzlGHGVcxptS2Wh/5xzXquZNxD1KBoqp/zm5twa2Yhz0jlNcl9E+3s4qkY6iVUoFEAG91ixZvW6HNiZUBi8APyd4hP3IkiyNHLmylk9gSl9qehT0THQ9ZTGcxQ+lw/sWZX5VldZduqIVWdW2IeIdOXACU6803FQGtJi6LDi+Knu01Ea3YNBQ/l5bf7BhyM6GH8vswft6qmeuVJ55I7KEEzkHlWenMeYAVdkkz6r3GpTSovMpOVIUVMHRaKubClIccE5FDOUs2e6em2r5Kl76qCVf+SjsOQvl/xKJR78GrkUjgKIzCUhR5mGMN6XKfvAQc+9ssqv5D0on+LMylbEoS18VwgHT2RuKOI2HjveKC92Rl/rYhz8Uc/sLpZ9Z8fcr541dVdO7lGgr3UDpgew1DXY9iNy4TJedNtpEZzmrHLMoy1hqJtmEFAdUFdnHc83kKE71jLuVM9rG+QPyhcxpyGIysPYf7XzmuSfnTdyOW9mTjumzsBCdBHt7+FRlm1+BQpHeDjfz5/tsTJIR++R/MN46YVdiMcmE5jKmZQ6udFBfh/35yynZEAxipVGJvlyMmYgKp+7oraUBfFCsQyFuFEY5PdMV5S7pYgdmf9B6TGmWgqLnlF6WZnBDXlGZVCcoKPKo3zJa7CdRwZDbpaXrwaltPn5IDdhltO0ZCv4NDjndGWaIlrrdq5NE5nFhLLuW4qZ8mphTgL58Z8Dk+VXOHUyV9Y5+SZlQxYR/Y1JBrkw3DBQy7bXGEHE2ZOUb9ohkYuBTvkxljBOTDMICC/qESrr7iD/1L/lpnqUC641bR9e9KVBJSvzob2UfJFhaPdS3stJeZA3/7VSGs3LGV1gCpXpmPnkoPRHj+fHyiBYW2Ot+NEWYh5pxlv5Dc4px+a/BQZF0ziqLPCRPLcyr03OGyrnzcxpa+ss1/fRfXCr9vekYDR0+9shzyk/AUOHgFoTyqNX88sqau1k0iSauiFfXSgCWxBliAGpxU95MBEOTWBJmSNc1z9zIpS6spylwtfie6YHVhxpjJTnkF3kHyv7oLKQ04IZadm9ACOUTOokjk8RrUuL8iex+JFPUh5KZvIPnMmbeLMyKM7W5SlFGr3PsqE8864Ru1LIQdt4H4nGZJN/SzFT/FQG+VOPvNQdZQpW4Y62aSIoHXiNtutgstTNfCfLmnmOyrdANtpFYMhk1JB4MDZMjUlN3I1uMNRSP1LeHCnjeF2v3W6U182wEUaMF9/kAvGnrbRp+gm7Tun9vKKwtW0/JRGPGCMKFuk22t4XikP+9MWx3ctu2tln8aRf0W9Rbm+ZzjqeZ2DXyBBjZm98UN3RNpbMa2vyJ4/e2FC014uf08Be8iLn5FivOINYy3/zeS3LQ99L2OZn8j9KD8t8JsupPKAYVx6fit8FsiH7rnOaZLmo9vdQ4DR0+48hzxm/WDWd2iqHBecltyQaH9cmpIqqmcDIi6+zNBMY6XRxJIrJLWGQ74l7VGeAwZYkueLFTiZLZBvdJclleJnzR1nItwlzBiMadlpZVBgYoEAc5LJ7NkgKq84fBorPQPClLiaP5niQ/Kn3WAX9Ws8YRuwEjcqgMOpn0/KIXy2hYCEzbkOS6d95GJGN+CjaDKrRx3Sb7lHaOH8ak0IZTpxECh9r04RTfyjRKGZy2u0aj5U0WdaS54R8tbLRhqn/t3J/0ZWUWrmMNbTJqfIryuYUk8nmjE/FUJjR7n7QldrY3vkqv7TbXpkP7by27U99RYtxi/FidKyqlGcsGgYx4xPH917o6im/Ywm38Fd+J6lD5XO28TxwWiHDpvPAivxvZU6jCibHemEzhPWe81rtvBHNp9adLGfJRGUem3NqZdt1TpN8F9f+HkoAN7oH7IMK2xp49cxKbhr05SalcaP8Nmcj+Y6awJQ+KZdZsBYOmwt7PEMa/TeS+Y3c0fPZCl+iLCyRqip/GGZcS2xTPvJPCqgeemEpwsDPjuUZyK3tpbw/bvu0nxbKhqEChhBGySCJ51SbJs0uitlcWUPYGfmqZBMP+tql97co8lW4wpSx+nMJi7GHcYcRsJfyvhSTqrZfwZQ5K/pQRfTFUTCO+dQwx/cwTk7aRpXvKevwLON5p0aWyLDHvLYkf+as3rxFnWX/XlinrM2j0uxRlob/3I3yv7R5rWremCtXN3yunBFf8abm3CrZxGPXOU38L6797WGUsJLbGnRVcAZ9OllD8ktHGxqP67nZewI7KRKqB1a3mChZDaWjnJTOnf9JC7tTZsIw+hYDDHW5hta267GVoDUyjKVZK9sYv938VReMf+w8IvNBz8+yy3FGnp/KoY5Q8CEmruaPNBVOOsIxMF/rAt/nuvDnCNgg3pkvK/K/0fWTnsudRGRCMU4KjlyOSpBHs8Or+1FSfNoXihbvBbG4hOy8G/E6h+n2PFTkv6rtK31gnT5CUPDbpEDiB9bpPRLd854lCz8cBxqsx26mikd7iWPJtINXumgbL3VBVe+piM9J6lD5nHU+AZBzy3Du/MHgFkg40mahVX1b6dbOG1V9M0m2/metbOtzvJKUT7aUU40IoCEGXSZaLo4wcbUMFSJdG6ks5QTGZHErhMLB8YVNOqP4gA0DyQvdMynP0ab5k9kKGUZl3JLXaCbrA0JRZGv8jWRd3M+UZnW7Vtqk6K4XfzrlMbJNc94nVPKieGKApBUu7vPzQS7GAVv/vCfBB0G4wC/VodyDnumHsTgQK21ssZM2xleidomdDFZKObpGfZaEkYQiG8RkzzM7DYuIPHQhF4YJXxRj5+RcY+EWbR8eH+nCaAOXrQnsqb+g17phvKulpq0oAXX7jS7GVXiAe7eu5TVNSrt3HV7CeH5uGc6d/2QjUBug7SyZoyf57RB4VN9W+TynbVwpW7aZKV4fffjAh7LapAThyUDdrLi1Y/WfFJeGgHLEClzaCZHL5McXemKCbSWUPxMtZ4PpJKzwrToaoHQovxhDq9IrrckIGAEjsAkCGofifaa0QwJT+aUdBrkoLA3pOYyVctxMOykKS+Om3Ke6BpXmnJ6xj1VqFGCU1ma81T0f3mBXoxkbdY9xNLrz0gg3cyM+jLso3ulokp43WdiYyfYqgoUF9Yqx2LQBBNczdTu7S6V46eMMchOm+Zn6/Vj3HMmijTG3Vs/Rit8jpXcd9lCxhxEwAudA4GHjTNNKnga55miW7nnBNG1fR156LidYdlE4i/hMF4bJJCltmnQHIpH+oPChldtYvRxI9uildGGIjcbZMkD5fTTGT2Hg8IOuWTwKHigYDe6Ff+v21OVsZe4HI3AhCEz1vz1EVH4oqCzQsNrdIvqtLvxe6oo+jAHSKPgK53mMGGMj3ZeKxGp8IvmTL+NIdwftncIa/o+xl/+KB2M7xhBjPzvj8ORPYqfkTRkpzknH3JTpBj+Se3Ts7rDHWGvqoghjDsPgaIzEIqy87dYRO2i0lYSt3JaxUyZcci8+d1eHS/BxXCNgBE6HwNZGCRNgd/KjNAzCiTQAMkGmATnfs+LDIDs7icFAcYeMDvyP2ilR+tqJBjF2JckCFnGEY9O8LqmcmxbMzIzAZSOAQQJNjXOMnyW9Lx/G7vN4cZDLGPhUV7lyjrHAGBtGS7BJOzHxsKFL/lUkmS5mzK0SeEEklQ0c2L3q4g4X6oedqkmjZCBty+CE0U7kOtwJWLM1AkZgGoHNjBINoEx+EDsfLVJYuSKHQcLnS5mAMTDYNeHYV+vlTD1fNEnmcrfnomW1cOdFQG1lsxVh8bpZRe68tbR77jEGTil8ESeE+SVuKl2OwTYr6TkNfq2FIrUhxt4hZTknqXfEK47+IPvRx8Hqc04LVJc8Bo/tkhyEGUYi7w7x+e3WKYKx8ise8yttp4kvv9SW5C5tJ61slP5sddgSxA9GwAjcPQKbGSVCkskPak2Aj16Pvxr8WC18LpcVIiZPzlZ/ld3HSFfwK3mZDH6W+7muTSb3Kyi2RVyBgNoHRvjku1m0J11HKRYrRHOSEyLAOJHrmHGyUSwRQf6xoJPeQzlCLMbXrmGDXys/Pb9Unq33WpbmqfS0a3gw3q82RsSHsRQFHordpNnjXzndqjFYacEb2T/T9a2usu9hsOHPOx9dLOVdTRgcUxizEEd9d+smZZDLRzgvuoMxC3gYM6VMvK8ylUfiNfajtJvU4Rh/+xsBI2AEliIwZ5QwYdQSqy0HDXSDSrr8mQgYZDc5B0teZyQmUbBhEh0s7xllc9aXhQAKWxjsPckURjtapVz1mNnjkhAYGjs/l4A/qM75YlU5bqCg8kWkckGH9EM8psoIz+YImPgx5j7TFcr+Ifv1drOnmJZhSs+HTFCQUaZnX9Yu047co3Q3R3J1z1FfjjY1L+qPpFs9BisPdimS8VHmHfnIj3nqfTwvdZUeZZ9yjJLi8B7Qe12f6irbQqSh7rj4ChHtoCWP/Ah7q2sxKe3WdbhYBie4TQTUtmj7vb4r/9XG820i5VKNIfAwEsBqDBNZr3GV8dXQGCz5RCFx08QnPwb0kojDyhMuq4XlxFvGu4p7yc9k8EYXna+Z7K9CeAt5UgTUVpj8J5UTha9Wrk5aGGdWhYDqHGWXOk1jnp4ZD/kvCYwOxj/eFUPR/EUuxBjCcxoX5TK+oKTj/6WeMSreyB1cUVdYQ4oDHwwe2hz8/0/X73Tx56jht/iYrNIydjPeIRf8J+cFxVlCX4kfL8jHvICBht+Ysn5Q2BZjcO9YWyE0BkPUT+FdfQvvVxWxUdQoy5BRAh68e0I4ZWa3lS9tUY8YbRg0s22CtJDi7lmHj5n49+4RUDsr32e7ezwMwHIEHkaSMEgyKTKxjpIaIAP3Lex8jJZxIIDJEgUDw+35QLi9jEAgwB+yTe2SbKFcRV52LwAB1Tdj5+iYmMeNZmegK7LCUUZDQe8Gzz4r/RDvUXnmGIofyixKMDsaWxojkTXyvouHSneLMZi+1+CisrGAwLuOzGmvK+UYjCYeDd/BCNlT8WgrQwbJIcvRqkv5YYRUGyKRt9LtXYeRld07RkDtDJ2RRRgWZroUf07K4gYLM4wpQcyRfLJ8sC9EJLv3gcCYUcJqDMexGPyv5bw7kwnXbiQs+Dfj+GIKE2nPaCNOFuAT3bcmld0EM+OLQyC3A/rRFG2hXE3xd5gROAoBtWPG1D2MkSSX+HdXVhkzy08ct+SnX+k6agxW+lCaUJSeKwOU9s+Cr9xmHtH91Y/nuTy71WGrgvxwlwiojdGH2PnjPVvefWJHtaX/5Djgg+HCEVJ0JPo6uhR+bqMC4d7pyRAAaiSs1MULdVi2m1NuoBz9OuieBoyVvZqUnnPC3QluNb9uQvFmZa1cweSTmi2ZFYfJLl7kp5OZ7hABtQMGaBSe0VVNhXWVq1ZbukPYXOQ7RyCPnyyGDX4OXeFbjcHwQXHiSBSKFIsH5diuxzQveTxPSPjHCMwjkPtTGPTPBlLgx4cl6Ff8t1HomKTx/CcQTIfD2E4J2GDlYs1+rcYT29r4b0LiSUOs2ubeJMPjmSArE9nLzIpOxC4SV9kRU0eTX2+SO14Ec7gUBFS/1P8LuUOG8NcK42z8ICnNkHL1ZTey4l39Km23TH42AkMI5P5En5l6eX6rMZjjIuX4zJjNe4IHyfFUDv2aBQWUKI/nAsFkBKYQUH8JHYg+xPwWBkeTTP7Rl+h/6JZBGClN+vC0e58IjBolakDsPLBNjmLEjsY1GRCb1qZwYFW7uxWJUsqqHi4vsOKCEccAylVweZluCQHVL4MuAyv1/K2uZkDVPUoNx7JYgR2jWeVK6Rmo2XXj613kZzICN4mA2jdjJy/p06cO+Rm3UWx0v+UYTH9qxnPxpv/GeXYWFDjf7vFcQJiMwAoEmN9Ko6PLgmPv5fzIQi87KCYjcHgyhYEGZhoOK0Z8c33ufPwUq6sNU7mZwBqlMwoi/5gwmbwO+ZkjW+90H2eeI7rdG0JA9YvBTt9AkUGJKYnV3nLALcMOSpeUK9LHVcRPbSkn8CptCzk/3CIC6gO0eeYWjvBizGOM03/e60okv83G4MwfvuVOSZkP/8LOjjjju8fzhIx/jMAiBOivYeS3Eqpf0d9ZuEs6VX6OPt+K64f7RODJXLHVaLB6mSS+0v1dvSeh8jJZUua0gic3kfw5shVGGsfb6ISm+0PgtYqMkcEge8guSs3YgFyrXDFw0+84RhJHuMjCZARuDQG+wkO/wI2LuSaUls3G4NyX2PWHeJ+EL4pxYRCxsstFnzYZASNwBALqT7Fo2+USBgsL3cxt6JZTRza76f184wg81JRPjYdP4LJjgkV7N6Qys8XfbPNHweXPhDkYFnHs3j4C9AldDL5f62JwHd0lUTyUqy91sULbvIcifwwa0kEYuKzSshOTFgDketftERv/3iACat8fTxVL4YPjrPwXj8G5L7k/TQHuMCNwJALqZ1Nf0eIjFvFqwJE5OfktIvDRhw8fbrFcJy+TOiLKJatwaStSz6NfXjq5cM5wNwRUz7xXRL1/rgujgh2Oo0l8WFHifZKeUXw0czMwAjeIgPrKZmPwlrxuEGoXyQisQkD9iq+WcnTZ+tEqBG8/kY2S269jl3BnBPJA+0zZsA09tm29SArxsVGyCDFHNgJGwAgYgUtFQHMaJwI4ssVJAQwTdjtNRqCFgI2SFhx+MALLEdDgym7JS7lb7ZJstuK7vDROYQSMgBEwAkbACBiB0yPw/wH5/2pI07v5IwAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle \\begin{cases} 0 & \\text{for}\\: w \\leq \\frac{L_{b}^{2} \\bar{\\tau} p}{2 A_\\mathrm{f} E_\\mathrm{f}} \\wedge x \\leq - \\frac{\\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{w}}{\\sqrt{\\bar{\\tau}} \\sqrt{p}} \\\\\\frac{\\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{w} + \\bar{\\tau} p x}{A_\\mathrm{f}} & \\text{for}\\: w \\leq \\frac{L_{b}^{2} \\bar{\\tau} p}{2 A_\\mathrm{f} E_\\mathrm{f}} \\wedge x > - \\frac{\\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{w}}{\\sqrt{\\bar{\\tau}} \\sqrt{p}} \\\\0 & \\text{for}\\: x \\leq \\frac{\\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{A_\\mathrm{f} E_\\mathrm{f} - 2 L_{b} \\bar{\\tau} p + 2 \\bar{\\tau} p w} - A_\\mathrm{f} E_\\mathrm{f}}{\\bar{\\tau} p} \\wedge w > \\frac{L_{b}^{2} \\bar{\\tau} p}{2 A_\\mathrm{f} E_\\mathrm{f}} \\\\E_\\mathrm{f} + \\frac{\\bar{\\tau} p x}{A_\\mathrm{f}} - \\frac{\\sqrt{E_\\mathrm{f}} \\sqrt{A_\\mathrm{f} E_\\mathrm{f} - 2 L_{b} \\bar{\\tau} p + 2 \\bar{\\tau} p w}}{\\sqrt{A_\\mathrm{f}}} & \\text{for}\\: w > \\frac{L_{b}^{2} \\bar{\\tau} p}{2 A_\\mathrm{f} E_\\mathrm{f}} \\wedge x > \\frac{\\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{A_\\mathrm{f} E_\\mathrm{f} - 2 L_{b} \\bar{\\tau} p + 2 \\bar{\\tau} p w} - A_\\mathrm{f} E_\\mathrm{f}}{\\bar{\\tau} p} \\end{cases}$"
      ],
      "text/plain": [
       "⎧                                                                             \n",
       "⎪                                                                             \n",
       "⎪                                                          0                  \n",
       "⎪                                                                             \n",
       "⎪                                                                             \n",
       "⎪                                                                             \n",
       "⎪                           ______________   ______________   ____________    \n",
       "⎪                      √2⋅╲╱ A_\\mathrm{f} ⋅╲╱ E_\\mathrm{f} ⋅╲╱ \\bar{\\tau} ⋅√p⋅\n",
       "⎪                      ───────────────────────────────────────────────────────\n",
       "⎪                                                     A_\\mathrm{f}            \n",
       "⎪                                                                             \n",
       "⎨                                                                             \n",
       "⎪                                                                             \n",
       "⎪                                                                             \n",
       "⎪                                                          0                  \n",
       "⎪                                                                             \n",
       "⎪                                                                             \n",
       "⎪                                  ______________   __________________________\n",
       "⎪               \\bar{\\tau}⋅p⋅x   ╲╱ E_\\mathrm{f} ⋅╲╱ A_\\mathrm{f}⋅E_\\mathrm{f}\n",
       "⎪E_\\mathrm{f} + ────────────── - ─────────────────────────────────────────────\n",
       "⎪                A_\\mathrm{f}                                         ________\n",
       "⎪                                                                   ╲╱ A_\\math\n",
       "⎩                                                                             \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "√w + \\bar{\\tau}⋅p⋅x                                                           \n",
       "───────────────────                                                           \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                     ______________   ________\n",
       "                                                   ╲╱ A_\\mathrm{f} ⋅╲╱ E_\\math\n",
       "                                           for x ≤ ───────────────────────────\n",
       "                                                                              \n",
       "                                                                              \n",
       "_________________________________________                  2                  \n",
       " - 2⋅L_b⋅\\bar{\\tau}⋅p + 2⋅\\bar{\\tau}⋅p⋅w                L_b ⋅\\bar{\\tau}⋅p     \n",
       "─────────────────────────────────────────  for w > ───────────────────────────\n",
       "______                                             2⋅A_\\mathrm{f}⋅E_\\mathrm{f}\n",
       "rm{f}                                                                         \n",
       "                                                                              \n",
       "\n",
       "                          2                               ______________   ___\n",
       "                       L_b ⋅\\bar{\\tau}⋅p            -√2⋅╲╱ A_\\mathrm{f} ⋅╲╱ E_\n",
       "          for w ≤ ─────────────────────────── ∧ x ≤ ──────────────────────────\n",
       "                  2⋅A_\\mathrm{f}⋅E_\\mathrm{f}                     ____________\n",
       "                                                                ╲╱ \\bar{\\tau} \n",
       "                                                                              \n",
       "                          2                               ______________   ___\n",
       "                       L_b ⋅\\bar{\\tau}⋅p            -√2⋅╲╱ A_\\mathrm{f} ⋅╲╱ E_\n",
       "          for w ≤ ─────────────────────────── ∧ x > ──────────────────────────\n",
       "                  2⋅A_\\mathrm{f}⋅E_\\mathrm{f}                     ____________\n",
       "                                                                ╲╱ \\bar{\\tau} \n",
       "                                                                              \n",
       "______   ___________________________________________________________________  \n",
       "rm{f} ⋅╲╱ A_\\mathrm{f}⋅E_\\mathrm{f} - 2⋅L_b⋅\\bar{\\tau}⋅p + 2⋅\\bar{\\tau}⋅p⋅w  -\n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                 \\bar{\\tau}⋅p                                 \n",
       "                                                                              \n",
       "         ______________   ______________   ___________________________________\n",
       "       ╲╱ A_\\mathrm{f} ⋅╲╱ E_\\mathrm{f} ⋅╲╱ A_\\mathrm{f}⋅E_\\mathrm{f} - 2⋅L_b⋅\n",
       " ∧ x > ───────────────────────────────────────────────────────────────────────\n",
       "                                                                   \\bar{\\tau}⋅\n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "___________                                                 \n",
       "\\mathrm{f} ⋅√w                                              \n",
       "───────────────                                             \n",
       "                                                            \n",
       "⋅√p                                                         \n",
       "                                                            \n",
       "___________                                                 \n",
       "\\mathrm{f} ⋅√w                                              \n",
       "───────────────                                             \n",
       "                                                            \n",
       "⋅√p                                                         \n",
       "                                                            \n",
       "                                         2                  \n",
       " A_\\mathrm{f}⋅E_\\mathrm{f}            L_b ⋅\\bar{\\tau}⋅p     \n",
       "────────────────────────── ∧ w > ───────────────────────────\n",
       "                                 2⋅A_\\mathrm{f}⋅E_\\mathrm{f}\n",
       "                                                            \n",
       "________________________________                            \n",
       "\\bar{\\tau}⋅p + 2⋅\\bar{\\tau}⋅p⋅w  - A_\\mathrm{f}⋅E_\\mathrm{f}\n",
       "────────────────────────────────────────────────────────────\n",
       "p                                                           \n",
       "                                                            \n",
       "                                                            "
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aw_up = -Pw_up_pull/p/tau\n",
    "bw_down = -Pw_down_pull/p/tau\n",
    "sig_f_x = sp.Piecewise(\n",
    "    (0, ((w <= w_argmax) & (x <= aw_up)) ),\n",
    "    (-Pw_up_pull/A_f/aw_up*(x-aw_up), ((w <= w_argmax) & (x > aw_up)) ),\n",
    "    (0, ((w > w_argmax) & (x <= bw_down)) ),\n",
    "    (-Pw_down_pull/A_f/bw_down*(x-bw_down), ((w > w_argmax) & (x > bw_down)) ),\n",
    ")\n",
    "sp.simplify(sig_f_x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/latex": [
       "$\\displaystyle \\left( w, \\  \\bar{\\tau}, \\  p, \\  L_{b}, \\  A_\\mathrm{f}, \\  A_\\mathrm{m}, \\  E_\\mathrm{f}, \\  E_\\mathrm{m}\\right)$"
      ],
      "text/plain": [
       "(w, \\bar{\\tau}, p, L_b, A_\\mathrm{f}, A_\\mathrm{m}, E_\\mathrm{f}, E_\\mathrm{m}\n",
       ")"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp_vars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "get_sig_f_x = sp.lambdify((x,) + sp_vars, sig_f_x)\n",
    "get_aw_up = sp.lambdify(sp_vars, aw_up)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2b9ee650254e4287a6602f0dbd024217",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f15279ce820>]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.warnings.filterwarnings('ignore', category=np.VisibleDeprecationWarning)                 \n",
    "w_range = np.linspace(0,2,50)\n",
    "x_range = np.linspace(-1,0,100)\n",
    "params = {w: 0.4, A_f:1, E_f:2, A_m:1, E_m:4, tau:1, p:1, L_b:1}\n",
    "param_vals = tuple(params[map_py2sp[py_var]] for py_var in py_vars)\n",
    "get_sig_f_x(0, *param_vals), get_aw_up(*param_vals)\n",
    "fix, ax = plt.subplots(1,1, figsize=(8,2))\n",
    "ax.plot(x_range, get_sig_f_x(x_range, *param_vals))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# ds = 0.2\n",
    "po_paper = poui.ModelInteract(\n",
    "    models=[PO_SF_M_RG],\n",
    "    py_vars=list(py_vars),\n",
    "    map_py2sp=map_py2sp,\n",
    "    w=.1, A_f=np.pi*(ds/2)**2, \n",
    "    E_f=200000, L_b=9.75, p=np.pi*ds, tau=6.56\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "po_paper.interact_geometry()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Task: use the parameters of the test to fit the response\n",
    "Assume the length of the bond zone $L_b = 6.5m$ and $L_b = 9.75$, $E_\\mathrm{f}=200000$ MPa and the diameter $d = 0.2$ mm. Identify the bond stress $\\bar{\\tau}$ rendering the pullout curve with the maximum force $P_\\max$ = 49 N and final pullout displacement with zero force of 10 mm. "
   ]
  }
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