Coagulation 3 (Project).ipynb

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   "id": "a2627f08",
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   "source": [
    "# Project: PFR  reactor design\n",
    "\n",
    "In this project you will design a PFR (plug flow reactor) optimized to produce a given particle number distribution. First we introduce the governing equations."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f9ff271",
   "metadata": {},
   "source": [
    "The general dynamic equation which incorporates convective diffusion is given by (Friedlander, 2000; p. 306-307):\n",
    "\n",
    "$$\n",
    "\\frac{\\partial n_{k}}{\\partial t}+\\nabla \\cdot n_{k} \\mathbf{v}=\\nabla \\cdot D \\nabla n_{k}+\\left[\\frac{\\partial n_{k}}{\\partial t}\\right]_{\\text {growth }}+\\left[\\frac{\\partial n_{k}}{\\partial t}\\right]_{c_{k} \\phi}-\\nabla \\cdot \\mathbf{c} n_{k}\n",
    "$$\n",
    "\n",
    "The mass balance in the PFR with a volume $B$ is given by\n",
    "\n",
    "$$\n",
    "\\frac {d F_N}{dV} = r_N\n",
    "$$\n",
    "\n",
    "And the Smoluchowski type aggregation model:\n",
    "\n",
    "$$\n",
    "\\begin{split}\n",
    "& \\frac{\\partial n(v_p,t)}{\\partial t} =\n",
    "\\frac{1}{2}\\int_0^{v_p} \\beta(\\tilde{v_p},v_p-\\tilde{v_p}) \\, n(\\tilde{v_p},t) \\, n(v_p-\\tilde{v_p},t) \\, d\\tilde{v_p} \n",
    "- \\int_0^{\\infty} \\beta(v_p,\\tilde{v_p}) \\, n(v_p,t) \\, n(\\tilde{v_p},t) \\, d\\tilde{v_p} \n",
    "\\end{split}\n",
    "$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "498961ec",
   "metadata": {},
   "source": [
    "providing:\n",
    "$$\n",
    "\\frac {d F_N}{dV} = \\frac{\\partial n(v_p,t)}{\\partial t} \n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db0cc94d",
   "metadata": {},
   "source": [
    "where $F_N$ is a vector of the number flowrates of particles of each volume.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2bc54d9",
   "metadata": {},
   "source": [
    "Task 1 (20%): For a residence time of $\\tau = B/Q = 2$ s, and a reactor of size $B = 1$ m$^3$, write a simulation of a PFR reactor with an initial input steam that has the following variables:\n",
    "\n",
    "- $F_{0} = 10^{17}$ $(\\#$ particles s$^{-1}$)\n",
    "- $n_{0}= F_{0} \\delta\\left(v-v_{0}\\right)$ (monodisperse as above)\n",
    "- $Q = 0.5~($m$^{3}$s$^{-1}$)\n",
    "\n",
    "For the particle volumes use\n",
    "- $d_p$ (min) $= 0.5 \\times 10^{-9}$ (m)\n",
    "- $d_p$ (max) $= 1000 \\times 10^{-9}$ (m)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "Task 2 (20%): For a conservation of mass validation comparing the mass flow compute the volume of the particles entering and leaving the reactor.\n",
    "\n",
    "Task 3 (60%): Add in a recycle stream to your PFR reactor. Find the recyle ratio $R$ that produces the number average particle distribution of $d_{p, avg} = 3.5 \\times 10^{-9}$. "
   ]
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  {
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   "id": "abcca7d2",
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   "source": [
    "<img src=\"PFR.svg\">"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7abb60ff",
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   "source": [
    "The number average particle distribution can be found using the following function from a vector $n$:\n",
    "\n",
    "```python\n",
    "# Function for computing number average particle distribution\n",
    "def dp_avg(n, dp):\n",
    "    return np.sum(n * dp) / np.sum(n)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7dfd712e",
   "metadata": {},
   "source": [
    "Task 4 (30%): Use the solution from CSTR reactor below and compare the performance of the CSTR with the PFR reactor by sizing the materials for the same flowrates."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d3af4b1",
   "metadata": {},
   "source": [
    "Note that the marks total to $130$ points\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "3e68fd53",
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   "source": [
    "# imports and variables\n",
    "\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "t_total = 5e-0                           # [s], change from 2e-4 to 2e-0 or any \n",
    "                                         # other number   \n",
    "nt = 1000                                # number of iteration steps \n",
    "dt = t_total / nt                        # [s], small time step during the interation\n",
    "dp_min = 0.5e-9                          # [m]\n",
    "dp_max = 1000e-9                         # [m]\n",
    "vp_min = np.pi/6 * (dp_min)**3           # [m^3]\n",
    "vp_max = np.pi/6 * (dp_max)**3           # [m^3]\n",
    "# Initialization\n",
    "vp_num = int(np.log(vp_max / vp_min) // np.log(2) + 2)\n",
    "vp = np.zeros((vp_num))\n",
    "for i in range(vp_num): \n",
    "    vp[i] = vp_min * 2**i \n",
    "    \n",
    "n = np.zeros((vp_num))\n",
    "k_B = 1.380649e-23                       # [J / K = N m / K = kg m^2 / (s^2 * K)]\n",
    "mu = 17.2e-6                             # dynamische Viskosität Luft [Pa*s = N * s /m^2 = kg / ( m * s)] \n",
    "T = 293                                  # [K]\n",
    "\n",
    "beta_pre = (2*k_B*T)/(3*mu)              # [kg m^2 *K *m * s/ (s^2 * K * kg) = m^3/s]\n",
    "\n",
    "\n",
    "beta_n = np.zeros((vp_num, vp_num))\n",
    "for i in range(vp_num): \n",
    "    for j in range(vp_num): \n",
    "        beta_n[i,j] = beta_pre * (1/vp[i]**(1/3) + 1/vp[j]**(1/3)) *(vp[i]**(1/3) + vp[j]**(1/3))\n",
    "        # [m^3 /s * 1/m * m = m^3/s]\n",
    "        \n",
    "# Initial conditions\n",
    "n_0 = np.zeros((vp_num))\n",
    "start_bin = 1                 # this is an easy way to select a starting size\n",
    "n_0[start_bin] = 1e17         # [#/m^3]\n",
    "n = n_0.copy()                # copy the initial condition to our interation array \n",
    "Q = 1\n",
    "B = 1\n",
    "N_0 = 1e17\n",
    "\n",
    "n_zeit = np.zeros((nt))\n",
    "n_formed = np.zeros((vp_num))\n",
    "\n",
    "# Main solver loop\n",
    "nn = np.empty_like(n)\n",
    "n_formed = np.empty_like(n)\n",
    "n_in = np.empty_like(n)\n",
    "n_in[1] = N_0\n",
    "for t in range(nt - 1):\n",
    "    nn = n.copy()\n",
    "    for i in range(1, vp_num, 1):\n",
    "        sum1 = np.zeros((vp_num))\n",
    "        sum2 = np.zeros((vp_num))\n",
    "        sum3 = np.zeros((vp_num))\n",
    "        for j in range(0, i - 1, 1):\n",
    "            sum1[i] = sum1[i] + (2**(j-i+1) * beta_n[i-1,j] * nn[j])\n",
    "        for j in range(0, i - 0, 1):    \n",
    "            sum2[i] = sum2[i] + (2**(j-i) * beta_n[i,j] * nn[j])\n",
    "        for j in range(i, vp_num - 1, 1): \n",
    "            sum3[i]= sum3[i] + (beta_n[i,j] * nn[j])\n",
    "        n_formed[i] = nn[i] + dt * ( \\\n",
    "                             nn[i-1] * sum1[i] + \\\n",
    "                             1/2 * beta_n[i-1,i-1] * nn[i-1]**2 - \\\n",
    "                             nn[i] * sum2[i] - \\\n",
    "                             nn[i] * sum3[i]     \n",
    "                             )\n",
    "        n[i] = nn[i] + dt * (B * n_formed[i] + Q * n_in[i] - nn[i] * Q)\n",
    "\n",
    "            \n",
    "\n",
    "def fun_q(v): \n",
    "    return A * v **(1/3)\n",
    "\n",
    "def an_n(v): # analytic solution\n",
    "    return (1/(A * v**(1/3.0))) * np.exp((3/2.0) * (vp_min**(2/3.0) - v**(2/3.0))/(A * tau)) * (N_0 / tau)\n",
    "\n",
    "tau = B/Q  # Verweilzeit\n",
    "A = 1e-1\n",
    "q = np.array(fun_q(vp))\n",
    "n_an = np.zeros(vp_num)\n",
    "\n",
    "for j in range(1, vp_num, 1):\n",
    "    n_an[j] = an_n(vp[j])"
   ]
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  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "dc2a392e",
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       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', { width: x_pixels, height: y_pixels });\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_message = function (type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function () {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function (fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n",
       "    fig.rubberband_canvas.style.cursor = msg['cursor'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_message = function (fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message('ack', {});\n",
       "};\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function (fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            var img = evt.data;\n",
       "            if (img.type !== 'image/png') {\n",
       "                /* FIXME: We get \"Resource interpreted as Image but\n",
       "                 * transferred with MIME type text/plain:\" errors on\n",
       "                 * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "                 * to be part of the websocket stream */\n",
       "                img.type = 'image/png';\n",
       "            }\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src\n",
       "                );\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                img\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig['handle_' + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "};\n",
       "\n",
       "// from https://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function (e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e) {\n",
       "        e = window.event;\n",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n",
       "\n",
       "    return { x: x, y: y };\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * https://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys(original) {\n",
       "    return Object.keys(original).reduce(function (obj, key) {\n",
       "        if (typeof original[key] !== 'object') {\n",
       "            obj[key] = original[key];\n",
       "        }\n",
       "        return obj;\n",
       "    }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function (event, name) {\n",
       "    var canvas_pos = mpl.findpos(event);\n",
       "\n",
       "    if (name === 'button_press') {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.key_event = function (event, name) {\n",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.key === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.key;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.key !== 'Control') {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    else if (event.altKey && event.key !== 'Alt') {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    else if (event.shiftKey && event.key !== 'Shift') {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k' + event.key;\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n",
       "    if (name === 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message('toolbar_button', { name: name });\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "\n",
       "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
       "// prettier-ignore\n",
       "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "var comm_websocket_adapter = function (comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.binaryType = comm.kernel.ws.binaryType;\n",
       "    ws.readyState = comm.kernel.ws.readyState;\n",
       "    function updateReadyState(_event) {\n",
       "        if (comm.kernel.ws) {\n",
       "            ws.readyState = comm.kernel.ws.readyState;\n",
       "        } else {\n",
       "            ws.readyState = 3; // Closed state.\n",
       "        }\n",
       "    }\n",
       "    comm.kernel.ws.addEventListener('open', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('close', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('error', updateReadyState);\n",
       "\n",
       "    ws.close = function () {\n",
       "        comm.close();\n",
       "    };\n",
       "    ws.send = function (m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function (msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        var data = msg['content']['data'];\n",
       "        if (data['blob'] !== undefined) {\n",
       "            data = {\n",
       "                data: new Blob(msg['buffers'], { type: data['blob'] }),\n",
       "            };\n",
       "        }\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(data);\n",
       "    });\n",
       "    return ws;\n",
       "};\n",
       "\n",
       "mpl.mpl_figure_comm = function (comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element;\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error('Failed to find cell for figure', id, fig);\n",
       "        return;\n",
       "    }\n",
       "    fig.cell_info[0].output_area.element.on(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "    fig.resizeObserverInstance.unobserve(fig.canvas_div);\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable();\n",
       "    fig.parent_element.innerHTML =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "    fig.close_ws(fig, msg);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.close_ws = function (fig, msg) {\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message('ack', {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    if (event.target !== this) {\n",
       "        // Ignore bubbled events from children.\n",
       "        return;\n",
       "    }\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('tabindex', 0);\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "mpl.find_output_cell = function (html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i = 0; i < ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code') {\n",
       "            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] === html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "};\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel !== null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "dp_start = np.zeros((vp_num))\n",
    "dp_end = np.zeros((vp_num))\n",
    "dp_start = (6/np.pi * vp[start_bin])**(1/3)\n",
    "dp_end = (6/np.pi * vp)**(1/3)\n",
    "\n",
    "fig, ax1 = plt.subplots()\n",
    "color1 = \"tab:blue\"\n",
    "ax1.semilogx(dp_end, n, drawstyle=\"steps-mid\", \\\n",
    "             label=\"numeric solution\", color = color1) \n",
    "ax1.set_ylabel(\"particle number in #/m^3\", color = color1)\n",
    "ax1.tick_params(axis=\"y\", labelcolor = color1)\n",
    "title_string = \"normalized particle size distribution\" + \"\\n\" + \\\n",
    "    \"total time = \" + \\\n",
    "    str(np.format_float_scientific(t_total, precision=0))\n",
    "ax1.set_title(title_string)\n",
    "ax1.set_xlabel(\"particle diameter in m\")\n",
    "\n",
    "color2 = \"tab:red\"\n",
    "ax2 = ax1.twinx() \n",
    "ax2.semilogx(dp_end, n_an, drawstyle=\"steps-mid\", \\\n",
    "             label=\"analytic solution\", color = color2) \n",
    "ax2.set_ylabel(\"particle number in #/m^3\", color = color2)\n",
    "ax2.tick_params(axis=\"y\", labelcolor = color2)\n",
    "#ax2.set_ylim(1.2e24,1.22e24)\n",
    "\n",
    "\n",
    "# ask matplotlib for the plotted objects and their labels\n",
    "lines, labels = ax1.get_legend_handles_labels()\n",
    "lines2, labels2 = ax2.get_legend_handles_labels()\n",
    "ax2.legend(lines + lines2, labels + labels2, loc=0)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7e51684c",
   "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": "3.10.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}