{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "ed69d213",
   "metadata": {},
   "source": [
    "# Biot oscillations\n",
    "Supplementary material to _The essence of Biot waves in an oscillator with two degrees of freedom_ by [Dominik Kern](https://orcid.org/0000-0002-1958-2982) and [Thomas Nagel](https://orcid.org/0000-0001-8459-4616), 2024."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "b1f94559",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import sympy as sp\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import fsolve\n",
    "import tikzplotlib"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93ed51d1",
   "metadata": {},
   "source": [
    "Spatial discretization by the mode shape ($k$th mode) of an elastic bar and the assumption that the fluid moves proportional to the solid\n",
    "\\begin{align}\n",
    "u_\\text{f}(t,x) &= U_\\text{f}(t)\\sin\\biggl(\\Bigl(k+ \\frac{1}{2}\\Bigr)\\pi x \\biggr), \\\\\n",
    "u_\\text{s}(t,x) &= U_\\text{s}(t)\\sin\\biggl(\\Bigl(k+ \\frac{1}{2}\\Bigr)\\pi x \\biggr). \n",
    "\\end{align}\n",
    "corresponding to a bar of unit-length with boundary conditions fixed-symmetric for S-waves (one half of a fixed-fixed bar) or fixed-free for P-waves.\n",
    "Temporal discretization (exponential ansatz with $\\hat{U}_\\text{f}$, $\\hat{U}_\\text{s}$, $\\delta\\in\\mathbb{C}$), such that coefficients in characteristic equation remain in real domain ($a_i\\in\\mathbb{R}$)\n",
    "\\begin{align}\n",
    "U_\\text{f}(t) &= \\hat{U}_\\text{f}\\, e^{\\delta t}, \\\\\n",
    "U_\\text{s}(t) &=  \\hat{U}_\\text{s}\\, e^{\\delta t}.\n",
    "\\end{align}\n",
    "\n",
    "Note that the real part of the coefficient $\\mathfrak{R}\\{\\delta\\}$ describes decay and the imaginary part $\\mathfrak{I}\\{\\delta\\}$ oscillation.\n",
    "\n",
    "The original equations are related to domain length $L$ and reference time $T=L\\sqrt{m_\\text{v} \\rho_\\text{s}}$ to make them non-dimensional, note $c_\\mathrm{P}^\\mathrm{el}=\\frac{1}{\\sqrt{m_\\text{v} \\rho_\\text{s}}}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb9700fc",
   "metadata": {},
   "source": [
    "## Parameters\n",
    "The continuum parameters are\n",
    "- $L$ domain length [m],\n",
    "- $\\varrho_\\text{f}$ fluid density [kg m$^{-3}$],\n",
    "- $\\varrho_\\text{s}$ solid density [kg m$^{-3}$],\n",
    "- $m_\\text{v}$ one-dimensional soil compressibility (inverse P-wave modulus) [Pa$^{-1}$],\n",
    "- $G$ shear modulus (bulk) [Pa],\n",
    "- $S_\\text{p}$ storativity [Pa$^{-1}$],\n",
    "- $\\mu$ viscosity [Pa s],\n",
    "- $\\kappa$ permeability [m$^2$],\n",
    "- $\\alpha$ Biot coefficient,\n",
    "- $n$ porosity,\n",
    "- $\\tau$ tortuosity factor."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "597c7d09",
   "metadata": {},
   "source": [
    "Declare variables for dimensional and non-dimensional parameters (symbolic computations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "5c29b39e",
   "metadata": {},
   "outputs": [],
   "source": [
    "L, G, m_v, n, S, alpha, kappa, mu, rho_f, rho_s, tau = sp.symbols('L G m_v n S alpha kappa mu rho_f rho_s tau') \n",
    "I_11, I_12, I_22, M, D_P, D_S, RHO, x, k, g = sp.symbols('I_11 I_12 I_22 M D_P D_S RHO x k g') "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff620c9d",
   "metadata": {},
   "source": [
    "Example of some soil [Verruijt2010: table 5.1], except $\\tau\\ne 0$ to check the influence of tortuosity and bulk compressibility $m_\\text{v}<S_\\text{}p$ to make frequency dependency visible. A Poisson ratio $\\nu=0.2$ is assumed to derive the shear modulus from the bulk modulus (for S-waves)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "e1c85085",
   "metadata": {},
   "outputs": [],
   "source": [
    "rho_s_num = 2650\n",
    "rho_f_num = 1000\n",
    "kappa_num = 1e-10   # note, Verruijt lists hydraulic conductivity k=0.001 m/s\n",
    "n_num = 0.4\n",
    "tau_num = 0.1   # different from Verruijt's example (tau=0)\n",
    "alpha_num = 1.0\n",
    "m_v_num = 2e-9   # different from Verruijt's example (mb_v=2e-10)\n",
    "S_num = n_num*5e-10 + (alpha_num-n_num)*0   # S_p = n*C_f + (alpha-n)*C_s\n",
    "mu_num = 1e-3\n",
    "\n",
    "nu_num = 0.2   # Poisson ratio\n",
    "G_num = (1/m_v_num)*(1-2*nu_num)/(2*(1-nu_num))   # shear modulus"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b542af2c",
   "metadata": {},
   "source": [
    "Bar length, plausible values are some meters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "0b30c2a3",
   "metadata": {},
   "outputs": [],
   "source": [
    "L_num = 20    # influences eigenfrequency range, set to center it around f_crit"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0de6e1b6",
   "metadata": {},
   "source": [
    "Weight function integrals $I_{ij} = \\int_0^1 \\tilde{w}_i(x)\\tilde{w}_j(x)\\,\\text{d}x$ as they occur in Galerkin's method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "88858454",
   "metadata": {},
   "outputs": [],
   "source": [
    "I_11_k = sp.integrate(sp.sin(x*sp.pi*(1/2+k))**2, (x,0,1))\n",
    "I_12_k = sp.integrate(sp.sin(x*sp.pi*(1/2+k))**2, (x,0,1))\n",
    "I_22_k = sp.integrate(sp.sin(x*sp.pi*(1/2+k))**2, (x,0,1))\n",
    "k0 = 0 # base mode discretization\n",
    "I_11_k0 = float(I_11_k.subs(k, k0))\n",
    "I_12_k0 = float(I_12_k.subs(k, k0))\n",
    "I_22_k0 = float(I_22_k.subs(k, k0))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20497933",
   "metadata": {},
   "source": [
    "Lists to substitute numerical values into analytic expressions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "54f9805d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(L, 20),\n",
       " (n, 0.4),\n",
       " (alpha, 1.0),\n",
       " (G, 187499999.99999994),\n",
       " (m_v, 2e-09),\n",
       " (S, 2.0000000000000003e-10),\n",
       " (rho_f, 1000),\n",
       " (rho_s, 2650),\n",
       " (kappa, 1e-10),\n",
       " (mu, 0.001),\n",
       " (tau, 0.1)]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "continuum_num = [(L, L_num),\n",
    "                 (n, n_num),\n",
    "                 (alpha,   alpha_num),\n",
    "                 (G, G_num),\n",
    "                 (m_v, m_v_num),\n",
    "                 (S, S_num),\n",
    "                 (rho_f, rho_f_num), \n",
    "                 (rho_s, rho_s_num), \n",
    "                 (kappa, kappa_num), \n",
    "                 (mu, mu_num), \n",
    "                 (tau, tau_num)]\n",
    "\n",
    "display(continuum_num)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "846ba26a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(I_11, 0.5),\n",
       " (I_12, 0.5),\n",
       " (I_22, 0.5),\n",
       " (D_S, 22.698460868221083),\n",
       " (D_P, 13.899911768418223),\n",
       " (n, 0.4),\n",
       " (alpha, 1.0),\n",
       " (M, 9.999999999999998),\n",
       " (RHO, 2.65),\n",
       " (tau, 0.1)]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "RHO_num = float((rho_s/rho_f).subs(continuum_num).evalf())\n",
    "M_num =   float((m_v/S).subs(continuum_num).evalf())\n",
    "D_S_num = float((L*n*mu/(kappa*(G*rho_s)**(1/2))).subs(continuum_num).evalf())\n",
    "D_P_num = float((L*n*mu*sp.sqrt(m_v*rho_s)/(kappa*rho_s)).subs(continuum_num).evalf())\n",
    "\n",
    "nondim_num_k0 = [(I_11, I_11_k0),\n",
    "                 (I_12, I_12_k0),\n",
    "                 (I_22, I_22_k0),\n",
    "                 (D_S, D_S_num),\n",
    "                 (D_P, D_P_num),\n",
    "                 (n,   n_num),\n",
    "                 (alpha,   alpha_num),\n",
    "                 (M, M_num),\n",
    "                 (RHO, RHO_num),\n",
    "                 (tau, tau_num)]\n",
    "\n",
    "display(nondim_num_k0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee6f27cb",
   "metadata": {},
   "source": [
    "Non-dimensional Biot's characteristic frequency [Biot1956: equation (7.4)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "6dfff2c6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "f_crit = 5.862435116185167\n"
     ]
    }
   ],
   "source": [
    "f_characteristic = (mu*n/(2*sp.pi*kappa*rho_f))*L*(m_v*rho_s)**(1/2)\n",
    "f_characteristic_num = float(f_characteristic.subs(continuum_num).evalf())   \n",
    "print(\"f_crit = {}\".format(f_characteristic_num))   # non-dimensional"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f4db004",
   "metadata": {},
   "source": [
    "Wave velocities (elastic S, elastic P, undrained P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "b319a908",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "c_el_S = 265.997588299466 m/s\n",
      "c_el_P = 434.372242763069 m/s\n",
      "c_un_S = 306.954565901272 m/s\n",
      "c_un_P = 1662.47378790686 m/s\n"
     ]
    }
   ],
   "source": [
    "c_el_S = (G/rho_s)**(1/2)\n",
    "c_el_S_num = c_el_S.subs(continuum_num).evalf()\n",
    "c_el_P = (m_v*rho_s)**(-1/2)\n",
    "c_el_P_num = c_el_P.subs(continuum_num).evalf()\n",
    "c_un_S = (G/((1-n)*rho_s + n*rho_f))**(1/2)    # drained is same as elastic\n",
    "c_un_S_num = c_un_S.subs(continuum_num).evalf()\n",
    "c_un_P = (((1/m_v) + (alpha**2)/S)/((1-n)*rho_s + n*rho_f))**(1/2)\n",
    "c_un_P_num = c_un_P.subs(continuum_num).evalf()\n",
    "print(\"c_el_S = {} m/s\".format(c_el_S_num))\n",
    "print(\"c_el_P = {} m/s\".format(c_el_P_num))\n",
    "print(\"c_un_S = {} m/s\".format(c_un_S_num))\n",
    "print(\"c_un_P = {} m/s\".format(c_un_P_num))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1bfc932e",
   "metadata": {},
   "source": [
    "Variables for MBS models (same variables, but different expressions for S- and P-waves)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "9ef1e133",
   "metadata": {},
   "outputs": [],
   "source": [
    "m_1, m_2, m_Delta, d_Delta, c_1, c_2, c_Delta, delta= sp.symbols('m_1 m_2 m_Delta d_Delta c_1 c_2 c_Delta delta')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "de27edaf",
   "metadata": {},
   "source": [
    "## S-waves\n",
    "Use isochronic one-term Galerkin discretization of the poroelastic bar (1D) in non-dimensional formulation, with fixed BC on the left (x=0), symmetry BC on the right (x=1), to illustrate the motion of shear waves, since oscillations are standing waves and simpler to describe while wave velocity, wave length and frequency are still related ($c=\\frac{\\omega}{k}$ in non-dissipative case, otherwise close by).\n",
    "\n",
    "Non-dimensional equations of motion for fluid phase (total displacement $u_\\mathrm{f}$) and solid phase (total displacement $u_\\mathrm{s}$)\n",
    "\\begin{align}\n",
    "\\frac{n}{\\rho}\\ddot{u}_\\text{f} + \\frac{n\\tau}{\\rho}(\\ddot{u}_\\text{f} - \\ddot{u}_\\text{s}) + n D_S (\\dot{u}_\\text{f}-\\dot{u}_\\text{s}) &&=0, \\\\\n",
    "(1-n)\\ddot{u}_\\text{s} - \\frac{n\\tau}{\\rho}(\\ddot{u}_\\text{f} - \\ddot{u}_\\text{s}) - n D_S(\\dot{u}_\\text{f}-\\dot{u}_\\text{s})& - u_\\text{s}'' &=0,\n",
    "\\end{align}\n",
    "with $\\rho = \\frac{\\varrho_\\mathrm{s}}{\\varrho_\\mathrm{f}}$, and $D_\\mathrm{S}=\\frac{n \\mu L}{\\kappa \\sqrt{G \\varrho_\\mathrm{s}}}$, note the relation $D_\\mathrm{S} = \\frac{c_\\mathrm{P}^\\mathrm{el}}{c_\\mathrm{S}^\\mathrm{el}} D_\\mathrm{P}$ with $\\frac{c_\\mathrm{P}^\\mathrm{el}}{c_\\mathrm{S}^\\mathrm{el}} = \\sqrt{\\frac{1}{m_\\mathrm{v} G}}$. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8afe415c",
   "metadata": {},
   "source": [
    "### Multi-body system matrices"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ecaa8d8",
   "metadata": {},
   "source": [
    "Conversion between multi-body and non-dimensional continuum parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "5fe39e7f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "m_1(k=0) = 0.0754716981132076\n",
      "m_2(k=0) = 0.300000000000000\n",
      "m_Delta(k=0) = 0.00754716981132076\n",
      "d_Delta(k=0) = 4.53969217364422\n",
      "c_2(k=0) = 1.23370055013617\n"
     ]
    }
   ],
   "source": [
    "mbs2nondim_S = [(m_1,     I_11*(n/RHO)), \n",
    "                (m_2,     I_22*(1-n)), \n",
    "                (m_Delta, I_12*n*tau/RHO), \n",
    "                (d_Delta, I_12*n*D_S), \n",
    "                (c_2,     I_22*(sp.pi*(1/2+k))**2)]\n",
    "\n",
    "print(\"m_1(k=0) = {}\".format(m_1.subs(mbs2nondim_S).subs(nondim_num_k0).evalf()))\n",
    "print(\"m_2(k=0) = {}\".format(m_2.subs(mbs2nondim_S).subs(nondim_num_k0).evalf()))\n",
    "print(\"m_Delta(k=0) = {}\".format(m_Delta.subs(mbs2nondim_S).subs(nondim_num_k0).evalf()))\n",
    "print(\"d_Delta(k=0) = {}\".format(d_Delta.subs(mbs2nondim_S).subs(nondim_num_k0).evalf()))\n",
    "print(\"c_2(k=0) = {}\".format(c_2.subs(mbs2nondim_S).subs(nondim_num_k0 + [(k, k0)]).evalf()))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80deb975",
   "metadata": {},
   "source": [
    "mass matrix (symmetric)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "4cee07b4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}m_{1} + m_{\\Delta} & - m_{\\Delta}\\\\- m_{\\Delta} & m_{2} + m_{\\Delta}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[m_1 + m_Delta,      -m_Delta],\n",
       "[     -m_Delta, m_2 + m_Delta]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mass_S = sp.Matrix(((m_1+m_Delta, -m_Delta), (-m_Delta, m_2+m_Delta)))\n",
    "display(mass_S)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "793915e2",
   "metadata": {},
   "source": [
    "damping matrix (symmetric)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "217df3a1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}d_{\\Delta} & - d_{\\Delta}\\\\- d_{\\Delta} & d_{\\Delta}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[ d_Delta, -d_Delta],\n",
       "[-d_Delta,  d_Delta]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "damping_S = sp.Matrix(((d_Delta, -d_Delta), (-d_Delta, d_Delta)))\n",
    "display(damping_S)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0e86788",
   "metadata": {},
   "source": [
    "stiffness matrix (symmetric)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "8de78f68",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 0\\\\0 & c_{2}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[0,   0],\n",
       "[0, c_2]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "stiffness_S = sp.Matrix(((0, 0), (0, c_2)))\n",
    "display(stiffness_S)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "efa44a40",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c_{2} d_{\\Delta} \\delta + c_{2} \\delta^{2} m_{1} + c_{2} \\delta^{2} m_{\\Delta} + d_{\\Delta} \\delta^{3} m_{1} + d_{\\Delta} \\delta^{3} m_{2} + \\delta^{4} m_{1} m_{2} + \\delta^{4} m_{1} m_{\\Delta} + \\delta^{4} m_{2} m_{\\Delta}$"
      ],
      "text/plain": [
       "c_2*d_Delta*delta + c_2*delta**2*m_1 + c_2*delta**2*m_Delta + d_Delta*delta**3*m_1 + d_Delta*delta**3*m_2 + delta**4*m_1*m_2 + delta**4*m_1*m_Delta + delta**4*m_2*m_Delta"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.simplify(sp.Determinant(mass_S*delta**2+damping_S*delta+stiffness_S))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "95f578a6",
   "metadata": {},
   "source": [
    "_Swap relation_ [Hagedorn2012], to show that damping matrix cannot be diagonalized (except $c_2=0$ or $d_\\Delta=0$)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "47a2e453",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{c_{2} d_{\\Delta} m_{1} m_{\\Delta}}{\\left(m_{1} m_{2} + m_{1} m_{\\Delta} + m_{2} m_{\\Delta}\\right)^{2}}$"
      ],
      "text/plain": [
       "c_2*d_Delta*m_1*m_Delta/(m_1*m_2 + m_1*m_Delta + m_2*m_Delta)**2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{c_{2} d_{\\Delta} \\left(- m_{1} m_{\\Delta} + m_{2} m_{\\Delta} - m_{2} \\left(m_{1} + m_{\\Delta}\\right)\\right)}{\\left(m_{1} m_{2} + m_{1} m_{\\Delta} + m_{2} m_{\\Delta}\\right)^{2}}$"
      ],
      "text/plain": [
       "c_2*d_Delta*(-m_1*m_Delta + m_2*m_Delta - m_2*(m_1 + m_Delta))/(m_1*m_2 + m_1*m_Delta + m_2*m_Delta)**2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{c_{2} d_{\\Delta} m_{1} \\left(m_{1} + m_{\\Delta}\\right)}{\\left(m_{1} m_{2} + m_{1} m_{\\Delta} + m_{2} m_{\\Delta}\\right)^{2}}$"
      ],
      "text/plain": [
       "c_2*d_Delta*m_1*(m_1 + m_Delta)/(m_1*m_2 + m_1*m_Delta + m_2*m_Delta)**2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{c_{2} d_{\\Delta} m_{1} m_{\\Delta}}{\\left(m_{1} m_{2} + m_{1} m_{\\Delta} + m_{2} m_{\\Delta}\\right)^{2}}$"
      ],
      "text/plain": [
       "-c_2*d_Delta*m_1*m_Delta/(m_1*m_2 + m_1*m_Delta + m_2*m_Delta)**2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "inv_mass_S = sp.Matrix.inv(mass_S)\n",
    "zero_or_not = (inv_mass_S*damping_S)*(inv_mass_S*stiffness_S) - (inv_mass_S*stiffness_S)*(inv_mass_S*damping_S)\n",
    "display(sp.simplify(zero_or_not[0,0]))\n",
    "display(sp.simplify(zero_or_not[0,1]))\n",
    "display(sp.simplify(zero_or_not[1,0]))\n",
    "display(sp.simplify(zero_or_not[1,1])) "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cea5d110",
   "metadata": {},
   "source": [
    "### Free vibrations"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53e2a075",
   "metadata": {},
   "source": [
    "Eigenproblem and characteristic equation (MBS and non-dimensional formulation of 1D continuum) $a_4 \\delta^4 + a_3 \\delta^3 + a_2 \\delta^2 + a_1 \\delta + a_0 = 0$ with $a_4,a_3,a_2,a_1\\in\\mathbb{R}^+$ and $a_0=0$ on physical grounds ($0\\le \\tau, \\rho_\\mathrm{f}, \\rho_\\mathrm{s}, G, \\kappa, \\mu$ and $0\\le n\\le 1$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "6a25e904",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\delta \\left(c_{2} d_{\\Delta} + \\delta^{3} \\left(m_{1} m_{2} + m_{1} m_{\\Delta} + m_{2} m_{\\Delta}\\right) + \\delta^{2} \\left(d_{\\Delta} m_{1} + d_{\\Delta} m_{2}\\right) + \\delta \\left(c_{2} m_{1} + c_{2} m_{\\Delta}\\right)\\right)$"
      ],
      "text/plain": [
       "delta*(c_2*d_Delta + delta**3*(m_1*m_2 + m_1*m_Delta + m_2*m_Delta) + delta**2*(d_Delta*m_1 + d_Delta*m_2) + delta*(c_2*m_1 + c_2*m_Delta))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c_{2} d_{\\Delta} + \\delta^{3} \\left(m_{1} m_{2} + m_{1} m_{\\Delta} + m_{2} m_{\\Delta}\\right) + \\delta^{2} \\left(d_{\\Delta} m_{1} + d_{\\Delta} m_{2}\\right) + \\delta \\left(c_{2} m_{1} + c_{2} m_{\\Delta}\\right)$"
      ],
      "text/plain": [
       "c_2*d_Delta + delta**3*(m_1*m_2 + m_1*m_Delta + m_2*m_Delta) + delta**2*(d_Delta*m_1 + d_Delta*m_2) + delta*(c_2*m_1 + c_2*m_Delta)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "evp_mbs_S = (delta**2)*mass_S + delta*damping_S + stiffness_S\n",
    "ceq_mbs_S = sp.simplify(sp.Determinant(evp_mbs_S).doit())\n",
    "ceq_mbs_reduced_S = ceq_mbs_S/delta\n",
    "display(ceq_mbs_S.collect(delta))\n",
    "display(ceq_mbs_reduced_S.collect(delta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "d6f5f2b7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{n \\left(D_{S} I_{12} I_{22} \\rho^{2} \\left(\\delta^{2} \\cdot \\left(1 - n\\right) + \\pi^{2} \\left(k + 0.5\\right)^{2}\\right) + I_{11} I_{12} \\delta^{3} n \\tau + \\rho \\delta \\left(D_{S} I_{11} I_{12} \\delta n + \\pi^{2} I_{11} I_{22} \\left(k + 0.5\\right)^{2} + \\pi^{2} I_{12} I_{22} \\tau \\left(k + 0.5\\right)^{2} + \\delta^{2} \\left(- I_{11} I_{22} \\left(n - 1\\right) - I_{12} I_{22} \\tau \\left(n - 1\\right)\\right)\\right)\\right)}{\\rho^{2}}$"
      ],
      "text/plain": [
       "n*(D_S*I_12*I_22*RHO**2*(delta**2*(1 - n) + pi**2*(k + 0.5)**2) + I_11*I_12*delta**3*n*tau + RHO*delta*(D_S*I_11*I_12*delta*n + pi**2*I_11*I_22*(k + 0.5)**2 + pi**2*I_12*I_22*tau*(k + 0.5)**2 + delta**2*(-I_11*I_22*(n - 1) - I_12*I_22*tau*(n - 1))))/RHO**2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "evp_nondim_S = evp_mbs_S.subs(mbs2nondim_S)\n",
    "ceq_nondim_reduced_S = sp.simplify(ceq_mbs_reduced_S.subs(mbs2nondim_S))\n",
    "#display(evp_continuum_S)\n",
    "display(ceq_nondim_reduced_S.collect(delta))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca84011c",
   "metadata": {},
   "source": [
    "#### Numerical evaluation (example)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "216c7ec7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.0830188679245283 \\delta^{2} + 4.53969217364422 \\delta & - 0.00754716981132076 \\delta^{2} - 4.53969217364422 \\delta\\\\- 0.00754716981132076 \\delta^{2} - 4.53969217364422 \\delta & 0.307547169811321 \\delta^{2} + 4.53969217364422 \\delta + 1.23370055013617\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[  0.0830188679245283*delta**2 + 4.53969217364422*delta,                 -0.00754716981132076*delta**2 - 4.53969217364422*delta],\n",
       "[-0.00754716981132076*delta**2 - 4.53969217364422*delta, 0.307547169811321*delta**2 + 4.53969217364422*delta + 1.23370055013617]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 0.000569597721609114 \\delta^{3} + 1.36190765209327 \\delta^{2} + 0.150943396226415 \\delta \\left(0.165 \\delta^{2} + 2.26984608682211 \\delta + 0.678535302574893\\right) + 5.60062073207373$"
      ],
      "text/plain": [
       "0.000569597721609114*delta**3 + 1.36190765209327*delta**2 + 0.150943396226415*delta*(0.165*delta**2 + 2.26984608682211*delta + 0.678535302574893) + 5.60062073207373"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "evp_num_S = evp_nondim_S.subs(nondim_num_k0 + [(k,k0)]).evalf()\n",
    "ceq_num_reduced_S = ceq_nondim_reduced_S.subs(nondim_num_k0 + [(k,k0)]).evalf()\n",
    "display(evp_num_S)\n",
    "display(ceq_num_reduced_S)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "b0d0087d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(-66.89810038739164+0j),\n",
       " (-0.005486807020854653-1.8128000450300856j),\n",
       " (-0.005486807020854653+1.8128000450300856j)]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eigenvalue_sp_S = sp.solve(ceq_num_reduced_S, delta)\n",
    "eigenvalue_num_S = [complex(EVSP) for EVSP in eigenvalue_sp_S]\n",
    "display(eigenvalue_num_S)\n",
    "number_of_eigenvalues = len(eigenvalue_num_S)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "d54e3b6e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--- 0. mode ---\n",
      "eigenvalue = (-66.89810038739164+0j)  \n",
      "eigenvector = [(0.9698356306509386+0j), (-0.24375981933020907+0j)]\n",
      "--- 1. mode ---\n",
      "eigenvalue = (-0.005486807020854653-1.8128000450300856j)  \n",
      "eigenvector = [(0.706946409444054+0j), (0.706946134120384-0.021305812033437233j)]\n",
      "--- 2. mode ---\n",
      "eigenvalue = (-0.005486807020854653+1.8128000450300856j)  \n",
      "eigenvector = [(0.706946409444054+0j), (0.706946134120384+0.021305812033437233j)]\n",
      "t_scale = 0.014553731557971884\n",
      "Tr0 = 1.494811e-02   Tr1 = 1.822554e+02   Ti1 = 3.466011e+00\n"
     ]
    }
   ],
   "source": [
    "eigenvector_num_S = np.zeros((number_of_eigenvalues, 2), dtype=complex)\n",
    "for mode_n, delta_n in enumerate(eigenvalue_num_S):\n",
    "    EVP_S = evp_num_S.subs(delta, delta_n)\n",
    "    ev0r = np.array([1.0, -EVP_S[0,0].evalf()/EVP_S[0,1].evalf()], dtype=complex)   # first row --> eigenvector\n",
    "    ev0r_norm = np.linalg.norm(ev0r) \n",
    "    if ev0r_norm>0:\n",
    "        ev0rn = ev0r/ev0r_norm  # normalize\n",
    "    else:\n",
    "        ev0rn = ev0r\n",
    "    #ev1r = np.array([1.0, -EVP_S[1,0].evalf()/EVP_S[1,1].evalf()], dtype=complex)   # second row, redundant\n",
    "    #ev1rn = ev1r/np.linalg.norm(ev1r)   # normalize  \n",
    "    print(\"--- {}. mode ---\".format(mode_n))\n",
    "    print(\"eigenvalue = {}  \".format(delta_n))\n",
    "    print(\"eigenvector = [{}, {}]\".format(ev0rn[0], ev0rn[1]))\n",
    "    #print(\"eigenvector = [{}, {}] (redundant)\".format(ev1rn[0], ev1rn[1]))\n",
    "    eigenvector_num_S[mode_n,:] = ev0rn\n",
    "    \n",
    "t_scale = 1.0/(np.abs(min(np.imag(eigenvalue_num_S))) + np.abs(min(np.real(eigenvalue_num_S))))\n",
    "print(\"t_scale = {}\".format(t_scale))\n",
    "t_decay0 = 1/np.abs(np.real(eigenvalue_num_S[0]))\n",
    "t_decay1 = 1/np.abs(np.real(eigenvalue_num_S[1]))\n",
    "t_oscillation1 = 2*np.pi/np.abs(np.imag(eigenvalue_num_S[1]))\n",
    "print(\"Tr0 = {:e}   Tr1 = {:e}   Ti1 = {:e}\".format(t_decay0, t_decay1, t_oscillation1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c8d215d",
   "metadata": {},
   "source": [
    "#### Visualize modes\n",
    "The real root leads to exponential decay, note that state of rest can be for any relative displacement between masses $m_1$ and $m_2$. The pair of complex-conjugated roots leads to damped oscillations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "47054775",
   "metadata": {},
   "outputs": [],
   "source": [
    "t_modeshow = np.linspace(0, 25*t_scale)   # try to show oscillation and decay\n",
    "timesteps_modeshow = len(t_modeshow)\n",
    "u_f = np.zeros((number_of_eigenvalues, timesteps_modeshow))\n",
    "u_s = np.zeros((number_of_eigenvalues, timesteps_modeshow))\n",
    "\n",
    "for mode_n, delta_n in enumerate(eigenvalue_num_S):\n",
    "    u_f[mode_n,:] = np.real(eigenvector_num_S[mode_n,0]*np.exp(delta_n*t_modeshow))\n",
    "    u_s[mode_n,:] = np.real(eigenvector_num_S[mode_n,1]*np.exp(delta_n*t_modeshow))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce97d8ac",
   "metadata": {},
   "source": [
    "Note that for complex-conjugated pairs the real parts of its contributions are identical (imaginary parts cancel on summation)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "5391757a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t_modeshow,u_f[0,:],'b',   t_modeshow,u_s[0,:],'k');\n",
    "plt.xlabel(\"$t$\");\n",
    "plt.ylabel(\"$u_\\\\mathrm{f}$,$u_\\\\mathrm{s}$\");\n",
    "#plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ac68354",
   "metadata": {},
   "source": [
    "Solid (black) and fluid (blue) move towards each other and slow down to rest."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "9d637e2d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t_modeshow, u_f[1,:],'b',   t_modeshow, u_s[1,:],'k');\n",
    "plt.xlabel(\"$t$\");\n",
    "plt.ylabel(\"$u_\\\\mathrm{f}$,$u_\\\\mathrm{s}$\");\n",
    "#plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17aa6510",
   "metadata": {},
   "source": [
    "Solid (black) and fluid (blue) motion are almost in phase with almost same amplitudes.  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7bcd4724",
   "metadata": {},
   "source": [
    "Note, that second root of complex-conjugated pair gives the same plot as first."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "552fe957",
   "metadata": {},
   "source": [
    "### Discriminant\n",
    "There is a discriminant for cubic polynomials indicating the number of real roots. However, for now we claim that there always is the rigid body mode ($\\delta_0=0$), a decaying mode ($\\delta_1\\in\\mathbb{R}$ and $\\delta_1<0$) and an oscillation mode ($\\delta_2, \\delta_3\\in\\mathbb{C}$ and $\\delta_2=\\bar{\\delta}_3$), i.e. S-waves exist always for physically plausible values. \n",
    "For the proof, we refer to this characteristic polynomial (S-waves) as a special case ($c_1=c_\\Delta=0$) of the more general characteristic polynomial for the P-wave model in the next section (same structure, only different values of the coefficients)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "738852e7",
   "metadata": {},
   "source": [
    "### Higher modes"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5baacc40",
   "metadata": {},
   "source": [
    "Characteristics of S-waves (takes some seconds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "e9c5d40d",
   "metadata": {},
   "outputs": [],
   "source": [
    "Nk = 1000\n",
    "d = np.zeros(Nk)   # decay constant\n",
    "c = np.zeros(Nk)   # phase velocity approximation\n",
    "f = np.zeros(Nk)   # frequency\n",
    "AR = np.zeros(Nk)   # amplitude ratio\n",
    "phi = np.zeros(Nk)   # phase angle\n",
    "\n",
    "index_S = 1    # second and third eigenvalue compose wave mode\n",
    "\n",
    "for k_num in range(Nk):\n",
    "    \n",
    "    I_11_num = float(I_11_k.subs(k, k_num))\n",
    "    I_12_num = float(I_12_k.subs(k, k_num))\n",
    "    I_22_num = float(I_22_k.subs(k, k_num))\n",
    "    \n",
    "    # redefine, since I_ij changes with higher modes\n",
    "    nondim_num_k = [(I_11,  I_11_num),\n",
    "                    (I_12,  I_12_num),\n",
    "                    (I_22,  I_22_num),\n",
    "                    (D_S,   D_S_num),\n",
    "                    (D_P,   D_P_num),\n",
    "                    (n,     n_num),\n",
    "                    (alpha, alpha_num),\n",
    "                    (M,     M_num),\n",
    "                    (RHO,   RHO_num),\n",
    "                    (tau,   tau_num)]\n",
    "    \n",
    "    ceq_num_reduced_Sk = ceq_nondim_reduced_S.subs(nondim_num_k + [(k, k_num)]).evalf()\n",
    "    eigenvalue_sp = sp.solve(ceq_num_reduced_Sk, delta)\n",
    "    eigenvalue_num = [complex(EVSP) for EVSP in eigenvalue_sp]\n",
    "    d[k_num] = np.real(eigenvalue_num[index_S])\n",
    "    omega = np.abs(np.imag(eigenvalue_num[index_S]))\n",
    "    c[k_num] = omega/((k_num+1/2)*np.pi)    \n",
    "    f[k_num] = omega/(2*np.pi)\n",
    "    \n",
    "    evp_num_Sk = evp_nondim_S.subs(nondim_num_k + [(k, k_num)]).evalf()\n",
    "    EVP = evp_num_Sk.subs(delta, eigenvalue_num[index_S])\n",
    "    evkr = np.array([1.0, -EVP[0,0].evalf()/EVP[0,1].evalf()], dtype=complex)   # first row --> eigenvector\n",
    "    us_uf = evkr[1]/evkr[0]   # TODO exclude division by zero\n",
    "    AR[k_num] = 1.0/np.absolute(us_uf)   # fluid-to-solid\n",
    "    phi[k_num] = np.angle(us_uf)   #np.abs(np.angle(us_uf))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "33b00d8c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "nondimensional c_el_S = 0.612372435695794\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"nondimensional c_el_S = {}\".format(c_el_S_num/c_el_P_num))\n",
    "\n",
    "fig1, ax1 = plt.subplots()\n",
    "ax2 = ax1.twinx()\n",
    "ax1.semilogx(f, c, 'g')\n",
    "ax2.semilogx(f, np.abs(d)/f, 'b')\n",
    "ax1.set_xlabel('frequency');\n",
    "ax1.set_xticks(list(ax1.get_xticks()) + [f_characteristic_num], list(ax1.get_xticklabels()) + ['$f_c$'])   # with extra tick\n",
    "ax1.set_ylabel('phase velocity', color='g');\n",
    "ax2.set_ylabel('decay constant', color='b');\n",
    "tikzplotlib.save(\"s_wave_eigenvalue.tex\", axis_height = '\\\\figH', axis_width = '\\\\figW')  \n",
    "\n",
    "fig2, ax3 = plt.subplots()\n",
    "ax4 = ax3.twinx()\n",
    "ax3.semilogx(f, AR, 'g')\n",
    "ax4.semilogx(f, phi, 'b')\n",
    "ax3.set_xlabel('frequency');\n",
    "ax3.set_xticks(list(ax3.get_xticks()) + [f_characteristic_num], list(ax3.get_xticklabels()) + ['$f_c$'])   # with extra tick\n",
    "ax3.set_ylabel('amplitude ratio', color='g');\n",
    "ax4.set_ylabel('phase angle [RAD]', color='b');\n",
    "tikzplotlib.save(\"s_wave_eigenvector.tex\", axis_height = '\\\\figH', axis_width = '\\\\figW') "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72ef048f",
   "metadata": {},
   "source": [
    "Numbers for TikZ-plots (complex amplitudes and time history)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "1c63917b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.2885160880037486\n",
      "0.019017334731030195\n",
      "0.9990929254273743\n",
      "0.03011047807705776\n"
     ]
    }
   ],
   "source": [
    "k_num = 500   # 0, 50, 500\n",
    "print(f[k_num])\n",
    "print(-d[k_num]/f[k_num])   # delta, with time axis scaled to period\n",
    "print(AR[k_num]*np.cos(phi[k_num])) # u_fluid, real part, with u_solid = 1\n",
    "print(AR[k_num]*np.sin(phi[k_num])) # u_fluid, imaginary part, with u_solid = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1a2ca07",
   "metadata": {},
   "source": [
    "## P-waves\n",
    "Non-dimensional equations of motion for fluid phase (displacement $u_\\text{f}$) and solid phase (displacement $u_\\text{s}$)\n",
    "\\begin{align}\n",
    "\\frac{n}{\\rho}\\ddot{u}_\\mathrm{f} + &\\frac{n\\tau}{\\rho}(\\ddot{u}_\\mathrm{f}- \\ddot{u}_\\mathrm{s}) &+& n D_\\text{P} (\\dot{u}_\\mathrm{f}-\\dot{u}_\\mathrm{s}) &-& nM\\bigl(n u_\\mathrm{f}'' - (n-\\alpha)u_\\mathrm{s}''\\bigr) &=0, \\\\\n",
    "(1-n) \\ddot{u}_\\mathrm{s} -& \\frac{n\\tau}{\\rho} (\\ddot{u}_\\mathrm{f} - \\ddot{u}_\\mathrm{s}) &-& n D_\\text{P} (\\dot{u}_\\mathrm{f}-\\dot{u}_\\mathrm{s}) &-& (n-\\alpha)M \\bigl(-n u_\\mathrm{f}'' + (n-\\alpha)u_\\mathrm{s}''\\bigr) - u_\\mathrm{s}'' &=0,\n",
    "\\end{align}\n",
    "with $\\rho = \\frac{\\varrho_\\text{s}}{\\varrho_\\text{f}}$, $M = \\frac{m_\\text{v}}{S_\\text{p}}$ and $D_\\mathrm{P} = \\frac{n\\mu L\\,\\sqrt{m_\\text{v}}\\, }{\\kappa \\sqrt{\\varrho_\\text{s}}}$, note relation $D_\\mathrm{P} = \\frac{c_\\mathrm{S}^\\mathrm{el}}{c_\\mathrm{P}^\\mathrm{el}}D_S$ with $\\frac{c_\\mathrm{S}^\\mathrm{el}}{c_\\mathrm{P}^\\mathrm{el}} = \\sqrt{m_\\text{v} G}$. \n",
    "\n",
    "**Remarks** about the resulting formulation as multi-body system\n",
    "- negative masses (interaction mass $m_\\Delta$ in off-diagonal entries of mass matrix),\n",
    "- complex eigenvectors (diagonalization of damping matrix with undamped eigenvectors is impossible),\n",
    "- non-dimensional damping $D_\\mathrm{P}$ in P-waves is similar to the ratio $\\frac{L f_\\mathrm{c}}{V_\\mathrm{c}}$ with bar length $L$ times characteristic frequency $f_\\mathrm{c}$ \\[Biot1956: eq.(7.4)\\], which divides low- from high-frequency range, and reference velocity $V_\\mathrm{c}$ in his notation \\[Biot1956: equation (5.4)\\],\n",
    "- Biot refers to the velocity of dilatational waves in the undrained case $V_\\mathrm{c} = \\sqrt{\\frac{1/m_\\text{v} + \\alpha^2/S_\\text{p}}{(1-n)\\varrho_\\text{s} + n \\varrho_\\text{f}}}$ and a characteristic frequency $f_c=\\frac{1}{2\\pi}\\frac{\\mu n}{\\kappa \\varrho_\\text{f}}$ \\[Biot1956: equations (5.4) and (7.4)\\]. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7f27916",
   "metadata": {},
   "source": [
    "### Multi-body system matrices"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16115758",
   "metadata": {},
   "source": [
    "Conversion between multi-body and non-dimensional continuum parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "2e0e6e4e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "m_1(k=0)     = 0.0754716981132076\n",
      "m_2(k=0)     = 0.300000000000000\n",
      "m_Delta(k=0) = 0.00754716981132076\n",
      "d_Delta(k=0) = 2.77998235368364\n",
      "c_1(k=0)     = 4.93480220054468\n",
      "c_2(k=0)     = 8.63590385095319\n",
      "c_Delta(k=0) = -2.96088132032681\n"
     ]
    }
   ],
   "source": [
    "mbs2nondim_P = [(m_1,     I_11*n/RHO), \n",
    "                (m_2,     I_22*(1-n)), \n",
    "                (m_Delta, I_12*n*tau/RHO), \n",
    "                (d_Delta, I_12*n*D_P), \n",
    "                (c_1,     I_11*(((k+1/2)*sp.pi)**2)*n*M*alpha),\n",
    "                (c_2,     I_22*(((k+1/2)*sp.pi)**2)*(1 - (n-alpha)*M*alpha)),\n",
    "                (c_Delta, I_12*(((k+1/2)*sp.pi)**2)*(n-alpha)*M*n)]\n",
    "\n",
    "m_1_num_P =         m_1.subs(mbs2nondim_P).subs(nondim_num_k0).evalf()\n",
    "m_2_num_P =         m_2.subs(mbs2nondim_P).subs(nondim_num_k0).evalf()\n",
    "m_Delta_num_P = m_Delta.subs(mbs2nondim_P).subs(nondim_num_k0).evalf() \n",
    "d_Delta_num_P = d_Delta.subs(mbs2nondim_P).subs(nondim_num_k0).evalf()\n",
    "c_1_num_P =         c_1.subs(mbs2nondim_P).subs(nondim_num_k0 + [(k,k0)]).evalf()\n",
    "c_2_num_P =         c_2.subs(mbs2nondim_P).subs(nondim_num_k0 + [(k,k0)]).evalf()\n",
    "c_Delta_num_P = c_Delta.subs(mbs2nondim_P).subs(nondim_num_k0 + [(k,k0)]).evalf()\n",
    "# masses\n",
    "print('m_1(k=0)     = ' + str(m_1_num_P))\n",
    "print('m_2(k=0)     = ' + str(m_2_num_P))\n",
    "print('m_Delta(k=0) = ' + str(m_Delta_num_P))\n",
    "# damping\n",
    "print('d_Delta(k=0) = ' + str(d_Delta_num_P))\n",
    "# springs\n",
    "print('c_1(k=0)     = ' + str(c_1_num_P))\n",
    "print('c_2(k=0)     = ' + str(c_2_num_P))\n",
    "print('c_Delta(k=0) = ' + str(c_Delta_num_P))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f97c692",
   "metadata": {},
   "source": [
    "mass matrix (symmetric)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "77f2a02f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}m_{1} + m_{\\Delta} & - m_{\\Delta}\\\\- m_{\\Delta} & m_{2} + m_{\\Delta}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[m_1 + m_Delta,      -m_Delta],\n",
       "[     -m_Delta, m_2 + m_Delta]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mass_P = sp.Matrix(((m_1+m_Delta, -m_Delta), (-m_Delta, m_2+m_Delta)))\n",
    "display(mass_P)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "65bc46e4",
   "metadata": {},
   "source": [
    "damping matrix (symmetric)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "f65ec0ff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}d_{\\Delta} & - d_{\\Delta}\\\\- d_{\\Delta} & d_{\\Delta}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[ d_Delta, -d_Delta],\n",
       "[-d_Delta,  d_Delta]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "damping_P = sp.Matrix(((d_Delta, -d_Delta), (-d_Delta, d_Delta)))\n",
    "display(damping_P)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da641df5",
   "metadata": {},
   "source": [
    "stiffness matrix (symmetric)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "114e059e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}c_{1} + c_{\\Delta} & - c_{\\Delta}\\\\- c_{\\Delta} & c_{2} + c_{\\Delta}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[c_1 + c_Delta,      -c_Delta],\n",
       "[     -c_Delta, c_2 + c_Delta]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "stiffness_P = sp.Matrix(((c_1+c_Delta, -c_Delta), (-c_Delta, c_2+c_Delta)))\n",
    "display(stiffness_P)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a46ba276",
   "metadata": {},
   "source": [
    "check (swap relation) whether diagonalization with eigenvectors of undamped system is possible (answer is no, except degenerate cases)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "198cf63f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d_{\\Delta} \\left(- m_{1} \\left(c_{\\Delta} \\left(m_{2} + m_{\\Delta}\\right) - m_{\\Delta} \\left(c_{2} + c_{\\Delta}\\right)\\right) + m_{2} \\left(c_{\\Delta} \\left(m_{1} + m_{\\Delta}\\right) - m_{\\Delta} \\left(c_{1} + c_{\\Delta}\\right)\\right)\\right)}{\\left(m_{1} m_{2} + m_{1} m_{\\Delta} + m_{2} m_{\\Delta}\\right)^{2}}$"
      ],
      "text/plain": [
       "d_Delta*(-m_1*(c_Delta*(m_2 + m_Delta) - m_Delta*(c_2 + c_Delta)) + m_2*(c_Delta*(m_1 + m_Delta) - m_Delta*(c_1 + c_Delta)))/(m_1*m_2 + m_1*m_Delta + m_2*m_Delta)**2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d_{\\Delta} \\left(m_{1} \\left(c_{\\Delta} \\left(m_{2} + m_{\\Delta}\\right) - m_{\\Delta} \\left(c_{2} + c_{\\Delta}\\right)\\right) - m_{2} \\left(c_{\\Delta} m_{\\Delta} - \\left(c_{1} + c_{\\Delta}\\right) \\left(m_{2} + m_{\\Delta}\\right)\\right) + m_{2} \\left(c_{\\Delta} m_{\\Delta} - \\left(c_{2} + c_{\\Delta}\\right) \\left(m_{1} + m_{\\Delta}\\right)\\right) - m_{2} \\left(c_{\\Delta} \\left(m_{2} + m_{\\Delta}\\right) - m_{\\Delta} \\left(c_{2} + c_{\\Delta}\\right)\\right)\\right)}{\\left(m_{1} m_{2} + m_{1} m_{\\Delta} + m_{2} m_{\\Delta}\\right)^{2}}$"
      ],
      "text/plain": [
       "d_Delta*(m_1*(c_Delta*(m_2 + m_Delta) - m_Delta*(c_2 + c_Delta)) - m_2*(c_Delta*m_Delta - (c_1 + c_Delta)*(m_2 + m_Delta)) + m_2*(c_Delta*m_Delta - (c_2 + c_Delta)*(m_1 + m_Delta)) - m_2*(c_Delta*(m_2 + m_Delta) - m_Delta*(c_2 + c_Delta)))/(m_1*m_2 + m_1*m_Delta + m_2*m_Delta)**2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d_{\\Delta} \\left(m_{1} \\left(c_{\\Delta} m_{\\Delta} - \\left(c_{1} + c_{\\Delta}\\right) \\left(m_{2} + m_{\\Delta}\\right)\\right) - m_{1} \\left(c_{\\Delta} m_{\\Delta} - \\left(c_{2} + c_{\\Delta}\\right) \\left(m_{1} + m_{\\Delta}\\right)\\right) - m_{1} \\left(c_{\\Delta} \\left(m_{1} + m_{\\Delta}\\right) - m_{\\Delta} \\left(c_{1} + c_{\\Delta}\\right)\\right) + m_{2} \\left(c_{\\Delta} \\left(m_{1} + m_{\\Delta}\\right) - m_{\\Delta} \\left(c_{1} + c_{\\Delta}\\right)\\right)\\right)}{\\left(m_{1} m_{2} + m_{1} m_{\\Delta} + m_{2} m_{\\Delta}\\right)^{2}}$"
      ],
      "text/plain": [
       "d_Delta*(m_1*(c_Delta*m_Delta - (c_1 + c_Delta)*(m_2 + m_Delta)) - m_1*(c_Delta*m_Delta - (c_2 + c_Delta)*(m_1 + m_Delta)) - m_1*(c_Delta*(m_1 + m_Delta) - m_Delta*(c_1 + c_Delta)) + m_2*(c_Delta*(m_1 + m_Delta) - m_Delta*(c_1 + c_Delta)))/(m_1*m_2 + m_1*m_Delta + m_2*m_Delta)**2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d_{\\Delta} \\left(m_{1} \\left(c_{\\Delta} \\left(m_{2} + m_{\\Delta}\\right) - m_{\\Delta} \\left(c_{2} + c_{\\Delta}\\right)\\right) - m_{2} \\left(c_{\\Delta} \\left(m_{1} + m_{\\Delta}\\right) - m_{\\Delta} \\left(c_{1} + c_{\\Delta}\\right)\\right)\\right)}{\\left(m_{1} m_{2} + m_{1} m_{\\Delta} + m_{2} m_{\\Delta}\\right)^{2}}$"
      ],
      "text/plain": [
       "d_Delta*(m_1*(c_Delta*(m_2 + m_Delta) - m_Delta*(c_2 + c_Delta)) - m_2*(c_Delta*(m_1 + m_Delta) - m_Delta*(c_1 + c_Delta)))/(m_1*m_2 + m_1*m_Delta + m_2*m_Delta)**2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "inv_mass_P = sp.Matrix.inv(mass_P)\n",
    "zero_or_not = (inv_mass_P*damping_P)*(inv_mass_P*stiffness_P) - (inv_mass_P*stiffness_P)*(inv_mass_P*damping_P)\n",
    "display(sp.simplify(zero_or_not[0,0]))\n",
    "display(sp.simplify(zero_or_not[0,1]))\n",
    "display(sp.simplify(zero_or_not[1,0]))\n",
    "display(sp.simplify(zero_or_not[1,1]))        "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0357f83",
   "metadata": {},
   "source": [
    "### Free vibrations"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24520e27",
   "metadata": {},
   "source": [
    "Eigenproblem and characteristic equation (MBS and non-dimensional formulation of 1D continuum) $a_4 \\delta^4 + a_3 \\delta^3 + a_2 \\delta^2 + a_1 \\delta + a_0 = 0$ with $a_4,a_3,a_2,a_1,a_0\\in\\mathbb{R}^+$ on physical grounds ($0\\le \\tau, \\rho_\\mathrm{f}, \\rho_\\mathrm{s}, m_\\mathrm{v}, S_\\mathrm{p}, \\kappa, \\mu$ and $0\\le \\alpha,n\\le 1$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "7a9797e0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c_{1} c_{2} + c_{1} c_{\\Delta} + c_{2} c_{\\Delta} + \\delta^{4} \\left(m_{1} m_{2} + m_{1} m_{\\Delta} + m_{2} m_{\\Delta}\\right) + \\delta^{3} \\left(d_{\\Delta} m_{1} + d_{\\Delta} m_{2}\\right) + \\delta^{2} \\left(c_{1} m_{2} + c_{1} m_{\\Delta} + c_{2} m_{1} + c_{2} m_{\\Delta} + c_{\\Delta} m_{1} + c_{\\Delta} m_{2}\\right) + \\delta \\left(c_{1} d_{\\Delta} + c_{2} d_{\\Delta}\\right)$"
      ],
      "text/plain": [
       "c_1*c_2 + c_1*c_Delta + c_2*c_Delta + delta**4*(m_1*m_2 + m_1*m_Delta + m_2*m_Delta) + delta**3*(d_Delta*m_1 + d_Delta*m_2) + delta**2*(c_1*m_2 + c_1*m_Delta + c_2*m_1 + c_2*m_Delta + c_Delta*m_1 + c_Delta*m_2) + delta*(c_1*d_Delta + c_2*d_Delta)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "evp_mbs_P = (delta**2)*mass_P + delta*damping_P + stiffness_P\n",
    "ceq_mbs_P = sp.simplify(sp.Determinant(evp_mbs_P).doit())\n",
    "display(ceq_mbs_P.collect(delta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "908c9966",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{n \\left(I_{11} I_{12} \\delta^{4} n \\tau + \\rho^{2} \\left(- D_{P} I_{12} I_{22} \\delta^{3} \\left(n - 1\\right) - \\pi^{4} I_{11} I_{12} M^{2} \\alpha n \\left(\\alpha - n\\right) \\left(k + 0.5\\right)^{4} + \\pi^{4} I_{11} I_{22} M \\alpha \\left(k + 0.5\\right)^{4} \\left(M \\alpha \\left(\\alpha - n\\right) + 1\\right) - \\pi^{4} I_{12} I_{22} M \\left(\\alpha - n\\right) \\left(k + 0.5\\right)^{4} \\left(M \\alpha \\left(\\alpha - n\\right) + 1\\right) + \\delta^{2} \\left(- \\pi^{2} I_{11} I_{22} M \\alpha \\left(k + 0.5\\right)^{2} \\left(n - 1\\right) + \\pi^{2} I_{12} I_{22} M \\left(\\alpha - n\\right) \\left(k + 0.5\\right)^{2} \\left(n - 1\\right)\\right) + \\delta \\left(\\pi^{2} D_{P} I_{11} I_{12} M \\alpha n \\left(k + 0.5\\right)^{2} + \\pi^{2} D_{P} I_{12} I_{22} \\left(k + 0.5\\right)^{2} \\left(M \\alpha \\left(\\alpha - n\\right) + 1\\right)\\right)\\right) + \\rho \\delta^{2} \\left(D_{P} I_{11} I_{12} \\delta n + \\pi^{2} I_{11} I_{12} M \\alpha n \\tau \\left(k + 0.5\\right)^{2} - \\pi^{2} I_{11} I_{12} M n \\left(\\alpha - n\\right) \\left(k + 0.5\\right)^{2} + \\pi^{2} I_{11} I_{22} \\left(k + 0.5\\right)^{2} \\left(M \\alpha \\left(\\alpha - n\\right) + 1\\right) + \\pi^{2} I_{12} I_{22} \\tau \\left(k + 0.5\\right)^{2} \\left(M \\alpha \\left(\\alpha - n\\right) + 1\\right) + \\delta^{2} \\left(- I_{11} I_{22} \\left(n - 1\\right) - I_{12} I_{22} \\tau \\left(n - 1\\right)\\right)\\right)\\right)}{\\rho^{2}}$"
      ],
      "text/plain": [
       "n*(I_11*I_12*delta**4*n*tau + RHO**2*(-D_P*I_12*I_22*delta**3*(n - 1) - pi**4*I_11*I_12*M**2*alpha*n*(alpha - n)*(k + 0.5)**4 + pi**4*I_11*I_22*M*alpha*(k + 0.5)**4*(M*alpha*(alpha - n) + 1) - pi**4*I_12*I_22*M*(alpha - n)*(k + 0.5)**4*(M*alpha*(alpha - n) + 1) + delta**2*(-pi**2*I_11*I_22*M*alpha*(k + 0.5)**2*(n - 1) + pi**2*I_12*I_22*M*(alpha - n)*(k + 0.5)**2*(n - 1)) + delta*(pi**2*D_P*I_11*I_12*M*alpha*n*(k + 0.5)**2 + pi**2*D_P*I_12*I_22*(k + 0.5)**2*(M*alpha*(alpha - n) + 1))) + RHO*delta**2*(D_P*I_11*I_12*delta*n + pi**2*I_11*I_12*M*alpha*n*tau*(k + 0.5)**2 - pi**2*I_11*I_12*M*n*(alpha - n)*(k + 0.5)**2 + pi**2*I_11*I_22*(k + 0.5)**2*(M*alpha*(alpha - n) + 1) + pi**2*I_12*I_22*tau*(k + 0.5)**2*(M*alpha*(alpha - n) + 1) + delta**2*(-I_11*I_22*(n - 1) - I_12*I_22*tau*(n - 1))))/RHO**2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "evp_nondim_P = evp_mbs_P.subs(mbs2nondim_P)\n",
    "ceq_nondim_P = sp.simplify(ceq_mbs_P.subs(mbs2nondim_P))\n",
    "#display(evp_continuum)\n",
    "display(ceq_nondim_P.collect(delta))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d9be3853",
   "metadata": {},
   "source": [
    "#### Numerical evaluation (example)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "e6b909b3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.0830188679245283 \\delta^{2} + 2.77998235368364 \\delta + 1.97392088021787 & - 0.00754716981132076 \\delta^{2} - 2.77998235368364 \\delta + 2.96088132032681\\\\- 0.00754716981132076 \\delta^{2} - 2.77998235368364 \\delta + 2.96088132032681 & 0.307547169811321 \\delta^{2} + 2.77998235368364 \\delta + 5.67502253062638\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[  0.0830188679245283*delta**2 + 2.77998235368364*delta + 1.97392088021787, -0.00754716981132076*delta**2 - 2.77998235368364*delta + 2.96088132032681],\n",
       "[-0.00754716981132076*delta**2 - 2.77998235368364*delta + 2.96088132032681,    0.307547169811321*delta**2 + 2.77998235368364*delta + 5.67502253062638]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 0.000569597721609114 \\delta^{4} + 0.833994706105093 \\delta^{3} + 0.150943396226415 \\delta^{2} \\cdot \\left(0.165 \\delta^{2} + 1.38999117684182 \\delta + 3.51604656788808\\right) + 0.592176264065361 \\delta^{2} + 37.7263233501919 \\delta + 2.43522727585006$"
      ],
      "text/plain": [
       "0.000569597721609114*delta**4 + 0.833994706105093*delta**3 + 0.150943396226415*delta**2*(0.165*delta**2 + 1.38999117684182*delta + 3.51604656788808) + 0.592176264065361*delta**2 + 37.7263233501919*delta + 2.43522727585006"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "evp_num_P = evp_nondim_P.subs(nondim_num_k0 + [(k, k0)]).evalf()\n",
    "ceq_num_P = ceq_nondim_P.subs(nondim_num_k0 + [(k, k0)]).evalf()\n",
    "display(evp_num_P)\n",
    "display(ceq_num_P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "ea9229fb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(-40.78145835271035+0j),\n",
       " (-0.06466681553935676+0j),\n",
       " (-0.06357372407901675-6.020244454235613j),\n",
       " (-0.06357372407901675+6.020244454235613j)]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eigenvalue_sp_P = sp.solve(ceq_num_P, delta)\n",
    "eigenvalue_num_P = [complex(EVSP) for EVSP in eigenvalue_sp_P]\n",
    "display(eigenvalue_num_P)\n",
    "number_of_eigenvalues = len(eigenvalue_num_P)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb9c199d",
   "metadata": {},
   "source": [
    "Plot characteristic equation, intersections of zero-levels of real- and imaginary parts are roots of characteristic equation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "fca9170a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Xmin = min(np.real(eigenvalue_num_P))\n",
    "Xmax = max(np.real(eigenvalue_num_P))\n",
    "dX = Xmax - Xmin\n",
    "Ymin = min(np.imag(eigenvalue_num_P))\n",
    "Ymax = max(np.imag(eigenvalue_num_P))\n",
    "dY = Ymax - Ymin\n",
    "X = np.linspace(Xmin-dX, Xmax+dX, 500)\n",
    "Y = np.linspace(Ymin-0.5*dY, Ymax+0.5*dY, 500)\n",
    "XX, YY = np.meshgrid(X, Y)\n",
    "\n",
    "ceq_f = sp.lambdify(delta, ceq_num_P, modules='numpy')\n",
    "ZZ = ceq_f(XX+1j*YY)\n",
    "\n",
    "plt.contour(XX, YY, np.real(ZZ), [0], colors='r');\n",
    "plt.contour(XX, YY, np.imag(ZZ), [0], colors='b');\n",
    "plt.xlabel(\"$\\mathfrak{R}\\{\\delta\\}$\");\n",
    "plt.ylabel(\"$\\mathfrak{I}\\{\\delta\\}$\");\n",
    "#plt.show();\n",
    "#tikzplotlib.save(\"characteristic_roots.tex\", axis_height = '\\\\figH', axis_width = '\\\\figW')   # im,re "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "f6f5f0d5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--- 0. mode ---\n",
      "eigenvalue = (-40.78145835271035+0j)  \n",
      "eigenvector = [(0.9685229369356281+0j), (-0.24892432711485973+0j)]\n",
      "--- 1. mode ---\n",
      "eigenvalue = (-0.06466681553935676+0j)  \n",
      "eigenvector = [(0.8682605181150567+0j), (-0.49610852913709647+0j)]\n",
      "--- 2. mode ---\n",
      "eigenvalue = (-0.06357372407901675-6.020244454235613j)  \n",
      "eigenvector = [(0.7145586095621932+0j), (0.6937985335885932+0.08971949782997472j)]\n",
      "--- 3. mode ---\n",
      "eigenvalue = (-0.06357372407901675+6.020244454235613j)  \n",
      "eigenvector = [(0.7145586095621932+0j), (0.6937985335885932-0.08971949782997472j)]\n"
     ]
    }
   ],
   "source": [
    "eigenvector_num_P = np.zeros((number_of_eigenvalues, 2), dtype=complex)\n",
    "for mode_n, delta_n in enumerate(eigenvalue_num_P):\n",
    "    EVP_P = evp_num_P.subs(delta, delta_n)\n",
    "    ev0r = np.array([1.0, -EVP_P[0,0].evalf()/EVP_P[0,1].evalf()], dtype=complex)   # first row --> eigenvector\n",
    "    ev0rn = ev0r/np.linalg.norm(ev0r)   # normalize\n",
    "    #ev1r = np.array([1.0, -EVP_P[1,0].evalf()/EVP_P[1,1].evalf()], dtype=complex)   # second row, redundant\n",
    "    #ev1rn = ev1r/np.linalg.norm(ev1r)   # normalize  \n",
    "    print(\"--- {}. mode ---\".format(mode_n))\n",
    "    print(\"eigenvalue = {}  \".format(delta_n))\n",
    "    print(\"eigenvector = [{}, {}]\".format(ev0rn[0], ev0rn[1]))\n",
    "    #print(\"eigenvector = [{}, {}] (redundant)\".format(ev1rn[0], ev1rn[1]))\n",
    "    eigenvector_num_P[mode_n,:] = ev0rn\n",
    "t_scale = 1.0/(np.abs(min(np.imag(eigenvalue_num_P))) + np.abs(min(np.real(eigenvalue_num_P))))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35d1e576",
   "metadata": {},
   "source": [
    "#### Visualize modes\n",
    "Real roots lead to real coefficients, slow and fast decay, two of them together can match initial position and initial velocity of one component (either $u_\\mathrm{f}$ or $u_\\mathrm{s}$). Pair of complex-conjugated roots leads to damped oscillations, which can match initial conditions by amplitude and phase shift."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "ea4f0acb",
   "metadata": {},
   "outputs": [],
   "source": [
    "t_modeshow = np.linspace(0, 20*t_scale)\n",
    "timesteps_modeshow = len(t_modeshow)\n",
    "u_f = np.zeros((number_of_eigenvalues, timesteps_modeshow))\n",
    "u_s = np.zeros((number_of_eigenvalues, timesteps_modeshow))\n",
    "\n",
    "for mode_n, delta_n in enumerate(eigenvalue_num_P):\n",
    "    u_f[mode_n,:] = np.real(eigenvector_num_P[mode_n,0]*np.exp(delta_n*t_modeshow))\n",
    "    u_s[mode_n,:] = np.real(eigenvector_num_P[mode_n,1]*np.exp(delta_n*t_modeshow))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e19a5c0",
   "metadata": {},
   "source": [
    "From the solution list above we see that first (0) and second mode (1) correspond to aperiodic decay (real roots), and third and fourth mode to damped oscillations (complex-conjugated roots):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "0d184bf7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t_modeshow,u_f[0,:],'b',   t_modeshow,u_s[0,:],'k');\n",
    "plt.plot(t_modeshow,u_f[1,:],'b--', t_modeshow,u_s[1,:],'k--');\n",
    "plt.xlabel(\"$t$\");\n",
    "plt.ylabel(\"$u_f$,$u_s$\");\n",
    "#plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6cffaf7f",
   "metadata": {},
   "source": [
    "Solid motion (black) and fluid (blue) of first mode (solid line) and second mode (dashed line)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "c601341a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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37hzt2rUjS5YszJo1K3l/gIiI/Cu7WmcoNWidIXno/n3jrtCSJcax1WrsefbRR0ZQio+7d+/y+eefM2rUKB7+V69w4cIsX76cEiVKJFPPRUQcT7pcZ0gktbm7w+LFxsrVTZtCbKzxKK10aZg0KX41MmbMyIgRI/j9998pWLAgYIwnKlWqFB06dND6RCIiqUBhSCSBypaFFStg6VJ4/nkICTFWry5TBp4ySfExFStWJCQkhGnTpuHu7o7NZmPOnDlkzZqVxYsXJ+8PEBGRRygMiSRSy5Zw+LAxywyM9/nzw8iR8a/RtWtXbty4QcuWLQG4ffs2bdu2ZcCAAdy6dcvkHouIyJMoDIkkQbZscOwYfP65sb9ZTAyMGmWEouDg+NVwd3dn6dKl7NmzBz8/P2JjY/nyyy8pXrw4X331lWadiYgkM4UhERMMGmRs6+HnZxyfPWvMRBs1Kv41KlasyN69e1m9ejWFChXi4sWL9OvXjxw5crBp06bk6biIiCgMiZjF2xv27oWZM/+ehj9yJLRrBzduxL/Oyy+/zKFDh2jVqhVg7MtXr149mjVrRmR8FjgSEZEEURgSMVnnznD1KrzzjrF449y5xuDqKVPiXyNDhgwsWbKENWvWkDVrVgBWrlxJtmzZWL58eTL1XETEMSkMiSSDTJlg6lT47Tdjw9c//4QePYxQdOVK/Os0bNiQ0NBQOnfuDMCdO3do0aIFL7/8MlFRUcnUexERx6IwJJKMqlSBwECoWNE4PnwY8uSJ38avD1mtVmbOnMnvv/+Oj48PAGvXrqVy5cra/FVExAQKQyLJLGNG2LPHWKDRaoWoKGPj11q14H/2EP5XlSpV4tKlS/Tt25esWbMSFBREpUqV6N27N+Hh4cn3A0RE0jmFIZEUMmQI/PEHPNjInu3bwccHli2Lfw2r1cqECRMIDg7mlVdeISYmhm+++QYfHx+mJ+R2k4iIxFEYEklBBQrAqVMwYABYLHDvHrz6Knz7rTH7LL5y5MjBwoUL+fLLL7FYLERERPD2229To0YNbifkdpOIiCgMiaSG8eNh/35jX7OoKOje3QhF168nrE6/fv04fvw4BR7cbtqxYwc+Pj6acSYikgAKQyKppFw5Y9PX8ePBxcXYBDZnTpg8OWF1ihQpwqlTpxg4cCAWi4V79+7RokULWrVqpY1fRUTiQWFIJBVZrcYjsx07IHNm4y5Rz55Qrx4kdH3FL774gv379/Pcc88B8PPPP9OwYUMuxHf3WBERB6UwJJIGVKxo7HH2cHD1pk3G4Oo9exJWp1y5cly+fJnXX38dNzc3Nm3aRJkyZZgzZ475nRYRSScUhkTSiFy5jMHV77xjHIeFGesUDRuWsDpWq5WffvqJgwcPUqlSJW7evEmHDh3w9fXl1KlT5ndcRMTOKQyJpDFTp8K6dcb6RDYbfPopNG4MEREJq1O0aFF+++03+vXrB8C5c+coUqQI//nPf8zvtIiIHVMYEkmDGjSAv/4CPz/jePVqqF0bzp5NWB0XFxe+/PJLvv/+e1xcXIiNjWXgwIHUqlWL+/fvm99xERE7pDAkkkZlygR798KSJZA1K/z+O5QvD4m5sdOlSxcuXLhAsWLFANi+fTs+Pj7s3LnT5F6LiNgfhSGRNK5VK2N/s0qV4MYNGDjQ2MojobPNfHx8OHbsGL179wbg1q1b1KxZk4ULFyZDr0VE7IfCkIgd8PWFrVuNXe/B2MojZ044ciThtSZOnMivv/6Kh4cHsbGxtG3blp49e+qxmYg4LIUhETvh7g4HD0KPHsbxjRtQtixMmZLwWnXr1uXq1au89957AEyePJnSpUuzcuVKE3ssImIfFIZE7MykScbmrq6uEBtrhKMWLYz3CZEhQwbGjRvHmjVryJ49OyEhITRr1ow33niD2IQWExGxYwpDInaoeXNjZlm+fMbx8uXQqBGEhye8VsOGDdm0aRNZs2YFYObMmRQqVIgrV66Y2GMRkbRLYUjETuXMCadPw2uvgZOTsTZR1apw4kTCa5UtW5YrV67g7+8PwJkzZ8iXLx+rV682udciImmPwpCIHbNaYd48Y2+z3LkhONhYm2jkyITXcnZ2Zu3atUycOBGr1UpERASNGzemf//+pvdbRCQtURgSSQcqVzbWJKpSBW7fhlGjoH59iIlJeK3evXsTGBiIl5cXABMmTKBv375EJnQuv4iInVAYEkkncuaEDRugVCnjeONGY0zRxYsJr1W2bFkuX75M3bp1AWM6ft26dblw4YJ5HRYRSSMUhkTSkUyZ4PBh6NTJOL54EQoWNIJRQrm7u/Prr7+ybNkyvLy82LlzJ4ULF2bcuHHmdlpEJJUpDImkQ7NmwbRpxpiiiAhjr7MxYxJXq3nz5uzbt4+8efMSERHB4MGDqVevHtHR0eZ2WkQklSgMiaRTXbvCvn3G3SKbDYYPh08/Nd4nVKFChThw4EDc3mabNm0iV65cnE3ozrEiImmQwpBIOlauHPz5J1SoYBwPGwbt2sG9ewmvlTVrVo4dO8Zbb70FwNWrVylSpAjLly83r8MiIqlAYUgknfP0NO4QTZ0Kzs7GVPxixSAoKHH1pk+fzuzZs3FyciIqKooWLVowbNgwU/ssIpKSFIZEHMQ778D69ZAxI5w/DxUrwty5iavVvn17Dh06RJYsWQD49NNPGTFihLbxEBG7pDAk4kDq1v17X7OYGOOR2ZAhiatVokQJLl68yKuvvgrA6NGjadmyJTdv3jStvyIiKUFhSMTB1K9vbNmRPbtx/Nln0LBhwjd6BWOz1wULFjBr1izc3NxYsWIFOXPm1DYeImJXFIZEHJCvL1y4AGXKGMfr1kHhwpDYmzqdOnVi+/btuLq6xm3jMXz4cNP6KyKSnBSGRByUuzscPAgBAcbx6dNQsyb89Vfi6lWsWJF9+/bh6ekJwJgxY6hXr57GEYlImqcwJOLg5s41HpVlyABHjhj7nB08mLhapUuX5uLFi5R5cMtp06ZN5M+fn+vXr5vYYxERcykMiQjvvw+BgVCkCJw7B9Wrw9ixiavl4eHBwYMH6dy5MwDnz58nb968HD582MQei4iYx+7C0OTJkylQoADu7u74+fmxbdu2eH3vt99+w9nZmXLlyiVvB0XsVLFisGsX1KgBd+7ABx/AgzyTKDNnzmTixIlYLBbu3r2Lv78/+/btM6/DIiImsaswNH/+fPr168ewYcMIDAykVq1aNGrUiHPnzj3ze2FhYXTq1Il69eqlUE9F7FO2bLBqFRQoYBz/8IMRjhK7DVnv3r3ZtGkTxYoV49KlS9SqVYsFCxaY12ERERNYbLbE7FSUOqpUqUKFChWYMmVK3LkSJUrQsmVLxj7jnn5AQABFihTBycmJn3/+maBnLL0bERFBRERE3HF4eDh58+YlLCwsbmCoSHoXGwsvvghbtxrH+fLBgQPwYI3FBAsPDycgICBuyn3dunXZuHEjVqtd/e8xEbEj4eHheHl5xevvt938mygyMpJ9+/bh7+//yHl/f3927Njx1O99//33hISEMGLEiHi1M3bsWLy8vOJeefPmTVK/ReyR1QpbtsCDbcg4d86Yjn/yZOLqeXp6smLFCtq2bQvA5s2bKVCggAZWi0iaYDdhKDQ0lJiYGHLkyPHI+Rw5cnD58uUnfufkyZMMGTKEOXPm4OzsHK92hg4dSlhYWNzr/PnzSe67iL2aPh3GjTPeh4cbG76GhCSulpOTE/Pnz6dTp04AnDt3jnz58rF//36Teisikjh2E4YeslgsjxzbbLbHzgHExMTQrl07Ro0aRdGiReNd383NDU9Pz0deIo7svfdg6VJwc4Pbt6FqVdi5M/H1Zs2axZdffonFYuHOnTtUqlSJ+fPnm9dhEZEEspsw5O3tjZOT02N3ga5cufLY3SKAW7dusXfvXnr16oWzszPOzs6MHj2aAwcO4OzszKZNm1Kq6yJ2r2VLY1FGPz8IDTXGE331VeLr9evXjw0bNuDq6kpsbCwBAQGMHj3atP6KiCSE3YQhV1dX/Pz8WL9+/SPn169fT/Xq1R/7vKenJ4cOHSIoKCju1b17d4oVK0ZQUBBVqlRJqa6LpAvPP2+MI2rWDCIioF8/eOWVxNd76aWXOHHiBFmzZgVg5MiRTJ482ZzOiogkgN2EIYABAwYwffp0vvvuO4KDg+nfvz/nzp2je/fugDHe5+F4BKvVSunSpR95+fj44O7uTunSpfHw8EjNnyJilzw8jEdmD/c0W7wYqlVL3CavAL6+vpw7d46GDRtis9no2bMngwYN0hYeIpKi7CoMvfbaa0yYMIHRo0dTrlw5tm7dyqpVq/D19QXg0qVL/7rmkIgkjZMTBAVB/frG8a5dxsrVd+8mrl6mTJlYvXo1Y8aMAWD8+PEUKlSI0NBQczosIvIv7GqdodSQkHUKRBzNm2/C998b77Nnh8OHIWfOxNebM2cOHTt2xGaz4eHhwa5duyhdurQ5nRURh5Iu1xkSkbTnu+9g5Ejj/bVrUKgQnD2b+Hrt27eP28Ljzp07lC9fnpUrV5rSVxGRp1EYEpEkGTHCCEUWi/GorF49+OOPxNfr1asXq1evxtnZmejoaJo3b85//vMf8zosIvIPCkMikmRvvAHbtkH+/MaijNWrw549ia/XsGFDDh8+TObMmbHZbAwcODBuooSIiNkUhkTEFDVqGIsxli8PV68aizM+GBOdKMWKFePcuXNxW+J8++23fPrpp2iYo4iYTWFIREyTM6exFlHBgsZ0++HDoWfPxNfLkiULp06dombNmgAMGzaMPn36EBMTY1KPRUQUhkTEZJkzGzvcP1jxgsmT4dVXE1/P2dmZbdu2xW3h8c0331CjRg1t8ioiplEYEhHTZcpkDKIuW9Y4XrQI6tZN/OKMYGzhMW/ePJycnNi9ezcFChQgJLG7xoqI/A+FIRFJFs7OEBho7GMGxuOzcuUgOjrxNdu2bcsXX3wBGGuIlCxZkh07diS9syLi0BSGRCTZWK2waRO89ppxfOgQtGkDkZGJr9mvXz+WLFmC1WolMjKSWrVqsWDBAnM6LCIOSWFIRJLdvHnQu7exlcfy5dCiBdy5k/h6rVq1YteuXbi5uREbG8trr73G559/bl6HRcShKAyJSIqYOBFWroQMGWDNGmPq/alTia9XqVIljh8/jpeXFwDvv/++FmcUkURRGBKRFPPyy7BhgzHA+vBhKFkS9u9PfL2Hu94/XIto4MCBTJw40aTeioijUBgSkRRVvTrMmmWMJ4qIgCpVjHFFieXp6cmpU6fo1asXAH379mXw4MHEJmXqmog4FIUhEUlxrVvDr78aM86io6FBA1i2LPH1nJ2dmThxIh9//DEA48aNo3Tp0kQmZaS2iDgMhSERSRW1a8O+feDmZqw/1KoVzJ6d+HoWi4UPP/ww7g5RcHAwBQsWJDw83KQei0h6pTAkIqmmbFk4cgQ8PMBmg44d4Ycfklbz66+/ZuDAgQD8+eef5M+fnwsXLpjQWxFJrxSGRCRVFSoEJ07Ag0lhvPMOrF2btJpffPFF3OKMN27coGjRohw5ciSJPRWR9EphSERSXa5cxjT7hg3h/n1o1gyWLElazYEDBzJ79mwsFgv37t2jfPnybN261ZwOi0i6ojAkImlCtmzGgoyvvgpRUcZK1d26Ja1m+/btWbt2Lc7OzkRFRfHKK69w6NAhczosIumGwpCIpBmurjB3rrGpK8C0adC2bdJqNmjQgN27d1O4cGGuXr1K7dq12blzZ5L7KiLph8KQiKQpTk6wfr2xqSvAwoXGYo1JUaFCBfbs2UONGjW4efMmL774Iv/3f/+X5L6KSPqgMCQiaY6zszHtvlYt43jtWqhZ05iCn1hZsmRh7dq1VK9enYiICIYOHcrgwYPN6bCI2DWFIRFJk6xW2LoVGjc2jn/7DSpXTlog8vDwYM2aNeTOnRswFmfs2rWrCb0VEXumMCQiadovvxiDqsG4WxQQkLRAlDlzZk6dOkWRIkUAmDFjBq1btzahpyJirxSGRCTNW7AAOnUy3i9cCG+/DTExia/n6urKsWPHqFChAgBLly7lxRdf1H5mIg5KYUhE7MKsWfDjj8bjs+++M+4W3b+f+HpWq5U9e/bw0ksvAbB582aaNGmiQCTigBSGRMRudOgA8+YZM86WLoXCheH27cTXs1qtbNy4kTZt2gCwZs0a3nrrLaKjo03qsYjYA4UhEbErr74Kw4cb7//809jO4+bNpNVctGgRM2fOxMnJiZkzZ9K2bVtu3bqV5L6KiH1QGBIRuzNiBIwZY7y/csW4QxQamrSanTt3ZtGiRbi4uLB06VIKFizItWvXkt5ZEUnzFIZExC4NGwbjxxvvr12DIkXg8uWk1WzZsiVTp04FIDQ0lEKFCnHx4sUk9lRE0jqFIRGxWwMGwOTJxvubN6FoUbhwIWk133zzTb755hsAwsLCKFasGKdPn05aURFJ0xSGRMSuvfsuzJwJFgvcugUtWkBYWNJq9uzZk1mzZmGxWLh9+zYlS5bk6NGjpvRXRNIehSERsXudO8OcOeDlBfv3Q4MGSR9U3alTJxYuXIjFYuH+/fuUL1+effv2mdJfEUlbFIZEJF14/XXYvBmyZ4c9e6BiRQgJSVrNNm3asHr1apycnIiMjKRp06acOXPGjO6KSBqiMCQi6Ua5cvDrr5A5sxGEypSBkyeTVrNhw4Zs3ryZHDlycPnyZWrXrs2JEydM6a+IpA0KQyKSrpQpY6xUbbHAvXtQtiwEByetZs2aNdm3bx/Fixfn/Pnz1KhRg6VLl5rTYRFJdQpDIpLutGgBy5cbW3fcvw/ly8Phw0mrmTt3brZs2ULJkiUJDQ2lTZs2zJ4925wOi0iqUhgSkXSpaVNYudIIRBER4OcHBw8mraaPjw8rV67Ew8MDm81Gx44dmTFjhjkdFpFUozAkIulWo0awbp2xl1lkJFSqBMeOJa1mgQIFOHHiBJ6engB07dqVSZMmmdBbEUktCkMikq7VqwcbNvwdiJo1M/Y0S4pcuXJx8uRJsmTJAkCvXr0Y/3A5bBGxO3YXhiZPnkyBAgVwd3fHz8+Pbdu2PfWzS5YsoUGDBjz33HN4enpSrVo11q5dm4K9FZG0oG5d+P13yJcP/vgDXnwx6YHIx8eHkJAQsmfPDsCgQYMYN25c0jsrIinOrsLQ/Pnz6devH8OGDSMwMJBatWrRqFEjzp0798TPb926lQYNGrBq1Sr27dvHiy++SLNmzQgMDEzhnotIaqtQAbZsAV9fY7p9qVKwd2/SambLlo0//vgDHx8fAD788ENWrlxpQm9FJCVZbDabLbU7EV9VqlShQoUKTJkyJe5ciRIlaNmyJWPHjo1XjVKlSvHaa6/x0Ucfxevz4eHheHl5ERYWFjdGQETs15kzxvT727fBxQV27jQGVyfF7du3CQgI4JdffsHFxYV58+bRunVrU/orIomTkL/fdnNnKDIykn379uHv7//IeX9/f3bs2BGvGrGxsdy6dYts2bI99TMRERGEh4c/8hKR9CN/fli92hhDFBUF1apBUnfZyJQpEz///DMBAQFERUXxyiuv0KdPH1P6KyLJz27CUGhoKDExMeTIkeOR8w9XhY2P8ePHc+fOHdq2bfvUz4wdOxYvL6+4V968eZPUbxFJe2rWNLbuMDMQOTs7M3v2bBo2bIjNZuPrr7+mW7dupvRXRJKX3YShhywWyyPHNpvtsXNPMnfuXEaOHMn8+fPjnu8/ydChQwkLC4t7nT9/Psl9FpG0JzkCkZOTEytXrqRYsWIATJs2jS5duiS5ryKSvOwmDHl7e+Pk5PTYXaArV648drfon+bPn89bb73FggULqF+//jM/6+bmhqen5yMvEUmf/hmIatSACxeSVtPZ2ZnDhw9TpkwZAGbNmkWHDh2S3lkRSTZ2E4ZcXV3x8/Nj/fr1j5xfv3491atXf+r35s6dS5cuXfjpp59o0qRJcndTROzMw0Dk4mKsVP3SS0mfdu/s7ExQUBDlypUDYM6cObz22mtJ7quIJA+7CUMAAwYMYPr06Xz33XcEBwfTv39/zp07R/fu3QHjEVenTp3iPj937lw6derE+PHjqVq1KpcvX+by5cuEhYWl1k8QkTSoZk1jZeqH0+7NWIfIarWyb98+/B5MVVuwYAH9+/c3obciYja7CkOvvfYaEyZMYPTo0ZQrV46tW7eyatUqfH19Abh06dIjaw59++23REdH07NnT55//vm4V9++fVPrJ4hIGlWwoHGH6GEgKlwYDhxIWk2r1crvv/9OlSpVAJgwYQJffvll0jsrIqayq3WGUoPWGRJxLCEhUKKEMYbI1dUYVF26dNJqxsbGMnz4cD799FPAmLU6ZMgQE3orIk+TLtcZEhFJCYUKwZo1f+9lVrEiHDmStJpWq5UxY8YwYsQIwHik37BhQxN6KyJmUBgSEfmHl16CtWvBajUGVVesCMePJ62mxWJh5MiRvPLKKwCsW7eOevXqmdBbEUkqhSERkSeoVw9WrTIC0f37UK6cMZYoqRYuXBi3kv6mTZuoW7cusbGxSS8sIommMCQi8hQNG8KKFX8HourV4fr1pNddu3YtjRs3BmDLli3UqVNHgUgkFSkMiYg8Q+PGsHQpuLlBaCj4+8PNm0mv+8svv9C8eXMAtm/fTu3atRWIRFKJwpCIyL9o3hz27gVvb2N2mb8//PVX0usuW7aMli1bAvDbb7/Rt29fNMFXJOUpDImIxEPp0rBxI2TLBnv2GOsQJXXrDoClS5fGDar+5ptvGDZsmAKRSApTGBIRiaeyZWHePLBY4PZtKFkS/rFdYqIsXLiQr776CjDWIOrVq5cemYmkIIUhEZEEaNAAfvzRCES3bkHx4sZYoqTq06cPEydOBGDy5MlUr15dgUgkhSgMiYgkUPv2MGOG8T4sDIoVM2eWWe/eveM2dN29ezfVqlVTIBJJAQpDIiKJ8MYbMHWq8f76dSMQmbEH9Lx583j11VcB+P3336lataoCkUgyUxgSEUmkd96BB0+2CA01HqFFRia97oIFC2jbti0Ae/bsoUqVKgpEIslIYUhEJAl694YvvgBnZ2OWWUCAsclrUs2fPz/ukdnevXupXLmyApFIMlEYEhFJooED4ZdfjF3uly6Ftm2NFauTat68eQQEBACwb98+Bg0apGn3IslAYUhExAT+/rBkiXGH6OefoUQJcx6ZzZ07l+7duwPw5ZdfMnjwYAUiEZMlOgx16NCB8PBwAFatWsXSpUtN65SIiD1q0gSGDTPenzljrEMUHZ30ulOmTGHSpEkAfP7557Rt21aPzERMlOgwdPDgQTw9PTl69CiDBg1izZo19OvXz8SuiYjYn5EjjcdmACEhUKYMmJFbevTowTfffAPAokWLqFGjhgKRiEkSHYZcXFyw2WzMnDmTYcOG8e2337Jt2zYz+yYiYpe++AJ69TLeHzsG5cubE4h69uwZN+1+165d1KxZU4FIxASJDkPvvPMOlSpVYtGiRXEbDd65c8esfomI2LWvv4auXY33Bw9ClSrmBKIFCxbE7WW2c+dOatWqpUAkkkTxDkPX/7G8ardu3diwYQMHDx7Ew8ODP/74gypVqpjeQRERezVtGnToYLzfuxcGDTKn7sKFC2nTpg0AO3bsoHbt2gpEIklgscVzWoLVaiVPnjy88MILj7yKFCmCxWJJ7n6mmvDwcLy8vAgLC8PT0zO1uyMidqhDB5gzx3j/8cfw4Yfm1G3dunXc5JWaNWuydevWdP3vY5GESMjf73jfGTp69Cjjxo2jZMmS7Nmzhx49elCiRAkyZ86sO0IiIs8wezZ8/rnxfvhwGDrUnLpLliyJG6awfft2Ro4caU5hEQcT7zBUvHhxAgIC+Oyzz1i7di1Xrlxh5cqV5MyZk3r16iVnH0VE7N6gQTBmjPH+//4PHjzlSrKlS5fy/vvvAzB69GhGjRplTmERB5LoAdQWi4VGjRoxe/ZsLl68aGafRETSpWHDoFYt4/2SJdC+vTl1P/vsM8aPHw/AyJEjad68uTmFRRxEvMPQ0wbnVa1alc2bN5vVHxGRdG3zZqhUyXj/009/zzhLqgEDBvDJJ58AsGLFCho0aGBOYREHEO8wlClTJipXrky3bt2YNGkSv/32G6GhoaxatYrbt28nZx9FRNINqxV27YIXXjCOZ8yAnj3Nqf3BBx/w8ssvA7Bhw4a49yLybPEOQ0uWLKFNmzbcvn2bSZMmUbduXXLkyEHz5s0Z+HC5VRER+VdWK+zfb+xfBjB5Mrz3njm1V69eHXdXaO3atTRu3NicwiLpWLyn1v/T/fv3CQkJIXv27OTMmdPsfqUZmlovIsklOtoIRH/8YQSk5cuN/c3MUK9ePTZt2gRA06ZNWbFihTmFRexEskyt/yd3d3dKlSqVroOQiEhycnaGI0egcmVjdeo2bWD9enNqb9y4kbp16wKwcuVK2rZta05hkXQo0WFIRESSztUVtm+HVq0gIgKaN4eZM82p/euvv1LrwfS1hQsX8tVXX5lTWCSdMSUMWa1WXnrpJfbt22dGORERh+LiAvPmwcsvw/378MYb8N//mlN78+bNDBgwAIB+/frF7XwvIn8zJQx999131KlThz59+phRTkTE4bi6wty5kDWrcfzOO8bK1UlltVr54osvGDJkCAC9e/cmICAg6YVF0pEED6D+7LPPGDx4cHL1J83RAGoRSUlXrkCRIhAeDhYLLFgADzapTxKbzcabb77JzAfP4Nq1a8echxumiaRDyTqAevaD/6nycGCeiIiYx8cHgoPBwwNsNmjbFlauTHpdi8XCjBkz8PPzA+Cnn36ic+fOSS8skg4kOAxVrFiRxo0bc+rUKZYtW0ZISEhy9EtExGHlymXMMsuQwQhELVrAxo1Jr2u1Wvn9998pV64cAD/88ANvvvlm0guL2LlErTN04MABmjRpQtu2bTl06BAhISF4e3tTqlQpvv/+++ToZ6rRYzIRSS0nT0KZMsYss+eegz17wNc36XVjY2MpX748Bw8eBKBr165MmzYt6YVF0pCE/P12jm/R69evky1bNgBeeOEF1q9fT4mHy6cCoaGhHDp0KJFdFhGRfypSBPbuhcaN4fx5eOkl2LoVcudOWl2r1UpgYCBly5blyJEjTJ8+neeff57Ro0eb03EROxPvO0NWq5U8efLwwgsvPPIqUqQIFoslufuZanRnSERS259/Qu3acOoUFChgrFRdunTS60ZHR1O2bFmCg4OxWCzMmTOH119/PemFRdKAZBlAffToUcaNG0fJkiXZs2cPPXr0oESJEmTOnJkqVaokudMiIvJkuXPDpk2QMyecPg0VK8KJE0mv6+zszMGDB3nrrbew2Wx06NCBBQsWJL2wiJ2JdxgqXrw4AQEBfPbZZ6xdu5YrV66wcuVKcubMSb169ZKzjyIiDs/X11h3yGo1xhCVKwdnzya9rrOzM//973/p0qULsbGxBAQEaPNtcTiJXnTRYrHQqFEjZs+ezcWLF83sk4iIPEG9erBsmbH+0L17xqMyM/71a7VamT59OpUrV8Zms/Gf//zHodaTE4l3GIqNjX3i+apVq7J582az+vOvJk+eTIECBXB3d8fPz49t27Y98/NbtmzBz88Pd3d3ChYsyNSpU1OopyIi5mvaFObPNwLR7dtQsiSEhia9rpOTE9u2bSN//vwAjBs3jmHDhiW9sIgdiHcYypQpE5UrV6Zbt25MmjSJ3377jdDQUFatWsXt27eTs49x5s+fT79+/Rg2bBiBgYHUqlWLRo0ace7cuSd+/vTp0zRu3JhatWoRGBjIBx98QJ8+fVi8eHGK9FdEJDm8+irMmmW8DwuDYsXg5s2k13V1dSU4OJh8+fIB8Omnn/LRRx8lvbBIGhfv2WRr1qzhwIEDHDhwgKCgIE6ePElsbCwWi4WPP/6YoUOHJndfqVKlChUqVGDKlClx50qUKEHLli0ZO3bsY58fPHgwy5cvJzg4OO5c9+7dOXDgADt37oxXm5pNJiJp1bffQvfuxnt/f1ixwtjjLKnu379P0aJFOX/+PACjRo1SKBK7k5C/34ladBGM/7KEhISQPXt2cubMmaiOJkRkZCQZM2Zk4cKFtGrVKu583759CQoKYsuWLY99p3bt2pQvX56vvvoq7tzSpUtp27Ytd+/excXF5bHvREREEBEREXccHh5O3rx5FYZEJE2aMgX69zcGVbdpA/PmgXO8V5B7urt371K0aFH+/PNPABYvXkzr1q2TXlgkhSTr3mQPubu7U6pUqRQJQmAs6hgTE0OOHDkeOZ8jRw4uX778xO9cvnz5iZ+Pjo4m9CkP2ceOHYuXl1fcK2/evOb8ABGRZPDuu8agaldXWLwYGjSAyMik182YMSMnTpyI+3dgu3bt2LBhQ9ILi6RBiQ5DqeWfCzzabLZnLvr4pM8/6fxDQ4cOJSwsLO718DaxiEha1bAhLFxoTLvfvNmYZRYdnfS6GTNm5I8//qB58+ZERETQrFkz1q1bl/TCImmM3YQhb29vnJycHrsLdOXKlcfu/jyUM2fOJ37e2dmZ7NmzP/E7bm5ueHp6PvISEUnrmjeHfv2M9ydPGusQPWUScIK4urqyYMECmjRpwv3793n55ZeZMGFC0guLpCF2E4ZcXV3x8/Nj/fr1j5xfv3491atXf+J3qlWr9tjn161bR8WKFZ84XkhExJ6NH//3gOojR6BSJXMCkZubG4sXLyZ37tzYbDb69+/P119/nfTCImmE3YQhgAEDBjB9+nS+++47goOD6d+/P+fOnaP7g//2Dx06lE6dOsV9vnv37pw9e5YBAwYQHBzMd999x4wZMxg0aFBq/QQRkWQ1ZQo8/Nfg/v1QqxYkbprMo9zc3Dh8+HDcXfU+ffowefLkpBcWSQNMmHOQcl577TWuXbvG6NGjuXTpEqVLl2bVqlX4+voCcOnSpUfWHCpQoACrVq2if//+TJo0iVy5cjFx4kTatGmTWj9BRCTZzZplrFC9cCHs2AH168PGjUmvmyVLFk6cOEGRIkW4fv06PXv2xMnJiXfeeSfpxUVSUaKn1jsKrTMkIvaqWTNYudJ4P24cvPeeOXVDQ0MpWrQoN27cAGDatGl07drVnOIiJkmRqfUiIpK2rVgBD2/avP8+mDXMx9vbmxMnTpAlSxbAGJLw+++/m1NcJBUoDImIpGNTp8LDLcb69IGePc2p6+3tzfHjx8mdOzcxMTH4+/uzZ88ec4qLpDCFIRGRdO7jj6F3b+P95MnQrZs5dX18fDh27Bi1atUiLCwMf39/LcwodklhSEQknbNYYMIEYzFGgGnToG9fc2pnypSJVatWUaNGDW7evIm/vz9z5swxp7hIClEYEhFxAFYrBAYaO9wDTJwIgwebUztTpkwsX76czJkzY7PZ6NixI/PnzzenuEgKUBgSEXEQzs5w8CAULGgcjxsHI0eaUztbtmwcPXqUTJkyYbPZeP3111mwYIE5xUWSmcKQiIgDcXU1Vqd+uAf1qFHw2Wfm1M6TJw9HjhzBw8MDm81GQEAAixYtMqe4SDJSGBIRcTDu7nDsGDz/vHE8YgRs2WJO7Xz58nHkyBEyZsyIzWajbdu2LF261JziIslEYUhExAFlzGgEorp1ISICmjQxVqs2g6+vL4cPH44LRJ06deLw4cPmFBdJBgpDIiIOytMTVq82tuu4cwcaNDC28jBDgQIFOHz4ML6+vty+fZuXXnqJI0eOmFNcxGQKQyIiDszdHZYtg3Ll4O5deOMNMGsiWIECBdi/fz/ly5fn6tWr1K1bl19++cWc4iImUhgSEXFwGTPCqlWQObOxw/3rrxsByQzZsmVjw4YNlC1bltDQUJo1a8by5cvNKS5iEoUhERHh+efh8GEjGNls0Lq1EZDMkC1bNpYsWUKGDBmw2Wy0atWKlQ93kBVJAxSGREQEgHz5jHWIMmSA2Fhj1/v1682pXahQIQ4cOECGDBmIjY2lRYsWCkSSZigMiYhInEKFjJWq3dyMQNSoEfz2mzm1ixQpwoEDB3B3d48LRKvMuv0kkgQKQyIi8ohixWDfPmOBxpgYaNcOzp41p3aRIkUICgqKC0TNmjVTIJJUpzAkIiKPKVXKCESFC8O5c/DSS3Dhgjm1ixUr9kgg6ty5M8ePHzenuEgiKAyJiMgTlS4Nv/5q7GV26hS88AIEBZlT+2EgKlKkCKGhodStW5djx46ZU1wkgRSGRETkqfLkgU2bjAUar1+HKlWMWWdmKFasGDt27KBs2bJcvnyZ6tWra1C1pAqFIREReSZfX1i+HJycIDISKlYEs55qeXt7s3HjRgoXLsyNGzdo0aKF1iGSFKcwJCIi/6pOHVizBqxWYy+z8uUhJMSc2t7e3qxatSpuDFHLli0ViCRFKQyJiEi81K8PK1aAxQL37kGZMnD6tDm1ixQpwsGDB+MWZmzZsiXLzFoGW+RfKAyJiEi8NW4MS5c+GoiuXzen9sN1iP53peqff/7ZnOIiz6AwJCIiCdKiBSxcaASiO3eMgBQebk7tIkWKcOjQobhA1Lp1a1avXm1OcZGnUBgSEZEEa9PGWJk6WzbYvdtYqfrWLXNqFypU6JFA1KlTJw6bNYVN5AkUhkREJFGqVTP2LsuSBXbsMLbyuHzZnNqFChXi6NGjVKhQgdDQUF588UUOHjxoTnGRf1AYEhGRRKtQAdauNWaZXb0KxYvDlSvm1M6fPz8bNmygYsWKhIaGUqVKFebNm2dOcZH/oTAkIiJJUrkyTJ9uvA8LM/Y2Cw01p3bWrFlZv349efPm5f79+7Rr1445c+aYU1zkAYUhERFJsjfegGnTjPc3b0LRoubNMsuSJQvbt28nU6ZM2Gw2OnTowMyZM80pLoLCkIiImKRrV5g82Xh/44YRiG7eNKd2vnz5OHbsGJ6engC88cYbTH94O0okiRSGRETENO++C19/bby/ds3Y3PX+fXNq586dm+PHj+Pl5QXA22+/zbfffmtOcXFoCkMiImKqXr1gwgRjHaJz56B1a/MCUc6cOTlx4gRZsmQBoHv37lqHSJJMYUhEREzXty9s2AAZMsDq1UYgunfPnNo+Pj6cPHmS7NmzA/DKK6+wefNmc4qLQ1IYEhGRZPHSS/DLL38HIl9f88YQeXt7c+7cOfz9/bl79y6NGzdm3bp15hQXh6MwJCIiyebFF2H2bOP91avmDqrOmDEjy5Yto1GjRty7d4+XX36ZTz75xJzi4lAUhkREJFm1bg3jxxvvzQ5E7u7uLF26FF9fX2w2Gx9++CEfffSROcXFYSgMiYhIshswIPkCkZubG4cPH+b5558H4OOPP+b99983p7g4BIUhERFJEQMGwBdfGO/NDkSZMmXijz/+IF++fAB8/vnn9OnTx5ziku4pDImISIoZOPDRQFSnjnnT7jNmzMjJkycpVKgQAF9//TVvv/22OcUlXVMYEhGRFPUwEDk7w8GD5q5D5OrqyrFjxyhWrBgA06dPZ8qUKeYUl3RLYUhERFLcwIHGbvcPp903b25s4WEGZ2dnjhw5QtWqVQHo0aMHkyZNMqe4pEt2E4Zu3LhBx44d8fLywsvLi44dO3LzGQ+bo6KiGDx4MGXKlMHDw4NcuXLRqVMnLl68mHKdFhGRp/rfdYjWr4fChY0tPMzg5OTEjh07GDhwIAC9evVi0KBB5hSXdMduwlC7du0ICgpizZo1rFmzhqCgIDp27PjUz9+9e5f9+/czfPhw9u/fz5IlSzhx4gTNmzdPwV6LiMizvPgifPWV8f76dShSBEJDzaltsVj4/PPP+eCDDwAYP348DRo0MKe4pCsWm81mS+1O/Jvg4GBKlizJrl27qFKlCgC7du2iWrVqjzwb/jd79uyhcuXKnD17Nm7GwT9FREQQERERdxweHk7evHkJCwuL2y1ZRETMNXky9OxpvM+SBYKDIWdO8+rXq1ePTZs2AVCrVi02b96M1Wo39wMkEcLDw/Hy8orX32+7+E/Czp078fLyigtCAFWrVsXLy4sdO3bEu05YWBgWiyVug78nGTt2bNyjOC8vL/LmzZuUrouISDz06AEPN6C/eROKFQMzRzVs3LiRRo0aAbBt2zYqVapEbGyseQ2IXbOLMHT58mV8fHweO+/j48Ply5fjVeP+/fsMGTKEdu3aPTMhDh06lLCwsLjX+fPnE91vERGJv27dYPp04314OBQvDhcumFd/1apVtGnTBoD9+/dTunRpoqOjzWtA7FaqhqGRI0disVie+dq7dy9gPPv9J5vN9sTz/xQVFUVAQACxsbFMnjz5mZ91c3PD09PzkZeIiKSMt96CmTPBYoFbt6BxYwgLM6/+okWL6NKlC2AMwShatCiRkZHmNSB2yTk1G+/VqxcBAQHP/Ez+/Pk5ePAgf/3112P/7OrVq+TIkeOZ34+KiqJt27acPn2aTZs2KdyIiKRxnTsbaxC9+y4cOgT+/sY0/GeMcEiQ77//Hk9PTyZOnMjp06d5/fXXmTt3Lq6uruY0IHbHrgZQ7969m8qVKwOwe/duqlat+swB1A+D0MmTJ/n111957rnnEtx2QgZgiYiIeYKCoH59Y7p9iRKwYgU8WFzaFBMnTmTQoEFERUXRqFEjFi9eTIYMGcxrQFJVQv5+20UYAmjUqBEXL17k2wcj7Lp164avry8rVqyI+0zx4sUZO3YsrVq1Ijo6mjZt2rB//35Wrlz5yB2kbNmyxft/ASgMiYiknkOHoHZtY1C1uzvs328EI7Ns2LCBFi1acPfuXfLmzcuuXbvIlSuXeQ1Iqkl3s8kA5syZQ5kyZfD398ff35+yZcvy448/PvKZ48ePE/bg4fKFCxdYvnw5Fy5coFy5cjz//PNxr4TMQBMRkdRTpgzMmgVWq7FlR/nyxh0js9SvX5+1a9fi7OzM+fPnKVasGKdPnzavAbELdnNnKLXozpCISOpbuxaaNIGYGHBxgW3b4H9WW0myH374gS5dumCz2ciQIQP79u2jhJm3oCTFpcs7QyIi4rgaNoSNG42B1VFRULMmbN1qXv1OnTqxcOFCrFYr9+7do1y5cuzZs8e8BiRNUxgSERG7UKeOcUfIxQWio429zTZvNq9+mzZtWLVqFU5OTkRGRlKtWjXWr19vXgOSZikMiYiI3ahaFXbvBldX45FZQAAcPWpe/YYNG7Jt2zZcXFyIiYmhUaNGBAYGmteApEkKQyIiYlfKl4fAQChdGv76y7hjdOCAefWrVatGYGAgHh4exMTE8NJLL2niTTqnMCQiInanZEnjEZmfn7HLfdWq8MMP5tUvVaoU58+fp0aNGty8eZMGDRqwbNky8xqQNEVhSERE7FL27LBhAxQsaEy779wZpkwxr37WrFlZt24dL7/8Mnfv3qVly5a899575jUgaYbCkIiI2K0sWYxB1V5exnGPHjBunHn1M2bMyLJlyyhYsCAAX3zxBW+++aZ5DUiaoDAkIiJ2LVcu+OMP404RwODB8MEH5tV3dXWN29QVjL3NWrZsaV4DkuoUhkRExO55e8OpU0YwAhg7Fnr2NK/+w0BUsWJFAJYtW0bt2rWJjY01rxFJNQpDIiKSLnh6QkiIMYYIYPJk+PRT8+pbrVZ2795NgwYNANi2bRtly5YlMjLSvEYkVSgMiYhIuuHuDsePG9PuAYYNg/HjzatvtVpZt24dAQEBABw5coR27doRERFhXiOS4hSGREQkXXF2hoMHYcgQ43jQIGMckZlPtObOncsHH3yAs7MzixcvpkmTJty6dcu8BiRFKQyJiEi6Y7EY44YePiYbNw4qVTI3EH3yySesXr2aTJkysXHjRkqUKMFRM5fDlhSjMCQiIunW0KHG+kMA+/cbizWaOcSnfv36/Prrr2TMmJE///yTcuXKsX37dvMakBShMCQiIunazJnw1lvG++PHoXBhuH3bvPoVK1ZkyZIlODk5ERUVRZ06dVi8eLF5DUiyUxgSEZF0b/p0GDDAeH/+POTPD1eumFe/YcOG7Nq1Czc3N2JjY3n11VeZYuZy2JKsFIZERMQhjB8PY8YY769dg0KFjKn4ZqlYsSJHjx4lc+bM2Gw2evTowUcffWReA5JsFIZERMRhDBsG06YZA6xv34bGjeHPP82rX7BgQU6dOoWPjw8AH3/8MV9++aV5DUiyUBgSERGH0rUrLFkCPj5w4gTUrAknT5pX39vbm9OnT1OoUCEABgwYwMcff4zNZjOvETGVwpCIiDicli1h925jMPWZM1CxIsyfb179jBkzcuLECYYOHQrARx99RIcOHbh//755jYhpFIZERMQh5c8P27cbY4fCwyEgAL75xrz6VquVTz/9lEmTJgHw008/4evryxUzR26LKRSGRETEYeXIAZs2GfuaAfTuDWaPee7RowcjRowA4MqVKxQsWJDg4GBzG5EkURgSERGHli8fnD5tBCOAjz+G7t3NbWPkyJFMnToVi8XCnTt3eOGFF9i0aZO5jUiiKQyJiIjDy5YNTp36e8f7b7+Fpk3N3b7jnXfeYeXKlXGLM9avX58ffvjBvAYk0RSGREREgIwZjRWq/fyM419+gTZtzA1EjRs3Zu/evWTIkAGbzUbnzp354osvzGtAEkVhSERE5AFnZ9i717grBPDzz9CuHUREmNdGuXLlOHHiBNmyZQNg8ODBzJgxw7wGJMEUhkRERP5hxQqYPRtcXIwp9w0bwoUL5tXPkycPZ8+epU2bNsTGxtK1a1c++OADYmJizGtE4k1hSERE5Anat4dVq8DDA7ZsgSJFICjIvPqZMmVi4cKFcVt2jB07lgIFCnDz5k3zGpF4URgSERF5ivr14aefwGqF+/eNxRlXrzavvsViYdSoUUyYMAGA8+fPky9fPo4dO2ZeI/KvFIZERESeoXlz2LjReGQWEwNNmoDZQ3z69u0bN5D61q1blClThrVr15rbiDyVwpCIiMi/qFsXAgONR2Y2m7G/2ciR5rYxcOBAVqxYgbOzM9HR0TRq1IhvzFwSW55KYUhERCQeSpWCP/4Ab2/jeNQoeOMNc9to2rQpgYGBeHh4YLPZ6N27Nz169DC3EXmMwpCIiEg85cwJZ88aG7wCzJwJQ4aYuxZR6dKlOXPmDLly5QJgypQp2vU+mSkMiYiIJMDDxRl79zaOP/vMWIvIzA3pvb29OXv2LM2aNQOMXe+7dOlChJkLHkkchSEREZEEslph4kSYNctYqHH+fHj+eTh50rw2nJ2dWb58OVOmTMHJyYkffviBfPnyceTIEfMaEUBhSEREJNE6dTLWIrJa4eZNY1yR2fuvdu/endWrV+Pi4sKVK1d44YUXWLx4sbmNODiFIRERkSRo0ACWLgUnJ4iKMtYm+u9/zW6jAcuWLcPFxYWYmBheeeUVhg8fbm4jDkxhSEREJImaN4f9+43xRDYbvPMOvPeeuW00atSI4OBgsmbNCsCYMWNo3LgxsWaO3nZQCkMiIiImKFsWTp2CHDmM4y++MEKSmVmlUKFCXLhwgZIlSwKwevVqihYtSnh4uHmNOCCFIREREZPkyAHnzkGZMsbxihXQvbvx+MwsGTNm5PDhw7z66qsAhISEUL9+fa5cuWJeIw7GbsLQjRs36NixI15eXnh5edGxY8cEbWb3zjvvYLFY4vZ/ERERSQ6ursaGrgEBxvG0afDyy3D9unltWCwWFixYwKeffkqmTJnYs2cPlStX5uDBg+Y14kDsJgy1a9eOoKAg1qxZw5o1awgKCqJjx47x+u7PP//M7t274xawEhERSU5WK8ydC8uXQ6ZMxgyzwoXB7O3Ghg4dyp49eyhcuDBnz56lcuXKDBo0yNxGHIBdhKHg4GDWrFnD9OnTqVatGtWqVWPatGmsXLmS48ePP/O7f/75J7169WLOnDm4uLikUI9FRESgWTP47TfIkgVu3IBGjYyxRGYqXrw4u3fvpmrVqkRERDB+/Hhq1KhBZGSkuQ2lY3YRhnbu3ImXlxdVqlSJO1e1alW8vLzYsWPHU78XGxtLx44dee+99yhVqlS82oqIiCA8PPyRl4iISGKVLQvbthl3iGw2Y5ZZhw7mtpEtWzZ+/fVX/Pz8ANixYwd58uTh7Nmz5jaUTtlFGLp8+TI+Pj6Pnffx8eHy5ctP/d5nn32Gs7Mzffr0iXdbY8eOjRuX5OXlRd68eRPVZxERkYdKl4bz5yF/fuN4zhwoX97cLTzc3d3Zu3cv7777LgBXr16lSJEiLF++3LxG0qlUDUMjR47EYrE887V3717AGCz2Tzab7YnnAfbt28dXX33FzJkzn/qZJxk6dChhYWFxr/Pnzyfux4mIiPyPLFkgJMRYlBGMQdb58hmzz8w0efJkZs+ejZOTE1FRUbRo0YIhQ4aY20g645yajffq1YuAh8PtnyJ//vwcPHiQv/7667F/dvXqVXI8XNDhH7Zt28aVK1fIly9f3LmYmBgGDhzIhAkTOHPmzBO/5+bmhpubW/x/hIiISDxZrbB+PQwcCP/5D1y9CnXqwMaNULCgee20b9+eChUqUL16dW7evMlnn32Gq6srI0eOxGq1i4dCKcpis9lsqd2JfxMcHEzJkiXZvXs3lStXBogbLHbs2DGKFSv22HeuXbvGpUuXHjnXsGFDOnbsyBtvvPHE7zxJeHg4Xl5ehIWF4enpmfQfIyIiAvzwA/Tta+xpli2bsdnrw7tGZrl//z5NmjRh04MN05o2bcrs2bPx8vIyt6E0KCF/v+0iHpYoUYKXX36Zt99+m127drFr1y7efvttmjZt+kioKV68OEuXLgUge/bslC5d+pGXi4sLOXPmjHcQEhERSS6dOsHhw1C5srEGkb8/tGhh7orV7u7ubNy4kR9++AE3NzdWrlxJ3rx54/5WisEuwhDAnDlzKFOmDP7+/vj7+1O2bFl+/PHHRz5z/PhxwsLCUqmHIiIiCZM7N2zZAu3bGzPNli+HQoXg2jVz2+nYsSO//fYbmTNn5tatW7Ru3TpuoLXYyWOy1KTHZCIiktxiY6FtW1i82DjOkMEYR1StmrntBAcHU7NmTa4/WA67ZMmS7Ny5M13+fUt3j8lERETSM6sVFi2CL78EiwXu3YMaNWDiRHPbKVGiBJcuXaJ27doAHD16lOeff57t27eb25CdURgSERFJI/r1MxZozJDBeGzWt69xx8jMcUSurq5s2bKFjz/+GIvFwt27d6lduzafffaZeY3YGYUhERGRNKRGDWPtIV9f43jhQnjrLYiIMLedDz/8kG3btuHh4YHNZmPIkCF8+OGHxMTEmNuQHVAYEhERSWO8veHUKWjVynhsNnMm1KoFZu+uUaNGDS5evEjbtm0B+OSTT2jYsCHnzF4JMo1TGBIREUmDrFZYsgTWrIGsWWHPHiheHMaMMbcdT09P5s+fz5w5c8iYMSMbN26kYMGCfP311+Y2lIZpNtm/0GwyERFJbWfOGAsyhoQYx7VrGytZu7qa287hw4epVKkS9x9smvbiiy+yZs0aXM1uKAVoNpmIiEg6kj8/7N8PJUsax1u3Qq5ccPy4ue2ULl2a06dPU/DB3iC//vorPj4+cfuEplcKQyIiInbA0xOOHIF33jGOr12DUqVgxgxz28mZMychISF069YNgLCwMCpXrsyIESPMbSgNURgSERGxI1OnGmOJXFwgJga6dv17BWszffvtt6xZs4YMGTJgs9kYPXo0HTp0IMLsaW1pgMKQiIiInWnVyphtlju3cfzTT0Ygun3b3HYaNmzI5cuXKVeuHGBsjVWjRg3++OMPcxtKZQpDIiIidihPHmM9ot69wdkZ5s6FSpVg925z2/H09CQwMJClS5eSLVs29u3bxwsvvECvXr3MbSgVKQyJiIjYKavV2LJj82ZjQPWxY1C1KgQEmLtqNUDLli05cOAAtWrV4u7du0yaNImCBQty1uzFj1KBwpCIiIidq1EDDhwwdrwHmD/fuHN06pS57eTJk4cNGzZQp04dAE6fPk2hQoWYMGGCuQ2lMIUhERGRdMDbG06cgBYtjONLl6BoUZgyxdx2XF1d2bx5M99++y3Ozs7ExMTQv39/KlasyM2bN81tLIUoDImIiKQTViv8/DP8+OPfs8169IAGDSAy0ty2unXrxvnz5ylevDgA+/btI2fOnKxatcrchlKAwpCIiEg606GDsWp1/vzG8YYNULo0XLxobjs5c+YkODiY4cOHY7FYiIiIoEWLFowbN86uNnxVGBIREUmHcuUytu/o2tW4Y3TyJLzwAiTHjZvRo0dz5MgRXnzxRaKjoxk8eDB169Zl165d5jeWDBSGRERE0imrFaZNM1auLlcOQkOhSROoXt14b6YSJUqwceNGZsyYQaZMmdi+fTvVqlWjS5cuxJo9tc1kCkMiIiLpXPHisHMn9OljHO/cadw5+v57c9uxWCy8+eabBAUF4eXlBcCsWbN47rnn+O2338xtzEQKQyIiIg7A3R2++grGjjXuGEVFwZtvQt26cPeuuW0VKlSIK1eu0KRJEwCuX79OzZo1CQgIIDo62tzGTKAwJCIi4kCGDDGm4OfLZxxv2QI+PrB6tbntuLq6snLlStasWYOnpycA8+fPx9vbm02bNpnbWBIpDImIiDiYQoXg7Fno1QssFrhzBxo3NgZbm73ha8OGDbl27RqvvPIKAGFhYTRu3Jgvv/wyzcw4UxgSERFxUF9/bexlljWrcTxjBjRqZP4UfGdnZxYuXMjmzZspWbIkERERDBgwgJo1a6aJGWcKQyIiIg6sUiW4cgXee88YV7R2rbEm0Zgx5u9vVqdOHQ4fPsx///tfMmfOzK5du6hWrRo9evRI1bFEFpvN7Bti6Ut4eDheXl6EhYXFPfMUERFJj4KDjQUb9+83jp97DlauhMqVzW/r/Pnz1K5dmzNnzuDp6UlwcDC5cuUyrX5C/n7rzpCIiIgAUKIE7NoFLVsax1evQpUqRkAye3hP3rx5CQkJYcqUKUyZMsXUIJRQujP0L3RnSEREHNHy5dC+Pdy+bRxnyQKLF8NLL6Vqt+JNd4ZEREQkSZo3h2vX/r5LdPMm1KsHr75q/l2i1KYwJCIiIk/k6gpLl8KmTcadIYBFi6BmTWN8UXqhMCQiIiLP9OKLxl5mPXpApkzGuKJy5YzjmzdTu3dJpzAkIiIi/8rJCSZNgqNHjQUaIyNhyhRjxtmYMandu6RRGBIREZF4y5vXmG7/2WfGHmfR0TB8OOTJA3v2pHbvEkdhSERERBLEYoH33ze29KhQwTj355/GekQtWpi/8WtyUxgSERGRRMmTB/btg/nzjbFEYEzJz54d1q9P3b4lhMKQiIiIJEnbtnDjBnTpYtw1un8f/P3hzTeNhRvTOoUhERERSTJnZ/j+ezh2zFisEYzjggWhaVMID0/d/j2LwpCIiIiYpmhRmD0bduyA8uWNFax/+cV4dPbee+Zv/moGhSERERExXbVqxuyyt976e9bZF19AtmxGWEpLFIZEREQkWTg5wfTpxkyzWrWMc2Fh0LEjFC5sDL5OCxSGREREJFnlzAlbtxorV+fPb5wLCYGqVWH06NSfiq8wJCIiIimiShU4fdq4W5Qtm/HobMQIY5zRn3+mXr/sJgzduHGDjh074uXlhZeXFx07duRmPDZECQ4Opnnz5nh5eZE5c2aqVq3KuXPnkr/DIiIi8kRvvWXsdTZvHvj6Go/McuVKvf7YTRhq164dQUFBrFmzhjVr1hAUFETHjh2f+Z2QkBBq1qxJ8eLF2bx5MwcOHGD48OG4u7unUK9FRETkSSwWeO01Yyr+7NnGcar1xWaz2VKv+fgJDg6mZMmS7Nq1iypVqgCwa9cuqlWrxrFjxyhWrNgTvxcQEICLiws//vhjotsODw/Hy8uLsLAwPD09E11HREREUk5C/n7bxZ2hnTt34uXlFReEAKpWrYqXlxc7dux44ndiY2P55ZdfKFq0KA0bNsTHx4cqVarw888/P7OtiIgIwsPDH3mJiIhI+mUXYejy5cv4+Pg8dt7Hx4fLly8/8TtXrlzh9u3b/N///R8vv/wy69ato1WrVrRu3ZotW7Y8ta2xY8fGjUvy8vIib968pv0OERERSXtSNQyNHDkSi8XyzNfevXsBsDzhYaLNZnvieTDuDAG0aNGC/v37U65cOYYMGULTpk2ZOnXqU/s0dOhQwsLC4l7nz5834ZeKiIhIWuWcmo336tWLgICAZ34mf/78HDx4kL/++uuxf3b16lVy5MjxxO95e3vj7OxMyZIlHzlfokQJtm/f/tT23NzccHNzi0fvRUREJD1I1TDk7e2Nt7f3v36uWrVqhIWF8fvvv1O5cmUAdu/eTVhYGNWrV3/id1xdXalUqRLHjx9/5PyJEyfw9fVNeudFREQkXbCLMUMlSpTg5Zdf5u2332bXrl3s2rWLt99+m6ZNmz4yk6x48eIsXbo07vi9995j/vz5TJs2jT/++INvvvmGFStW0KNHj9T4GSIiIpIG2UUYApgzZw5lypTB398ff39/ypYt+9iU+ePHjxMWFhZ33KpVK6ZOncq4ceMoU6YM06dPZ/HixdSsWTOluy8iIiJplF2sM5SatM6QiIiI/Ul36wyJiIiIJBeFIREREXFoCkMiIiLi0BSGRERExKEpDImIiIhDS9VFF+3Bw8l22rBVRETEfjz8ux2fSfMKQ//i1q1bANqwVURExA7dunULLy+vZ35G6wz9i9jYWC5evEjmzJmfuilsYoWHh5M3b17Onz+vNYzSKF0j+6DrZB90ndK+9HSNbDYbt27dIleuXFitzx4VpDtD/8JqtZInT55kbcPT09Pu/0OX3uka2QddJ/ug65T2pZdr9G93hB7SAGoRERFxaApDIiIi4tAUhlKRm5sbI0aMwM3NLbW7Ik+ha2QfdJ3sg65T2ueo10gDqEVERMSh6c6QiIiIODSFIREREXFoCkMiIiLi0BSGRERExKEpDCWzyZMnU6BAAdzd3fHz82Pbtm3P/PyWLVvw8/PD3d2dggULMnXq1BTqqeNKyDW6dOkS7dq1o1ixYlitVvr165dyHXVwCblOS5YsoUGDBjz33HN4enpSrVo11q5dm4K9dUwJuUbbt2+nRo0aZM+enQwZMlC8eHG+/PLLFOyt40ro36WHfvvtN5ydnSlXrlzydjA12CTZzJs3z+bi4mKbNm2a7ejRo7a+ffvaPDw8bGfPnn3i50+dOmXLmDGjrW/fvrajR4/apk2bZnNxcbEtWrQohXvuOBJ6jU6fPm3r06ePbdasWbZy5crZ+vbtm7IddlAJvU59+/a1ffbZZ7bff//dduLECdvQoUNtLi4utv3796dwzx1HQq/R/v37bT/99JPt8OHDttOnT9t+/PFHW8aMGW3ffvttCvfcsST0Oj108+ZNW8GCBW3+/v62F154IWU6m4IUhpJR5cqVbd27d3/kXPHixW1Dhgx54ufff/99W/HixR85984779iqVq2abH10dAm9Rv+rTp06CkMpJCnX6aGSJUvaRo0aZXbX5AEzrlGrVq1sHTp0MLtr8j8Se51ee+0124cffmgbMWJEugxDekyWTCIjI9m3bx/+/v6PnPf392fHjh1P/M7OnTsf+3zDhg3Zu3cvUVFRydZXR5WYayQpz4zrFBsby61bt8iWLVtydNHhmXGNAgMD2bFjB3Xq1EmOLgqJv07ff/89ISEhjBgxIrm7mGq0UWsyCQ0NJSYmhhw5cjxyPkeOHFy+fPmJ37l8+fITPx8dHU1oaCjPP/98svXXESXmGknKM+M6jR8/njt37tC2bdvk6KLDS8o1ypMnD1evXiU6OpqRI0fStWvX5OyqQ0vMdTp58iRDhgxh27ZtODun38iQfn9ZGmGxWB45ttlsj537t88/6byYJ6HXSFJHYq/T3LlzGTlyJMuWLcPHxye5uick7hpt27aN27dvs2vXLoYMGULhwoV5/fXXk7ObDi++1ykmJoZ27doxatQoihYtmlLdSxUKQ8nE29sbJyenx9L2lStXHkvlD+XMmfOJn3d2diZ79uzJ1ldHlZhrJCkvKddp/vz5vPXWWyxcuJD69esnZzcdWlKuUYECBQAoU6YMf/31FyNHjlQYSiYJvU63bt1i7969BAYG0qtXL8B45Gyz2XB2dmbdunW89NJLKdL35KYxQ8nE1dUVPz8/1q9f/8j59evXU7169Sd+p1q1ao99ft26dVSsWBEXF5dk66ujSsw1kpSX2Os0d+5cunTpwk8//USTJk2Su5sOzaz/LtlsNiIiIszunjyQ0Ovk6enJoUOHCAoKint1796dYsWKERQURJUqVVKq68kv9cZup38PpzDOmDHDdvToUVu/fv1sHh4etjNnzthsNpttyJAhto4dO8Z9/uHU+v79+9uOHj1qmzFjhqbWJ7OEXiObzWYLDAy0BQYG2vz8/Gzt2rWzBQYG2o4cOZIa3XcYCb1OP/30k83Z2dk2adIk26VLl+JeN2/eTK2fkO4l9Bp98803tuXLl9tOnDhhO3HihO27776zeXp62oYNG5ZaP8EhJObfef8rvc4mUxhKZpMmTbL5+vraXF1dbRUqVLBt2bIl7p917tzZVqdOnUc+v3nzZlv58uVtrq6utvz589umTJmSwj12PAm9RsBjL19f35TttANKyHWqU6fOE69T586dU77jDiQh12jixIm2UqVK2TJmzGjz9PS0lS9f3jZ58mRbTExMKvTcsST033n/K72GIYvN9mCEroiIiIgD0pghERERcWgKQyIiIuLQFIZERETEoSkMiYiIiENTGBIRERGHpjAkIiIiDk1hSERERByawpCIiIg4NIUhERERcWgKQyLisPr160fLli1TuxsiksoUhkTEYe3Zs4fKlSundjdEJJVpbzIRcThRUVF4eHgQFRUVd65y5crs3r07FXslIqnFObU7ICKS0pycnNi+fTtVqlQhKCiIHDly4O7untrdEpFUojAkIg7HarVy8eJFsmfPzgsvvJDa3RGRVKYxQyLikAIDAxWERARQGBIRBxUUFKQwJCKAwpCIOKhDhw5RtmzZ1O6GiKQBCkMi4pBiY2M5ePAgFy9eJCwsLLW7IyKpSGFIRBzSmDFjmD9/Prlz52b06NGp3R0RSUVaZ0hEREQcmu4MiYiIiENTGBIRERGHpjAkIiIiDk1hSERERByawpCIiIg4NIUhERERcWgKQyIiIuLQFIZERETEoSkMiYiIiENTGBIRERGHpjAkIiIiDu3/AcvQ4PITro4fAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t_modeshow, u_f[2,:],'b',   t_modeshow, u_s[2,:],'k');\n",
    "plt.plot(t_modeshow, u_f[3,:],'b--', t_modeshow, u_s[3,:],'k--');\n",
    "plt.xlabel(\"$t$\");\n",
    "plt.ylabel(\"$u_f$,$u_s$\");\n",
    "#plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ead6946c",
   "metadata": {},
   "source": [
    "Solid motion (black) and fluid (blue) of third mode (solid line) and fourth mode (dashed line)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ae99c1f",
   "metadata": {},
   "source": [
    "Note: \n",
    "- for complex-conjugated roots the curves of two modes are identical (no difference between dashed line and solid line) \n",
    "- the  waves (oscillations in reduced model) where fluid and solid move in counter-phase decay fast than waves with motion in-phase (physically due to higher dissipation). "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7cd6daa",
   "metadata": {},
   "source": [
    "#### Specific initial conditions \n",
    "$U_\\mathrm{f}(0)$, $\\dot{U}_\\mathrm{f}(0)$, $U_\\mathrm{s}(0)$, $\\dot{U}_\\mathrm{s}(0)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "id": "7e29a44d",
   "metadata": {},
   "outputs": [],
   "source": [
    "u_f0 = 2.0\n",
    "ut_f0 = 3.0\n",
    "u_s0 = 0.7\n",
    "ut_s0 = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "db2adcf8",
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.matrix([[eigenvector_num_P[mode_n, 0] for mode_n in range(number_of_eigenvalues)],\n",
    "               [eigenvector_num_P[mode_n, 1] for mode_n in range(number_of_eigenvalues)],\n",
    "               [eigenvector_num_P[mode_n, 0]*eigenvalue_num_P[mode_n] for mode_n in range(number_of_eigenvalues)],\n",
    "               [eigenvector_num_P[mode_n, 1]*eigenvalue_num_P[mode_n] for mode_n in range(number_of_eigenvalues)]],\n",
    "              dtype=complex)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "ed1289bd",
   "metadata": {},
   "outputs": [],
   "source": [
    "b = np.matrix([[u_f0], [u_s0], [ut_f0], [ut_s0]], dtype=complex)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "413b72e0",
   "metadata": {},
   "outputs": [],
   "source": [
    "amplitude = np.linalg.solve(A, b)   # matrix with one column "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "ef342a8a",
   "metadata": {},
   "outputs": [],
   "source": [
    "u_f_fit = lambda N,T: amplitude[N,0]*eigenvector_num_P[N,0]*np.exp(eigenvalue_num_P[N]*T) \n",
    "u_s_fit = lambda N,T: amplitude[N,0]*eigenvector_num_P[N,1]*np.exp(eigenvalue_num_P[N]*T) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "e0baceec",
   "metadata": {},
   "outputs": [],
   "source": [
    "t_oscillation = np.linspace(0, 30*t_scale, 250)\n",
    "timesteps_oscillation = len(t_oscillation)\n",
    "u_f_oscillation = np.zeros(timesteps_oscillation, dtype=complex)\n",
    "u_s_oscillation = np.zeros(timesteps_oscillation, dtype=complex)\n",
    "\n",
    "for mode_n in range(number_of_eigenvalues):\n",
    "    u_f_oscillation += u_f_fit(mode_n, t_oscillation)\n",
    "    u_s_oscillation += u_s_fit(mode_n, t_oscillation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "0abca9bb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t_oscillation,np.real(u_f_oscillation),'b', t_oscillation,np.real(u_s_oscillation),'k');\n",
    "plt.xlabel(\"$t$\");\n",
    "plt.ylabel(\"$u_f$, $u_s$\");\n",
    "#plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14e201c8",
   "metadata": {},
   "source": [
    "### Discriminant\n",
    "Discriminant $D_4$ of a quartic equation $ax^4 + bx^3 + cx^2 + dx + e = 0 $. For real coefficients $a,b,c,d,e \\in \\mathbb{R}$\n",
    "- $D_4 = 0$ at least two roots are equal,\n",
    "- $D_4 < 0$ two real roots and one complex-conjugated pair,\n",
    "- $D_4 > 0$ four real roots or two complex-conjugated pairs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "2a641cc2",
   "metadata": {},
   "outputs": [],
   "source": [
    "quartic_discriminant = lambda a,b,c,d,e: 256 * a**3 * e**3 \\\n",
    "    -192 * a**2 * b * d * e**2 \\\n",
    "    -128 * a**2 * c**2 * e**2 \\\n",
    "    +144 * a**2 * c * d**2 * e \\\n",
    "    -27 * a**2 * d**4 \\\n",
    "    +144 * a * b**2 * c * e**2 \\\n",
    "    -6 * a * b**2 * d**2 * e \\\n",
    "    -80 * a * b * c**2 * d * e \\\n",
    "    +18 * a * b * c * d**3 \\\n",
    "    +16 * a * c**4 *e \\\n",
    "    -4 * a * c**3 * d**2 \\\n",
    "    -27 * b**4 * e**2 \\\n",
    "    +18 * b**3 * c * d * e \\\n",
    "    -4 * b**3 * d**3 \\\n",
    "    -4 * b**2 * c**3 * e \\\n",
    "    + b**2 * c**2 * d**2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93c689c4",
   "metadata": {},
   "source": [
    "#### Dependency on MBS parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "10651986",
   "metadata": {},
   "outputs": [],
   "source": [
    "coefficients_mbs_P = ceq_mbs_P.collect(delta, evaluate=False)\n",
    "a4_mbs_P = coefficients_mbs_P[delta**4] \n",
    "a3_mbs_P = coefficients_mbs_P[delta**3] \n",
    "a2_mbs_P = coefficients_mbs_P[delta**2] \n",
    "a1_mbs_P = coefficients_mbs_P[delta] \n",
    "a0_mbs_P = coefficients_mbs_P[sp.S.One] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "1d539759",
   "metadata": {},
   "outputs": [],
   "source": [
    "D4_mbs = sp.simplify(quartic_discriminant(a4_mbs_P, a3_mbs_P, a2_mbs_P, a1_mbs_P, a0_mbs_P))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "68dad06b",
   "metadata": {},
   "outputs": [],
   "source": [
    "D4_mbs_num = D4_mbs.subs([(m_1,m_1_num_P), (m_2,m_2_num_P), (m_Delta,m_Delta_num_P), (c_1,c_1_num_P), (c_2,c_2_num_P), (c_Delta, c_Delta_num_P)])\n",
    "D4_mbs_d = sp.lambdify(d_Delta, D4_mbs_num, modules='numpy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "01772b89",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d_Delta_range = np.linspace(0.0, 0.0215*float(d_Delta_num_P))\n",
    "D4_mbs_range = D4_mbs_d(d_Delta_range)\n",
    "plt.plot(d_Delta_range, D4_mbs_range, color='black', linewidth=2);\n",
    "plt.plot([0,0.3],[0, 0], color='gray', linewidth=1);\n",
    "#plt.xlim((0,0.3))\n",
    "#plt.ylim((-2,2))\n",
    "plt.xlabel('$d_\\Delta$');\n",
    "plt.ylabel('$D_4$');\n",
    "#plt.show();\n",
    "tikzplotlib.save(\"d_crit.tex\", axis_height = '\\\\figH', axis_width = '\\\\figW')   "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fbdbd7a3",
   "metadata": {},
   "source": [
    "The value of $d_\\Delta$, when the discriminant $D_4$ changes its sign, corresponds to the change from oscillation ($D_4>0$), i.e. slow P-wave exists, to asymptotic decay ($D_4<0$), i.e. no slow P-wave."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "af6b803a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "critical d_Delta = 0.2353623276385464\n"
     ]
    }
   ],
   "source": [
    "d_Delta_crit_P = fsolve(D4_mbs_d, 0.8)\n",
    "print('critical d_Delta = '+ str(d_Delta_crit_P[0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76f2628a",
   "metadata": {},
   "source": [
    "The dissipation seems most relevant, as it introduces the asymmetry to the characteristic polynomial, however the precise value of the critical $d_\\Delta$ also depends on other parameters."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cfd2aed2",
   "metadata": {},
   "source": [
    "### Higher modes"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b1625c2",
   "metadata": {},
   "source": [
    "Find wave characteristics for increasing values of eigenfrequencies (higher modes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "e39a713d",
   "metadata": {},
   "outputs": [],
   "source": [
    "Nk = 1000\n",
    "# slow P-wave\n",
    "d1 = np.zeros(Nk)   # decay constant\n",
    "c1 = np.zeros(Nk)   # phase velocity approximation\n",
    "f1 = np.zeros(Nk)   # frequency \n",
    "AR1 = np.zeros(Nk)  # amplitude ratio\n",
    "phi1 = np.zeros(Nk) # phase angle  \n",
    "# fast P-wave\n",
    "d2 = np.zeros(Nk)   # decay constant\n",
    "c2 = np.zeros(Nk)   # phase velocity approximation\n",
    "f2 = np.zeros(Nk)   # frequency\n",
    "AR2 = np.zeros(Nk)  # amplitude ratio\n",
    "phi2 = np.zeros(Nk) # phase angle  \n",
    "\n",
    "index_slow = 0      # first and second eigenvalue compose first mode (slow)\n",
    "index_fast = 2      # third and fourth eigenvalue compose first mode (fast) \n",
    "\n",
    "for k_num in range(Nk):\n",
    "    \n",
    "    I_11_num = float(I_11_k.subs(k, k_num))\n",
    "    I_12_num = float(I_12_k.subs(k, k_num))\n",
    "    I_22_num = float(I_22_k.subs(k, k_num))  \n",
    "\n",
    "    # redefine, since I_ij changes with higher modes\n",
    "    nondim_num_k = [(I_11,  I_11_num),\n",
    "                    (I_12,  I_12_num),\n",
    "                    (I_22,  I_22_num),\n",
    "                    (alpha, alpha_num),  \n",
    "                    (M,     M_num),\n",
    "                    (D_P,   D_P_num),\n",
    "                    (n,     n_num),\n",
    "                    (RHO,   RHO_num),\n",
    "                    (tau,   tau_num)]\n",
    "    \n",
    "    ceq_num_P = ceq_nondim_P.subs(nondim_num_k + [(k, k_num)]).evalf()  \n",
    "    eigenvalue_sp = sp.solve(ceq_num_P, delta)\n",
    "    eigenvalue_num = [complex(EVSP) for EVSP in eigenvalue_sp]\n",
    "    \n",
    "    \n",
    "    d1[k_num] = np.real(eigenvalue_num[index_slow])   \n",
    "    omega = np.abs(np.imag(eigenvalue_num[index_slow]))\n",
    "    c1[k_num] = omega/((k_num+1/2)*np.pi)   \n",
    "    f1[k_num] = omega/(2*np.pi)\n",
    "    \n",
    "    d2[k_num] = np.real(eigenvalue_num[index_fast])   \n",
    "    omega = np.abs(np.imag(eigenvalue_num[index_fast]))\n",
    "    c2[k_num] = omega/((k_num+1/2)*np.pi)   \n",
    "    f2[k_num] = omega/(2*np.pi)\n",
    "    \n",
    "    evp_num_P = evp_nondim_P.subs(nondim_num_k + [(k, k_num)]).evalf()\n",
    "    \n",
    "    EVP = evp_num_P.subs(delta, eigenvalue_num[index_slow])\n",
    "    evkr = np.array([1.0, -EVP[0,0].evalf()/EVP[0,1].evalf()], dtype=complex)   # first row --> eigenvector\n",
    "    us_uf = evkr[1]/evkr[0]   # TODO exclude division by zero\n",
    "    AR1[k_num] = 1.0/np.absolute(us_uf)   # fluid-to-solid\n",
    "    phi1[k_num] = np.angle(us_uf)   # np.abs(np.angle(us_uf))\n",
    "    \n",
    "    EVP = evp_num_P.subs(delta, eigenvalue_num[index_fast])\n",
    "    evkr = np.array([1.0, -EVP[0,0].evalf()/EVP[0,1].evalf()], dtype=complex)   # first row --> eigenvector\n",
    "    us_uf = evkr[1]/evkr[0]   # TODO exclude division by zero\n",
    "    AR2[k_num] = 1.0/np.absolute(us_uf)  # fluid-to-solid\n",
    "    phi2[k_num] = np.angle(us_uf)   # np.abs(np.angle(us_uf))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d78de00c",
   "metadata": {},
   "source": [
    "Slow P-waves may exist only above a threshold frequency (depending on parameters, particularly dissipation). Maybe the actual threshold frequency is lower, but cannot be resolved more accurately by an integer number of modes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "728f1e67",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Slow P-waves exist from 7. mode on corresponding to a frequency of f = 1.3407949028585218\n"
     ]
    }
   ],
   "source": [
    "nonzero_f = f1.nonzero();    # only when there is an frequency (wave exists)\n",
    "index_first_nonzero_f = nonzero_f[0][0]\n",
    "print(\"Slow P-waves exist from {}. mode on corresponding to a frequency of f = {}\".format(index_first_nonzero_f+1, f1[index_first_nonzero_f]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c8384a8",
   "metadata": {},
   "source": [
    "Characteristics of slow P-waves"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "fa62ebee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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GjYKPjw9MTEwwZcqUcmU2b96MoKAg2Nvbw8rKCgEBAfjxx/Kf74sWLUKzZs1gaWmJdu3a4cCBA7p8aVphUkgksbJRyL/+/StuF96WOBoydO+9Bzx4APToAQwZInU0RMbNzc0Nc+bMQXJyMpKTk9GzZ09ERETgzJkzFZZXKpVwcnJCTEwM/P39Kyzj6OiImJgYJCUl4dSpUxg7dizGjh2LnTt3qsqsX78eU6ZMQUxMDE6ePIkuXbogLCwMV69e1cvrrCqZwLkwysnIyIC7uzvS09Ph5uYmdThUBwR+HwhFtgKL+i3CxPYTpQ6HDNT+/UC3boCJCXDyJODnJ3VERIZFF9/fjo6OmDdvHsaPH//Ect27d0dAQADmz5//1Drbtm2L/v3745NPPgEAdOzYEW3btsXixYtVZZ599lkMHDgQs2fP1ipuXeCdQiID8PichUQVKS19NLjk1VeZEBI9SV5eHnJzc1WbUvn0gXwlJSWIjY1FQUEBgoODdRKHIAjYs2cPzp07h67/LDdUVFSE48ePIzQ0VK1saGgoDh8+rJPraotJIZEBGNVmFExkJjiScQTnb5+XOhwyQD/+CJw4AdjaAv/cbCCiSvj6+sLOzk61PenuW0pKCqytrWFhYYEJEyYgLi4Ovr6+1bp+Tk4OrK2tIZfL0b9/f3zzzTfo3bs3AODWrVsoKSmBs7Oz2jnOzs7Izs6u1nWry0zSqxMRAKCxdWOEeoUi/kI8fjz1Iz7u8bHUIZEBKSwEYmLE/WnTACcnaeMhMnSpqalo0qSJ6rGFhUWlZX18fKBQKHDv3j1s2rQJUVFR2LdvX7USQxsbGygUCuTn52PPnj2YOnUqmjdvju7du6vKyP41uaggCOWO1TTeKSQyEGVzFv546keUCqUSR0OG5KuvgMxMwNNTXMWEiJ7MxsZGNaLY1tb2iUmhXC6Ht7c3goKCMHv2bPj7+2PBggXVur6JiQm8vb0REBCAt99+G0OGDFHdrWzYsCFMTU3L3RW8ceNGubuHNY1JIZGBiGgZARu5DS7fu4xDVw9JHQ4ZiJs3xXkJAXGdY0tLaeMhqu0EQahSH0Rt65TL5WjXrh0SEhLUyiQkJKBTp046va6m2HxMZCDqm9fHEN8hWKFYgR9P/YguHl2kDokMwCefAHl5QLt2XN+YSNc++OADhIWFwd3dHXl5eYiNjUViYiLi4+MBANHR0cjMzMTq1Y8GASoUCgBAfn4+bt68CYVCAblcrmpunj17NoKCguDl5YWioiJs374dq1evVhtpPHXqVERGRiIoKAjBwcFYsmQJrl69igkTJtTci6+ApHcK9+/fj/DwcLi6ukImk2HLli1PLP/yyy9DJpOV21q1aqVWbv78+fDx8UG9evXg7u6Ot956Cw8ePNDjKyHSjbJRyD+f+RkPivlvtq67dAn47jtx/7PPxKloiEh3rl+/jsjISPj4+KBXr144evQo4uPjVYNCsrKyys0dGBgYiMDAQBw/fhxr165FYGAg+vXrp3q+oKAA//3vf9GqVSt06tQJGzduxE8//YRXXnlFVWb48OGYP38+Pv74YwQEBGD//v3Yvn07PDw8auaFV0LSeQp37NiBQ4cOoW3bthg8eDDi4uIwcODASsvn5OTg/v37qsfFxcXw9/fHG2+8gRkzZgAA1qxZg/Hjx2P58uXo1KkT/v77b7z88ssYPnw4vvrqqyrFxXkKSSqlQik853siPTcdPw/5GUNbDZU6JJLQ6NHA2rVAaCjw2Ly3RFQJfn9Xj6TNx2FhYQgLC6ty+bKh5WW2bNmCu3fvYuzYsapjSUlJeP755zFq1CgAgKenJ0aOHIk//vhDd4ET6YmJzAQv+b2E2QdnY/Wp1UwK67BTp4B168R9CeeyJaI6xKgbI5YtW4aQkBC1262dO3fG8ePHVUngpUuXsH37dvTv37/SepRKpdokl3l5eXqPnagyZU3I8RficaPghsTRkFSmTQMEARg2DGjbVupoiKguMNqkMCsrCzt27FBroweAESNG4JNPPkHnzp1hbm4OLy8v9OjRA++//36ldc2ePVttksvqTlpJVB3POj2LINcgFJcWI/Z0rNThkASOHgV++UXsQ/gxp6wkohpitEnhypUrYW9vX64PYmJiImbNmoVFixbhxIkT2Lx5M3799VfVeoMViY6ORk5OjmpLTU3Vc/RET/b4nIVU93z4ofgzKgrw8ZE2FiKqO4wyKRQEAcuXL0dkZCTkcrnacx9++CEiIyPxyiuvoE2bNnjxxRfx6aefYvbs2SgtrXhCYAsLC7VJLm1sbGriZRBVakTrETAzMUPytWScvXlW6nCoBu3fDyQkAObmwEcfSR0NEdUlRpkU7tu3DxcuXMD48ePLPVdYWAiTf83bYGpqCkEQIOFAayKNOFk5IcxbHITFu4V1y/Tp4s/x48UVTIiIaoqkSWF+fj4UCoVqIsi0tDQoFArVnEDR0dEYM2ZMufOWLVuGjh07onXr1uWeCw8Px+LFixEbG4u0tDQkJCTgww8/xIABA2BqaqrX10OkS2UDTn469ROXvasjEhPFTS4HPvhA6miIqK6RdEqa5ORk9OjRQ/V46tSpAICoqCisXLmywkkjc3JysGnTpkrXJZw2bRpkMhmmTZuGzMxMODk5ITw8HLNmzdLfCyHSg3CfcNhZ2CE9Nx37Lu9Dj2Y9nn4SGbX//U/8+corgLu7tLEQUd0j6eTVhoqTX5Kh+M8v/8HSE0vxcsDLWBGxQupwSI/27we6dRP7El68yKSQSBv8/q4eo+xTSFRXjPEXu09sTN2IwoeFEkdD+lQ29cz48UwIiUgaTAqJDNjz7s+jmX0z5BflY8tfW6QOh/QkKQnYswcwMwOeMKUqEZFeMSkkMmAymUw14ISjkGuvsi7PY8YAjy3QRERUo5gUEhm4l/xeAgDsurgLWXlZEkdDuqZQAL/9Jq5ewruERCQlJoVEBu6ZBs8g2C0YpUIp1p1eJ3U4pGNz5og/hw0DnnlG2liIqG5jUkhkBMqakFf/uVriSEiXLlwANmwQ96OjpY2FiIhJIZERGN56OMxNzPHn9T9x6vopqcMhHZk3DygtBfr3B/z8pI6GiOo6JoVERsCxniNeaPECAODHPzngpDbIzgZWrRL3/+//pI2FiAhgUkhkNMrmLFyTsgYlpSUSR0PVtWABoFQCwcFA585SR0NExKSQyGj0e6YfHOs5Iis/C3vS9kgdDlVDXh6weLG4/957gEwmbTxERACTQiKjITeVY0SrEQA44MTYLVsG5OQALVoAAwZIHQ0RkYhJIZERifQXRyHH/RWHPGWexNGQNoqLga++Evffflucn5CIyBDw44jIiHRs0hHPOD6DwoeFiPsrTupwSAubNgFXrwJOTkBkpNTREBE9wqSQyIjIZDIMbzUcALD9/HaJoyFNCQLw5Zfi/qRJQL160sZDRPQ4JoVERqaPdx8AQMKlBI5CNjJJScAffwAWFsDEiVJHQ0SkjkkhkZHp2KQjbOQ2uHP/Dk5mn5Q6HNJAWV/Cl14CGjWSNhYion9jUkhkZMxNzdGzWU8AwK6LuySOhqrqyhVg82Zxf8oUSUMhIqoQk0IiI9THS2xCZlJoPL79VlzSrlcvoHVrqaMhIiqPSSGREQr1CgUAHE4/zKlpjEBBAbB0qbg/ebK0sRARVYZJIZER8nL0QnOH5nhY+hD7ruyTOhx6ijVrgHv3AC8voH9/qaMhIqoYk0IiIxXaXLxbyCZkwyYIwDffiPuTJnGyaiIyXPx4IjJSZU3ITAoN2/79wOnTQP36wNixUkdDRFQ5JoVERqpHsx4wlZni3O1zuHLvitThUCUWLhR/RkYC9vaShkJE9ERMComMlL2lPTq6dQQgTmRNhufaNSDun9UIJ02SNhYiKm/x4sXw8/ODra0tbG1tERwcjB07dlRaPisrC6NGjYKPjw9MTEwwpYL5pZYuXYouXbrAwcEBDg4OCAkJwR9//KFWZsaMGZDJZGpb48aNdf3yNMakkMiIsV+hYVu6FCgpAbp0Adq0kToaIvo3Nzc3zJkzB8nJyUhOTkbPnj0RERGBM2fOVFheqVTCyckJMTEx8Pf3r7BMYmIiRo4cib179yIpKQlNmzZFaGgoMjMz1cq1atUKWVlZqi0lJUXnr09TZlIHQETaC/UKxYx9M7D70m6UlJbA1MRU6pDoHw8fAkuWiPv//a+0sRBRxcLDw9Uez5o1C4sXL8aRI0fQqlWrcuU9PT2xYMECAMDy5csrrHPNmjVqj5cuXYqNGzdiz549GDNmjOq4mZmZQdwdfBzvFBIZsfZN2sPOwg53H9zF8azjUodDj9m2TWw+btQIGDRI6miI6pa8vDzk5uaqNqVS+dRzSkpKEBsbi4KCAgQHB+sslsLCQjx8+BCOjo5qx8+fPw9XV1c0a9YMI0aMwKVLl3R2TW0xKSQyYmYmZujVvBcANiEbmu+/F3+OHw/I5dLGQlTX+Pr6ws7OTrXNnj270rIpKSmwtraGhYUFJkyYgLi4OPj6+uoslvfffx9NmjRBSEiI6ljHjh2xevVq7Ny5E0uXLkV2djY6deqE27dv6+y62mBSSGTk2K/Q8Fy4ACQkADIZ8OqrUkdDVPekpqYiJydHtUVHR1da1sfHBwqFAkeOHMHEiRMRFRWF1NRUncQxd+5crFu3Dps3b4alpaXqeFhYGAYPHow2bdogJCQEv/32GwBg1apVOrmuttinkMjIlc1XmJSRhFxlLmwtbCWOiMr6EvbtCzRrJm0sRHWRjY0NbG2r9lkol8vh7e0NAAgKCsKxY8ewYMECfF92u19Ln3/+OT799FPs3r0bfn5+TyxrZWWFNm3a4Pz589W6ZnXxTiGRkWvm0Azejt4oLi1G4uVEqcOp84qKgJUrxf3XXpM0FCLSgiAIVeqD+CTz5s3DJ598gvj4eAQFBT21vFKpxNmzZ+Hi4lKt61YXk0KiWoBNyIZj61bg5k3A1ZXrHBMZug8++AAHDhzA5cuXkZKSgpiYGCQmJmL06NEAgOjoaLURwwCgUCigUCiQn5+PmzdvQqFQqDU3z507F9OmTcPy5cvh6emJ7OxsZGdnIz8/X1XmnXfewb59+5CWloajR49iyJAhyM3NRVRUVM288Eqw+ZioFgj1CsWi5EVMCg1AWdPxuHGAGT9hiQza9evXERkZiaysLNjZ2cHPzw/x8fHo3bs3AHGy6qtXr6qdExgYqNo/fvw41q5dCw8PD1y+fBkAsGjRIhQVFWHIkCFq502fPh0zZswAAGRkZGDkyJG4desWnJyc8Nxzz+HIkSPw8PDQ34utApkgCIKkERigjIwMuLu7Iz09HW5ublKHQ/RUucpcOH7miBKhBJfevIRmDuzIJoVLlwAvL3GAyaVLgKen1BER1S38/q4eNh8T1QK2FrYIdhfn1eLdQumUzWXbuzcTQiIyPkwKiWoJVb/CS0wKpVBS8miAySuvSBoKEZFWmBQS1RJlU9PsubQHxaXFEkdT9+zcCWRmAg0aAAMGSB0NEZHmmBQS1RJBrkFwsHRAjjIHxzKPSR1OnbNsmfgzMhKwsJA2FiIibTApJKolTE1MEdJcXEaJ/Qpr1s2b4lrHgLisHRGRMZI0Kdy/fz/Cw8Ph6uoKmUyGLVu2PLH8yy+/DJlMVm5r1aqVWrl79+5h0qRJcHFxgaWlJZ599lls375dj6+EyDCUNSGzX2HN+uknoLgYaN8eaN1a6miIiLQjaVJYUFAAf39/LFy4sErlFyxYgKysLNWWnp4OR0dHDB06VFWmqKgIvXv3xuXLl7Fx40acO3cOS5cuRZMmTfT1MogMRu/m4txaRzOO4t6De9IGU0cIArBihbg/dqy0sRARVYekU6uGhYUhLCysyuXt7OxgZ2enerxlyxbcvXsXYx/7JF6+fDnu3LmDw4cPw9zcHAAknwySqKZ42HvAp4EPzt0+h71pe/Hisy9KHVKtp1AAKSliP8IRI6SOhohqq6lTNT9n2jTA0bHq5Y16vv1ly5YhJCRELenbtm0bgoODMWnSJGzduhVOTk4YNWoU/u///g+mpqYV1qNUKtXWOczLy9N77ET6EuoVinO3z2HXxV1MCmtA2V3CgQMBBwdJQyGiWmz+fCA4GJDLq1b+4EHg9dfrSFKYlZWFHTt2YO3atWrHL126hN9//x2jR4/G9u3bcf78eUyaNAnFxcX46KOPKqxr9uzZ+N///lcTYRPpXahXKL754xv2K6wBRUVA2UfQyy9LGgoR1QFxcUCjRlUra2Ojef1GO/p45cqVsLe3x8CBA9WOl5aWolGjRliyZAnatWuHESNGICYmBosXL660rujoaOTk5Ki2xxe2JjI23T27w9zEHJfuXsLFOxelDqdW274duH0bcHERVzEhItKXFSuAx3rQPdX33wPOzppdwyiTQkEQsHz5ckRGRkL+r/uoLi4uaNGihVpT8bPPPovs7GwUFRVVWJ+FhQVsbW1Vm4026TWRgbCWW6OTeycAnJpG31avFn++9BJQSe8UIiKdiIrSbA7UUaMAKyvNrmGUSeG+fftw4cIFjK9gQrDnn38eFy5cQGlpqerY33//DRcXl3IJJFFtxalp9O/2beDXX8X9MWOkjYWI6hZBAJKTgY0bgU2bgBMnxGPVJWlSmJ+fD4VCAYVCAQBIS0uDQqHA1atXAYjNumMq+LRdtmwZOnbsiNYVTAg2ceJE3L59G5MnT8bff/+N3377DZ9++ikmTZqk19dCZEjKksLf037Hw5KHEkdTO8XGAg8fAm3bcm5CIqo5e/cCXl5Ax47AsGHA0KHiHKnPPAPs31+9uiVNCpOTkxEYGIjAwEAAwNSpUxEYGKgaEJKVlaVKEMvk5ORg06ZNFd4lBAB3d3fs2rULx44dg5+fH958801MnjwZ77//vn5fDJEBCWwciAb1GiBXmYs/Mv+QOpxaqazpmHcJiaimXLgAvPAC4OkJbN4MnD0LpKYCGzYAbm5Av37ApUva1y8TBF3ccKxdMjIy4O7ujvT0dLi5uUkdDpFWRmwcgfVn1uOjrh/hfz04ul6Xzp8HWrQQ+xFmZmremZuI9KO2f3+//rqYCO7ZU/45QQBCQgBfX+Cbb7Sr3yj7FBLR07Ffof6sWSP+DA1lQkhENScxEZgypeLnZDLxub17ta+/WklhRm4GMnMzq1MFEelJ2ZJ3f2T+gbv370ocTe0hCOJax4A46piIqKZcvQq0aVP5861bA1euaF+/xklhqVCKj/d9DLs5dvCY74Gm85vCfo49Ptn3CUqF0qdXQEQ1wt3OHc82fBalQil+T/td6nBqjaNHgYsXxakeIiKkjoaI6pL8fKB+/cqfr18fKCzUvn6NVzSJ2RODZSeXYU6vOXi+6fMQBAGH0g9hRuIMPCh+gFm9ZmkfDRHpVKhXKM7eOotdF3dhsO9gqcOpFcqajl98UfM5wIiIqis1FcjOrvi5W7eqV7fGSeGqP1fhhwE/YIDPANUx/8b+aGLTBP/d/l8mhUQGJNQrFAuOLsDOizshCAJkMpnUIRm14mJg/Xpxf/RoaWMhorqpV6+K5ySUycTj1fmY1zgpvHP/Dlo2bFnueMuGLXHn/h3tIyEinevm0Q3mJua4knMFF+5cwDMNnpE6JKO2Zw9w8ybg5CSO8iMiqklpafqtX+M+hf6N/bHwj4Xlji/8YyH8nf11EhQR6YaV3Aqdm3YGwCXvdGHtWvHnsGGAmcZ/UhMRVY+Hx9O3u9UYV6jxx9rckLnov7Y/dl/ajWC3YMhkMhxOP4z03HRsH7Vd+0iISC9CvUKx9/Je7Ly4E5M6cGUfbd2/D8TFifsjR0obCxHR43JyxP7OP/wA/PknUFKiXT0a3yns5tkNf7/xN15s+SLuKe/hzv07GPTsIJx7/Ry6eHTRLgoi0puy+Qr3Xt6LopIiiaMxXr/9BuTliX+JBwdLHQ0REfD77+LUWC4u4oTV/fqJayJrS6sGEFcbVw4oITISAY0D4FTfCTcLb+JIxhF09egqdUhGad068eeIEYAJp/0nIolkZAArVwLLlwMFBWJ3locPgU2bxNVMqqNKSeGp66fQulFrmMhMcOr6qSeW9XP2q15ERKRTJjIT9PbqjbUpa7Hr4i4mhVrIzRXvFAJsOiYi6fTrBxw8KK5//M03QN++4nKb332nm/qrlBQGfBeA7Hey0ciqEQK+C4BMJkNFSybLZDKUfKRlQzYR6U1o81BVUjiz50ypwzE627YBSiXQsiXgx797iUgiu3YBb74JTJwIPKOHySSqlBSmTU6DU30n1T4RGZfeXuKSd8nXknG78DYa1G8gcUTGpWxuwuHDqzcHGBFRdRw4IDYbBwWJf6RGRoqfS7pSpZ4xHvYeqklvr+RcQRPbJvCw91Dbmtg2wZWcaiy4R0R642rjitaNWkOAgD1pe6QOx6jcvQvs3Cnu6/LDl4hIU8HBwNKlQFYW8NprQGws0KQJUFoKJCSIg+GqQ+Pu0j1W9ahwkuqcBznosapH9aIhIr0JbS6OQuZ8hZqJixM7cbdpAzz7rNTREBGJaxyPGyf2L0xJAd5+G5gzB2jUCBgw4OnnV0bjpFAQBMhQvv3k9v3bsDLnQqBEhqpsappdF3dV2CeYKvZ40zERkaHx8QHmzhVHJa9bV70uLlVOCgetH4RB6wdBJpPh5a0vqx4PWj8IEbER6PNTH3Ry76R9JESkV108usDC1ALpuen469ZfUodjFG7dEpe2A8RpH4iodlm8eDH8/Pxga2sLW1tbBAcHY8eOHZWWz8rKwqhRo+Dj4wMTExNMmTKlXJmlS5eiS5cucHBwgIODA0JCQvDHH3+UK7do0SI0a9YMlpaWaNeuHQ4cOFCt12JqKk5aXZ2l8KqcFNpZ2sHO0g6CIMBGbqN6bGdph8ZWjfGftv/BT4N+0j4SItKr+ub1VUve7b60W+JojMOWLeKHbECAfkb6EZG03NzcMGfOHCQnJyM5ORk9e/ZEREQEzpw5U2F5pVIJJycnxMTEwN+/4qV9ExMTMXLkSOzduxdJSUlo2rQpQkNDkZmZqSqzfv16TJkyBTExMTh58iS6dOmCsLAwXL169akxL10KDB0KjBoFHD0qHvv9dyAwUBx40qk69+cEDc3YO0PIV+ZreppRSU9PFwAI6enpUodCpFNzDswRMAPCgHUDpA7FKISGCgIgCLNmSR0JEVWFLr6/HRwchB9++OGp5bp16yZMnjz5qeWKi4sFGxsbYdWqVapjHTp0ECZMmKBWrmXLlsL777//xLrmzRMEc3NBaNdOEOrXF7dZswShQQNBmDFDEG7efGo4T6Rxn8Lp3afDSs6+g0TGKKR5CABgb9peFJcWSxyNYbt9+1HT8dCh0sZCRJrJy8tDbm6ualMqlU89p6SkBLGxsSgoKECwDteyLCwsxMOHD+Ho6AgAKCoqwvHjxxEaGqpWLjQ0FIcPH35iXcuWiRNVJyeLE+rfvy/eJbxwAZg+HWjYsHqxarXM3cbUjfj5zM+4mnO13FqqJ147Ub2IiEhvAhoHwLGeI+7cv4M/Mv9gP+An2LpVbDr292fTMZGx8f3Xem/Tp0/HjBkzKiybkpKC4OBgPHjwANbW1oiLiyt3fnW8//77aNKkCUJCxD/Kb926hZKSEjg7O6uVc3Z2RnZ29hPrunIF+KcadO8OmJsDs2YB9va6iVXjO4VfH/0aY7eORSOrRjiZfRIdmnRAg/oNcOnuJYR5h+kmKiLSC1MTU/Rq1gsA+xU+zYYN4k/eJSQyPqmpqcjJyVFt0dHRlZb18fGBQqHAkSNHMHHiRERFRSE1NVUnccydOxfr1q3D5s2bYWlpqfac7F/DhAVBKHfs3x48AB6vRi4HnJx0EioALe4ULjq2CEteWIKRbUZi1Z+r8N7z76G5Q3N8tPejCucvJCLDEtI8BBtSN2D3pd34qNtHUodjkO7eBXb/kzMPGSJtLESkORsbG9ja2laprFwuh7e3NwAgKCgIx44dw4IFC/D9999XK4bPP/8cn376KXbv3g2/x9bHbNiwIUxNTcvdFbxx40a5u4cV+eEHwNpa3C8uBlauLN9s/Oab2sWscVJ4Neeqqsmpnlk95CnF6bMj/SLx3LLnsLDfQu0iIaIaUdavMCkjCflF+bCWW0sckeHZtk38sG3dWpwDjIjqDkEQqtQH8UnmzZuHmTNnYufOnQgKClJ7Ti6Xo127dkhISMCLL76oOp6QkICIiIgn1tu0qTj6uEzjxsCPP6qXkclqMClsbN0Yt+/fVi1vdyTjCPwb+yPtXhonxCUyAs0dmqOZfTOk3UvD/iv70e+ZflKHZHA2bRJ/Dh4sbRxEpF8ffPABwsLC4O7ujry8PMTGxiIxMRHx8fEAgOjoaGRmZmL16tWqcxQKBQAgPz8fN2/ehEKhgFwuV/VDnDt3Lj788EOsXbsWnp6eqjuC1tbWsP7nFt/UqVMRGRmJoKAgBAcHY8mSJbh69SomTJjwxHgvX9bxL+BfNE4KezbriV/O/YK2Lm0xPnA83tr5Fjae3Yjka8kY1HKQPmIkIh0LaR6CpSeWIuFiApPCf8nLA3b9sxIgk0Ki2u369euIjIxEVlYW7Ozs4Ofnh/j4ePTu3RuAOFn1v+cODAwMVO0fP34ca9euhYeHBy7/k7EtWrQIRUVFGPKvviePD3YZPnw4bt++jY8//hhZWVlo3bo1tm/fDg8PD/292CqQCRre3isVSlEqlMLMRMwnfz7zMw5ePQhvR29MCJoAualcL4HWpIyMDLi7uyM9PR1ubm5Sh0OkcxvObMCwjcPQulFrpExMkTocgxIbC4wcKY44PneuektGEVHNqs3f319/DfznP+oDTZ7ku++A0aMBG5uqX0Oj0cfFpcX4ZN8nyMrLUh0b1moYvg77Gm92fLNWJIREdUGPZj0ggwynb5xGdv6Tp0CoazZvFn8OHsyEkIgMx1tviS0ZVfXee8DNm5pdQ6PmYzMTM8w7PA9RAVGaXYWIDErD+g0R6BKIE1knsOfSHoz2Gy11SAbh/n1g+3Zxn03HRGRIBAHo1Qswq2Lmdv++5tfQuE9hSPMQJF5OxMsBL2t+NSIyGCHNQnAi6wR2p+1mUviPnTuBggLAwwNo107qaIiIHpk+XbPyERHAP4uoVJnGSWGYdxii90Tj9I3TaOfSrtySdwN8BmhaJRFJIKR5COYenouEiwlVmjS1LoiLE3+++CKbjonIsGiaFGpD46Rw4m8TAQBfJn1Z7jmZTIaSj0qqHxUR6V3npp1hYWqBzLxMnLt9Di0btpQ6JEkVFwO//CLuPzZ1GBFRnaFxUlg6vVQfcRBRDatnXg+dm3bGnrQ92H1pd51PCvfvF1cyadgQeP55qaMhIqp5Gq99TES1R9nqJlwH+VHT8YABgKmptLEQEUmBSSFRHVaWFO69vBfFpcUSRyMdQQC2bBH32XRMRHUVk0KiOiywcSAc6zkiV5mLY5nHpA5HMsePAxkZgJUVEBIidTRERFVTVCROsl+so7/pmRQS1WGmJqbo2awngLrdhFzWdBwWVvXVAoiIpFJYCIwfD9SvD7RqBZStxPfmm8CcOdrXy6SQqI4LafZPv8K0upsUljUdDxwoZRRERFUTHQ38+SeQmKj+h2xICLB+vfb1apUUXrxzEdN+n4aRm0biRsENAED8hXicuXFG+0iISBJl/QqT0pOQX5QvcTQ178IFIDVVXCWgf3+poyEierotW4CFC4HOndXnVPX1BS5e1L5ejZPCfZf3oc3iNjiaeRSbz25WfYmcun4K0xNrYGZFItKp5g7N4WnviYelD3HgygGpw6lx27aJP7t1A+ztJQ2FiKhKbt4EGjUqf7ygoHoT72ucFL6/533M7DkTCZEJkJvKVcd7ePZAUkaSRnXt378f4eHhcHV1hUwmw5ayNpxKvPzyy5DJZOW2Vq1aVVg+NjYWMpkMA9kmRFQpmUyG3s17AwASLiVIHE3N27pV/BkRIW0cRERV1b498Ntvjx6XJYJLlwLBwdrXq3FSmHI9BS+2LD9ng5OVE24X3taoroKCAvj7+2PhwoVVKr9gwQJkZWWptvT0dDg6OmLo0KHlyl65cgXvvPMOunTpolFMRHVRXZ2v8NYt4OBBcX8AV+gkIiMxezYQEwNMnCiOPF6wAOjdG1i5Epg1S/t6NU4K7S3tkZWfVe74yayTaGLbRKO6wsLCMHPmTAwaNKhK5e3s7NC4cWPVlpycjLt372Ls2LFq5UpKSjB69Gj873//Q/PmzTWKiaguKhuBnHIjBdn52RJHU3N++w0oLQX8/QEPD6mjISKqmk6dgEOHxFHIXl7Arl2AszOQlAS0a6d9vRonhaPajML/7f4/ZOdnQwYZSoVSHLp6CO8kvIMxfmO0j0QLy5YtQ0hICDz+9Wn+8ccfw8nJCePHj69SPUqlErm5uaotLy9PH+ESGayG9RsisHEgAOD3tN8ljqbmsOmYiIxVmzbAqlXA6dPiYLmffhKPVYfGSeGsnrPQ1K4pmnzZBPlF+fD91hddV3ZFJ/dOmNZ1WvWi0UBWVhZ27NiBV155Re34oUOHsGzZMixdurTKdc2ePRt2dnaqzdfXV9fhEhm8utaEfP8+sHOnuM+kkIgMXW5u1TdtmWl6grmpOdYMWoOPu3+Mk9knUSqUIrBxIJ5p8Iz2UWhh5cqVsLe3VxtEkpeXh5deeglLly5Fw4YNq1xXdHQ0pk6dqnqcmZnJxJDqnN7Ne2Pe4XlIuJQAQRAgq84QNiPw++9i04ubGxAYKHU0RERPZm//9JHFgiCWKSnR7hoaJ4VlvBy94OXope3p1SIIApYvX47IyEjI5Y9GQF+8eBGXL19GeHi46lhpaSkAwMzMDOfOnYOXV/mYLSwsYGFhoXqcW500m8hIdW7aGRamFsjIzcDft/+GT0MfqUPSq19+EX+Gh1dvCgciopqwd6/+r1GlpHDqzqlPL/SPL/t8qXUwVbVv3z5cuHChXJ/Bli1bIiUlRe3YtGnTkJeXhwULFsDd3V3vsREZq3rm9fB80+fxe9rv2H1pd61OCgUB+PVXcf+xvyGJiAxWt276v0aVksKT2SfVHh+/dhwlQgl8GohfGn/f/humJqZo56LZkJf8/HxcuHBB9TgtLQ0KhQKOjo5o2rQpoqOjkZmZidWrV6udt2zZMnTs2BGtW7dWO25paVnumP0/s9H++zgRlRfSLERMCtN2Y1KHSVKHozcnTwKZmYCVFdCjh9TREBFp5tSpio/LZOKyd02bAo81gFZZlZLCvVGP7ll+mfQlbOQ2WDVwFRzqOQAA7t6/i7Fbx6JLU83mBExOTkaPxz6Ry/r1RUVFYeXKlcjKysLVslWe/5GTk4NNmzZhwYIFGl2LiJ6ut1dvfPD7B9ibthfFpcUwM9G6h4lBK2s67t1bfd1QIiJjEBDw5G4v5ubA8OHA999r9hknEwRB0CSQJl82wa6XdqFVI/VVRE7fOI3QH0Nx7e1rmlRnkDIyMuDu7o709HS4ublJHQ5RjSkpLYHTPCfcfXAXSeOT8Jzbc1KHpBdBQcDx48CyZcC4cVJHQ0S6Ule+v7duBf7v/4B33wU6dBC7xBw7BnzxBTB9ujih9fvvi4nh559XvV6NbwPkKnNxveA6WkE9KbxRcAN5RZzfj8iYmZqYomeznth0dhN2X9pdK5PCa9fEhFAmA/r3lzoaIiLNzZolrmLSp8+jY35+4mwKH34I/PGH2D3m7bc1Swo1nqfwxZYvYuzWsdiYuhEZuRnIyM3AxtSNGL9tPAY9W7WVSYjIcNX2+QrLBph06CCuAEBEZGxSUipehcnDQ3wOEJuYs8ovQPdEGt8p/O6F7/DOrnfw0uaX8LD0oViJiRnGB47HvN7zNK2OiAxMWVJ4OP0wCooKYCW3kjgi3Xp8KhoiImPUsiUwZw6wZAlQNjPfw4fisZYtxceZmZr/4atxUljfvD4W9V+Eeb3n4eLdixAEAd6O3rXui4OorvJy8IKnvScu37uMA1cPoK93X6lD0pn794E9e8T9F16QNhYiIm19+y0wYIDYXOznJ3aHOXVKnLS6rDXk0iXgv//VrF6thxZaya3g5+yn7elEZKBkMhlCmoXgh5M/IOFiQq1KCvfuFRPDsg9SIiJj1KkTcPmyuN7x33+LA02GDAFGjQJsbMQykZGa16txUthjVQ/IUPk46N+jftc8CiIyKCHNxaRw58Wd+AJfSB2Ozvz2m/jzhRe4igkRGTdra2DCBN3WqXFSGOAcoPb4YelDKLIVOH3jNKL8o3QVFxFJKKR5CExkJjhz8wwycjPgZmv8UzsIwqOkkKOOicjY/f03kJgI3LgB/LOir8pHH2lXp8ajj7/q+5XatrDfQhwcdxBTnpsCc1Nz7aIgIoPSoH4DdGjSAQCw88JOiaPRjTNngCtXxIlce/aUOhoiMgSLFy+Gn58fbG1tYWtri+DgYOzYsaPS8llZWRg1ahR8fHxgYmKCKVOmlCtz5swZDB48GJ6enpDJZJg/f365MjNmzIBMJlPbGjduXOW4ly4FfH3F5G/jRiAu7tG2ZUuVqylH46SwMi/5vYTlJ5frqjoiklhfL7EvYfzFeIkj0Y2yu4Q9egD160sbCxEZBjc3N8yZMwfJyclITk5Gz549ERERgTNnzlRYXqlUwsnJCTExMfD396+wTGFhIZo3b445c+Y8MdFr1aoVsrKyVFtK2VwyVTBzpjhXYXY2oFCIS3eWbSdOVLmacnS2hlVSehIszbheFFFt0de7L2bsm4GEiwm1Ysm7x/sTEhEBQPi/5qaaNWsWFi9ejCNHjqBVq1blynt6eqqW2V2+vOIbYe3bt0f79u0BAO+//36l1zYzM9Po7uDj7t4Fhg7V6tQn0vhTftB69QmqBQjIystC8rVkfNj1Q50FRkTSCnINgmM9R9y5fwdHM47i+abPSx2S1u7cAQ4fFvfZn5Co9svLy0Nubq7qsYWFBSwsLJ54TklJCTZs2ICCggIEBwfrO0ScP38erq6usLCwQMeOHfHpp5+iefPmVTp36FBg1y4DGGhia2EL2WPD9kxgAp8GPvi4x8cI9QrVaXBEJB1TE1OEeoUi9nQs4i/EG3VSuHOnOH9Xq1YVrwJARLWLr6+v2uPp06djxowZFZZNSUlBcHAwHjx4AGtra8TFxZU7X9c6duyI1atXo0WLFrh+/TpmzpyJTp064cyZM2jQoMFTz/f2FpezO3IEaNMGMP/XkI4339QuLo2TwpUDV2p3JSIyOn29+opJ4cV4fNLzE6nD0dr27eJP3iUkqhtSU1PRpEkT1eMn3SX08fGBQqHAvXv3sGnTJkRFRWHfvn16TQzDwsJU+23atEFwcDC8vLywatUqTJ069annL1kiTkmzb5+4PU4mq8GksPmC5jj26jE0qK+eyd57cA9tv2+LS5MvaRcJERmcsrv/ydeScaPgBhpZNZI4Is2VlADx/4yVYVJIVDfY2NjA1ta2SmXlcjm8vb0BAEFBQTh27BgWLFiA77//Xp8hqrGyskKbNm1w/vz5KpVPS9NPHBqPPr587zJKhJJyx5XFSmTmZeokKCIyDC42LghoHAAASLiYIG0wWkpOBm7dAuzsgBroJkRERk4QBCiVyhq9plKpxNmzZ+Hi4lKj1/23Kt8p3HZum2p/54WdsLO0Uz0uKS3BnrQ98LT31GlwRCS9vl59ochWIP5iPEb7jZY6HI2VNR337l2+3w0R1W0ffPABwsLC4O7ujry8PMTGxiIxMRHx/zQvREdHIzMzE6tXr1ado1AoAAD5+fm4efMmFAoF5HK5qrm5qKgIqampqv3MzEwoFApYW1ur7ki+8847CA8PR9OmTXHjxg3MnDkTubm5iIqq+iIgGRnAtm3A1atAUZH6c19+qd3vo8pJ4cDYgQDEdVGjtqgHbW5qDk97T3wRWnuWwyIiUV/vvphzaA52XtiJUqEUJjKdTW9aI8rmoe3XT9o4iMjwXL9+HZGRkcjKyoKdnR38/PwQHx+P3r17AxAnq7569araOYGBgar948ePY+3atfDw8MDly5cBANeuXVMr8/nnn+Pzzz9Ht27dkJiYCADIyMjAyJEjcevWLTg5OeG5557DkSNH4FHFkXB79gADBgDNmgHnzgGtW4trIQsC0Lat9r8PmSAIgiYnNFvQDMdePYaG9Rtqf1UDl5GRAXd3d6Snp8PNzfiX9yKqjqKSIjSc2xB5RXlIfjUZ7VzbSR1SlV2/DpRNA3btGiBxywwR6Vld+f7u0AHo2xf4+GPAxgb480+gUSNg9Gjx+MSJ2tWr8Z/8aZPTanVCSETq5KZy9GreCwAQf8G4VjfZ+c8KfYGBTAiJqPY4exYoa2k2MwPu3xdHI3/8MfDZZ9rXW6Xm46+Pfo3/tPsPLM0s8fXRr59Y9s2OWo6DJiKD1derL7b8tQXxF+MR0zVG6nCqjE3HRFQbWVkBZWNhXF2BixfFeVgBcWCdtqqUFH515CuMbjMalmaW+OrIV5WWk0HGpJCoFurj3QeAuJzlvQf3YG9pL21AVVBc/OhO4WNTghERGb3nngMOHQJ8fcWptt5+G0hJATZvFp/TVpWSwrTJaRXuE1Hd4GnviZYNW+KvW39hz6U9GOw7WOqQnuroUXF9UAcHoGNHqaMhItKdL78E8vPF/RkzxP3168WVTr6q/N7dUxn3CvdEVGP6evXFX7f+QvyFeKNICsuajvv0EfvcEBHVFo8vkVy/PrBokW7qrdJH5dSdT19ypcyXfbScHIeIDFpf776Yf3Q+4i/GQxAEtTXQDVFZUti3r7RxEBEZiyolhSezT1apMhkM+0uCiLTX1aMrLM0skZGbgdSbqWjVqJXUIVXq+nXgxAlxn0khEVHVVCkp3Bu1V99xEJGBq2deD909uyP+QjziL8QbdFJYNsCkbVvA2VnaWIiIjEW1liZIz0lHRm6GrmIhIgPX10u87RZ/0bDnK/xnhSreJSQi0oDGSWFxaTE+/P1D2M2xg+cCT3jM94DdHDtM+30aHpY81EeMRGQg+nqLWdb+K/tRUFQgcTQVKynhVDREVDcUFYnL3BUX66Y+jZPC17e/jiUnlmBuyFycfO0kTr52EnND5mLZyWV4Y8cbuomKiAxSiwYt4GnviaKSIiReTpQ6nAolJwN37gB2dtWbr4uIyFAVFgLjx4sjj1u1AsqWZ37zTWDOHO3r1TgpXHd6HVZGrMRrQa/Bz9kPfs5+eC3oNSwfsBzrTq/TPhIiMngymexRE7KBLnlX1nTcuzenoiGi2ik6WlzvODERsLR8dDwkRJyvUFsaJ4WWZpbwtPcsd9zT3hNyU7n2kRCRUShrQjbUfoWcioaIarstW4CFC4HOnYHHZwfz9RWXvNOWxknhpPaT8Mn+T6AsVqqOKYuVmHVgFl5v/7r2kRCRUejZrCfMTMxw4c4FXLhzQepw1Ny+Dfzxh7jPpJCIaqubN4FGjcofLyhQTxI1pXHjysnsk9hzaQ/cvnKDv7M/AODP63+iqKQIvZr1wqD1g1RlNw/frH1kRGSQbCxs0LlpZyReTsTOCzvh3cFb6pBUdu0CBAFo0wZo0kTqaIiI9KN9e+C334A3/hnKUZYILl0KBAdrX6/GSaG9pX25Ja7c7dy1j4CIjE5fr75IvJyI+IvxmNRhktThqJT1J+SoYyKqzWbPFltDUlPFkccLFgBnzgBJScC+fdrXq3FSuCJihfZXI6Jaoa93X7y/533subQH9x/eRz3zelKHhNLSR1PR9OkjbSxERPrUqRNw6BDw+eeAl5fYStK2rZgUtmmjfb0cm0dEGvNz9kNTu6a4mnMVuy/tRrhPuNQh4dQpcXk7Kyux8zURUW3Wpg2wapVu69R4oMntwtuY9Nsk+H7ri4ZzG8LxM0e1jYhqP5lMhgEtBgAAtp7bKnE0orKm4549ATknQiCiWuzECSAl5dHjrVuBgQOBDz4QJ7TWlsZ3Cl+KewkX71zE+MDxcLZ2hgzVGOZCREYromUEFh5biF/+/gWlQilMZNVaNbPa2HRMRHXFa68B778v3i28dAkYPhwYNAjYsEGc2Hr+fO3q1TgpPHj1IA6OPQj/xv7aXZGIaoWuHl1ha2GLGwU3cDTjKILdqzHkrZry8sT+NQCnoiGi2u/vv4GAAHF/wwagWzdg7Vrxc3DECO2TQo3/tG/ZsCXuF9/X7mpEVGvITeXo90w/AMC2c9skjWXvXuDhQ7HDtZeXpKEQEemdIIiD6wBg926gn/hRDHd34NYt7evVOClc1G8RYn6Pwb7L+3C78DZylblqmyb279+P8PBwuLq6QiaTYcuWLU8s//LLL0Mmk5XbWrVqpSqzdOlSdOnSBQ4ODnBwcEBISAj+KJvNloh0ylD6FZY1HfMuIRHVBUFBwMyZwI8/ilPQ9O8vHk9LA5ydta9X46TQ3tIeOQ9y0HN1TzT6vBEcPnOAw2cOsJ9jD4fPHDSqq6CgAP7+/li4cGGVyi9YsABZWVmqLT09HY6Ojhg6dKiqTGJiIkaOHIm9e/ciKSkJTZs2RWhoKDIzMzWKjYieLuyZMJiZmOHsrbM4f/u8ZHGUDTJhf0IiqgvmzxcHm7z+OhATA3j/s4bAxo3idDXakgmCIGhyQoelHWBmYobJHSdXONCkm2c37QKRyRAXF4eBAwdW+ZwtW7Zg0KBBSEtLg4eHR4VlSkpK4ODggIULF2LMmDFVqjcjIwPu7u5IT0+Hm5tbleMhqotCVodgT9oefN77c7zd6e0av/6FC8AzzwDm5sCdO4C1dY2HQEQGoq5/fz94AJiaip+H2tB4oMnpG6dx8rWT8Gnoo90VdWjZsmUICQmpNCEEgMLCQjx8+BCOjpVPl6NUKqFUPlrLOS8vT6dxEtVmET4R2JO2B1vPbZUkKSy7S9i5MxNCIqrbLC2rd77GzcdBrkFIz02v3lV1ICsrCzt27MArr7zyxHLvv/8+mjRpgpCQkErLzJ49G3Z2dqrN19dX1+ES1VoDfMR+hYfSD+FWYTV6OGuJ/QmJqK4pKRFXM+nQAWjcGHB0VN+0pXFS+EaHNzA5fjJWKlbi+LXjOHX9lNpWU1auXAl7e/snNjfPnTsX69atw+bNm2H5hPQ5OjoaOTk5qi01NVUPERPVTh72HvB39kepUIrf/v6tRq+tVIojjwH2JySiuuN//wO+/BIYNgzIyQGmThXnKTQxAWbM0L5ejZuPh28cDgAYt3Wc6phMJoMgCJDJZCj5qET7aKpIEAQsX74ckZGRkFeydMHnn3+OTz/9FLt374afn98T67OwsICFhYXqcW6uZqOoieq6CJ8I/Hn9T2w9txVRAVE1dt1Dh4CCAvEv5af8NyciqjXWrAGWLhVHHf/vf8DIkeJ0XH5+wJEjwJtvalevxklh2uQ07a6kQ/v27cOFCxcwfvz4Cp+fN28eZs6ciZ07dyIoKKiGoyOqewb4DMDH+z/Gzos78aD4ASzNqtmxpYrKmo5DQwEZF1ciojoiO1tczQQQ+1Ln5Ij7L7wAfPih9vVqnBR62Fc+qENT+fn5uHDhgupxWloaFAoFHB0d0bRpU0RHRyMzMxOrV69WO2/ZsmXo2LEjWrduXa7OuXPn4sMPP8TatWvh6emJ7OxsAIC1tTWs2QudSC/aurRFE5smyMzLxJ5Le9C/Rf8auS6XtiOiusjNDcjKApo2Faej2bULaNsWOHYMeKzhU2NaL1aaejMV8Rfise3cNrVNE8nJyQgMDERgYCAAYOrUqQgMDMRHH30EQBxMcvXqVbVzcnJysGnTpkrvEi5atAhFRUUYMmQIXFxcVNvnn3+uxaskoqqQyWSqASc1tbpJdjbw55/iHcLevWvkkkREBuHFF4E9e8T9yZPFu4PPPAOMGQOMG/fkc59I0NDFOxcFv8V+gmyGTDD5n4kgmyFT7Zv8z0TT6gxSenq6AEBIT0+XOhQioxF/Pl7ADAiNP28slJSW6P16q1cLAiAI7drp/VJEZCQ0/f5etGiR0KZNG8HGxkawsbERnnvuOWH79u2Vlr927ZowcuRIoUWLFoJMJhMmT55crszp06eFQYMGCR4eHgIA4auvvqqwrm+//Vbw9PQULCwshLZt2wr79++vUswVSUoShC++EIStW7WuQhAEQdD4TuHk+MloZt8M19+5jvrm9XHmv2ewf+x+BLkGITEqsRrpKREZs+6e3WEjt0F2fjaOZR7T+/Ue709IRKQNNzc3zJkzB8nJyUhOTkbPnj0RERGBM2fOVFheqVTCyckJMTEx8Pf3r7BMYWEhmjdvjjlz5qBx48YVllm/fj2mTJmCmJgYnDx5El26dEFYWFi51tGqeu45cQTygAFana6icZ/CpPQk/B71O5ysnGAiM4GJzASdm3bG7F6z8Wb8mzj52snqRURERsnCzAJ9vftiQ+oGbDu3DR3dOurtWqWlYh8agP0JiUh74eHhao9nzZqFxYsX48iRI2jVqlW58p6enliwYAEAYPny5RXW2b59e7Rv3x6AOFdyRb788kuMHz9eNdfy/PnzsXPnTixevBizZ8+uUux//w0kJgI3boifiY/7pxeexjS+U1gilMBaLg7YaFi/Ia7lXQMAeNh54Nytc9pFQUS1QoRPBABg67mter2OQgHcvCmOugsO1uuliMgI5eXlITc3V7U9vmpZZUpKShAbG4uCggIE6/GDpaioCMePH0fov5o5QkNDcfjw4SrVsXQp4OsrJn8bNwJxcY+2LVu0j03jO4WtG7XGqeun0NyhOTo26Yi5h+dCbirHkhNL0NyhufaREJHRC3smDKYyU5y5eQYX71yEl6OXXq5T1nTcsydQyVSlRFSH/XtlsunTp2NGJbM6p6SkIDg4GA8ePIC1tTXi4uL0urLZrVu3UFJSAmdnZ7Xjzs7OqhlTnmbmTGDWLOD//k+3sWl8p3Bal2koFcT7lDN7zsSVe1fQZUUXbD+/HV+Hfa3b6IjIqDjWc0RXj64A9DsKmVPRENGTpKamqq1UFh0dXWlZHx8fKBQKHDlyBBMnTkRUVFSNrGwm+9fkqsI/i4BUxd27wNChuo9J4zuFfbwffQo3d2iO1EmpuHP/DhwsHar8Yoio9hrgMwB7L+/F5r82463gt3Ref16euJIJwKSQiCpmY2MDW1vbKpWVy+Xw9vYGAAQFBeHYsWNYsGABvv/+e73E1rBhQ5iampa7K3jjxo1ydw8rM3So2K96wgTdxqZxUlgRx3rVWH2ZiGqVwc8Oxls738Khq4eQmZuJJrZNdFr/3r1AcbG4pJOXflqniagOEwShSn0QtSWXy9GuXTskJCTgxRdfVB1PSEhAREREped9/VhjrLe3ODfhkSPiyibm5upla2yZOyKiJ3G3c0cn9044nH4YG1I3YMpzU3RaP6eiISJd+eCDDxAWFgZ3d3fk5eUhNjYWiYmJiI+PB4AKV1ZTKBQAxFXZbt68CYVCAblcruqHWFRUpGp+LioqQmZmJhQKBaytrVV3JKdOnYrIyEgEBQUhODgYS5YswdWrVzHhCbf+vvpK/bG1NbBvn7g9TiZjUkgkqdu3gQYNpI7CcAxvNRyH0w9j/Zn1eksK2XRMRNV1/fp1REZGIisrC3Z2dvDz80N8fDx6/7NMUkUrq5WtwgYAx48fx9q1a+Hh4YHLly8DAK5du6ZW5vPPP8fnn3+Obt26ITExEQAwfPhw3L59Gx9//DGysrLQunVrbN++HR4elS8lnJamoxf9BDJBEAT9X8a4ZGRkwN3dHenp6XBzc5M6HDJgWVlAWBhw6ZI4RUp11pysTa7lXYPbl24QIODy5Ms6WzP94kWx2cTMTEzEq9hliIjqiLr4/V2WxeliWIfWax8TEeDsLE4cmpf3aB1KAlxtXFWjkH8+87PO6i27S9ipExNCIqrbli0DWrcGLC3FrXVr4Icfqlcnk0KiajAxAQYOFPfj4iQNxeAMbzUcALD+zHqd1cmmYyIicZDJ5MlAeDiwYYO4hYcDb70FTJumfb1MComqqWzw2NatQEmJtLEYksG+g2EiM8HxrOO4cOdCtet7+BD4/Xdxn0khEdVlixeLq5rMni2udzxggLi/ZAnw3Xfa18ukkKiauncH7O3FPoVVXKGoTmhk1Qg9m/UEoJsm5KQkID8fcHICHuvDTURU55SUAEFB5Y+3aydO2aUtJoVE1WRuDrzwgrjPJmR1umxCLms67t1bbLYnIqqrXnpJvFv4b0uWAKNHa18vP1qJdGDQIPFnXNyjkWAEDHp2EMxMzHDq+in8deuvatXF/oRERI+UDTR55RVxa91abFI2MQGmTn20aYJJIZEO9OkD1KsHXL4M/DOvKUFc7ah3c3G+r/Wntb9bePMmcOKEuP/P9GFERHXW6dNA27Zid5qLF8XNyUk8dvo0cPKkuGn6fcTJq4l0oH59MTHcskW8W8g+b48MbzUcOy7swPoz6/FRt4+0WiM9IUG8A+vnB7i46CFIIiIjsnevfurlnUIiHSkbhcx+heoGthwIuakcZ2+dxekbp7Wqg03HRET6x6SQSEdeeAEwNRVv3V+o/gwstYadpR36evcFoN2AE0EAdu0S95kUEhHpD5NCIh1xdBSnpwF4t/DfykYh/3zmZ2i6suapU0B2tthE37mzPqIjIiKASSGRTrEJuWLhLcJhaWaJ83fOQ5Gt0OjcsruE3btzbWkiIn1iUkikQ2VL3iUlAVlZkoZiUGwsbND/mf4AgHWn12l0bny8+JNNx0RE+sWkkEiHmjQBOnQQ97dulTYWQzO6jTij6k+nfkJxadWm3M/PBw4cEPf79tVXZEREBDApJNI5NiFXrH+L/mhYvyGy8rOw6+KuKp2TmCiuedysGfDMM/qNj4iormNSSKRjZUnh778D9+5JGopBkZvKVXcLVyhWVOmcsqbjvn0BLaY3JCIiDTApJNIxHx/A11dclPy336SOxrCMDRgLANh2bhtuF95+avnHk0IiItIvJoVEesAm5Ir5N/ZHQOMAFJUUPXXAyYUL4tJNZmZAjx41FCARUR3GpJBID8qSwh07gPv3pY3F0JTdLXxaE3LZKiadOwM2NvqOioiImBQS6UHbtkDTpkBh4aN59kg0qs0omJuY40TWCZy6fqrScmw6JiKqWUwKifRAJns0ZyGbkNU1rN8Q4T7hAICVipUVllEqxYE6AJNCIqKawqSQSE/KmpB/+UUcdEKPlDUh/3TqJzwseVju+YMHxbusjRsDfn41HR0RUd3EpJBITzp3Bho0AO7cAfbvlzoaw9LXuy+crZxxs/Amfjtffoh2WX/CPn04FQ0RUU1hUkikJ2ZmwIAB4j6bkNWZmZgh0i8SQMVNyOxPSERU85gUEulRWRPyli2AIEgaisEZGyg2If92/jfcKLihOp6ZCaSkiHcIe/eWKjoiorqHSSGRHvXuDVhZARkZQHKy1NEYFl8nX3Ro0gHFpcX46dRPquNlTccdOojN70REVDOYFBLpkaUlEBYm7rMJubyyASdLTyyF8M+t1LKm4z59pIqKiKhuYlJIpGeDBok/mRSWN6rNKFjLrfHXrb+w9/JeFBc/mteR/QmJiGoWk0IiPevXDzA3B/76S9zoEVsLW4zxGwMAWPjHQiQlATk5YrNxhw4SB0dEVMdImhTu378f4eHhcHV1hUwmw5YtW55Y/uWXX4ZMJiu3tWrVSq3cpk2b4OvrCwsLC/j6+iKOt2hIQnZ2QK9e4j7/KZY3qcMkAMDWc1sRG5cDQLxLaGoqZVRERHWPpElhQUEB/P39sXDhwiqVX7BgAbKyslRbeno6HB0dMXToUFWZpKQkDB8+HJGRkfjzzz8RGRmJYcOG4ejRo/p6GURPVTYKefNmaeMwRL5OvujZrCdKhVJs3FoIQLy7SkRENUvSpDAsLAwzZ87EoLJOV09hZ2eHxo0bq7bk5GTcvXsXY8eOVZWZP38+evfujejoaLRs2RLR0dHo1asX5s+fr6dXQfR0ERHiFCvJyUB6utTRGJ5J7ScBOU1w45ILZDKBg0yIqEYsXrwYfn5+sLW1ha2tLYKDg7Fjx45Ky2dlZWHUqFHw8fGBiYkJpkyZUmG5p7VYzpgxo1yrZ+PGjXX50rRi1H0Kly1bhpCQEHh4eKiOJSUlITQ0VK1cnz59cPjw4UrrUSqVyM3NVW15eXl6i5nqJmdnoFMncf8pvSTqpAE+A2CfMQoA4NXmJqeiIaIa4ebmhjlz5iA5ORnJycno2bMnIiIicObMmQrLK5VKODk5ISYmBv7+/hWWqWqLZatWrdRaP1NSUnT++jRltElhVlYWduzYgVdeeUXteHZ2NpydndWOOTs7Izs7u9K6Zs+eDTs7O9Xm6+url5ipbitrQma/wvLMTMzgkj0eAPCgGX9BRFQzwsPD0a9fP7Ro0QItWrTArFmzYG1tjSNHjlRY3tPTEwsWLMCYMWNgZ2dXYZmqtliamZmptX46OTnp+uVpzGiTwpUrV8Le3h4DBw4s95zsX4ulCoJQ7tjjoqOjkZOTo9pSU1N1HS6RKincvx+4fVvaWAyNUglcOfEMACDD+XscyzwmcUREZMzy8vLUWgCVSuVTzykpKUFsbCwKCgoQHBys9bWr2mJ5/vx5uLq6olmzZhgxYgQuXbqk9TV1xSiTQkEQsHz5ckRGRkIul6s917hx43J3BW/cuFHu7uHjLCwsVP0JbG1tYWNjo5e4qW5r3hzw8wNKSoBffpE6GsNy4ABQWGACS/t7QGMFvj32rdQhEZER8/X1VWsBnD17dqVlU1JSYG1tDQsLC0yYMAFxcXHVajGsSotlx44dsXr1auzcuRNLly5FdnY2OnXqhNsS3zEwyqRw3759uHDhAsaPH1/uueDgYCQkJKgd27VrFzqVdegikhCbkCu2fbv4MyS0CDAREHs6FrcKb0kbFBEZrdTUVLUWwOjo6ErL+vj4QKFQ4MiRI5g4cSKioqKq3WL4tBbLsLAwDB48GG3atEFISAh+++03AMCqVauqdd3qkjQpzM/Ph0KhgEKhAACkpaVBoVDg6tWrAMRm3TFjxpQ7b9myZejYsSNat25d7rnJkydj165d+Oyzz/DXX3/hs88+w+7duysdIURUk8qSwl27gIICaWMxJGVJ4ZghTghyDYKyRInFxxZLGxQRGS0bGxu1FkALC4tKy8rlcnh7eyMoKAizZ8+Gv78/FixYoPW1tWmxtLKyQps2bXD+/Hmtr6sLkiaFycnJCAwMRGBgIABg6tSpCAwMxEcffQRAHExSliCWycnJwaZNmyq8SwgAnTp1QmxsLFasWAE/Pz+sXLkS69evR8eOHfX7YoiqwM8PaNYMePDg0Rq/dd3Fi8C5c+Jk1aGhMkx9bioA4Os/vkbhw0KJoyOiukYQhCr1QayMNi2WSqUSZ8+ehYuLi9bX1QUzKS/evXt3CIJQ6fMrV64sd8zOzg6FhU/+ohgyZAiGDBlS3fCIdE4mE9dC/uILsQl58GCpI5Je2ZRgnTuLq78MbTUUMb/HIO1eGlacXKFa8YSISNc++OADhIWFwd3dHXl5eYiNjUViYiLi//mrPTo6GpmZmVi9erXqnLLWzfz8fNy8eRMKhQJyuVzVD3Hy5Mno2rUrPvvsM0RERGDr1q3YvXs3Dh48qKrjnXfeQXh4OJo2bYobN25g5syZyM3NRVRUVM29+AoYZZ9CImNW1oT8669AUZG0sRiCsqbjslVMzEzM8G6ndwEA8w7Pw8OShxJFRkS13fXr1xEZGQkfHx/06tULR48eRXx8PHr37g2g4hbLshbO48ePY+3atQgMDES/x5ZhqkqLZUZGBkaOHAkfHx8MGjQIcrkcR44cUZt3WQoy4Um36uqojIwMuLu7Iz09HW5ublKHQ7VMaSng6gpcvw7s3An8a+aCOqWwEGjQQGxOT0kByroJ3394H54LPHGj4AZ+evEnjPYbLW2gRGQU+P1dPbxTSFTDTEzEZe8AroW8d6+YELq7A61aPTpez7weJnecDAD47NBnT+xmQkREusGkkEgCZU3IW7eKdw7rqm3bxJ8vvCD2t3zcf9v/FzZyG6TcSMGOC5WvRUpERLrBpJBIAj17Ara2QHY2UMlqSrVeaemjSbzL7pw+zt7SHq+1ew0AMOfgnBqMjIiobmJSSCQBuRzo31/cr6sTWScnA1lZgI0N0L17xWXeCn4LclM5Dlw9gMPphysuREREOsGkkEgij69uUhe7zG3dKv7s2xeobF5ZVxtXjPETJ7D/ZP8nNRQZEVHdxKSQSCJhYWIydPEicPq01NHUvLL+hBU1HT8uuks0zEzMEH8hHgevHnxyYSIi0hqTQiKJWFsD/0yFVeeakC9dEhNhU1MxOX6S5g7NMT5QXMEo5vcYjkQmItITJoVEEnq8CbkuKbtL2LUr4Oj49PLTuk6DhakF9l/Zj4RLCU8/gYiINMakkEhCAwaI8xYqFEBamtTR1Jyy/oRPazou42brholBEwHwbiERkb4wKSSSUMOG4t0yANiyRdJQasydO8CBA+L+gAFVPy+6SzSszK2QfC0ZW89t1U9wRER1GJNCIonVtSbk7duBkhKgTRugWbOqn9fIqpFqlZMP936IktISPUVIRFQ3MSkkktjAgeLPgwfF9ZBrO02bjh/3Tqd3YGdhh9M3TmPd6XW6DYyIqI5jUkgksaZNgXbtxLkKywZg1FZKJRAfL+5r0nRcxqGeA957/j0AQPSeaBQUFegwOiKiuo1JIZEBqCtNyHv3Avn5gKurmAhr463n3oKHnQcycjMw7/A83QZIRFSHMSkkMgBlSeGePUBurrSx6FNZ03HZqGtt1DOvh7m95wIA5h6ai/ScdB1FR0RUtzEpJDIAzz4LtGgBFBWJAzFqo9LSqq9i8jRDfYeiS9MuuF98H+/veb/6wREREZNCIkMgk9X+JuQTJ4Br18SVXHr0qF5dMpkM8/vOhwwyrE1Zi6T0JN0ESURUhzEpJDIQZUnh9u3AgwfSxqIPZclu377ims/V1dalLcYGjAUATI6fjFKhtPqVEhHVYUwKiQxE+/biAIz8fLFvYW0iCMD69eL+kCG6q3dWr1mwkdvg2LVj+C75O91VTERUBzEpJDIQJiaP5iysbU3Ix48DFy8C9esDL7ygu3obWzfG7F6zAQDv734fmbmZuquciKiOYVJIZEAGDRJ/btsmrvpRW8TGij/DwwErK93WPSFoAjo26Yi8ojy8seMN3VZORFSHMCkkMiBduwIODsDNm8ChQ1JHoxulpcDPP4v7I0bovn5TE1MsCV8CMxMzxP0Vhy1/bdH9RYiI6gAmhUQGxNxcvJsG1J4m5KQkID0dsLUVB5nog5+zH97t9C4A4PXtryNXWYsneyQi0hMmhUQG5vGpaQRB2lh0oazpeOBAwNJSf9f5sOuH8HLwQmZeJt6Kf0t/FyIiqqWYFBIZmNBQoF494MoV4ORJqaOpnpISYMMGcV8fTcePq2deD8sjlkMGGZYrlmPrX1v1e0EiolqGSSGRgalf/1Ezq7E3Ie/bB1y/Djg6AiEh+r9eV4+ueKfTOwCAV395Fdfzr+v/okREtQSTQiIDVFtWNylrOh48WOwvWRM+6fEJ2jRqg5uFN/HqL69CqA1t8ERENYBJIZEBeuEFwMwMOHMGOH9e6mi0U1QEbNok7uu76fhxFmYW+GnQT5CbyvHL37/g++Pf19zFiYiMGJNCIgPk4AB07y7uG+vdwt27gTt3AGdnoFu3mr22n7MfPu35KQBxCbwTWSdqNgAiIiPEpJDIQBl7E3LZsnZDhwKmpjV//beC30J4i3AUlRRh6IahuPfgXs0HQURkRJgUEhmoiAjx55EjwLVr0saiqQcPHiWzNdl0/DgTmQlWDVwFT3tPXLp7CeO2jmP/QiKiJ2BSSGSgmjQBnntO3N9qZLOr7NgB5OUB7u5AcLB0cTjUc8DPQ36G3FSOuL/iMPfQXOmCISIycEwKiQyYsTYhl406HjYMMJH4U6Z9k/ZY0HcBACB6TzS2ndsmbUBEZDAWL14MPz8/2NrawtbWFsHBwdixY0el5bOysjBq1Cj4+PjAxMQEU6ZMqbDcpk2b4OvrCwsLC/j6+iKugg/xRYsWoVmzZrC0tES7du1w4MABXb0srTEpJDJgZUnh3r3A3bvSxlJV+fnAL7+I+1I1Hf/bhKAJmBg0EQIEjN48GinXU6QOiYgMgJubG+bMmYPk5GQkJyejZ8+eiIiIwJkzZyosr1Qq4eTkhJiYGPj7+1dYJikpCcOHD0dkZCT+/PNPREZGYtiwYTh69KiqzPr16zFlyhTExMTg5MmT6NKlC8LCwnD16lW9vM6qkgnsZFNORkYG3N3dkZ6eDjc3N6nDoTqudWtxapoffwReeknqaJ7up5+AyEjAy0ucTkcmkzoi0cOSh+i7pi9+T/sdnvaeSBqfhMbWjaUOi4h0SBff346Ojpg3bx7Gjx//xHLdu3dHQEAA5s+fr3Z8+PDhyM3NVbvj2LdvXzg4OGDdunUAgI4dO6Jt27ZYvHixqsyzzz6LgQMHYvbs2VrFrQu8U0hk4IytCfnbb8WfUVGGkxACgLmpOTYM3QBvR29cvncZ/db0Q64yV+qwiEgP8vLykJubq9qUSuVTzykpKUFsbCwKCgoQXI3O0ElJSQgNDVU71qdPHxw+fBgAUFRUhOPHj5crExoaqiojFSaFRAauLCncsQMoLJQ2lqc5flwcLW1uDrz6qtTRlOdYzxE7Ru9AI6tGOJl9EoPWD4Ky+OlfFkRkXHx9fWFnZ6fannT3LSUlBdbW1rCwsMCECRMQFxcHX19fra+dnZ0NZ2dntWPOzs7Izs4GANy6dQslJSVPLCMVJoVEBi4wEPDwAO7fB3btkjqaJyu7SzhkCNDYQFtmvR29sX3UdljLrbEnbQ8i4yJRXFosdVhEpEOpqanIyclRbdHR0ZWW9fHxgUKhwJEjRzBx4kRERUUhNTW1WteX/auZRBCEcseqUqamSZoU7t+/H+Hh4XB1dYVMJsOWLVueeo5SqURMTAw8PDxgYWEBLy8vLF++XK3M/Pnz4ePjg3r16sHd3R1vvfUWHjx4oKdXQaRfMhkwcKC4b8hNyLdvA/90l8Hrr0sby9O0c22HzcM2w9zEHBtSN+DlLS+jpLRE6rCISEdsbGxUI4ptbW1hYWFRaVm5XA5vb28EBQVh9uzZ8Pf3x4IFC7S+duPGjcvd8btx44bqzmDDhg1hamr6xDJSkTQpLCgogL+/PxYuXFjlc4YNG4Y9e/Zg2bJlOHfuHNatW4eWLVuqnl+zZg3ef/99TJ8+HWfPnsWyZcuwfv36J/6VQGToypqQf/kFePhQ2lgqs3y5OGl1YKC0cxNWVW+v3tgwdAPMTMywJmUNxm8bj1KhVOqwiEhigiBUqQ9iZYKDg5GQkKB2bNeuXejUqRMAMQlt165duTIJCQmqMlIxk/LiYWFhCAsLq3L5+Ph47Nu3D5cuXYKjoyMAwNPTU61MUlISnn/+eYwaNUr1/MiRI/HHH3/oLG6imta5M9CwIXDrFrB/P9Crl9QRqSspAcoG0U2aZFgDTJ4komUEYgfHYvjG4Vj15yoUlxZjRcQKmJuaSx0aEdWADz74AGFhYXB3d0deXh5iY2ORmJiI+Ph4AEB0dDQyMzOxevVq1TkKhQIAkJ+fj5s3b0KhUEAul6v6IU6ePBldu3bFZ599hoiICGzduhW7d+/GwYMHVXVMnToVkZGRCAoKQnBwMJYsWYKrV69iwoQJNffiK2BUfQq3bduGoKAgzJ07F02aNEGLFi3wzjvv4P79+6oynTt3xvHjx1VJ4KVLl7B9+3b079+/0nqVSqXaKKW8vDy9vxYiTZiaAgMGiPuG2IS8YweQlgY4OAAjR0odjWYG+w7G2sFrVXcMh24YigfF7G5CVBdcv34dkZGR8PHxQa9evXD06FHEx8ejd+/eAMTJqv89d2BgYCACAwNx/PhxrF27FoGBgejXr5/q+U6dOiE2NhYrVqyAn58fVq5cifXr16Njx46qMsOHD8f8+fPx8ccfIyAgAPv378f27dvh4eFRMy+8MoKBACDExcU9sUyfPn0ECwsLoX///sLRo0eF3377TfDw8BDGjh2rVu7rr78WzM3NBTMzMwGAMHHixCfWO336dAFAuS09Pb26L4tIZ375RRAAQWjSRBBKSqSORl2fPmJsb78tdSTa+/Xcr4LFJxYCZkDotqKbcKfwjtQhEZGG0tPT+f1dDUZ1p7C0tBQymQxr1qxBhw4d0K9fP3z55ZdYuXKl6m5hYmIiZs2ahUWLFuHEiRPYvHkzfv31V3zyySeV1hsdHa02Sqm6o46I9CEkBLC2BjIzgeRkqaN55Px5YOdOscl44kSpo9Fe/xb9sWP0DtjIbbDvyj48v/x5XLl3ReqwiIhqjFElhS4uLmjSpAns7OxUx5599lkIgoCMjAwAwIcffojIyEi88soraNOmDV588UV8+umnmD17NkpLK+5EbmFhoTZKycbGpkZeD5EmLC2BshYKQ2pCXrRI/BkWJq5iYsx6NOuBg+MOoolNE5y9dRYdf+iIQ1cPSR0WEVGNMKqk8Pnnn8e1a9eQn5+vOvb333/DxMREtZxNYWEhTEzUX5apqSkEQYDAFf3IyBna6iYFBcCKFeK+oU9DU1V+zn448soR+Dn74XrBdfRY1QNLjy+VOiwiIr2TNCnMz8+HQqFQjeRJS0uDQqFQdeqMjo7GmDFjVOVHjRqFBg0aYOzYsUhNTcX+/fvx7rvvYty4cahXrx4AIDw8HIsXL0ZsbCzS0tKQkJCADz/8EAMGDICpqWmNv0YiXerXD5DLgXPngLNnpY4GWLMGyMkR7xD26SN1NLrjZuuGQ+MOYfCzg/Gw9CH+8+t/MG7rOBQ+NPAlZYiIqkHSpDA5OVk1igcQh2gHBgbio48+AlB+1I+1tTUSEhJw7949BAUFYfTo0QgPD8fXX3+tKjNt2jS8/fbbmDZtGnx9fTF+/Hj06dMH33//fc2+OCI9sLV9NB3Np58CUt78FoRHK5j897+AiVG1OzydtdwaG4ZuwKyes2AiM8EKxQp0/KEjTt84LXVoRER6IRPYplpORkYG3N3dkZ6ermqWJjIUBw8C3boBpaXAsmXAuHHSxHHgANC1K1Cvnjj4xcFBmjhqwt60vRi5aSSuF1yHhakFPgv5DG90fAMmslqWCRMZOX5/Vw8/0YiMTOfOwMyZ4v6kSUBKijRxlC1ENHp07U4IAXEAyp8T/kS/Z/pBWaLElJ1T0HNVT1y8c1Hq0IiIdIZJIZER+r//A/r2FZeVGzoUqOn51i9dAjZvFvcnTarZa0vF2doZv478FQvDFqK+eX3su7IPbRa3wZyDc/CwxEDXHiQi0gCTQiIjZGIC/Pgj0KSJOOhkwoSa618oCMBrrwHFxeLciQEBNXNdQyCTyTCpwySkTExBz2Y9cb/4PqL3RCPg+wDsubRH6vCIiKqFSSGRkWrYEFi/XlwCb+1aYGkNzZqyejWwe7c4b2LZHIV1TXOH5tgduRurBq5Cw/oNkXozFSE/hmBg7ED8desvqcMjItIKk0IiI/b88+IoZAB4803gn9md9Ob6deCtt8T9GTOAZ57R7/UMmUwmwxj/MTj3+jm80eENmMpMsfXcVrRe1BqvbnsVV3OuPr0SIiIDwqSQyMi98w7Qvz+gVALDhgG5ufq71uTJwN27YpPx1Kn6u44xcazniK/DvkbKxBQM8BmAEqEEP5z8Ac988wwm/DoBaXfTpA6RiKhKmBQSGTkTE2DVKsDdXVyH+D//0U//wl9+EZurTUyAH34AzM11fw1j9qzTs9g6YisOjj2IHp49UFRShO+Pf49nvnkGIzeNRPI1A1qwmoioAkwKiWqBBg3EhM3MTPz53Xe6rT83V5ygGgDefhto10639dcmzzd9Hr9H/Y79L+9HqFcoSoQSxJ6ORful7fH88uex5tQaPCh+IHWYRETlMCkkqiWCg4E5c8T9KVOAEyd0V/cHHwAZGUDz5mJfQnq6Lh5dsPOlnTjxnxN4ye8lmJuY43D6YbwU9xKafNkEk3dMxsmsk1yTnYgMBlc0qQBnRCdjJQjAwIHAtm1iAnfiBGBnV706Dx0CunQR6969+9Eye6SZ7Pxs/HDiByw5vgTpuemq475OvhjZeiSGtRqGFg1aSBghkfHj93f1MCmsAP9RkTG7excIDASuXAGGDAF+/hmQybSrS6kU6zp7Fhg7Fli+XLex1kUlpSXYdXEXVihWYNu5bVCWKFXPtW7UGgN9BiLcJxxBrkFcRo9IQ/z+rh4mhRXgPyoydn/8IS6H9/Ah8M03wOuva1fP9OnAxx8Dzs5Aairg6KjbOOu6nAc52Hx2M9afWY89aXtQXFqses6pvhNCvULRu3lv9GreC262/Cwiehp+f1cPk8IK8B8V1QYLFoh9C83NgcOHgaAgzc4/fRpo21ZMLH/+WVxOj/Tn7v27+O38b9h6bit2XdyFXKX63EJeDl7o6tEVnZt2Rif3TmjRoAXvJBL9C7+/q4dJYQX4j4pqA0EABg8G4uKAZs3E/oX29lU7t6BAXMLuyBFgwABgyxbtm6BJcw9LHuJw+mHsurgLu9N2I/laMkqFUrUy9pb2CHINQpBLENq6tEVA4wB4OXoxUaQ6jd/f1cOksAL8R0W1xb174t2+tDTgxReBTZsqT+6KioCdO4F164CtW4HCQsDGRmw25n8DaeU8yMGh9EM4cOUADqUfwrFrxyqc1qa+eX20cmqFVo1awbehL1o2bAmfhj5oZt8M5qacWJJqP35/Vw+TwgrwHxXVJsnJ4nJ4RUXA/PniqiRlSkqAffvERHDTJnGQSpnmzcUm6BdeqPGQ6SkeljxEyo0UHMs8huNZx3Ey+yRO3zhd6fyHpjJTNLVrCm9HbzSzbwZPe0942HugqV1TuNu6w8XGBXJTeQ2/CiLd4/d39TAprAD/UVFts3Ah8MYbYv/CAwfEY+vWiX0Fs7IelXNxAYYPB0aOBNq3Z5OxMSkuLcaFOxdw+sZpnLlxBmdvncW52+fw9+2/Ufiw8KnnN7JqBFcbV7hYu6CxdWM4WzmjkVUjNLJqhIb1G6Jh/YZoUL8BGtRrAGu5NWT8x0EGiN/f1cOksAL8R0W1jSCI6yJv3CguU1f6WPc0Bwdx6pqRI4GuXQFTU+niJN0TBAFZ+Vm4cOcCLt65iLR7abiScwVX7l1Bem46MnIzUFRSpFGdZiZmcLB0gEM9B9hZ2MHe0h4vtHgBb3Z8U0+vgqhq+P1dPWZSB0BE+ieTiesVnzwJXLwIWFkBERFiIhgaCsjZclhryWQyuNq4wtXGFV09upZ7XhAE3Cq8hcy8TFzLu4asvCxk52fjesF13Ci4gZuFN3Gr8BZuFd7C7cLbUJYoUVxajJuFN3Gz8KaqHm9H75p8WUSkB0wKieoIOztxdZKTJ8UVSqyspI6IDIFMJoOTlROcrJwQ0DjgiWUFQUDhw0LcfXAXd+/fxd0Hd3HvwT3kKnPh5eBVMwETkd4wKSSqQ5ydgb59pY6CjJVMJoOV3ApWcitOpk1UC3FCKyIiIiJiUkhERERETAqJiIiICEwKiYiIiAhMComIiIgITAqJiIiojlq8eDH8/Pxga2sLW1tbBAcHY8eOHU88Z9++fWjXrh0sLS3RvHlzfPfdd2rPP3z4EB9//DG8vLxgaWkJf39/xMfHq5WZMWMGZDKZ2ta4cWOdvz5NMSkkIiKiOsnNzQ1z5sxBcnIykpOT0bNnT0RERODMmTMVlk9LS0O/fv3QpUsXnDx5Eh988AHefPNNbNq0SVVm2rRp+P777/HNN98gNTUVEyZMwIsvvoiTJ0+q1dWqVStkZWWptpSUFL2+1qrgMncV4DI5RERExkcX39+Ojo6YN28exo8fX+65//u//8O2bdtw9uxZ1bEJEybgzz//RFJSEgDA1dUVMTExmDRpkqrMwIEDYW1tjZ9++gmAeKdwy5YtUCgUWsWoL7xTSERERLVKXl4ecnNzVZtSqXzqOSUlJYiNjUVBQQGCg4MrLJOUlITQ0FC1Y3369EFycjIePnwIAFAqlbC0tFQrU69ePRw8eFDt2Pnz5+Hq6opmzZphxIgRuHTpkiYvUS+YFBIREVGt4uvrCzs7O9U2e/bsSsumpKTA2toaFhYWmDBhAuLi4uDr61th2ezsbDg7O6sdc3Z2RnFxMW7dugVATBK//PJLnD9/HqWlpUhISMDWrVuRlZWlOqdjx45YvXo1du7ciaVLlyI7OxudOnXC7du3dfDqtcdl7oiIiKhWSU1NRZMmTVSPLSwsKi3r4+MDhUKBe/fuYdOmTYiKisK+ffsqTQxlMpna47JeeGXHFyxYgFdffRUtW7aETCaDl5cXxo4dixUrVqjOCQsLU+23adMGwcHB8PLywqpVqzB16lTNX7CO8E4hERER1So2NjaqEcW2trZPTArlcjm8vb0RFBSE2bNnw9/fHwsWLKiwbOPGjZGdna127MaNGzAzM0ODBg0AAE5OTtiyZQsKCgpw5coV/PXXX7C2tkazZs0qjcHKygpt2rTB+fPntXi1usOkkIiIiOgfgiBU2gcxODgYCQkJasd27dqFoKAgmJubqx23tLREkyZNUFxcjE2bNiEiIqLSayqVSpw9exYuLi7VfwHVwObjCpSWlgKAWvs/ERERGbay7+2y7/Gn+eCDDxAWFgZ3d3fk5eUhNjYWiYmJqnkFo6OjkZmZidWrVwMQRxovXLgQU6dOxauvvoqkpCQsW7YM69atU9V59OhRZGZmIiAgAJmZmZgxYwZKS0vx3nvvqcq88847CA8PR9OmTXHjxg3MnDkTubm5iIqK0tWvQjsClXPw4EEBADdu3Lhx48bNCLeDBw9W6ft+3LhxgoeHhyCXywUnJyehV69ewq5du1TPR0VFCd26dVM7JzExUQgMDBTkcrng6ekpLF68uNzzzz77rGBhYSE0aNBAiIyMFDIzM9XKDB8+XHBxcRHMzc0FV1dXYdCgQcKZM2e0S1p0iPMUVuDOnTto0KABTp8+DTs7O6nDUdO9e3ckJiYaVJ2anl/V8k8r96TnNXkuLy8Pvr6+SE1NhY2NzVPjqkl14f0u+/03b94c+/bt06oevt/6q5P/v/WH73fVntfkuZycHLRu3Rq3b9+Go6PjU+MidWw+roCZmfhrcXd3h62trcTRqJPL5TqfULu6dWp6flXLP63ck57X5Lnc3FwAQJMmTfh+6+H8p5Uv+/2bm5vz/a4D73dVy/H9lqZOY3+/y97jsu9x0gwHmhiZx2dIN5Q6NT2/quWfVu5Jz2v7nKGpS+/3q6++qnU9fL/1Vyf/f+sP3++qPV9b3m9jwObjCuTm5sLOzg45OTkG95cl6R7fb2nV9O+f73fdwve7buH7XT28U1gBCwsLTJ8+/YnzGlHtwfdbWjX9++f7Xbfw/a5b+H5XD+8UEhERERHvFBIRERERk0IiIiIiApNCIiIiIgKTQiIiIiICk0IiIiIiApNCnXjxxRfh4OCAIUOGSB0K6cGvv/4KHx8fPPPMM/jhhx+kDqfW+Pbbb+Hp6QkzMzO8++67Uoejwv/PdUd6ejq6d+8OX19f+Pn5YcOGDVKHRHqUl5eH9u3bIyAgAG3atMHSpUulDsngcEoaHdi7dy/y8/OxatUqbNy4UepwSIeKi4vh6+uLvXv3wtbWFm3btsXRo0e5pmY1nT59GoGBgdiyZQvatm0LOzs71K9fX+qwAPD/c12SlZWF69evIyAgADdu3EDbtm1x7tw5WFlZSR0a6UFJSQmUSiXq16+PwsJCtG7dGseOHUODBg2kDs1g8E6hDvTo0cPgFlon3fjjjz/QqlUrNGnSBDY2NujXrx927twpdVhGb9u2bWjXrh369+8PFxcXg0kIAf5/rktcXFwQEBAAAGjUqBEcHR1x584daYMivTE1NVV91jx48AAlJSXgfTF1tT4p3L9/P8LDw+Hq6gqZTIYtW7aUK7No0SI0a9YMlpaWaNeuHQ4cOFDzgZJeVPf9v3btGpo0aaJ67ObmhszMzJoIvdby8vJCTEwMjh49CplMhsjISJ3Vzf/vdYsu3+/k5GSUlpbC3d1dz1GTtnTxft+7dw/+/v5wc3PDe++9h4YNG9ZQ9Mah1ieFBQUF8Pf3x8KFCyt8fv369ZgyZQpiYmJw8uRJdOnSBWFhYbh69aqqTLt27dC6dety27Vr12rqZZCWqvv+V/RXpEwm02vMtV1SUhKaN2+OefPmISsrC4sWLdJZ3br4/07GQ1fv9+3btzFmzBgsWbKkJsImLeni/ba3t8eff/6JtLQ0rF27FtevX6+p8I2DUIcAEOLi4tSOdejQQZgwYYLasZYtWwrvv/++RnXv3btXGDx4cHVDJD3S5v0/dOiQMHDgQNVzb775prBmzRq9x1qbFRQUCCYmJkJSUpJer1Od/+/8/2x8tH2/Hzx4IHTp0kVYvXp1TYRJOqKL7/MJEyYIP//8s75CNEq1/k7hkxQVFeH48eMIDQ1VOx4aGorDhw9LFBXVlKq8/x06dMDp06eRmZmJvLw8bN++HX369JEi3Frj1KlTAIA2bdrU6HX5/71uqcr7LQgCXn75ZfTs2VOn3Rio5lXl/b5+/Tpyc3MBALm5udi/fz98fHxqPFZDZiZ1AFK6desWSkpK4OzsrHbc2dkZ2dnZVa6nT58+OHHiBAoKCuDm5oa4uDi0b99e1+GSjlXl/TczM8MXX3yBHj16oLS0FO+99x5HqlWTQqGAt7e3aoTnlStXMGnSJGRkZODhw4fYtWuXWj9OXanq/3f+f64dqvJ+Hzp0COvXr4efn5+qf9qPP/5Y43+wUPVV5f3OyMjA+PHjIQgCBEHA66+/Dj8/PynCNVh1Oiks8+8+YoIgaNRvjKNRjdvT3v8BAwZgwIABNR1WraVQKODv7w9A/Ou+f//+WLRoEbp27Yo7d+7A1tZWr9d/2vvN/8+1y5Pe786dO6O0tFSKsEhPnvR+t2vXDgqFQoKojEedbj5u2LAhTE1Ny90VvHHjRrm/Nqj24fsvDYVCoZoGJC4uDs899xy6du0KAHB0dISZmX7+VuX7Xbfw/a5b+H7rRp1OCuVyOdq1a4eEhAS14wkJCejUqZNEUVFN4ftf80pLS5GSkqK6U5iSklJjTbN8v+sWvt91C99v3aj1zcf5+fm4cOGC6nFaWhoUCgUcHR3RtGlTTJ06FZGRkQgKCkJwcDCWLFmCq1evYsKECRJGTbrC99+wmJiYoKCgQPXY2dkZp0+fBiCuNpCTk1Ot1WL4ftctfL/rFr7fNUC6gc81Y+/evQKAcltUVJSqzLfffit4eHgIcrlcaNu2rbBv3z7pAiad4vtv2HJzc4WwsDChVatWQkBAgHD06NFq1cf3u27h+1238P3WP659TERERER1u08hEREREYmYFBIRERERk0IiIiIiYlJIRERERGBSSERERERgUkhEREREYFJIRERERGBSSERERERgUkhENUwQBPznP/+Bo6MjZDIZFAqF1CEREREArmhCRDVqx44diIiIQGJiIpo3b46GDRvCzKzWL8NORGTw+ElMRDXq4sWLcHFxQadOnSp8vqioCHK5vIajIiIiNh8TUY15+eWX8cYbb+Dq1auQyWTw9PRE9+7d8frrr2Pq1Klo2LAhevfuDQBITU1Fv379YG1tDWdnZ0RGRuLWrVuqugoKCjBmzBhYW1vDxcUFX3zxBbp3744pU6aoyshkMmzZskUtBnt7e6xcuVL1ODMzE8OHD4eDgwMaNGiAiIgIXL58WS3mgQMH4vPPP4eLiwsaNGiASZMm4eHDh6oySqUS7733Htzd3WFhYYFnnnkGy5YtgyAI8Pb2xueff64Ww+nTp2FiYoKLFy9W/5dKRKQjTAqJqMYsWLAAH3/8Mdzc3JCVlYVjx44BAFatWgUzMzMcOnQI33//PbKystCtWzcEBAQgOTkZ8fHxuH79OoYNG6aq691338XevXsRFxeHXbt2ITExEcePH9consLCQvTo0QPW1tbYv38/Dh48CGtra/Tt2xdFRUWqcnv37sXFixexd+9erFq1CitXrlRLLMeMGYPY2Fh8/fXXOHv2LL777jtYW1tDJpNh3LhxWLFihdp1ly9fji5dusDLy0uL3yIRkZ4IREQ16KuvvhI8PDxUj7t16yYEBASolfnwww+F0NBQtWPp6ekCAOHcuXNCXl6eIJfLhdjYWNXzt2/fFurVqydMnjxZdQyAEBcXp1aPnZ2dsGLFCkEQBGHZsmWCj4+PUFpaqnpeqVQK9erVE3bu3CkIgiBERUUJHh4eQnFxsarM0KFDheHDhwuCIAjnzp0TAAgJCQkVvt5r164JpqamwtGjRwVBEISioiLByclJWLly5RN+S0RENY99ColIckFBQWqPjx8/jr1798La2rpc2YsXL+L+/fsoKipCcHCw6rijoyN8fHw0uu7x48dx4cIF2NjYqB1/8OCBWtNuq1atYGpqqnrs4uKClJQUAIBCoYCpqSm6detW4TVcXFzQv39/LF++HB06dMCvv/6KBw8eYOjQoRrFSkSkb0wKiUhyVlZWao9LS0sRHh6Ozz77rFxZFxcXnD9/vkr1ymQyCP+aYOHxvoClpaVo164d1qxZU+5cJycn1b65uXm5ektLSwEA9erVe2ocr7zyCiIjI/HVV19hxYoVGD58OOrXr1+l10BEVFOYFBKRwWnbti02bdoET0/PCqer8fb2hrm5OY4cOYKmTZsCAO7evYu///5b7Y6dk5MTsrKyVI/Pnz+PwsJCteusX78ejRo1gq2trVaxtmnTBqWlpdi3bx9CQkIqLNOvXz9YWVlh8eLF2LFjB/bv36/VtYiI9IkDTYjI4EyaNAl37tzByJEj8ccff+DSpUvYtWsXxo0bh5KSElhbW2P8+PF49913sWfPHpw+fRovv/wyTEzUP9J69uyJhQsX4sSJE0hOTsaECRPU7vqNHj0aDRs2REREBA4cOIC0tDTs27cPkydPRkZGRpVi9fT0RFRUFMaNG4ctW7YgLS0NiYmJ+Pnnn1VlTE1N8fLLLyM6Ohre3t5qzd5ERIaCSSERGRxXV1ccOnQIJSUl6NOnD1q3bo3JkyfDzs5OlfjNmzcPXbt2xYABAxASEoLOnTujXbt2avV88cUXcHd3R9euXTFq1Ci88847as229evXx/79+9G0aVMMGjQIzz77LMaNG4f79+9rdOdw8eLFGDJkCP773/+iZcuWePXVV1FQUKBWZvz48SgqKsK4ceOq8ZshItIfrmhCRLVG9+7dERAQgPnz50sdSjmHDh1C9+7dkZGRAWdnZ6nDISIqh30KiYj0SKlUIj09HR9++CGGDRvGhJCIDBabj4mI9GjdunXw8fFBTk4O5s6dK3U4RESVYvMxEREREfFOIRERERExKSQiIiIiMCkkIiIiIjApJCIiIiIwKSQiIiIiMCkkIiIiIjApJCIiIiIwKSQiIiIiMCkkIiIiIgD/Dx8SgFzH/nEkAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig3, ax5 = plt.subplots();\n",
    "ax6 = ax5.twinx();\n",
    "ax5.semilogx(f1[nonzero_f], c1[nonzero_f], 'g');\n",
    "ax6.semilogx(f1[nonzero_f], np.abs(d1[nonzero_f])/f1[nonzero_f], 'b');   # frequency may be zero so decay instead of damping ratio\n",
    "ax5.set_xlabel('frequency');\n",
    "#ax5.set_ylim([0, 1])\n",
    "ax5.set_xticks(list(ax5.get_xticks()) + [f_characteristic_num], list(ax5.get_xticklabels()) + ['$f_c$'])   # with extra tick\n",
    "ax5.set_ylabel('phase velocity', color='g');\n",
    "ax6.set_ylabel('decay constant', color='b');   \n",
    "#ax6.set_ylim([0, 10])\n",
    "tikzplotlib.save(\"p_wave_slow_eigenvalue.tex\", axis_height = '\\\\figH', axis_width = '\\\\figW')   \n",
    "\n",
    "fig4, ax7 = plt.subplots();\n",
    "ax8 = ax7.twinx();\n",
    "ax7.semilogx(f1[nonzero_f], AR1[nonzero_f], 'g');\n",
    "ax8.semilogx(f1[nonzero_f], phi1[nonzero_f], 'b');\n",
    "ax7.set_xlabel('frequency');\n",
    "#ax7.set_ylim([0,2.5])\n",
    "ax7.set_xticks(list(ax7.get_xticks()) + [f_characteristic_num], list(ax7.get_xticklabels()) + ['$f_c$'])   # with extra tick\n",
    "ax7.set_ylabel('amplitude ratio', color='g');\n",
    "ax8.set_ylabel('phase angle [RAD]', color='b');\n",
    "#ax8.set_ylim([-1.2,0])\n",
    "tikzplotlib.save(\"p_wave_slow_eigenvector.tex\", axis_height = '\\\\figH', axis_width = '\\\\figW') "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d0c5b13",
   "metadata": {},
   "source": [
    "Characteristics of fast P-waves"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "c987bd6b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "nondimensional c_un_P = 3.82730207927597\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"nondimensional c_un_P = {}\".format(c_un_P_num/c_el_P_num))\n",
    "\n",
    "fig5, ax9 = plt.subplots();\n",
    "ax10 = ax9.twinx();\n",
    "ax9.semilogx(f2, c2, 'g');\n",
    "ax10.semilogx(f2, np.abs(d2)/f2, 'b');\n",
    "#ax9.set_ylim([0,2])\n",
    "ax9.set_xlabel('frequency');\n",
    "ax9.set_xticks(list(ax9.get_xticks()) + [f_characteristic_num], list(ax9.get_xticklabels()) + ['$f_c$'])   # with extra tick\n",
    "ax9.set_ylabel('phase velocity', color='g');\n",
    "ax10.set_ylabel('decay constant', color='b');\n",
    "#ax10.set_ylim([0,1.2e-5])\n",
    "tikzplotlib.save(\"p_wave_fast_eigenvalue.tex\", axis_height = '\\\\figH', axis_width = '\\\\figW')   \n",
    "\n",
    "fig6, ax11 = plt.subplots();\n",
    "ax12 = ax11.twinx();\n",
    "#ax11.set_ylim([0,1])\n",
    "ax11.semilogx(f2, AR2, 'g');\n",
    "ax12.semilogx(f2, phi2, 'b');\n",
    "ax11.set_xlabel('frequency');\n",
    "#ax12.set_ylim([-1.0,0])\n",
    "ax11.set_xticks(list(ax11.get_xticks()) + [f_characteristic_num], list(ax11.get_xticklabels()) + ['$f_c$'])   # with extra tick\n",
    "ax11.set_ylabel('amplitude ratio', color='g');\n",
    "ax12.set_ylabel('phase angle [RAD]', color='b');\n",
    "tikzplotlib.save(\"p_wave_fast_eigenvector.tex\", axis_height = '\\\\figH', axis_width = '\\\\figW') "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79c44a23",
   "metadata": {},
   "source": [
    "Numbers for TikZ-plots (complex amplitudes and time history)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "11a55570",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.9898895956380023\n",
      "5.9753425815780306\n",
      "-0.5706367402874353\n",
      "-0.02584887298505585\n",
      "--\n",
      "17.341531239807598\n",
      "0.1511413067811696\n",
      "1.9655891777113743\n",
      "0.48258074380282207\n"
     ]
    }
   ],
   "source": [
    "k_num = index_first_nonzero_f   # first mode with slow P-wave\n",
    "print(k_num)\n",
    "print('--')\n",
    "print(f1[k_num])\n",
    "print(-d1[k_num]/f1[k_num])   # delta, with time axis scaled to period\n",
    "print((1/AR1[k_num])*np.cos(-phi1[k_num])) # u_solid, real part, with u_fluid = 1\n",
    "print((1/AR1[k_num])*np.sin(-phi1[k_num])) # u_solid, imaginary part, with u_fluid = 1\n",
    "print('--')\n",
    "print(f2[k_num])\n",
    "print(-d2[k_num]/f2[k_num])   # delta, with time axis scaled to period\n",
    "print(1/AR2[k_num]*np.cos(-phi2[k_num])) # u_solid, real part, with u_fluid = 1\n",
    "print(1/AR2[k_num]*np.sin(-phi2[k_num])) # u_solid, imaginary part, with u_fluid = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "924d9256",
   "metadata": {},
   "source": [
    "## References\n",
    "- \\[Biot1956\\]   M.A. Biot; _Theory of Propagation of Elastic Waves in a Fluid-saturated Porous Solid -- I. Low-frequency Range_; Journal of the Acoustical Society of America 28(2); 1956.\n",
    "- \\[Verruijt2010\\]   A. Verruijt; _An Introduction to Soil Dynamics_; Springer Dordrecht Heidelberg London New York; 2010.\n",
    "- \\[Hagedorn2012\\] P. Hagedorn, D. Hochlehnert; _Technische Schwingungslehre: Schwingungen linearer diskreter mechanischer Systeme_; Europa-Lehrmittel, 2021."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.18"
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 },
 "nbformat": 4,
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