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template
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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<script src="https://cdn.bokeh.org/bokeh/release/bokeh-2.4.2.min.js"
crossorigin="anonymous"></script>
<script src="https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.4.2.min.js"
crossorigin="anonymous"></script>
<script src="https://cdn.bokeh.org/bokeh/release/bokeh-api-2.4.2.min.js"
crossorigin="anonymous"></script>
<script src="themodel.js"></script>
<script src=https://cdnjs.cloudflare.com/ajax/libs/mathjs/10.0.0/math.js></script>
<!-- use KaTeX for nice equations -->
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.15.2/dist/katex.min.css" integrity="sha384-MlJdn/WNKDGXveldHDdyRP1R4CTHr3FeuDNfhsLPYrq2t0UBkUdK2jyTnXPEK1NQ" crossorigin="anonymous">
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.15.2/dist/katex.min.js" integrity="sha384-VQ8d8WVFw0yHhCk5E8I86oOhv48xLpnDZx5T9GogA/Y84DcCKWXDmSDfn13bzFZY" crossorigin="anonymous"></script>
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.15.2/dist/contrib/auto-render.min.js" integrity="sha384-+XBljXPPiv+OzfbB3cVmLHf4hdUFHlWNZN5spNQ7rmHTXpd7WvJum6fIACpNNfIR" crossorigin="anonymous"
onload="renderMathInElement(document.body);"></script>
<title>model</title>
<style type="text/css">
html, body {
height: 100%;
}
/* Style the body */
body {
margin: 0;
display: flex;
flex-direction: column;
background-color: lightslategray;
}
/* this contains the main content */
.content {
flex: 1 0 auto;
}
/* Column container */
.row {
display: flex;
}
/* Create two unequal columns that sit next to each other */
/* Sidebar/left column */
.side {
background-color: white;
padding: 20px;
}
/* Main column */
.main {
background-color: white;
padding: 20px;
}
/* Responsive layout - when the screen is less than ###px wide, make the two columns stack on top of each other instead of next to each other */
@media screen and (max-width: 1000px) {
.row {
flex-direction: column;
}
.side {
border-bottom: 2px dashed #262626;
}
}
</style>
</head>
<body>
<div class="content" style="width: 90%; margin:auto; min-width: 400px; max-width: 1500px;">
<div class="side" style="flex: 3; border-bottom: 2px dashed #262626;">
This numerical model solves a 1-D transport problem, representative of a column experiment. The compound is subject to advection, dispersion, sorption and reaction.
The model employes a fully implicit Crank-Nicholson scheme to compute reactive and dispersive processes:<br>
<div style="text-align: center;">
<div style=" border: solid 2px black; display: inline-block">
Top Cell: \( (-s) c_{2}^{k+1} + (1 +s + r) c_{1}^{k+1} = c_{1}^{k} \) <br>
Internal Cells: \( (-s) c_{i-1}^{k+1} + (1 +s + r) c_{i}^{k+1} + (-s) c_{i+1}^{k} = c_{i}^{k} \) <br>
Bottom Cell: \( (-s) c_{N-1}^{k+1} + (1 +s + r) c_{N}^{k+1} = c_{N}^{k} \)
</div>
</div>
With s = \( \mathrm{\frac{D * dt}{dx^2}} \) and r = \( \lambda *\mathrm{dt} \), dispersion coefficient D, first-order rate constant \( \lambda \), time step dt, distance between cells dx, number of cells N, index of cell i and timestep k
</div>
<div class="row">
<div class="main" style="flex: 7">
+placeholder1+
</div>
<div class="side" style="flex: 3; border-left: 2px solid #262626;">
+placeholder2+
</div>
</div>
<div class="row">
<div class="main" style="flex: 7; border-top: 2px dashed #262626;">
+placeholder3+
</div>
<div class="side" style="flex: 3; border-left: 2px solid #262626;">
+placeholder4+
</div>
</div>
</div>
</div>
</div>
</body>
</html>