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https://github.com/vale981/neutrino_oscillations
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init
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88
index.html
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index.html
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<!DOCTYPE html>
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<html>
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<head>
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<title>Neutrino Oscillations</title>
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<link rel="stylesheet" href="main.css" type="text/css" media="screen" />
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<link rel="stylesheet" href="https://cdn.rawgit.com/Chalarangelo/mini.css/v3.0.1/dist/mini-default.min.css">
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<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous">
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<!-- The loading of KaTeX is deferred to speed up page rendering -->
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<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.js" integrity="sha384-g7c+Jr9ZivxKLnZTDUhnkOnsh30B4H0rpLUpJ4jAIKs4fnJI+sEnkvrMWph2EDg4" crossorigin="anonymous"></script>
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<!-- To automatically render math in text elements, include the auto-render extension: -->
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<script defer src="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/contrib/auto-render.min.js" integrity="sha384-mll67QQFJfxn0IYznZYonOWZ644AWYC+Pt2cHqMaRhXVrursRwvLnLaebdGIlYNa" crossorigin="anonymous"
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onload="renderMathInElement(document.body);"></script>
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</head>
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<body>
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<header>
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<a href="#" class="logo">Neutrino Oscillation Playground</a>
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</header>
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<div class="container">
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<div class="row">
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<div id="neutrinos" class="card fluid">
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<canvas id="neutrinorender"></canvas>
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</div>
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</div>
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<div class="row">
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<div class="card fluid" id="settings">
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<h3>Current Settings</h3>
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<div class="row">
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<div class="col-sm-6" id="pmns">
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</div>
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<div class="col-sm-3" id="sliders_1">
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</div>
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<div class="col-sm-3" id="sliders_2">
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</div>
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</div>
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</div>
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</div>
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<div class="row">
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<form id="controls">
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<div class="row">
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<div class="col-sm-6">
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<fieldset>
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<legend>Mixing Angles in \(^\circ\)</legend>
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<label for="t12">\(\theta_{12}\)</label>
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<input type="range" step=".1" min="0" max="90" id="t12" />
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<br>
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<label for="t13">\(\theta_{13}\)</label>
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<input type="range" step=".1" max="90" id="t13" />
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<br>
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<label for="t23">\(\theta_{23}\)</label>
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<input type="range" step=".1" min="0" max="90" id="t23" />
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</fieldset>
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<fieldset>
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<legend>Squared Mass Differences \([10^{-4}\text{eV}^{2}]\)</legend>
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<label for="ms13">\(\Delta m_{13}^2\)</label>
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<input type="range" step=".1" min="0" max="30" id="ms13" />
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<br>
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<label for="ms23">\(\Delta m_{23}^2\)</label>
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<input type="range" step=".1" min="0" max="30" id="ms23" />
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</fieldset>
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</div>
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<div class="col-sm-6">
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<fieldset>
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<legend>Observatory Settings</legend>
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<label for="L_max">\(L_{\text{max}}\) [km]</label>
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<input type="range" min="0" max="1000" id="L_max" />
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<br>
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<label for="energy">\(E\) [MeV]</label>
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<input type="range" step=".1" min="0" max="1000" id="energy" />
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</fieldset>
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</div>
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</div>
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</form>
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</div>
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</div>
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<script src="lib/chart.min.js"></script>
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<script src="lib/math.min.js"></script>
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<script src="index.js"></script>
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</body>
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</html>
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256
index.js
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index.js
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///////////////////////////////////////////////////////////////////////////////
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// Setup/Globals //
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///////////////////////////////////////////////////////////////////////////////
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const ctx = document.getElementById('neutrinorender').getContext('2d');
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const render = new Chart(ctx, {
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type: 'line',
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options: {
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responsive: true,
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maintainAspectRatio: false,
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tooltips: {
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mode: 'index',
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intersect: false,
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},
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animation: {
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duration: 0,
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},
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scales: {
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x: {
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scaleLabel: {
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display: true,
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labelString: "Distance [km]"
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}
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},
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y: {
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scaleLabel: {
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display: true,
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labelString: "Survival Probability"
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}
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}
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}
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},
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});
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const controls = document.forms.controls;
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const settings = document.getElementById('settings');
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// Mixing Angle Experimental Values, degrees
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const t12 = 33.44;
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const t23 = 49;
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const t13 = 8.57;
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// squared mass differences, 1e-4 eV^2
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const ms13 = 25.1;
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const ms23 = 24.4;
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// default settings
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const defaultNeutrinoData =
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{
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t12,
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t23,
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t13,
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ms13,
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ms23,
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L_range: [0, 100],
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E: 6 // MeV
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};
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///////////////////////////////////////////////////////////////////////////////
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// Util //
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///////////////////////////////////////////////////////////////////////////////
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function deg_to_rad(x) {
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return (x / 180) * math.pi
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}
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///////////////////////////////////////////////////////////////////////////////
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// Neutrino Mixing Specifics //
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///////////////////////////////////////////////////////////////////////////////
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/**
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* Compute the PMNS Matrix.
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*
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* Angle Arguments in Degrees.
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*/
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function pmns(t12, t23, t13) {
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t12 = deg_to_rad(t12);
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t13 = deg_to_rad(t13);
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t23 = deg_to_rad(t23);
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// Compute all sines, cosines
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let c12 = math.cos(t12);
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let c13 = math.cos(t13);
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let c23 = math.cos(t23);
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let s12 = math.sin(t12);
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let s13 = math.sin(t13);
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let s23 = math.sin(t23);
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return math.matrix([
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[c12 * c13, s12 * c13, s13],
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[-s12 * c23 - c12 * s23 * s13, c12 * c23 - s12 * s23 * s13, s23 * c13],
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[s12 * s23 - c12 * c23 * s13, -c12 * s23 - s12 * c23 * s13, c23 * c13]
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]);
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}
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function propagation_step(pmns_matrix, ms13, ms23, dL, E) {
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E = E / 1000;
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ms13 = ms13 * 1e-4;
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ms23 = ms23 * 1e-4;
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const propagator = math.matrix([[math.exp(math.complex(0, -ms13 * 2.54 * dL / E)), 0, 0],
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[0, math.exp(math.complex(0, -ms23 * 2.54 * dL / E)), 0],
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[0, 0, 1]]);
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return math.multiply(pmns_matrix, propagator, math.transpose(pmns_matrix));
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}
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function propagate(initial_state, pmns_matrix, ms13, ms23, L, E) {
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const propagator = propagation_step(pmns_matrix, ms13, ms23, L, E);
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return math.multiply(propagation_step, initial_state);
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}
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function state_to_probabilies(state) {
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return state.map(value => math.multiply(value.conjugate(), value).re);
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}
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function plot_propagation(state, neutrino_data) {
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const {t12, t23, t13, ms13, ms23, L_range, E} = neutrino_data;
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pmns_matrix = pmns(t12, t23, t13);
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dL = ((L_range[1] - L_range[0]) / 1000);
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lengths = math.range(L_range[0], L_range[1], dL);
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common_options = {
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pointRadius: 0,
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};
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datasets = [
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{
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data: [],
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borderColor: 'green',
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label: 'electron',
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...common_options
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},
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{
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data: [],
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borderColor: 'blue',
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label: 'muon',
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...common_options
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},
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{
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data: [],
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borderColor: 'red',
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label: 'tauon',
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...common_options
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}
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];
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propagator = propagation_step(pmns_matrix, ms13, ms23, dL, E)
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for (const length of lengths._data) {
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state = math.multiply(propagator, state);
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probs = state_to_probabilies(state);
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probs.forEach((p, index) => {
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datasets[index[0]].data.push(p);
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})
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}
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render.data.labels = lengths.map(l => math.round(l, 2))._data;
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render.data.datasets = datasets;
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render.update({
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duration: 0,
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easing: 'easeInOutBack'
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});
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}
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function initForm() {
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controls.elements.t13.value = t13;
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controls.elements.t12.value = t12;
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controls.elements.t23.value = t23;
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controls.elements.L_max.value = defaultNeutrinoData.L_range[1];
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controls.elements.energy.value = defaultNeutrinoData.E;
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controls.elements.ms13.value = ms13;
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controls.elements.ms23.value = ms23;
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}
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function getNeutrinoData() {
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return {
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...defaultNeutrinoData,
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t13: controls.elements.t13.value,
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t12: controls.elements.t12.value,
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t23: controls.elements.t23.value,
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ms13: controls.elements.ms13.value,
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ms23: controls.elements.ms23.value,
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E: controls.elements.energy.value,
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L_range: [0, controls.elements.L_max.value],
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};
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}
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function renderPmnsMatrix(pmns_matrix) {
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let result = "$$U=\\begin{pmatrix}\n";
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for (let row of pmns_matrix._data) {
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for (let val of row) {
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result += `${math.round(val, 3)} &`
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}
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result = result.slice(0, -1);
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result += "\\\\\n";
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}
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result += "\\end{pmatrix}$$";
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return result;
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}
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function displayCurrentSettings() {
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const {t12, t23, t13, ms13, ms23, L_range, E} = getNeutrinoData();
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pmns_matrix = pmns(t12, t23, t13);
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// render pmns
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settings.querySelector("#pmns").textContent = renderPmnsMatrix(pmns_matrix);
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settings.querySelector("#sliders_1").innerHTML = `
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\\(\\theta_{12} = ${t12}^\\circ\\)
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<br>
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\\(\\theta_{13} = ${t13}^\\circ\\)
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<br>
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\\(\\theta_{23} = ${t23}^\\circ\\)
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`;
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settings.querySelector("#sliders_2").innerHTML = `
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\\(\\Delta m_{13}^2 = ${ms13}\\cdot 10^{-4}\\text{GeV}\\)
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<br>
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\\(\\Delta m_{23}^2 = ${ms23}\\cdot 10^{-4}\\text{GeV}\\)
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<br>
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\\(L_\\text{max} = ${L_range[1]}\\text{km}\\)
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<br>
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\\(E = ${E}\\text{MeV}\\)
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`;
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renderMathInElement(settings);
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};
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document.addEventListener("DOMContentLoaded", (event) => {
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initForm();
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displayCurrentSettings();
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plot_propagation(math.matrix([
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[1],
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[0],
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[0]
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]), defaultNeutrinoData);
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});
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controls.addEventListener('input', () => {
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displayCurrentSettings();
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plot_propagation(math.matrix([
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[1],
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[0],
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[0]
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]), getNeutrinoData());
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});
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13
lib/chart.min.js
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lib/chart.min.js
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lib/math.min.js
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lib/math.min.js
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main.css
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main.css
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.container {
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max-width: 1500px !important;
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}
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#neutrinos {
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position: relative;
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width: 100%;
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height: 20vw;
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}
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#controls {
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width: 100%;
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}
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#settings {
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width: 100%;
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}
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