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    "# Python toolkit for simulation of the Josephson junction dynamics under the influence of external electromagnetic\n",
    "\n",
    "In this notebook the toolkit for modeling of the Josephson junction dynamics under the influence of external radiation is presented:\n",
    "* algorithm for calculation of the Josephson junctions current-voltage characteristic under the influence of external radiation;\n",
    "* algorithm for calculation of the amplitude dependence of Shapiro step width;\n",
    "* algorithm for calculation of the amplitude dependence of Shapiro step width in parallel regime using the Joblib library;\n",
    "* results of analysis of the parallel computing efficiency.\n",
    "\n",
    "The study is based on papers:\n",
    "1. _Josephson B.D._ __Possible new effects in superconductive tunnelling__ // Physics Letters - 1962. - V. 1, no. 7. - P. 251-253.\n",
    "2. _Shapiro S._ __Josephson currents in superconducting tunneling: The effect of microwavesand other observations__ // Phys. Rev. Lett. - 1963. - V. 11, no. 2. - P.80-82.\n",
    "3. _McCumber D.E._ __Effect of ac Impedance on dc Voltage-Current Characteristics of Superconductor Weak-Link Junctions__ // Journal of Applied Physics - 1968. - V. 39, no. 7. - P.3113-3118."
   ]
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    "## 1. Model description\n",
    "\n",
    "__Josephson effect and Josephson junction__\n",
    "\n",
    "The coupling of two superconducting layers through a thin layer of non-superconducting barrier forms a structure called a Josephson junction (in honor of the British scientist _Brian Josephson_). When an electric current is passed through a Josephson junction (JJ), depending on the current value, a stationary and non-stationary Josephson effect is observed.\n",
    "\n",
    "_Stationary Josephson effect._ When a current passes below the critical value $(I<I_{c})$, there is no voltage in the junction and a superconducting current flows through the junction. This current is proportional to the sine of the phase difference of the order parameters of the superconductor layers:\n",
    "\n",
    "$\n",
    "\\begin{eqnarray}\n",
    "I_{s}=I_{c}\\sin\\varphi.\n",
    "\\label{eq1}\n",
    "\\tag{1}\n",
    "\\end{eqnarray}\n",
    "$\n",
    "\n",
    "_Non-stationary Josephson effect._ When the current increases above the critical value $(I>I_{c})$, an AC voltage appears in the JJ, which is proportional to the time derivative of the phase difference\n",
    "\n",
    "$\n",
    "\\begin{eqnarray}\n",
    "V=\\frac{\\hbar}{2e}\\frac{d\\varphi}{dt}.\n",
    "\\label{eq2}\n",
    "\\tag{2}\n",
    "\\end{eqnarray}\n",
    "$\n",
    "\n",
    "__System of equations for description of the JJ's dynamics:__\n",
    "\n",
    "The dynamics of the JJ can be described within the framework of the RCSJ model (Resitively Capasitevily Shunted Junction) [3]. Within this model, the JJ is modeled as a parallel connection of a capacitor, resistor and superconductor:\n",
    "\n",
    "![RCSJ-model](rcsj.jpg)\n",
    "\n",
    "A displacement current flows through the capacitor $\\displaystyle I_{disp}=C\\frac{dV}{dt}$, through the resistor - quasiparticle current $\\displaystyle I_{qp}=\\frac{V}{R}$ and through the superconductor Josephson (superconducting) current $I_{s}=I_{c}\\sin\\varphi$.\n",
    "\n",
    "The total current passing through the system is equal to the sum of the above mentioned currents\n",
    "\n",
    "$\n",
    "\\begin{eqnarray}\n",
    "I=C\\frac{dV}{dt}+\\frac{V}{R}+I_{c}\\sin\\varphi.\n",
    "\\label{eq3}\n",
    "\\tag{3}\n",
    "\\end{eqnarray}\n",
    "$\n",
    "\n",
    "Using (2) and (3) in normalized quantities, we can write a coupled system of differential equations with respect to $V$ and $\\varphi$\n",
    "\n",
    "$\n",
    "\\begin{eqnarray}\n",
    "\\begin{cases}\n",
    "    \\displaystyle \\frac{dV}{dt} = I-\\beta V-\\sin\\varphi,\\\\\n",
    "    \\displaystyle \\frac{d\\varphi}{dt}=V,\n",
    "\\end{cases}\n",
    "\\label{eq4}\n",
    "\\tag{4}\n",
    "\\end{eqnarray}\n",
    "$\n",
    "\n",
    "where $\\displaystyle \\beta=\\frac{\\hbar \\omega_{p}}{2 e I_{c}R}$ - dissipation parameter, $\\displaystyle\\omega_{p}=\\sqrt{\\frac{2 e I_{c}}{\\hbar C}}$ - plasma frequency. In the system of equations (\\ref{eq4}) time is normalized to $\\omega_{p}$, voltage is normalized to $\\displaystyle V_{0}=\\frac{\\hbar \\omega_{p}}{2 e}$ and the current is normalized to $I_{c}$.\n",
    "\n",
    "__The influence of external radiation on the JJ's dynamics and Shapiro step__\n",
    "\n",
    "Under the influence of external radiation, in case of multiple Josephson frequency to the external radiation frequency a time-independent superconducting current arises as a result of frequency locking of Josephson oscillation by the external radiation. This superconducting current appears on the current-voltage characteristic (I-V characteristic) as a constant voltage step, called the Shapiro step [2]. The width of the Shapiro step depends on the frequency and amplitude of the external radiation.\n",
    "\n",
    "In order to modeling of this phenomena, in the system of equations of the RCSJ model should be taken into account additional AC current $I_{R}$, created by the external radiation with amplitude $A$ and frequency $\\omega$, i.e. $I_{R}=A\\sin(\\omega t)$.\n",
    "\n",
    "The calculation algorithm of current voltage characteristic is based on solution of system of equations at a fixed current value with a choosen step. We should note that during the solution of the system of equations for each current value, the time changes from zero to $T_{\\max}$. In this case, if the equations depend explicitly on time, then it becomes necessary to realise continuously changing of time for all current intervals. \n",
    "\n",
    "  \n",
    "In order to realise it we need to count the number of current steps and multiply by $T_{\\max}$ and add reults to the time value. This complexity can be leveled by adding to the system of equations an additional equation like $du/dt=\\omega$. Then it is only necessary to transfer the initial condition to the next current step, which simplifies the calculation process.\n",
    "\n",
    "Thus, the final form of the system of equations takes the form:\n",
    "\n",
    "$\n",
    "\\begin{eqnarray}\n",
    "\\begin{cases}\n",
    "    \\displaystyle \\frac{dV}{dt} = I+A\\sin(u)-\\beta V-\\sin\\varphi,\\\\\n",
    "    \\displaystyle \\frac{d\\varphi}{dt}=V,\\\\\n",
    "    \\displaystyle \\frac{du}{dt}=\\omega.\n",
    "\\end{cases}\n",
    "\\label{eq5}\n",
    "\\tag{5}\n",
    "\\end{eqnarray}\n",
    "$ \n",
    "\n",
    "Model parameters:\n",
    "* $\\beta$ - dissipation parameter;\n",
    "* $A$ - external radiation amplitude;\n",
    "* $V$ - voltage;\n",
    "* $I$ - external current;\n",
    "* $\\omega$ - radiation frequency;\n",
    "* $\\varphi$ - phase difference.\n",
    "\n",
    "__Formulation of the problem:__\n",
    "\n",
    "Calculate the current-voltage characteristic of a Josephson junction under the influence of external radiation and plot it."
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    "## 2. Calculation of current-voltage characteristics\n",
    "\n",
    "__Algorithm for calculation of the current-voltage characteristic:__\n",
    "\n",
    "1. We set the values of the model parameters, numerical calculation parameters and initial conditions.\n",
    "\n",
    "2. We numerically solve the Cauchy problem for a system of ordinary differential equations (5), (for example, by the fourth order Runge-Kutta method) for fixed value of current $I$, and find the time dependence of the phase difference $\\varphi(t)$ and voltage $V(t)$.\n",
    "\n",
    "3. We average the resulting $V(t)$ by time:\n",
    "\n",
    "$\n",
    "\\displaystyle <V>=\\frac{1}{T_{\\max}-T_{\\min}}\\int\\limits_{T_{\\min}}^{T_{\\max}}V(t)dt\n",
    "$\n",
    "\n",
    "As a result, we obtain the voltage value for a given value of current, i.e. we obtain one point on the current-voltage characteristic.\n",
    "\n",
    "4. We change the current value to $\\delta I$ and repeat step 2, using $\\varphi(T_{\\max})$ and $V(T_{\\max})$ as the initial condition from the previos value of current and for the resulting $V(t)$ perform step 3 to find the average voltage value.\n",
    "\n",
    "5. We carry out calculations until $I_{\\max}$.\n",
    "\n",
    "6. We carry out calculations by decreasing the current value $I$ from $I_{\\max}$ to zero.\n",
    "\n",
    "Now, let's move directly to the implementation of this algorithm."
   ]
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   "metadata": {},
   "source": [
    "__Importing libraries__"
   ]
  },
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   "cell_type": "code",
   "execution_count": 17,
   "id": "e08f8354-927f-4843-af46-e6814bab9083",
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import solve_ivp\n",
    "from functools import partial\n",
    "from scipy.integrate import odeint\n",
    "import time\n",
    "\n",
    "import seaborn as sns\n",
    "sns.set()\n",
    "sns.set(style=\"whitegrid\")\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b88f2ef-7fe2-4780-a431-98ad043abfa7",
   "metadata": {},
   "source": [
    "__Determination of the right sides of the equations__"
   ]
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   "cell_type": "code",
   "execution_count": 18,
   "id": "7ddaac53",
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   "source": [
    "# Function for determination of right side of equation\n",
    "def shortjj(t, S, beta, Iext, A, omega):\n",
    "    ''' Defines the right-hand sides of an ODE system (5),\n",
    "        beta, A, omega - model parameters,\n",
    "        S=[phi,V,u] - required solution '''\n",
    "    ph = S[0]\n",
    "    V = S[1]\n",
    "    u = S[2]\n",
    "    dph = V\n",
    "    dV = Iext - np.sin(ph) - beta * V + A * np.sin(u)\n",
    "    du = omega\n",
    "    dS = [dph, dV, du]\n",
    "    return dS"
   ]
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   "cell_type": "markdown",
   "id": "096f6fcc-dc25-4784-978f-a6a82c300c39",
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   "source": [
    "### Calculation of the time dependence of voltage\n",
    "We define a function for calculation of the time dependence of voltage and phase at a fixed value of the external current, which, using the initial conditions, values of model parameters and numerical calculations, returns the corresponding time dependences."
   ]
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   "cell_type": "markdown",
   "id": "9e202fa0-c8f6-47dc-aa7b-d5bbfe47bcb5",
   "metadata": {},
   "source": [
    "__We define a function for the numerical solution of the Cauchy problem__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "4da3b9d8-675d-4979-96d9-9055ed2ed7ab",
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   "source": [
    "def jjsolution(s0, Iext, beta, A, omega, nt, t0, deltat):\n",
    "    ''' Numerical solution of the Cauchy problem for an ODE system (5),\n",
    "        beta, A, omega - model parameters,\n",
    "        nt - number of points in time at which the solution is located,\n",
    "        t0 - initial time value,\n",
    "        deltat - time step,\n",
    "        Iext - external current value,\n",
    "        s0=[phi0, V0, u0] - initial conditions,\n",
    "        output: [phtime, Vtime, utime] - arrays of calculated time dependencies for phase, voltage and the introduced auxiliary function u '''\n",
    "    f = partial(shortjj, beta=beta, Iext=Iext, A=A, omega=omega)\n",
    "    t_e = np.linspace(t0, nt*deltat, nt)\n",
    "    sol_1 = solve_ivp(f, [t0, nt*deltat], s0, t_eval=t_e, method='RK45',\n",
    "                      rtol=1e-8, atol=1e-8)\n",
    "    phtime = sol_1.y[0]\n",
    "    Vtime = sol_1.y[1]\n",
    "    utime = sol_1.y[2]\n",
    "    return [phtime, Vtime, utime]"
   ]
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   "source": [
    "In order to check the correctness of the implemented computational scheme, we will find the time dependences of voltage in two modes:\n",
    "1. in a state with zero average voltage,\n",
    "2. in finite average voltage state.\n",
    "\n",
    "According to the physics of the Josephson junction, as the result we should get in the first case a damped voltage, and in the second case voltage oscillation with a finite average value.\n",
    "\n",
    "To do this, it is necessary to select the current values at which the implementation of such solutions is possible (For example $I=0.4$) and we need to solve a system of equations with different initial conditions for voltage (For example, $V=0$ for first case and $V=3$ for second one). For simplicity, we consider the case without external radiation, i.e.. $A=0$."
   ]
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   "metadata": {},
   "source": [
    "__Model parameters__"
   ]
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   "cell_type": "code",
   "execution_count": 20,
   "id": "7ca0d2b0",
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   "source": [
    "beta = 0.2  # Dissipation parameter\n",
    "A = 0  # External radiation amplitude\n",
    "omega = 2 # External radiation frequency"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9740da4-9056-474a-9dd8-d5e8e0c96047",
   "metadata": {},
   "source": [
    "__Numerical parameters__"
   ]
  },
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   "cell_type": "code",
   "execution_count": 21,
   "id": "f1ca9a8c-738b-4b40-a20a-439b9a0fcf6d",
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   "source": [
    "Tmax = 100 # Maximum time value\n",
    "deltat = 0.05  # time step\n",
    "t0 = 0\n",
    "nt = int(Tmax/deltat)"
   ]
  },
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   "cell_type": "markdown",
   "id": "3863d4ad-03a8-4dac-8e35-f8144238cc1a",
   "metadata": {},
   "source": [
    "#### 1. Solution for zero average voltage state"
   ]
  },
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   "cell_type": "code",
   "execution_count": 22,
   "id": "a310933f-a031-4149-b6a1-6df9b2e1fd1c",
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   "source": [
    "Iext = 0.4  # External current value\n",
    "V0 = 0  # Voltage value at the initial time\n",
    "\n",
    "time_array = np.linspace(0, Tmax, num=nt)\n",
    "s0 = np.array([0, V0, 0])\n",
    "res = jjsolution(s0, Iext, beta, A, omega, nt, t0, deltat)\n",
    "Vtime = res[1]"
   ]
  },
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   "cell_type": "markdown",
   "id": "2077cb26-2444-412d-81e0-ef2d0be7afa7",
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   "source": [
    "We draw a time dependence $V(t)$"
   ]
  },
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   "execution_count": 24,
   "id": "a3d90388-5dd3-4d7b-9efe-f78c2cf46135",
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    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(8, 6))\n",
    "plt.plot(time_array, Vtime, label='Time dependence', linewidth=3.0)\n",
    "plt.xlabel('Time', size=12)\n",
    "plt.ylabel('V', size=12)\n",
    "plt.legend(loc='upper right')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6f0d378-f054-4243-966c-39d38508be4d",
   "metadata": {},
   "source": [
    "> ***Fig. 1. Voltage versus time plot with zero average voltage***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c1701d4-fb5b-48c7-9b60-ac0d9e144dc8",
   "metadata": {},
   "source": [
    "To save the resulting Figure, we can use [Matplotlib library method](https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.savefig.html):\n",
    "```python\n",
    "fig.savefig('Vtime1.png')\n",
    "```\n",
    "\n",
    "To save calculation results to a file, we can use\n",
    " [NumPy library method](https://numpy.org/doc/stable/reference/generated/numpy.savetxt.html):\n",
    "```python\n",
    "time_dep = np.column_stack((time_array, Vtime))\n",
    "np.savetxt('Vtime1.dat', time_dep)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "693accc2-e20a-4eb1-914e-540874d1ae7d",
   "metadata": {},
   "source": [
    "As it was noted above, according to JJ physics, the voltage value should tend to zero. As can be seen from Fig. 1, at the beginning of the integration interval, the voltage value, oscillating, tends to zero and stabilizes starting from time $T_{min}=60$. Therefore, further for averaging it is necessary to take this fact into account, i.e. we need to calculate the average value after the stabilization of the solution."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b974a12-cfe5-49a0-ad71-c30a6e1efd64",
   "metadata": {},
   "source": [
    "#### 2. Solution for the finite average voltage state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "0febcf08-e05b-49e5-ac25-33462012a041",
   "metadata": {},
   "outputs": [],
   "source": [
    "Iext = 0.4  # External current value\n",
    "V0 = 3  # Voltage value at the initial time\n",
    "\n",
    "time_array = np.linspace(0, Tmax, num=nt)\n",
    "s0 = np.array([0, V0, 0])\n",
    "res = jjsolution(s0, Iext, beta, A, omega, nt, t0, deltat)\n",
    "Vtime = res[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c059568-d39d-4af7-b67d-495bffa6e785",
   "metadata": {},
   "source": [
    "Let's build a time dependence graph $V(t)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "2a2beee3-9817-4b15-af36-c481da49b051",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(8, 6))\n",
    "plt.plot(time_array, Vtime, label='Time dependence', linewidth=3.0)\n",
    "plt.xlabel('Time', size=12)\n",
    "plt.ylabel('V', size=12)\n",
    "plt.legend(loc='upper right')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fdb5667c-2a95-47d7-84f2-4ddffd6e0ae6",
   "metadata": {},
   "source": [
    "> ***Fig. 2. Voltage versus time plot with final voltage***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90377a91-6e02-4ebf-937d-ae5c7f10836a",
   "metadata": {},
   "source": [
    "At this stage, the step 2 of the algorithm for calculation of the current-voltage characteristic has been implemented. Now we define a function for averaging of voltage $V(t)$ and calculation of one point of the current-voltage characteristic."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4dc16732-e98e-44ec-8a5a-71721569a45d",
   "metadata": {},
   "source": [
    "### We average the calculated voltage values at a given external current value"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e5e9fc9-3399-44ca-8411-47db0c65977c",
   "metadata": {},
   "source": [
    "__We set a function for averaging the time dependence of voltage__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "fa4c697b-ccdd-4cae-acc3-d92f1e004bac",
   "metadata": {},
   "outputs": [],
   "source": [
    "def averageV(ntmin, nt, deltat, V):\n",
    "    intV = 0\n",
    "    for i in range(ntmin, nt):\n",
    "        intV += V[i]*deltat\n",
    "    Vav = intV/((nt-ntmin)*deltat)\n",
    "    return Vav"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a57d1cb6-2f69-4564-862f-5c52d0332d38",
   "metadata": {},
   "source": [
    "__We set a function for calculation of one point of the current-voltage characteristic__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "f7b3b6df-2175-4e3e-be94-e797c7a605a2",
   "metadata": {},
   "outputs": [],
   "source": [
    "def cvcpoint(s0, Iext, beta, A, omega, nt, t0, ntmin, deltat):\n",
    "    solution = jjsolution(s0, Iext, beta, A, omega, nt, t0, deltat)\n",
    "    phtime = solution[0]\n",
    "    Vtime = solution[1]\n",
    "    utime = solution[2]\n",
    "    s0 = np.array([phtime[nt-1], Vtime[nt-1], utime[nt-1]])\n",
    "    Vav = averageV(ntmin, nt, deltat, Vtime)\n",
    "    return [Vav, s0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "856b83ed-60d3-4c62-a53d-8b712e16b5e1",
   "metadata": {},
   "source": [
    "### Calculation of the current-voltage characteristic\n",
    "\n",
    "__Set the parameter values for calculation of the current-voltage characteristic__\n",
    "\n",
    "We note that in case of calculation, it is necessary to approve time characteristics with the period of external radiation in order to avoid the accumulation of errors during averaging. To do this, we need to calculate the period of external radiation $T=2\\pi/\\omega$. From the  above demonstrated time dependencies it is clear that the solution stabilizes after $T_{\\min}=60$ (for $\\omega=2$), this corresponds approximately $T_{\\min}=20T$ (start of the averaging interval). In order to calculate the current-voltage characteristic, if we select a time interval $T_{\\max}=250$ this will correspond approximately $T_{\\max} = 80T$ (maximum time value) and, respectively, the time step $\\Delta t=T/50$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "d356c346-b16b-471c-8b6a-15affdc74fcb",
   "metadata": {},
   "outputs": [],
   "source": [
    "T = 2 * np.pi/omega  # Period of external radiation\n",
    "Tmin = 20 * T  # Beginning of the interval for integration for averaging\n",
    "Tmax = 80 * T  # Maximum time value\n",
    "deltat = T/50  # time step\n",
    "ntmin = int(Tmin/deltat)\n",
    "nt = int(Tmax/deltat)\n",
    "\n",
    "deltaIext = 0.01\n",
    "Iext = 0.0\n",
    "a = 1.0\n",
    "Iext_max = 1.2\n",
    "A = 0.5\n",
    "Vplot = []\n",
    "Iplot = []\n",
    "s0 = np.array([0, 0, 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef21546b-e957-4ce8-bd5d-01e1f6f10a66",
   "metadata": {},
   "source": [
    "We enter the parameter `Ilimit`, limiting the range of current changes to avoid calculation cycling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "49a7749c-f343-43a0-a453-8fe49465af09",
   "metadata": {},
   "outputs": [],
   "source": [
    "Ilimit = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "898b57c8-2dc3-465f-a9d9-471189ff5930",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Execution time 78.31276488304138 s\n"
     ]
    }
   ],
   "source": [
    "t_start = time.time()\n",
    "\n",
    "while Iext < Ilimit:\n",
    "    res = cvcpoint(s0, Iext, beta, A, omega, nt, t0, ntmin, deltat)\n",
    "    Vav = res[0]\n",
    "    s0 = res[1]\n",
    "    Vplot.append(Vav)\n",
    "    Iplot.append(Iext)\n",
    "    Iext += a * deltaIext\n",
    "    if(Iext > Iext_max):\n",
    "        a = - 1\n",
    "    if ((Iext < 0) and (a == - 1)):\n",
    "        break\n",
    "t_finish = time.time()\n",
    "\n",
    "print(f'Execution time {t_finish - t_start} s')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a61965ca-ba96-4ad0-b26b-13f044cc27b2",
   "metadata": {},
   "source": [
    "##### We draw the current-voltage characteristic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "a303b644",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(8, 6))\n",
    "plt.plot(Iplot, Vplot, label='CVC', linewidth=3.0)\n",
    "plt.xlabel('I', size=12)\n",
    "plt.ylabel('V', size=12)\n",
    "plt.legend(loc='upper left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b3c5810-d047-44bb-a702-4f7f6c149f47",
   "metadata": {},
   "source": [
    "> ***Fig. 3. Current-voltage characteristic under the external radiation with  $\\omega=2$ and amplitude $A=0.5$***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bfca23cb-2680-4149-a2b3-f75a20c4c4df",
   "metadata": {},
   "source": [
    "As can be seen from Fig. 3 on the current-voltage characteristic at frequency $\\omega=V=2$ a constant voltage step has formed, i.e. Shapiro step. For comparison, we can calculate the current-voltage characteristic at $A=0$, i.e. without external radiation and make sure there is no step.\n",
    "\n",
    "For further comparison, we should save the calculated current-voltage characteristics with external radiation in arrays `Iplotrad` and `Vplotrad`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "c353fbe5-069f-439e-b03f-906a5df4eec6",
   "metadata": {},
   "outputs": [],
   "source": [
    "Iplotrad = Iplot\n",
    "Vplotrad = Vplot"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b80784fe-d6e5-491d-b7d6-785623f591fb",
   "metadata": {},
   "source": [
    "##### Calculation of current-voltage characteristics without external radiation $(A=0)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "86269b16-232b-47a8-9a60-e92b76f13c4f",
   "metadata": {},
   "outputs": [],
   "source": [
    "A = 0\n",
    "a = 1\n",
    "Iext = 0.0\n",
    "s0 = np.array([0, 0, 0])\n",
    "Vplot = []\n",
    "Iplot = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "7ee0c696-b459-408b-9f7d-cb92e12cdfdf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Execution time 46.573830127716064 s\n"
     ]
    }
   ],
   "source": [
    "t_start = time.time()\n",
    "\n",
    "while Iext < Ilimit:\n",
    "    res = cvcpoint(s0, Iext, beta, A, omega, nt, t0, ntmin, deltat)\n",
    "    Vav = res[0]\n",
    "    s0 = res[1]\n",
    "    Vplot.append(Vav)\n",
    "    Iplot.append(Iext)\n",
    "    Iext += a * deltaIext\n",
    "    if(Iext > Iext_max):\n",
    "        a = - 1\n",
    "    if ((Iext < 0) and (a == - 1)):\n",
    "        break\n",
    "t_finish = time.time()\n",
    "print(f'Execution time {t_finish - t_start} s')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "504d6e45-e923-41bb-9b2e-d3e4f27faae1",
   "metadata": {},
   "source": [
    "Now we can plot the obtained current-voltage characteristics with and without external radiation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "f3ad2465-4974-4cbe-99a4-749cb9b6f9fd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(8, 6))\n",
    "plt.plot(Iplotrad, Vplotrad, label='CVC with radiation', linewidth=3.0)\n",
    "plt.plot(Iplot, Vplot, label='CVC without radiation', linewidth=3.0)\n",
    "plt.xlabel('I', size=12)\n",
    "plt.ylabel('V', size=12)\n",
    "plt.legend(loc='upper left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1f18fc5-6ccc-45d3-a055-62422374dbff",
   "metadata": {},
   "source": [
    "> ***Fig. 4. Current-voltage characteristic with ($A=0.5$) and without ($A=0$) external radiation***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca281646-9772-4d69-8ae0-749ed4f562de",
   "metadata": {},
   "source": [
    "## 3. Calculation of the amplitude dependence of the Shapiro step width\n",
    "\n",
    "### Algorithm for calculation of the amplitude dependence of the Shapiro step width\n",
    "\n",
    "1. Set parameter values\n",
    "\n",
    "2. We calculatoion of the current-voltage characteristic for a fixed amplitude of external radiation. During the calculation process, we save all values of current for which are realised the condition $V=n_{harm}\\omega$ with precision $\\varepsilon$ ($\\varepsilon>|V-n_{harm}\\omega|$) and as the difference between the maximum and minimum values from the obtained values of current, we determine the Shapiro step width. Here $n_{harm}$ indicates the harmonic number.   \n",
    "\n",
    "3. Then increasing the amplitude value by $\\Delta A$ repeat step 2\n",
    "\n",
    "In order to perform step 2, we will define a function that calculates the current-voltage characteristic and retuns the value of Shapiro step width."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c432ad90-84d9-4fe8-a2e5-ccd27fc424ef",
   "metadata": {},
   "source": [
    "### Calculation of the amplitude dependence of the Shapiro step width"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7aaaf47f-76dd-4cbf-aedb-375761376d20",
   "metadata": {},
   "source": [
    "We create a function to calculate the current-voltage characteristic and find the Shapiro step width"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "212afe7b-69c3-49f4-a74a-a8ec2885a616",
   "metadata": {},
   "outputs": [],
   "source": [
    "def Shapirostepsize(A, omega, n_harm, epsilon, Ilimit,\n",
    "                    beta, deltaIext, ntmin, nt, deltat):\n",
    "    a = 1\n",
    "    t0 = 0\n",
    "    Iext = 0\n",
    "    Istep_list = []\n",
    "    s0 = np.array([0, 0, 0])\n",
    "    getstep = False  # Variable for checking whether a step is hit\n",
    "    while Iext < Ilimit:\n",
    "        res = cvcpoint(s0, Iext, beta, A, omega, nt, t0, ntmin, deltat)\n",
    "        Vav = res[0]\n",
    "        s0 = res[1]\n",
    "        # Condition for reversing the direction of the current when first hitting a step\n",
    "        # Required to fully obtain a step\n",
    "        if ((a == -1) and (getstep == False) and np.abs(Vav-(n_harm*omega)) < epsilon):\n",
    "            a = 1\n",
    "            getstep = True\n",
    "            \n",
    "        if ( (a==1) and (getstep==False) and np.abs(Vav-(n_harm*omega))<epsilon):\n",
    "            getstep=True\n",
    "        \n",
    "        #Algorithm for determining the maximum and minimum current values when hitting a step\n",
    "        if(np.abs(Vav-(n_harm*omega))<epsilon):\n",
    "            Istep_list.append(Iext)  \n",
    "        Iext+=a * deltaIext\n",
    "        #The condition for changing the direction of the current when exiting the step\n",
    "        if(Vav>n_harm*omega+0.05):\n",
    "            a=-1\n",
    "        #Condition for stopping the current cycle\n",
    "        if (Vav<n_harm*omega-0.05 and a==-1):\n",
    "            break\n",
    "        #End of current cycle\n",
    "     \n",
    "    #Calculation of step width    \n",
    "    Istep = max(Istep_list)-min(Istep_list)\n",
    "    \n",
    "    return Istep"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8eb51c03-2fc7-4990-9826-626cdad76f22",
   "metadata": {},
   "source": [
    "Let us calculate the width of the Shapiro step for $n_{harm}=1$ and $A=1$ with precision $\\varepsilon=0.01$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "8ac46aa0-8435-4382-ad99-5ef4bb058a4d",
   "metadata": {},
   "outputs": [],
   "source": [
    "A = 1\n",
    "n_harm = 1\n",
    "epsilon = 0.01"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "eb6fa832-0c88-44a2-8f88-9b611b6c023f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Execution time 62.509164810180664 s\n",
      "0.2300000000000002\n"
     ]
    }
   ],
   "source": [
    "t_start = time.time()\n",
    "k = Shapirostepsize(A, omega, n_harm, epsilon, Ilimit,\n",
    "                    beta, deltaIext, ntmin, nt, deltat)\n",
    "t_finish = time.time()\n",
    "print(f'Execution time {t_finish - t_start} s')\n",
    "print(k)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "55895ac3-55b7-43c6-ad1e-abf470b2e4be",
   "metadata": {},
   "source": [
    "#### Calculation of the amplitude dependence of the Shapiro step width in serial mode"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11d94e2a-71d3-4d8f-a746-93aac8f239fc",
   "metadata": {},
   "source": [
    "We introduce parameters for calculation of the amplitude dependence of the Shapiro step width\n",
    "* npoint - number of points in the range of amplitude values;\n",
    "* Amin -  minimum amplitude value;\n",
    "* Amax - maximum amplitude value;\n",
    "* deltaA - amplitude change step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "16721a63-c259-4242-a217-74b5b8a2c0a4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.24842767295597484\n"
     ]
    }
   ],
   "source": [
    "npoint = 160\n",
    "Amin = 0.5\n",
    "Amax = 40\n",
    "deltaA = (Amax - Amin) / (npoint-1)\n",
    "print(deltaA)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b38f92d4-ab00-4c80-8278-17232450a660",
   "metadata": {},
   "source": [
    "We create an array of amplitude values for which we need to calculate the width of the Shapiro step "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "6aadf5ae-09e3-4c25-b83a-b38f0e589b08",
   "metadata": {},
   "outputs": [],
   "source": [
    "A_array = np.linspace(Amin, Amax, num=npoint)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f6c7cf57-3f5d-4d29-a64b-f69c79fe3971",
   "metadata": {},
   "source": [
    "Create an empty array for the Shapiro step width values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "eec99482-8b32-47c5-b8ec-bd045965f0ef",
   "metadata": {},
   "outputs": [],
   "source": [
    "Step_array = np.zeros(npoint)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b44b656f-4e1b-4842-83cf-f25ef28338c0",
   "metadata": {},
   "source": [
    "We create a function to calculate the dependence of the width of the Shapiro step on the amplitude of external radiation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "d1ecb7b6-2a2f-4c28-9d56-a2482293b20b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def funk_ShapiroA(j, A, omega, n_harm, epsilon, Ilimit,\n",
    "                    beta, deltaIext, ntmin, nt, deltat):\n",
    "    A = Amin + deltaA * j\n",
    "\n",
    "    step = Shapirostepsize(A, omega, n_harm, epsilon, Ilimit,\n",
    "                    beta, deltaIext, ntmin, nt, deltat)\n",
    "\n",
    "    return step"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "74c5699a-c51c-4fdc-b289-856ee93d00fc",
   "metadata": {},
   "source": [
    "##### Calculation of the amplitude dependence of the Shapiro step width in serial mode"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "acf5c0a3-e5bc-422c-852e-e40826651505",
   "metadata": {},
   "outputs": [],
   "source": [
    "%%time\n",
    "for i in range(0, npoint):\n",
    "    Shapirostep = funk_ShapiroA(i, A, omega, n_harm, epsilon, Ilimit,\n",
    "                    beta, deltaIext, ntmin, nt, deltat)\n",
    "    Step_array[i] = Shapirostep"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "de93fb42-d7ff-40e9-8b6a-c76afe396e28",
   "metadata": {},
   "source": [
    "##### We can plot the amplitude dependence of the Shapiro step width"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3bb1ed36-9d2f-4abb-b853-f8261caae72c",
   "metadata": {},
   "outputs": [],
   "source": [
    "fig = plt.figure(figsize=(8, 6))\n",
    "plt.plot(A_array, Step_array, label='Shapiro step width', linewidth=3.0)\n",
    "plt.xlabel('A', size=12)\n",
    "plt.ylabel('Stepwidth', size=12)\n",
    "plt.legend(loc='upper right')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7c416af-4b6f-42a9-85bb-3d0f461c457e",
   "metadata": {},
   "source": [
    "> ***Fig. 5. Amplitude dependence of the Shapiro step width***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bee9b2a3-8b0f-40b8-ad87-8104e503d5a4",
   "metadata": {},
   "source": [
    "The calculation takes a long time, so we will carry out the calculations in parallel mode."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb2e79e1-9f98-40ef-9e9c-3224e86730a2",
   "metadata": {},
   "source": [
    "### Parallel implementation of a computational scheme for finding the amplitude dependence of the Shapiro step width\n",
    "\n",
    "__Calculation in parallel mode using the library Joblib__\n",
    "\n",
    "To parallelize calculations by parameter $A$ use the library functionality [Joblib](https://joblib.readthedocs.io/en/latest/), which allows using the method _Parallel_ distribute calculations over a given number of physical processor cores ```n_jobs```. A detailed description of the library's capabilities is presented in a separate section HLIT Jbook."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8d5aaf8-72b2-4cbc-a367-7a7c7131ac47",
   "metadata": {},
   "source": [
    "##### We import the necessary libraries for parallel computing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "0a6d1a79-97d1-4ca5-b334-c6479482a022",
   "metadata": {},
   "outputs": [],
   "source": [
    "import joblib\n",
    "from joblib import Parallel, delayed\n",
    "import time\n",
    "import os"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "4ca5654c-2f91-4ba4-893f-777e297144c2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of cpu: 88\n"
     ]
    }
   ],
   "source": [
    "print(f\"Number of cpu: {joblib.cpu_count()}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61347076-d497-40cd-ab2c-1f22d20fb96c",
   "metadata": {},
   "source": [
    "Now we can calculate the amplitude dependence of the Shapiro step width in parallel mode"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "3774121e-664e-4641-8967-4e3a4383281a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def funk_parallel(j, A, omega, n_harm, epsilon, Ilimit,\n",
    "                    beta, deltaIext, ntmin, nt, deltat):\n",
    "    A = Amin + deltaA * j\n",
    "\n",
    "    step = Shapirostepsize(A, omega, n_harm, epsilon, Ilimit,\n",
    "                    beta, deltaIext, ntmin, nt, deltat)\n",
    "\n",
    "    return step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "817547f7-621e-446b-bf70-854c218ef382",
   "metadata": {},
   "outputs": [],
   "source": [
    "t_start = time.time()\n",
    "rez = Parallel(n_jobs=20)(delayed(funk_parallel)(i, A, omega, n_harm, epsilon, Ilimit,\n",
    "                    beta, deltaIext, ntmin, nt, deltat) for i in range(npoint))\n",
    "t_finish = time.time()\n",
    "print(f'Execution time {t_finish - t_start} s')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "41693f28-762e-48e5-ab11-bd231eac6da2",
   "metadata": {},
   "outputs": [],
   "source": [
    "Step_array_parr = np.array(rez)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "91b02693-33f7-4482-8d1e-1dd0a5e2fdcb",
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'A_array' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m/tmp/ipykernel_144054/3045894480.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mfig\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfigure\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfigsize\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m8\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m6\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m plt.plot(A_array, Step_array_parr, label='Shapiro step width',\n\u001b[0m\u001b[1;32m      3\u001b[0m          linewidth=3.0)\n\u001b[1;32m      4\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mxlabel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'A'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msize\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m12\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mylabel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Stepwidth'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msize\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m12\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'A_array' is not defined"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 800x600 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(8, 6))\n",
    "plt.plot(A_array, Step_array_parr, label='Shapiro step width',\n",
    "         linewidth=3.0)\n",
    "plt.xlabel('A', size=12)\n",
    "plt.ylabel('Stepwidth', size=12)\n",
    "plt.legend(loc='upper right')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "061dce76-7a97-4266-8116-ead82a72487f",
   "metadata": {},
   "source": [
    "> ***Fig. 6. The amplitude dependence of the Shapiro step width***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8dd0e99b-dfb3-4b81-aa26-6ac139a47889",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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