{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "2e9149d6",
   "metadata": {
    "tags": []
   },
   "source": [
    "# Python-инструментарий для моделирования динамики джозефсоновского перехода под воздействием внешнего излучения\n",
    "\n",
    "В блокноте представлен инструментарий для моделирования динамики джозефсоновского перехода под воздействием внешнего излучения:\n",
    "* алгоритм для вычисления вольт-амперной характеристики джозефсоновского перехода под воздействием внешнего излучения;\n",
    "* алгоритм вычисления зависимости ширины ступеньки Шапиро от амплитуды;\n",
    "* алгоритм параллельного вычисления зависимости ширины ступеньки Шапиро от амплитуды с использованием библиотеки Joblib;\n",
    "* результаты анализа эффективности параллельных вычислений.\n",
    "\n",
    "Исследование основано на материалах статей:\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."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2a1b38e-3709-443a-8f3b-1bbd1f8d6fe9",
   "metadata": {
    "tags": []
   },
   "source": [
    "## 1. Описание модели\n",
    "\n",
    "__Эффект Джозефсона и джозефсоновский переход__\n",
    "\n",
    "Связь двух сверхпроводящих слоев посредством тонкого слоя несверхпроводящего барьера образует структуру называемую джозефсоновским переходом (в честь английского ученого _Брайана Джозефсона_). При пропускании электрического тока через джозефсоновский переход (ДП) в зависимости от величины тока наблюдается стационарный и нестационарный эффект Джозефсона.\n",
    "\n",
    "_Стационарный эффект Джозефсона._ При пропускании тока ниже критического значения $(I<I_{c})$ в ДП отсутствует напряжение и через переход течет сверхпроводящий ток. Данный ток пропорционален синусу разности фаз параметров порядка сверхпроводящих слоев образующих ДП:\n",
    "\n",
    "$\n",
    "\\begin{eqnarray}\n",
    "I_{s}=I_{c}\\sin\\varphi.\n",
    "\\label{eq1}\n",
    "\\tag{1}\n",
    "\\end{eqnarray}\n",
    "$\n",
    "\n",
    "_Нестационарный эффект Джозефсона._ При увеличении тока выше критического значения $(I>I_{c})$ возникает переменное напряжение в ДП и оно пропорционально производной разности фаз\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",
    "__Система уравнений для описания динамики ДП:__\n",
    "\n",
    "Динамика ДП описывается в рамках RCSJ-модели (Resitively Capasitevily Shunted Junction) [3]. В рамках этой модели ДП моделируется как параллельное соединение конденсатора, резистора и сверхпроводника:\n",
    "\n",
    "![RCSJ-model](rcsj.jpg)\n",
    "\n",
    "Через конденсатор течет ток смещения $\\displaystyle I_{disp}=C\\frac{dV}{dt}$, через резистор - квазичастичный ток $\\displaystyle I_{qp}=\\frac{V}{R}$ и через сверхпроводник джозефсоновский (сверхпроводящий) ток $I_{s}=I_{c}\\sin\\varphi$.\n",
    "\n",
    "Полный ток, проходящий через систему, равен сумме вышеперечисленных токов\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",
    "Используя (2) и (3) в нормированных величинах можно написать замкнутую систему дифференциальных уравнений относительно $V$ и $\\varphi$\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",
    "где $\\displaystyle \\beta=\\frac{\\hbar \\omega_{p}}{2 e I_{c}R}$ - параметр диссипации, $\\displaystyle\\omega_{p}=\\sqrt{\\frac{2 e I_{c}}{\\hbar C}}$ - плазменная частота. В системе уравнений (\\ref{eq4}) время нормирован на $\\omega_{p}$, напряжение нормировано на $\\displaystyle V_{0}=\\frac{\\hbar \\omega_{p}}{2 e}$ и ток нормирован на $I_{c}$.\n",
    "\n",
    "__Влияние внешнего излучения на динамику ДП и ступеньки Шапиро__\n",
    "\n",
    "Под воздействием внешнего излучения, при условии кратности частоты Джозефсона к частоте внешнего излучения, в результате частотного захвата через ДП возникает не зависящий от времени сверпроводящий ток. Этот сверхпроводящий ток на вольт-амперной характеристике (ВАХ) проявляется в виде ступеньки постоянного напряжения, называемой ступенькой Шапиро [2]. Ширина ступеньки Шапиро зависит от величины частоты и амплитуды внешнего излучения.\n",
    "\n",
    "Для моделирования этого явления в системе уравнений RCSJ-модели учитывается дополнительный переменный ток $I_{R}$, создаваемый внешним излучением с амплитудой $A$ и частотой $\\omega$, т.е. $I_{R}=A\\sin(\\omega t)$.\n",
    "\n",
    "Алгоритм проведения расчетов основан на решении системы уравнений при фиксированном значении тока с выбранным шагом. Отметим, что, при решении системы уравнений для каждого значения тока, время меняется от нуля до $T_{\\max}$. В этом случае, если уравнения зависят в явном виде от времени, то возникает необходимость организовать изменения времени непрерывно во всем интервалам по току. Для этого нужно будет считать количество шагов по току и умножать на $T_{\\max}$ и прибавить к текущему значению времени. Эту сложность можно нивелировать, добавив к системе уравнений дополнительное уравнение типа $du/dt=\\omega$. Тогда на следующий шаг по току необходимо только передавать начальное условие, что упрощает процесс вычислений.\n",
    "\n",
    "Таким образом конечный вид системы уравнений принимает вид:\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",
    "Параметры модели:\n",
    "* $\\beta$ - параметр диссипации;\n",
    "* $A$ - амплитуда внешнего  излучения;\n",
    "* $V$ - напряжение;\n",
    "* $I$ - внешний ток;\n",
    "* $\\omega$ - частота излучения;\n",
    "* $\\varphi$ - разность фаз.\n",
    "\n",
    "__Постановка задачи:__\n",
    "\n",
    "Вычислить вольт-амперную характеристику джозефсоновского перехода под воздействием внешнего излучения и построить ее график."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "19af40a5-3fbb-42a2-be7d-7619b13b6e74",
   "metadata": {},
   "source": [
    "## 2. Вычисление вольт-амперной характеристики\n",
    "\n",
    "__Алгоритм вычисления вольт-амперной характеристики:__\n",
    "\n",
    "1. Задаем значения параметров модели, параметры численного счета, начальные условия.\n",
    "\n",
    "2. Численно решаем задачу Коши для системы обыкновенных дифференциальных уравнений (5), (например, методом Рунге-Кутта четвертого порядка) для фиксированного значения тока $I$, и находим временную зависимость разности фаз $\\varphi(t)$ и напряжения $V(t)$.\n",
    "\n",
    "3. Усредняем полученную зависимость $V(t)$ по времени:\n",
    "\n",
    "$\n",
    "\\displaystyle <V>=\\frac{1}{T_{\\max}-T_{\\min}}\\int\\limits_{T_{\\min}}^{T_{\\max}}V(t)dt\n",
    "$\n",
    "\n",
    "В результате получим значение напряжения для заданного значения тока, т.е. определяем одну точку на ВАХ.\n",
    "\n",
    "4. Меняем значение тока на $\\delta I$ и повторяем п. 2, используя при этом $\\varphi(T_{\\max})$ и $V(T_{\\max})$ из посчитанного значения тока в качестве начального условия, и для полученного $V(t)$ выполняем п. 3, и находим среднее значение напряжения.\n",
    "\n",
    "5. Проводим расчеты до $I_{\\max}$.\n",
    "\n",
    "6. Проводим расчеты, уменьшая значение тока $I$ от $I_{\\max}$ до нуля.\n",
    "\n",
    "Теперь, непостредственно переходим к реализации вышеописанного алгоритма."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db72dff5-1640-4956-b9b4-e91d0cc1c8f5",
   "metadata": {},
   "source": [
    "__Подключаем библиотеки__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "e08f8354-927f-4843-af46-e6814bab9083",
   "metadata": {},
   "outputs": [],
   "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": [
    "__Определяем правые части уравнений__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "7ddaac53",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Функция, определяющая правую часть систему уравнений\n",
    "def shortjj(t, S, beta, Iext, A, omega):\n",
    "    ''' Определяет правые части системы ОДУ (5),\n",
    "        beta, A, omega - параметры модели,\n",
    "        S=[phi,V,u] - искомое решение '''\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"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "096f6fcc-dc25-4784-978f-a6a82c300c39",
   "metadata": {},
   "source": [
    "### Вычисления временной зависимости напряжения\n",
    "Зададим функцию для вычисления временной зависимости напряжение и фазы при фиксированном значении внешнего тока, которая используя начальные условия, значения параметров модели и численного счета, возвращает соответствующие временные зависимости."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e202fa0-c8f6-47dc-aa7b-d5bbfe47bcb5",
   "metadata": {},
   "source": [
    "__Задаем функцию для численного решения задачи Коши__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "4da3b9d8-675d-4979-96d9-9055ed2ed7ab",
   "metadata": {},
   "outputs": [],
   "source": [
    "def jjsolution(s0, Iext, beta, A, omega, nt, t0, deltat):\n",
    "    ''' Численное решение задачи Коши для системы ОДУ (5),\n",
    "        beta, A, omega - параметры модели,\n",
    "        nt - количество точек по времени, в которых находится решение,\n",
    "        t0 - начальное значение времени,\n",
    "        deltat - шаг по времени,\n",
    "        Iext - значение внешнего тока,\n",
    "        s0=[phi0, V0, u0] - начальные условия,\n",
    "        output: [phtime, Vtime, utime] - массивы посчитанных временных зависимостей для фазы, напряжения и введенной вспомогательной функции 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]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34eaf9b8-daee-4e3c-8417-442530ca3393",
   "metadata": {},
   "source": [
    "Для проверки корректности реализованной вычислительной схемы найдем временные зависимости напряжения в двух режимах:\n",
    "1. в состоянии с нулевым средним напряжением,\n",
    "2. в состоянии с конечным средним напряжением.\n",
    "\n",
    "Согласно физики джозефсоновского перехода, в качестве результата мы должны получить в первом случае - затухающую зависимость напряжения от времени, а во втором - осцилляцию напряжения с конечным средним значением. Для этого  необходимо выбрать значения тока при котором реализации таких решений возможно (например $I=0.4$) и нужно решить систему уравнений с разными начальными условиями для напряжения (например, $V=3$). Для простоты рассмотрим случай без внешнего излучения, т.е. $A=0$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c49b6c4-7894-4889-b33e-248c45a61bb3",
   "metadata": {},
   "source": [
    "__Параметры модели__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "7ca0d2b0",
   "metadata": {},
   "outputs": [],
   "source": [
    "beta = 0.2  # Параметр диссипации\n",
    "A = 0  # Амплитуда внешнего излучения\n",
    "omega = 2 # Частота внешнего излучения"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9740da4-9056-474a-9dd8-d5e8e0c96047",
   "metadata": {},
   "source": [
    "__Параметры численного счета__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "f1ca9a8c-738b-4b40-a20a-439b9a0fcf6d",
   "metadata": {},
   "outputs": [],
   "source": [
    "Tmax = 100 # Максимальное значение времени\n",
    "deltat = 0.05  # шаг по времени\n",
    "t0 = 0\n",
    "nt = int(Tmax/deltat)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3863d4ad-03a8-4dac-8e35-f8144238cc1a",
   "metadata": {},
   "source": [
    "#### 1. Решение для состояния с нулевым средним напряжением"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "a310933f-a031-4149-b6a1-6df9b2e1fd1c",
   "metadata": {},
   "outputs": [],
   "source": [
    "Iext = 0.4  # Значение внешнего тока\n",
    "V0 = 0  # Значение напряжение в начальный момент времени\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": "2077cb26-2444-412d-81e0-ef2d0be7afa7",
   "metadata": {},
   "source": [
    "Построим график временной зависимости $V(t)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "a3d90388-5dd3-4d7b-9efe-f78c2cf46135",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": [
    "> ***Рис. 1. График зависимости напряжения от времени с нулевым средним напряжением***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c1701d4-fb5b-48c7-9b60-ac0d9e144dc8",
   "metadata": {},
   "source": [
    "Для сохранения полученных графиков можно использовать [метод библиотеки Matplotlib](https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.savefig.html):\n",
    "```python\n",
    "fig.savefig('Vtime1.png')\n",
    "```\n",
    "\n",
    "Для сохранения результатов расчетов в файл можно использовать [метод библиотеки NumPy](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": [
    "Как отмечалось выше, согласно физике ДП, значение напряжения должно стремиться к нулю. Как видно из Рис. 1, в начале интервала интегрирования значение напряжения, осцилируя, стремится к нулю и стабилизируется начиная от времени $T_{min}=60$. Поэтому далее при усреднении необходимо это учитывать, т.е. нужно вычислять среднее после стабилизации решения."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b974a12-cfe5-49a0-ad71-c30a6e1efd64",
   "metadata": {},
   "source": [
    "#### 2. Решение для состояния с конечным средним напряжением"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "0febcf08-e05b-49e5-ac25-33462012a041",
   "metadata": {},
   "outputs": [],
   "source": [
    "Iext = 0.4  # Значение внешнего тока\n",
    "V0 = 3  # Значение напряжение в начальный момент времени\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": [
    "Построим график временной зависимости $V(t)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "2a2beee3-9817-4b15-af36-c481da49b051",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": [
    "> ***Рис. 2. График зависимости напряжения от времени с конечным средним напряжением***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90377a91-6e02-4ebf-937d-ae5c7f10836a",
   "metadata": {},
   "source": [
    "На данном этапе реализован п. 2 алгоритма вычисления ВАХ. Определим функцию для усреднения напряжения $V(t)$ и вычисления одной точки ВАХ."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4dc16732-e98e-44ec-8a5a-71721569a45d",
   "metadata": {},
   "source": [
    "### Усредняем посчитанные значения напряжения при заданном значении внешнего тока"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e5e9fc9-3399-44ca-8411-47db0c65977c",
   "metadata": {},
   "source": [
    "__Задаем функцию для усреднения временной зависимости напряжения__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "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": [
    "__Задаем функцию для вычисления одной точки ВАХ__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "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": [
    "### Вычисляем ВАХ\n",
    "\n",
    "__Задаем значения параметров для вычисления ВАХ__\n",
    "\n",
    "Отметим, что при вычислении необходимо согласовать все временных характеристики с периодом внешнего излучения во избежании накоплении ошибок при усреднении. Для этого нужно вычислить период внешнего излучения $T=2\\pi/\\omega$. Из построенных выше графиков видно, что решения стабилизируется после $T_{\\min}=60$ (для $\\omega=2$), это соответствует примерно $T_{\\min}=20T$ (начало интервала для усреднения). Для вычисления ВАХ если выберем временной интервал $T_{\\max}=250$ это будет соответствовать примерно $T_{\\max} = 80T$ (максимальное значение времени) и, соответственно, шаг по времени $\\Delta t=T/50$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "d356c346-b16b-471c-8b6a-15affdc74fcb",
   "metadata": {},
   "outputs": [],
   "source": [
    "T = 2 * np.pi/omega  # Период внешнего излучение\n",
    "Tmin = 20 * T  # Начало интервала для интегрирования для усреднения\n",
    "Tmax = 80 * T  # Максимальное значение времени\n",
    "deltat = T/50  # шаг по времени\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": [
    "Введем параметр `Ilimit`, ограничивающий интервал изменеия по току для избежания зацикливания расчета."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "49a7749c-f343-43a0-a453-8fe49465af09",
   "metadata": {},
   "outputs": [],
   "source": [
    "Ilimit = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "898b57c8-2dc3-465f-a9d9-471189ff5930",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Execution time 69.81972432136536 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": [
    "##### Построим график ВАХ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "a303b644",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": [
    "> ***Рис. 3. График ВАХ при значении внешнего излучения $A=0.5$***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bfca23cb-2680-4149-a2b3-f75a20c4c4df",
   "metadata": {},
   "source": [
    "Как видно из Рис. 3 на ВАХ при частоте $\\omega=V=2$ образовалась ступенька постоянного напряжения, т.е. ступенька Шапиро. Для сравнения можно вычислить ВАХ при $A=0$, т.е. без внешнего излучения и убедится в отсутствии ступеньки.\n",
    "\n",
    "Для дальнейшего сравнения сохраним рассчитанные занчения ВАХ с внешним излучением в массивах `Iplotrad` и `Vplotrad`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "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": [
    "##### Вычисления ВАХ без внешнего излучения $(A=0)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "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": 96,
   "id": "7ee0c696-b459-408b-9f7d-cb92e12cdfdf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Execution time 41.52426719665527 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": [
    "Построим графики ВАХ с внешним излучением без внешнего излучения"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "f3ad2465-4974-4cbe-99a4-749cb9b6f9fd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": [
    "> ***Рис. 4. Графики ВАХ с внешним излучением ($A=0.5$) и без внешнего излучения***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca281646-9772-4d69-8ae0-749ed4f562de",
   "metadata": {},
   "source": [
    "## 3. Вычисление зависимости ширины ступеньки Шапиро от амплитуды внешнего излучения\n",
    "\n",
    "### Алгоритм вычисления зависимости ширины ступеньки Шапиро от амплитуды внешнего излучения\n",
    "\n",
    "1. Задаем значения параметров\n",
    "\n",
    "2. Вычислим ВАХ при фиксированном значении амплитуды внешнего излучения. В процессе вычисления сохраняем все значения тока для которых выполняется условия $V=n_{harm}\\omega$ с точностью $\\varepsilon$ ($\\varepsilon>|V-n_{harm}\\omega|$) и как разность максимального и минимального значений из полученных значений тока определяем ширины ступеньки Шапиро. Здесь $n_{harm}$ обозначает номер гармоники.   \n",
    "\n",
    "3. Затем увеличивая значение амплитуды на $\\Delta A$ повторяем п.2\n",
    "\n",
    "Для выполнения п.2 зададим функцию, которая вычисляет ВАХ и ширину ступеньки Шапиро."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c432ad90-84d9-4fe8-a2e5-ccd27fc424ef",
   "metadata": {},
   "source": [
    "### Вычисления зависимости ширины ступеньки Шапиро от амплитуды внешнего излучения"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7aaaf47f-76dd-4cbf-aedb-375761376d20",
   "metadata": {},
   "source": [
    "Зададимфункцию для вычисления ВАХ и нахождения ширины ступеньки Шапиро"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "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  # Переменная для проверки попадание на ступеньку\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",
    "        # Условие для поворота направления тока при первом попадании на ступеньку\n",
    "        # Необходимо для полного получения ступеньки\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",
    "        #Алгоритм определения максимального и минимального значения тока при попадании на ступеньку\n",
    "        if(np.abs(Vav-(n_harm*omega))<epsilon):\n",
    "            Istep_list.append(Iext)  \n",
    "        Iext+=a * deltaIext\n",
    "        #Условие изменении направлении тока при выходе из ступеньки\n",
    "        if(Vav>n_harm*omega+0.05):\n",
    "            a=-1\n",
    "        #Условие для остановки цикла по току\n",
    "        if (Vav<n_harm*omega-0.05 and a==-1):\n",
    "            break\n",
    "        #Конец цикла по току\n",
    "     \n",
    "    #Вычисление ширины ступеньки    \n",
    "    Istep = max(Istep_list)-min(Istep_list)\n",
    "    \n",
    "    return Istep"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8eb51c03-2fc7-4990-9826-626cdad76f22",
   "metadata": {},
   "source": [
    "Вычислим ширину ступеньки Шапиро для $n_{harm}=1$ и $A=1$ с точностью $\\varepsilon=0.01$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8ac46aa0-8435-4382-ad99-5ef4bb058a4d",
   "metadata": {},
   "outputs": [],
   "source": [
    "A = 1\n",
    "n_harm = 1\n",
    "epsilon = 0.01"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "eb6fa832-0c88-44a2-8f88-9b611b6c023f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Execution time 55.185770988464355 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": [
    "#### Последовательное вычисление зависимости ширины ступеньки Шапиро от амплитуды внешнего излучения"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11d94e2a-71d3-4d8f-a746-93aac8f239fc",
   "metadata": {},
   "source": [
    "Вводим параметры для вычисления зависимости ширины ступеньки Шапиро от амплитуды внешнего излучения\n",
    "* npoint - количество точек в интервале значений амлитуды;\n",
    "* Amin -  минимальное значение амлитуды;\n",
    "* Amax - максимальное значение амплитуды;\n",
    "* deltaA - шаг изменения амплитуды."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "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": [
    "Создаем массив значений амплитуды, для которых нужно вычислить ширины ступеньки Шапиро "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "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": [
    "Создаем пустой массив для значений ширины ступеньки Шапиро"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "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": [
    "Создаем функцию для вычисления зависимости ширины ступеньки Шапиро от амплитуды внешнего излучения"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "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": [
    "##### Вычислим зависимости ширины ступеньки Шапиро от амплитуды в последовательном режиме"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "acf5c0a3-e5bc-422c-852e-e40826651505",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1h 38min 42s, sys: 1.86 s, total: 1h 38min 44s\n",
      "Wall time: 1h 38min 56s\n"
     ]
    }
   ],
   "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": [
    "##### Построим график зависимости ширины ступеньки Шапиро от амплитуды внешнего излучения"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "3bb1ed36-9d2f-4abb-b853-f8261caae72c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "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": [
    "> ***Рис. 5. График зависимости ширины ступеньки Шапиро от амплитуды внешнего излучения***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bee9b2a3-8b0f-40b8-ad87-8104e503d5a4",
   "metadata": {},
   "source": [
    "Расчет занимает продолжительное время, поэтому проведем расчеты в параллельном режиме."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb2e79e1-9f98-40ef-9e9c-3224e86730a2",
   "metadata": {},
   "source": [
    "### Параллельная реализация вычислительной схемы нахождения зависимости ширины ступеньки Шапиро от амплитуды внешнего излучения\n",
    "\n",
    "__Проведение расчетов в параллельном режиме с использованием библиотеки Joblib__\n",
    "\n",
    "Для распараллеливания вычислений по параметру $V$ используем функционал библиотеки [Joblib](https://joblib.readthedocs.io/en/latest/), которая позволяет с помощью метода _Parallel_ распределить вычисления по заданному количеству физических ядер процесоров ```n_jobs```. Подробное описание возможностей библиотеки представленно в отдельном разделе HLIT Jbook."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8d5aaf8-72b2-4cbc-a367-7a7c7131ac47",
   "metadata": {},
   "source": [
    "##### Подключаем необходимые библиотеки для параллельного вычисления"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "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": 68,
   "id": "4ca5654c-2f91-4ba4-893f-777e297144c2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of cpu: 80\n"
     ]
    }
   ],
   "source": [
    "print(f\"Number of cpu: {joblib.cpu_count()}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61347076-d497-40cd-ab2c-1f22d20fb96c",
   "metadata": {},
   "source": [
    "Вычислим зависимость ширины ступеньки Шапиро от амплитуды внешнего излучения в параллельном режиме"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "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": 111,
   "id": "817547f7-621e-446b-bf70-854c218ef382",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Execution time 323.6772277355194 s\n"
     ]
    }
   ],
   "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": 106,
   "id": "41693f28-762e-48e5-ab11-bd231eac6da2",
   "metadata": {},
   "outputs": [],
   "source": [
    "Step_array_parr = np.array(rez)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "91b02693-33f7-4482-8d1e-1dd0a5e2fdcb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": [
    "> ***Рис. 6. График зависимости ширины ступеньки Шапиро от амплитуды внешнего излучения***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0dd47062-bc1c-4af2-b26c-8c16d490a32e",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.8.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}