<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <link rel="stylesheet" href="{{VENDOR_CDN}}/katex.min.css">
  <script src="{{VENDOR_CDN}}/katex.min.js"></script>
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background: #ffffff;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      padding: 12px 16px;
      min-height: 100%;
      width: 100%;
      user-select: none;
    }

    .diagram-stage {
      width: 100%;
      max-width: 580px;
      position: relative;
    }

    svg {
      width: 100%;
      height: auto;
      display: block;
      overflow: visible;
    }

    /* Math & Cards */
    .steps-row {
      display: flex;
      gap: 8px;
      width: 100%;
      max-width: 580px;
      margin-top: 8px;
    }

    .step-card {
      flex: 1;
      background: #f8fafc;
      border: 2px solid #e2e8f0;
      border-radius: 8px;
      padding: 8px 6px;
      text-align: center;
      cursor: pointer;
      transition: border-color 0.25s ease, background 0.25s ease, box-shadow 0.25s ease;
    }

    .step-card.active {
      background: #f0f9ff;
      border-color: #0284c7;
      box-shadow: 0 2px 8px rgba(2, 132, 199, 0.15);
    }

    .step-num {
      font-size: 11px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.5px;
      color: #64748b;
      margin-bottom: 4px;
    }

    .step-card.active .step-num {
      color: #0284c7;
    }

    .step-math {
      font-size: 14px;
      min-height: 26px;
      display: flex;
      align-items: center;
      justify-content: center;
    }

    /* Controls */
    .control-bar {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 12px;
      margin-top: 6px;
    }

    .btn-ctrl {
      background: #f1f5f9;
      border: 1px solid #cbd5e1;
      border-radius: 6px;
      padding: 4px 10px;
      font-size: 13px;
      font-weight: 600;
      color: #334155;
      cursor: pointer;
      display: flex;
      align-items: center;
      gap: 4px;
    }

    .btn-ctrl:active {
      background: #e2e8f0;
    }

    .p-trail {
      stroke-dasharray: 4 4;
      animation: dash 1s linear infinite;
    }

    @keyframes dash {
      to { stroke-dashoffset: -8; }
    }
  </style>
</head>
<body>

  
  <div class="diagram-stage">
    <svg viewBox="0 0 540 230">
      <defs>
        
        <linearGradient id="wallGrad" x1="0%" y1="0%" x2="100%" y2="100%">
          <stop offset="0%" stop-color="#38bdf8" stop-opacity="0.35"/>
          <stop offset="100%" stop-color="#0284c7" stop-opacity="0.6"/>
        </linearGradient>
        <linearGradient id="backWallGrad" x1="0%" y1="0%" x2="100%" y2="100%">
          <stop offset="0%" stop-color="#94a3b8" stop-opacity="0.12"/>
          <stop offset="100%" stop-color="#64748b" stop-opacity="0.2"/>
        </linearGradient>
        <linearGradient id="molGrad" x1="0%" y1="0%" x2="100%" y2="100%">
          <stop offset="0%" stop-color="#f43f5e"/>
          <stop offset="100%" stop-color="#be123c"/>
        </linearGradient>

        <marker id="arrowRight" viewBox="0 0 10 10" refX="6" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
          <path d="M 0 1.5 L 8 5 L 0 8.5 z" fill="#e11d48"/>
        </marker>
        <marker id="arrowLeft" viewBox="0 0 10 10" refX="6" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
          <path d="M 0 1.5 L 8 5 L 0 8.5 z" fill="#2563eb"/>
        </marker>
        <marker id="arrowDim" viewBox="0 0 10 10" refX="5" refY="5" markerWidth="5" markerHeight="5" orient="auto-start-reverse">
          <path d="M 0 2 L 6 5 L 0 8 z" fill="#64748b"/>
        </marker>
      </defs>

      
      <polygon points="60,40 100,10 100,130 60,160" fill="url(#backWallGrad)" stroke="#94a3b8" stroke-width="1.5"/>

      
      <line x1="100" y1="10" x2="460" y2="10" stroke="#cbd5e1" stroke-width="1.5" stroke-dasharray="4 4"/>
      <line x1="100" y1="130" x2="460" y2="130" stroke="#cbd5e1" stroke-width="1.5" stroke-dasharray="4 4"/>

      
      <line x1="60" y1="40" x2="420" y2="40" stroke="#64748b" stroke-width="1.5"/>
      <line x1="60" y1="160" x2="420" y2="160" stroke="#64748b" stroke-width="1.5"/>

      
      <polygon id="wallA" points="420,40 460,10 460,130 420,160" fill="url(#wallGrad)" stroke="#0284c7" stroke-width="2"/>
      
      
      <g transform="translate(440, 85)">
        <circle cx="0" cy="0" r="13" fill="#ffffff" fill-opacity="0.9" stroke="#0284c7" stroke-width="1.5"/>
        <text x="0" y="4" text-anchor="middle" font-size="12" font-weight="700" fill="#0369a1">A</text>
      </g>

      
      <g transform="translate(0, 190)">
        <line x1="60" y1="0" x2="420" y2="0" stroke="#64748b" stroke-width="1.5"/>
        <line x1="60" y1="-8" x2="60" y2="8" stroke="#64748b" stroke-width="1.5"/>
        <line x1="420" y1="-8" x2="420" y2="8" stroke="#64748b" stroke-width="1.5"/>
        <path d="M 66 0 L 76 -3 L 76 3 Z" fill="#64748b"/>
        <path d="M 414 0 L 404 -3 L 404 3 Z" fill="#64748b"/>
        <rect x="225" y="-12" width="30" height="24" fill="#ffffff" rx="4"/>
        <text x="240" y="5" text-anchor="middle" font-size="14" font-weight="700" fill="#334155" font-style="italic">L</text>
      </g>

      
      <line x1="80" y1="100" x2="420" y2="100" stroke="#e2e8f0" stroke-width="2" stroke-dasharray="3 3"/>

      
      <g id="vectorGroup">
        
        <g id="vecRight">
          <line x1="240" y1="75" x2="310" y2="75" stroke="#e11d48" stroke-width="2.5" marker-end="url(#arrowRight)"/>
          <text x="275" y="66" text-anchor="middle" font-size="12" font-weight="700" fill="#e11d48">+v<tspan dy="2" font-size="9">x</tspan></text>
        </g>
        
        <g id="vecLeft" opacity="0.9">
          <line x1="310" y1="125" x2="240" y2="125" stroke="#2563eb" stroke-width="2.5" marker-end="url(#arrowLeft)"/>
          <text x="275" y="142" text-anchor="middle" font-size="12" font-weight="700" fill="#2563eb">-v<tspan dy="2" font-size="9">x</tspan></text>
        </g>
      </g>

      
      <g id="molecule" transform="translate(240, 100)">
        <circle cx="0" cy="0" r="11" fill="url(#molGrad)" filter="drop-shadow(0 2px 4px rgba(225,29,72,0.3))"/>
        <text x="0" y="4" text-anchor="middle" font-size="11" font-weight="700" fill="#ffffff">m</text>
      </g>

      
      <circle id="impactRing" cx="420" cy="100" r="16" fill="none" stroke="#f43f5e" stroke-width="2.5" opacity="0"/>
    </svg>
  </div>

  
  <div class="steps-row">
    <div class="step-card active" id="card0" onclick="setStep(0)">
      <div class="step-num">1. Momentum Change</div>
      <div class="step-math" id="math0"></div>
    </div>
    <div class="step-card" id="card1" onclick="setStep(1)">
      <div class="step-num">2. Time Between Hits</div>
      <div class="step-math" id="math1"></div>
    </div>
    <div class="step-card" id="card2" onclick="setStep(2)">
      <div class="step-num">3. Force on Wall</div>
      <div class="step-math" id="math2"></div>
    </div>
  </div>

  
  <div class="control-bar">
    <button class="btn-ctrl" id="playBtn" onclick="togglePlay()">
      <span id="playIcon">⏸</span> <span id="playText">Pause</span>
    </button>
  </div>

  <script>
    // Render KaTeX expressions cleanly
    window.addEventListener('DOMContentLoaded', () => {
      katex.render("\\Delta p = 2mv_x", document.getElementById('math0'), { displayMode: false });
      katex.render("\\Delta t = \\frac{2L}{v_x}", document.getElementById('math1'), { displayMode: false });
      katex.render("F = \\frac{m v_x^2}{L}", document.getElementById('math2'), { displayMode: false });
    });

    let currentStep = 0;
    let isPlaying = true;
    let autoTimer = null;
    let animFrame = null;

    const mol = document.getElementById('molecule');
    const ring = document.getElementById('impactRing');
    const vecRight = document.getElementById('vecRight');
    const vecLeft = document.getElementById('vecLeft');

    // Particle motion animation parameters
    const minX = 75;
    const maxX = 420;
    let posX = 160;
    let velX = 2.4;

    function animate() {
      if (isPlaying) {
        posX += velX;

        // Bounce right wall (Impact on Area A)
        if (posX >= maxX) {
          posX = maxX;
          velX = -Math.abs(velX);
          triggerImpact();
        } 
        // Bounce left wall
        else if (posX <= minX) {
          posX = minX;
          velX = Math.abs(velX);
        }

        mol.setAttribute('transform', `translate(${posX}, 100)`);

        // Highlight active direction
        if (velX > 0) {
          vecRight.setAttribute('opacity', '1');
          vecLeft.setAttribute('opacity', '0.25');
        } else {
          vecRight.setAttribute('opacity', '0.25');
          vecLeft.setAttribute('opacity', '1');
        }
      }
      animFrame = requestAnimationFrame(animate);
    }

    function triggerImpact() {
      ring.setAttribute('r', '8');
      ring.setAttribute('opacity', '1');
      ring.setAttribute('stroke-width', '3');
      
      let start = performance.now();
      function expand(time) {
        let elapsed = (time - start) / 300;
        if (elapsed < 1) {
          ring.setAttribute('r', 8 + elapsed * 18);
          ring.setAttribute('opacity', 1 - elapsed);
          requestAnimationFrame(expand);
        } else {
          ring.setAttribute('opacity', '0');
        }
      }
      requestAnimationFrame(expand);
    }

    function setStep(index) {
      currentStep = index;
      for (let i = 0; i < 3; i++) {
        document.getElementById(`card${i}`).classList.toggle('active', i === index);
      }
    }

    function togglePlay() {
      isPlaying = !isPlaying;
      document.getElementById('playIcon').textContent = isPlaying ? '⏸' : '▶';
      document.getElementById('playText').textContent = isPlaying ? 'Pause' : 'Play';
      if (isPlaying) {
        startStepTimer();
      } else {
        clearInterval(autoTimer);
      }
    }

    function startStepTimer() {
      clearInterval(autoTimer);
      autoTimer = setInterval(() => {
        if (isPlaying) {
          currentStep = (currentStep + 1) % 3;
          setStep(currentStep);
        }
      }, 4000);
    }

    // Start loops
    animate();
    startStepTimer();
  </script>
</body>
</html>

Kinetic Particle Theory of Gases: Motion, Collisions, and Space

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <title>Maxwell-Boltzmann Speed Distribution</title>
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      color: #1e293b;
      background: #ffffff;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      padding: 10px 14px 8px;
      width: 100vw;
      height: 100vh;
      overflow: hidden;
      user-select: none;
      -webkit-user-select: none;
    }
    .graph-container {
      width: 100%;
      max-width: 680px;
      flex: 1;
      min-height: 0;
      position: relative;
    }
    svg {
      width: 100%;
      height: 100%;
      display: block;
      overflow: visible;
    }
    .axis-line { stroke: #64748b; stroke-width: 1.5; stroke-linecap: round; }
    .grid-line { stroke: #f1f5f9; stroke-width: 1; }
    .tick-text { font-size: 11px; fill: #64748b; font-variant-numeric: tabular-nums; }
    .axis-label { font-size: 12.5px; font-weight: 600; fill: #334155; }
    
    .curve-cold { stroke: #1d4ed8; stroke-width: 2.2; fill: rgba(29, 78, 216, 0.08); }
    .curve-hot { stroke: #ea580c; stroke-width: 2.2; fill: rgba(234, 88, 12, 0.08); }
    .curve-live { stroke: #0284c7; stroke-width: 3; fill: rgba(2, 132, 199, 0.16); }

    .rms-cold { stroke: #1d4ed8; stroke-width: 1.5; stroke-dasharray: 4,4; opacity: 0.85; }
    .rms-hot { stroke: #ea580c; stroke-width: 1.5; stroke-dasharray: 4,4; opacity: 0.85; }
    .rms-live { stroke: #0284c7; stroke-width: 2; stroke-dasharray: 4,4; }

    .tag-bg {
      fill: #ffffff;
      fill-opacity: 0.94;
      stroke-width: 1;
      filter: drop-shadow(0 1px 2px rgba(0,0,0,0.08));
    }
    .rms-tag {
      font-size: 10.5px;
      font-weight: 700;
      font-variant-numeric: tabular-nums;
    }

    .legend-box {
      font-size: 11.5px;
      font-weight: 700;
    }

    .controls {
      width: 100%;
      max-width: 540px;
      display: flex;
      flex-direction: column;
      gap: 6px;
      padding-top: 4px;
    }
    .slider-row {
      display: flex;
      align-items: center;
      justify-content: space-between;
      gap: 12px;
    }
    .slider-label {
      font-size: 12.5px;
      font-weight: 600;
      color: #475569;
      white-space: nowrap;
    }
    .temp-badge {
      font-size: 13.5px;
      font-weight: 700;
      color: #0369a1;
      background: #e0f2fe;
      border: 1px solid #bae6fd;
      padding: 3px 10px;
      border-radius: 6px;
      min-width: 82px;
      text-align: center;
      font-variant-numeric: tabular-nums;
    }
    input[type=range] {
      flex: 1;
      height: 6px;
      -webkit-appearance: none;
      appearance: none;
      background: #e2e8f0;
      border-radius: 3px;
      outline: none;
      cursor: pointer;
    }
    input[type=range]::-webkit-slider-thumb {
      -webkit-appearance: none;
      width: 18px;
      height: 18px;
      border-radius: 50%;
      background: #0284c7;
      border: 2px solid #ffffff;
      box-shadow: 0 1px 4px rgba(0,0,0,0.25);
      cursor: pointer;
    }
    input[type=range]::-moz-range-thumb {
      width: 18px;
      height: 18px;
      border-radius: 50%;
      background: #0284c7;
      border: 2px solid #ffffff;
      box-shadow: 0 1px 4px rgba(0,0,0,0.25);
      cursor: pointer;
    }
    .presets {
      display: flex;
      gap: 8px;
      justify-content: center;
    }
    .btn {
      font-size: 11.5px;
      font-weight: 600;
      padding: 4px 14px;
      border-radius: 6px;
      border: 1px solid #cbd5e1;
      background: #f8fafc;
      color: #475569;
      cursor: pointer;
      transition: background 0.15s, color 0.15s, border-color 0.15s;
    }
    .btn:hover {
      background: #f1f5f9;
      border-color: #94a3b8;
    }
    .btn.active {
      background: #0284c7;
      color: #ffffff;
      border-color: #0284c7;
    }

    @media (max-width: 480px) {
      .axis-label { font-size: 11px; }
      .tick-text { font-size: 9.5px; }
      .rms-tag { font-size: 9.5px; }
      .slider-label { font-size: 11.5px; }
      .temp-badge { font-size: 12px; min-width: 72px; padding: 2px 8px; }
      .btn { font-size: 11px; padding: 3px 10px; }
    }
  </style>
</head>
<body>

  <div class="graph-container">
    <svg id="svgGraph" viewBox="0 0 580 340">
      
      <g id="grid"></g>

      
      <path id="pathCold" class="curve-cold" />
      <path id="pathHot" class="curve-hot" />

      
      <path id="pathLive" class="curve-live" />

      
      <g id="rmsColdGroup">
        <line id="lineRmsCold" class="rms-cold" />
        <rect id="bgRmsCold" class="tag-bg" stroke="#1d4ed8" rx="4" />
        <text id="textRmsCold" class="rms-tag" fill="#1d4ed8" text-anchor="middle" dominant-baseline="central"></text>
      </g>

      <g id="rmsHotGroup">
        <line id="lineRmsHot" class="rms-hot" />
        <rect id="bgRmsHot" class="tag-bg" stroke="#ea580c" rx="4" />
        <text id="textRmsHot" class="rms-tag" fill="#ea580c" text-anchor="middle" dominant-baseline="central"></text>
      </g>

      <g id="rmsLiveGroup">
        <line id="lineRmsLive" class="rms-live" />
        <rect id="bgRmsLive" class="tag-bg" stroke="#0284c7" rx="4" stroke-width="1.5" />
        <text id="textRmsLive" class="rms-tag" fill="#0284c7" text-anchor="middle" dominant-baseline="central"></text>
      </g>

      
      <line x1="52" y1="285" x2="560" y2="285" class="axis-line" />
      <line x1="52" y1="25" x2="52" y2="285" class="axis-line" />

      
      <text x="306" y="325" text-anchor="middle" class="axis-label">Particle Speed v (m/s)</text>
      <text x="16" y="155" text-anchor="middle" class="axis-label" transform="rotate(-90 16 155)">Probability Density P(v)</text>

      
      <g class="legend-box" transform="translate(190, 42)">
        <rect x="-6" y="-12" width="94" height="18" rx="4" fill="#ffffff" fill-opacity="0.9" stroke="#93c5fd" stroke-width="1"/>
        <text x="41" y="-3" fill="#1d4ed8" text-anchor="middle" dominant-baseline="central">300 K (Cold)</text>
      </g>

      <g class="legend-box" transform="translate(380, 118)">
        <rect x="-6" y="-12" width="88" height="18" rx="4" fill="#ffffff" fill-opacity="0.9" stroke="#fdba74" stroke-width="1"/>
        <text x="38" y="-3" fill="#ea580c" text-anchor="middle" dominant-baseline="central">900 K (Hot)</text>
      </g>
    </svg>
  </div>

  <div class="controls">
    <div class="slider-row">
      <span class="slider-label">Temperature T:</span>
      <input type="range" id="tempSlider" min="200" max="1000" step="10" value="450" aria-label="Temperature slider">
      <div id="tempVal" class="temp-badge">450 K</div>
    </div>
    <div class="presets">
      <button class="btn" onclick="setTemp(300)">300 K</button>
      <button class="btn" onclick="setTemp(600)">600 K</button>
      <button class="btn" onclick="setTemp(900)">900 K</button>
    </div>
  </div>

  <script>
    const X_MIN = 0, X_MAX = 2000;
    const Y_MIN = 0, Y_MAX = 0.0028;
    const LEFT = 52, RIGHT = 560, TOP = 25, BOTTOM = 285;
    const WIDTH = RIGHT - LEFT;
    const HEIGHT = BOTTOM - TOP;

    const M = 0.028; // Nitrogen molar mass (kg/mol)
    const R = 8.314; // J/(mol·K)

    function mb(v, T) {
      const a = M / (2 * R * T);
      return 4 * Math.PI * Math.pow(a / Math.PI, 1.5) * v * v * Math.exp(-a * v * v);
    }

    function vRMS(T) {
      return Math.sqrt(3 * R * T / M);
    }

    function mapX(v) {
      return LEFT + (v / X_MAX) * WIDTH;
    }

    function mapY(p) {
      return BOTTOM - (p / Y_MAX) * HEIGHT;
    }

    function buildPath(T) {
      let d = `M ${mapX(0).toFixed(1)} ${BOTTOM}`;
      const steps = 180;
      for (let i = 0; i <= steps; i++) {
        const v = (i / steps) * X_MAX;
        const p = mb(v, T);
        d += ` L ${mapX(v).toFixed(1)} ${mapY(p).toFixed(1)}`;
      }
      d += ` L ${mapX(X_MAX).toFixed(1)} ${BOTTOM} Z`;
      return d;
    }

    function initGrid() {
      const grid = document.getElementById('grid');
      let html = '';
      for (let v = 400; v <= 2000; v += 400) {
        const x = mapX(v);
        html += `<line x1="${x}" y1="${TOP}" x2="${x}" y2="${BOTTOM}" class="grid-line" />`;
        html += `<text x="${x}" y="${BOTTOM + 18}" text-anchor="middle" class="tick-text">${v}</text>`;
      }
      grid.innerHTML = html;
    }

    function updateMarker(idPrefix, T, yPosOffset, customLabel) {
      const v = vRMS(T);
      const x = mapX(v);
      const p = mb(v, T);
      const yPeak = mapY(p);

      const line = document.getElementById(`line${idPrefix}`);
      line.setAttribute('x1', x);
      line.setAttribute('y1', yPeak);
      line.setAttribute('x2', x);
      line.setAttribute('y2', BOTTOM);

      const text = document.getElementById(`text${idPrefix}`);
      const bg = document.getElementById(`bg${idPrefix}`);

      const label = customLabel || `v_rms: ${Math.round(v)} m/s`;
      text.textContent = label;

      // Position badge safely above curve peak / point to prevent overlap
      const tagY = Math.max(TOP + 12, yPeak - yPosOffset);
      text.setAttribute('x', x);
      text.setAttribute('y', tagY);

      // Dynamically size background pill
      const bbox = text.getBBox();
      const padX = 6;
      const padY = 3;
      bg.setAttribute('x', bbox.x - padX);
      bg.setAttribute('y', bbox.y - padY);
      bg.setAttribute('width', bbox.width + padX * 2);
      bg.setAttribute('height', bbox.height + padY * 2);
    }

    const slider = document.getElementById('tempSlider');
    const tempVal = document.getElementById('tempVal');
    const pathLive = document.getElementById('pathLive');
    const pathCold = document.getElementById('pathCold');
    const pathHot = document.getElementById('pathHot');

    function renderLive(T) {
      tempVal.textContent = `${T} K`;
      pathLive.setAttribute('d', buildPath(T));

      // Show/hide live marker if overlapping exact reference temps or update badge
      const isExactCold = (T === 300);
      const isExactHot = (T === 900);

      document.getElementById('rmsColdGroup').style.opacity = isExactCold ? '0.3' : '1';
      document.getElementById('rmsHotGroup').style.opacity = isExactHot ? '0.3' : '1';

      updateMarker('RmsLive', T, 16, `Live v_rms (${Math.round(vRMS(T))} m/s)`);

      document.querySelectorAll('.presets .btn').forEach(btn => {
        btn.classList.toggle('active', btn.textContent.trim() === `${T} K`);
      });
    }

    function setTemp(T) {
      slider.value = T;
      renderLive(T);
    }

    slider.addEventListener('input', (e) => {
      renderLive(Number(e.target.value));
    });

    // Initialize chart
    initGrid();
    pathCold.setAttribute('d', buildPath(300));
    pathHot.setAttribute('d', buildPath(900));
    
    // Position static 300 K and 900 K RMS markers with clear badges
    updateMarker('RmsCold', 300, 14, `v_rms (${Math.round(vRMS(300))} m/s)`);
    updateMarker('RmsHot', 900, 14, `v_rms (${Math.round(vRMS(900))} m/s)`);

    // Initial live state
    renderLive(450);
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <title>Mean Free Path & Collision Cylinder</title>
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      color: #1e293b;
      background: transparent;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: flex-start;
      padding: 10px;
      min-height: 100vh;
      box-sizing: border-box;
      user-select: none;
    }

    .container {
      width: 100%;
      max-width: 660px;
      display: flex;
      flex-direction: column;
      gap: 10px;
    }

    .panels-container {
      display: flex;
      flex-direction: row;
      gap: 10px;
      width: 100%;
      align-items: stretch;
    }

    .panel {
      flex: 1;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 8px;
      padding: 8px;
      display: flex;
      flex-direction: column;
      align-items: center;
    }

    .panel-title {
      font-size: 13px;
      font-weight: 700;
      color: #0369a1;
      margin-bottom: 4px;
      text-align: center;
    }
    .panel-title.walk-title {
      color: #334155;
    }

    .panel svg {
      width: 100%;
      height: auto;
      max-height: 200px;
      display: block;
    }

    .footer {
      width: 100%;
      display: flex;
      flex-wrap: wrap;
      align-items: center;
      justify-content: space-between;
      gap: 10px;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 8px;
      padding: 8px 12px;
    }

    .math-card {
      display: flex;
      align-items: center;
      flex-wrap: wrap;
      gap: 12px;
      font-size: 13px;
      color: #1e293b;
      font-weight: 500;
    }

    .formula-item {
      display: inline-flex;
      align-items: center;
      gap: 4px;
    }

    .fraction {
      display: inline-flex;
      flex-direction: column;
      vertical-align: middle;
      text-align: center;
      padding: 0 2px;
      font-size: 0.9em;
      line-height: 1.1;
    }
    .fraction .num {
      border-bottom: 1.5px solid #1e293b;
      padding-bottom: 1px;
    }
    .fraction .den {
      padding-top: 1px;
    }

    .divider-pipe {
      color: #cbd5e1;
      font-weight: 300;
    }

    .btn {
      background: #0284c7;
      color: #ffffff;
      border: none;
      border-radius: 6px;
      padding: 7px 16px;
      font-size: 13px;
      font-weight: 600;
      cursor: pointer;
      display: inline-flex;
      align-items: center;
      gap: 6px;
      transition: background-color 0.15s ease;
    }
    .btn:hover {
      background: #0369a1;
    }
    .btn:active {
      background: #075985;
    }

    @media (max-width: 520px) {
      .panels-container {
        flex-direction: column;
      }
      .panel svg {
        max-height: 180px;
      }
      .footer {
        flex-direction: column;
        align-items: stretch;
        text-align: center;
      }
      .math-card {
        justify-content: center;
      }
      .btn {
        justify-content: center;
        width: 100%;
      }
    }
  </style>
</head>
<body>

  <div class="container">
    
    <div class="panels-container">
      
      
      <div class="panel">
        <div class="panel-title">Collision Cylinder (Radius <i>d</i>, Length <i>λ</i>)</div>
        <svg viewBox="0 0 320 190" aria-label="Collision Cylinder Diagram">
          <defs>
            <linearGradient id="cylGrad" x1="0%" y1="0%" x2="0%" y2="100%">
              <stop offset="0%" stop-color="#0284c7" stop-opacity="0.18" />
              <stop offset="50%" stop-color="#0284c7" stop-opacity="0.06" />
              <stop offset="100%" stop-color="#0284c7" stop-opacity="0.22" />
            </linearGradient>
            <radialGradient id="particleGrad" cx="35%" cy="35%" r="65%">
              <stop offset="0%" stop-color="#38bdf8" />
              <stop offset="70%" stop-color="#0284c7" />
              <stop offset="100%" stop-color="#0369a1" />
            </radialGradient>
            <radialGradient id="hitGrad" cx="35%" cy="35%" r="65%">
              <stop offset="0%" stop-color="#f87171" />
              <stop offset="70%" stop-color="#dc2626" />
              <stop offset="100%" stop-color="#991b1b" />
            </radialGradient>
            <radialGradient id="missGrad" cx="35%" cy="35%" r="65%">
              <stop offset="0%" stop-color="#cbd5e1" />
              <stop offset="70%" stop-color="#94a3b8" />
              <stop offset="100%" stop-color="#64748b" />
            </radialGradient>
            <marker id="arrow-blue" viewBox="0 0 10 10" refX="5" refY="5" markerWidth="5" markerHeight="5" orient="auto-start-reverse">
              <path d="M 0 1.5 L 8 5 L 0 8.5 z" fill="#0284c7" />
            </marker>
            <marker id="arrow-dim" viewBox="0 0 10 10" refX="5" refY="5" markerWidth="5" markerHeight="5" orient="auto-start-reverse">
              <path d="M 0 1.5 L 8 5 L 0 8.5 z" fill="#64748b" />
            </marker>
          </defs>

          
          <line x1="45" y1="95" x2="270" y2="95" stroke="#94a3b8" stroke-width="1.2" stroke-dasharray="3,3" />

          
          <path d="M 45,45 L 270,45 A 18,50 0 0,1 270,145 L 45,145 A 18,50 0 0,1 45,45 Z" fill="url(#cylGrad)" stroke="#0284c7" stroke-width="1.5" />
          
          
          <ellipse cx="45" cy="95" rx="18" ry="50" fill="none" stroke="#0284c7" stroke-width="1.2" stroke-dasharray="3,3" opacity="0.6" />
          
          
          <ellipse cx="270" cy="95" rx="18" ry="50" fill="#e0f2fe" fill-opacity="0.3" stroke="#0284c7" stroke-width="1.5" />

          
          <line x1="45" y1="95" x2="45" y2="47" stroke="#0369a1" stroke-width="1.8" marker-end="url(#arrow-blue)" />
          <text x="33" y="75" font-size="12" font-weight="700" fill="#0369a1">r = d</text>

          
          <line x1="45" y1="162" x2="270" y2="162" stroke="#64748b" stroke-width="1.2" marker-start="url(#arrow-dim)" marker-end="url(#arrow-dim)" />
          <line x1="45" y1="150" x2="45" y2="168" stroke="#94a3b8" stroke-width="1" />
          <line x1="270" y1="150" x2="270" y2="168" stroke="#94a3b8" stroke-width="1" />
          <text x="157" y="177" text-anchor="middle" font-size="12" font-weight="700" fill="#475569">λ (mean free path)</text>

          
          <circle cx="185" cy="72" r="11" fill="url(#hitGrad)" stroke="#b91c1c" stroke-width="1.2" />
          <circle cx="185" cy="72" r="22" fill="none" stroke="#ef4444" stroke-width="1" stroke-dasharray="2,2" opacity="0.7" />
          <text x="185" y="55" text-anchor="middle" font-size="10" font-weight="700" fill="#dc2626">Target (Hit)</text>

          
          <circle cx="215" cy="165" r="11" fill="url(#missGrad)" stroke="#64748b" stroke-width="1.2" />
          <text x="250" y="170" font-size="10" font-weight="600" fill="#64748b">Miss</text>

          
          <circle id="moving-mol" cx="45" cy="95" r="11" fill="url(#particleGrad)" stroke="#0284c7" stroke-width="1.5" />
          <path id="vel-vector" d="M 58 95 L 90 95" stroke="#0284c7" stroke-width="1.8" marker-end="url(#arrow-blue)" />
          <text x="45" y="118" text-anchor="middle" font-size="9" font-weight="700" fill="#0369a1">d</text>
        </svg>
      </div>

      
      <div class="panel">
        <div class="panel-title walk-title">Random Walk (Mean Path <i>λ</i>)</div>
        <svg viewBox="0 0 300 190" aria-label="Random Walk Diagram">
          
          <path d="M 35,150 L 95,50 L 190,130 L 265,35" fill="none" stroke="#94a3b8" stroke-width="2" stroke-linejoin="round" stroke-linecap="round" stroke-dasharray="4,3" />
          
          
          <text x="50" y="105" font-size="12" font-weight="700" fill="#0284c7">λ₁</text>
          <text x="145" y="85" font-size="12" font-weight="700" fill="#0284c7">λ₂</text>
          <text x="235" y="80" font-size="12" font-weight="700" fill="#0284c7">λ₃</text>

          
          <circle cx="35" cy="150" r="4" fill="#0284c7" />
          <circle cx="95" cy="50" r="6" fill="#dc2626" />
          <text x="95" y="38" text-anchor="middle" font-size="9" font-weight="600" fill="#dc2626">Collision</text>
          
          <circle cx="190" cy="130" r="6" fill="#dc2626" />
          <circle cx="265" cy="35" r="6" fill="#dc2626" />

          
          <circle id="walk-mol" cx="35" cy="150" r="9" fill="url(#particleGrad)" stroke="#0284c7" stroke-width="1.5" />
          
          <text x="150" y="175" text-anchor="middle" font-size="11" font-weight="600" fill="#64748b">
            Average straight segment = &langle;λ&rangle;
          </text>
        </svg>
      </div>

    </div>

    
    <div class="footer">
      <div class="math-card">
        <div class="formula-item">
          <span><b>Volume:</b> <i>V</i> = &pi; <i>d</i><sup>2</sup> <i>λ</i></span>
        </div>
        <span class="divider-pipe">|</span>
        <div class="formula-item">
          <span><b>Mean Free Path:</b> <i>λ</i> =</span>
          <span class="fraction">
            <span class="num">1</span>
            <span class="den">&radic;2 &pi; <i>d</i><sup>2</sup> <i>n</i></span>
          </span>
        </div>
      </div>
      <button id="animBtn" class="btn" aria-label="Toggle animation">
        <span id="btnIcon">▶</span> <span id="btnText">Animate</span>
      </button>
    </div>
  </div>

  <script>
    const molCyl = document.getElementById('moving-mol');
    const velVec = document.getElementById('vel-vector');
    const molWalk = document.getElementById('walk-mol');
    const animBtn = document.getElementById('animBtn');
    const btnIcon = document.getElementById('btnIcon');
    const btnText = document.getElementById('btnText');

    let isPlaying = false;
    let progress = 0;
    let animId = null;

    const walkPts = [
      { x: 35, y: 150 },
      { x: 95, y: 50 },
      { x: 190, y: 130 },
      { x: 265, y: 35 }
    ];

    function getWalkPos(t) {
      const numSegs = walkPts.length - 1;
      const scaled = t * numSegs;
      const idx = Math.min(Math.floor(scaled), numSegs - 1);
      const subT = scaled - idx;
      const p0 = walkPts[idx];
      const p1 = walkPts[idx + 1];
      return {
        x: p0.x + (p1.x - p0.x) * subT,
        y: p0.y + (p1.y - p0.y) * subT
      };
    }

    function animate() {
      progress = (progress + 0.006) % 1;

      // 1. Collision cylinder translation
      const curX = 45 + progress * 140;
      molCyl.setAttribute('cx', curX);
      velVec.setAttribute('d', `M ${curX + 13} 95 L ${curX + 45} 95`);

      // 2. Random walk translation
      const pos = getWalkPos(progress);
      molWalk.setAttribute('cx', pos.x);
      molWalk.setAttribute('cy', pos.y);

      if (isPlaying) {
        animId = requestAnimationFrame(animate);
      }
    }

    animBtn.addEventListener('click', () => {
      isPlaying = !isPlaying;
      if (isPlaying) {
        btnIcon.textContent = '⏸';
        btnText.textContent = 'Pause';
        animate();
      } else {
        btnIcon.textContent = '▶';
        btnText.textContent = 'Animate';
        if (animId) cancelAnimationFrame(animId);
      }
    });
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }

    body {
      width: 100%;
      height: 100%;
      background: #ffffff;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      padding: 12px;
      user-select: none;
      -webkit-user-select: none;
    }

    .header-bar {
      width: 100%;
      max-width: 600px;
      display: flex;
      flex-wrap: wrap;
      justify-content: space-between;
      align-items: center;
      gap: 6px;
      margin-bottom: 8px;
    }

    .badge-group {
      display: flex;
      flex-direction: column;
      gap: 4px;
      margin-left: auto;
    }

    .badge {
      font-size: 11px;
      font-weight: 600;
      padding: 3px 8px;
      border-radius: 6px;
      background: #f1f5f9;
      color: #475569;
      border: 1px solid #e2e8f0;
      white-space: nowrap;
      display: flex;
      align-items: center;
      gap: 5px;
    }

    .badge-dot {
      width: 6px;
      height: 6px;
      border-radius: 50%;
      background: #0284c7;
    }

    .legend {
      display: flex;
      align-items: center;
      gap: 6px;
      font-size: 12px;
      font-weight: 600;
      color: #0891b2;
    }

    .legend-dot {
      width: 10px;
      height: 10px;
      border-radius: 50%;
      background: #06b6d4;
      box-shadow: 0 0 6px rgba(6, 182, 212, 0.6);
    }

    .sim-container {
      position: relative;
      width: 100%;
      max-width: 600px;
      flex: 1;
      min-height: 240px;
      border: 2px solid #cbd5e1;
      border-radius: 12px;
      background: #f8fafc;
      overflow: hidden;
    }

    canvas {
      display: block;
      width: 100%;
      height: 100%;
    }

    .controls {
      width: 100%;
      max-width: 600px;
      display: flex;
      justify-content: center;
      align-items: center;
      gap: 12px;
      margin-top: 8px;
    }

    .btn {
      padding: 6px 14px;
      font-size: 12px;
      font-weight: 600;
      border-radius: 6px;
      border: 1px solid #cbd5e1;
      background: #ffffff;
      color: #334155;
      cursor: pointer;
      display: flex;
      align-items: center;
      gap: 6px;
      transition: background 0.15s ease, border-color 0.15s ease;
    }

    .btn:hover {
      background: #f1f5f9;
      border-color: #94a3b8;
    }

    .btn.active {
      background: #0ea5e9;
      color: #ffffff;
      border-color: #0284c7;
    }
  </style>
</head>
<body>

  <div class="header-bar">
    <div class="legend">
      <span class="legend-dot"></span>
      <span>Tracked Molecule</span>
    </div>
    <div class="badge-group">
      <div class="badge">
        <span class="badge-dot"></span>
        <span>Particle Volume ≪ Container Volume</span>
      </div>
      <div class="badge">
        <span class="badge-dot" style="background:#10b981;"></span>
        <span>Elastic Collisions: Energy Conserved</span>
      </div>
    </div>
  </div>

  <div class="sim-container" id="container">
    <canvas id="simCanvas"></canvas>
  </div>

  <div class="controls">
    <button class="btn" id="btnPlay">⏸ Pause</button>
    <button class="btn" id="btnSpeed">⏱ Slow Motion</button>
    <button class="btn" id="btnReset">↺ Reset Trail</button>
  </div>

  <script>
    const canvas = document.getElementById('simCanvas');
    const ctx = canvas.getContext('2d');
    const container = document.getElementById('container');
    const btnPlay = document.getElementById('btnPlay');
    const btnSpeed = document.getElementById('btnSpeed');
    const btnReset = document.getElementById('btnReset');

    let width = 0;
    let height = 0;
    let isRunning = true;
    let isSlow = false;
    let speedFactor = 1.0;

    const NUM_PARTICLES = 20;
    const RADIUS = 6;
    const TRAIL_MAX = 50;

    let particles = [];
    let trail = [];

    function resize() {
      const rect = container.getBoundingClientRect();
      const dpr = window.devicePixelRatio || 1;
      width = rect.width;
      height = rect.height;
      canvas.width = width * dpr;
      canvas.height = height * dpr;
      ctx.resetTransform();
      ctx.scale(dpr, dpr);
    }

    function initParticles() {
      particles = [];
      trail = [];
      const baseSpeed = 2.2;

      for (let i = 0; i < NUM_PARTICLES; i++) {
        let attempts = 0;
        let p;
        while (attempts < 200) {
          const angle = Math.random() * Math.PI * 2;
          p = {
            x: RADIUS + 10 + Math.random() * (width - 2 * RADIUS - 20),
            y: RADIUS + 10 + Math.random() * (height - 2 * RADIUS - 20),
            vx: Math.cos(angle) * baseSpeed,
            vy: Math.sin(angle) * baseSpeed,
            r: RADIUS,
            isCyan: i === 0
          };

          let overlap = false;
          for (let j = 0; j < particles.length; j++) {
            const dx = p.x - particles[j].x;
            const dy = p.y - particles[j].y;
            if (Math.hypot(dx, dy) < p.r + particles[j].r + 4) {
              overlap = true;
              break;
            }
          }
          if (!overlap) break;
          attempts++;
        }
        particles.push(p);
      }
    }

    function update() {
      if (!isRunning) return;

      const dt = isSlow ? 0.35 : 1.0;

      for (let i = 0; i < particles.length; i++) {
        const p = particles[i];
        p.x += p.vx * dt;
        p.y += p.vy * dt;

        // Wall collisions (elastic)
        if (p.x - p.r < 0) {
          p.x = p.r;
          p.vx = -p.vx;
        } else if (p.x + p.r > width) {
          p.x = width - p.r;
          p.vx = -p.vx;
        }

        if (p.y - p.r < 0) {
          p.y = p.r;
          p.vy = -p.vy;
        } else if (p.y + p.r > height) {
          p.y = height - p.r;
          p.vy = -p.vy;
        }
      }

      // Particle-particle collisions (elastic)
      for (let i = 0; i < particles.length; i++) {
        for (let j = i + 1; j < particles.length; j++) {
          const p1 = particles[i];
          const p2 = particles[j];

          const dx = p2.x - p1.x;
          const dy = p2.y - p1.y;
          const dist = Math.hypot(dx, dy);

          if (dist < p1.r + p2.r && dist > 0) {
            // Normal unit vector
            const nx = dx / dist;
            const ny = dy / dist;

            // Tangent unit vector
            const tx = -ny;
            const ty = nx;

            // Dot product velocities
            const v1n = p1.vx * nx + p1.vy * ny;
            const v1t = p1.vx * tx + p1.vy * ty;
            const v2n = p2.vx * nx + p2.vy * ny;
            const v2t = p2.vx * tx + p2.vy * ty;

            // Equal mass 1D elastic collision on normal component
            const newV1n = v2n;
            const newV2n = v1n;

            p1.vx = newV1n * nx + v1t * tx;
            p1.vy = newV1n * ny + v1t * ty;
            p2.vx = newV2n * nx + v2t * tx;
            p2.vy = newV2n * ny + v2t * ty;

            // Separate overlapping particles
            const overlap = (p1.r + p2.r) - dist;
            p1.x -= (overlap / 2) * nx;
            p1.y -= (overlap / 2) * ny;
            p2.x += (overlap / 2) * nx;
            p2.y += (overlap / 2) * ny;
          }
        }
      }

      // Record trail for highlighted cyan particle
      const cyan = particles[0];
      if (cyan) {
        trail.push({ x: cyan.x, y: cyan.y });
        if (trail.length > TRAIL_MAX) {
          trail.shift();
        }
      }
    }

    function render() {
      ctx.clearRect(0, 0, width, height);

      // Draw faint container grid
      ctx.strokeStyle = '#f1f5f9';
      ctx.lineWidth = 1;
      const gridSize = 30;
      for (let x = gridSize; x < width; x += gridSize) {
        ctx.beginPath();
        ctx.moveTo(x, 0);
        ctx.lineTo(x, height);
        ctx.stroke();
      }
      for (let y = gridSize; y < height; y += gridSize) {
        ctx.beginPath();
        ctx.moveTo(0, y);
        ctx.lineTo(width, y);
        ctx.stroke();
      }

      // Draw trail for highlighted particle
      if (trail.length > 1) {
        for (let i = 1; i < trail.length; i++) {
          const alpha = (i / trail.length) * 0.7;
          ctx.strokeStyle = `rgba(6, 182, 212, ${alpha})`;
          ctx.lineWidth = 2 * (i / trail.length) + 0.8;
          ctx.lineCap = 'round';
          ctx.beginPath();
          ctx.moveTo(trail[i - 1].x, trail[i - 1].y);
          ctx.lineTo(trail[i].x, trail[i].y);
          ctx.stroke();
        }
      }

      // Draw particles
      for (let i = 0; i < particles.length; i++) {
        const p = particles[i];
        ctx.beginPath();
        ctx.arc(p.x, p.y, p.r, 0, Math.PI * 2);

        if (p.isCyan) {
          // Glow
          ctx.shadowColor = 'rgba(6, 182, 212, 0.8)';
          ctx.shadowBlur = 8;
          ctx.fillStyle = '#06b6d4';
          ctx.fill();
          ctx.lineWidth = 1.5;
          ctx.strokeStyle = '#0891b2';
          ctx.stroke();
          ctx.shadowBlur = 0; // reset
        } else {
          ctx.fillStyle = '#94a3b8';
          ctx.fill();
          ctx.lineWidth = 1;
          ctx.strokeStyle = '#64748b';
          ctx.stroke();
        }
      }
    }

    function loop() {
      update();
      render();
      requestAnimationFrame(loop);
    }

    window.addEventListener('resize', () => {
      resize();
    });

    btnPlay.addEventListener('click', () => {
      isRunning = !isRunning;
      btnPlay.textContent = isRunning ? '⏸ Pause' : '▶ Play';
      btnPlay.classList.toggle('active', !isRunning);
    });

    btnSpeed.addEventListener('click', () => {
      isSlow = !isSlow;
      btnSpeed.classList.toggle('active', isSlow);
      btnSpeed.textContent = isSlow ? '⚡ Normal Speed' : '⏱ Slow Motion';
    });

    btnReset.addEventListener('click', () => {
      trail = [];
    });

    // Start simulation
    resize();
    initParticles();
    requestAnimationFrame(loop);
  </script>
</body>
</html>

OGS.13.PS.7

Aligned learning resources

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