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* Particle Sampler
* Generates particle positions using CDF sampling of quantum probability distributions
* Based on the approach from https://github.com/kavan010/Atoms
*/
class ParticleSampler {
constructor(quantumEngine) {
this.quantumEngine = quantumEngine;
// Pre-calculated particle cache for common orbitals
// Stores normalized particle positions (0-1 range) that can be scaled
this.particleCache = null;
this.initializeCache();
}
/**
* Initialize pre-calculated particle cache for common orbitals
* This significantly speeds up loading for frequently used orbitals
*/
initializeCache() {
console.log('Initializing particle cache for common orbitals...');
// Pre-generate particles for common orbitals with a base count
const baseCount = 10000; // Base particle count for cache
this.particleCache = {
// 1s orbital (most common)
'1_0_0': this.generateAndNormalizeParticles(1, 0, 0, baseCount),
// 2s orbital
'2_0_0': this.generateAndNormalizeParticles(2, 0, 0, baseCount),
// 2p orbitals
'2_1_-1': this.generateAndNormalizeParticles(2, 1, -1, baseCount),
'2_1_0': this.generateAndNormalizeParticles(2, 1, 0, baseCount),
'2_1_1': this.generateAndNormalizeParticles(2, 1, 1, baseCount),
// 3s orbital
'3_0_0': this.generateAndNormalizeParticles(3, 0, 0, baseCount),
// 3p orbitals
'3_1_-1': this.generateAndNormalizeParticles(3, 1, -1, baseCount),
'3_1_0': this.generateAndNormalizeParticles(3, 1, 0, baseCount),
'3_1_1': this.generateAndNormalizeParticles(3, 1, 1, baseCount),
// 3d orbitals
'3_2_-2': this.generateAndNormalizeParticles(3, 2, -2, baseCount),
'3_2_-1': this.generateAndNormalizeParticles(3, 2, -1, baseCount),
'3_2_0': this.generateAndNormalizeParticles(3, 2, 0, baseCount),
'3_2_1': this.generateAndNormalizeParticles(3, 2, 1, baseCount),
'3_2_2': this.generateAndNormalizeParticles(3, 2, 2, baseCount)
};
console.log('Particle cache initialized with', Object.keys(this.particleCache).length, 'orbitals');
}
/**
* Generate and normalize particles for caching
* @param {number} n - Principal quantum number
* @param {number} l - Azimuthal quantum number
* @param {number} m - Magnetic quantum number
* @param {number} count - Number of particles
* @returns {Array} Normalized particle data
*/
generateAndNormalizeParticles(n, l, m, count) {
const particles = [];
// Pre-calculate max probability for normalization
const sampleSize = 100;
let maxProb = 0;
for (let i = 0; i < sampleSize; i++) {
const r = this.sampleRadius(n, l);
const theta = this.sampleTheta(l, m);
const phi = this.samplePhi(m);
const prob = this.quantumEngine.probabilityDensity(n, l, m, r, theta, phi);
if (prob > maxProb) maxProb = prob;
}
// Generate particles
for (let i = 0; i < count; i++) {
const r = this.sampleRadius(n, l);
const theta = this.sampleTheta(l, m);
const phi = this.samplePhi(m);
const cartesian = this.sphericalToCartesian(
r * CONSTANTS.SCALE_FACTOR,
theta,
phi
);
const probability = this.quantumEngine.probabilityDensity(n, l, m, r, theta, phi);
particles.push({
position: cartesian,
probability: maxProb > 0 ? probability / maxProb : 0
});
}
return particles;
}
/**
* Get particles from cache or generate new ones
* @param {number} n - Principal quantum number
* @param {number} l - Azimuthal quantum number
* @param {number} m - Magnetic quantum number
* @param {number} particleCount - Desired particle count
* @returns {Array} Particle data
*/
getParticlesFromCache(n, l, m, particleCount) {
const key = `${n}_${l}_${m}`;
// Check if orbital is in cache
if (this.particleCache && this.particleCache[key]) {
const cached = this.particleCache[key];
const baseCount = cached.length;
console.log(`Using cached particles for orbital (${n},${l},${m})`);
// If requested count is close to base count, return cached particles
if (particleCount <= baseCount * 1.2) {
// Return subset or all cached particles
if (particleCount >= baseCount) {
return cached;
} else {
// Return random subset
const step = Math.floor(baseCount / particleCount);
return cached.filter((_, i) => i % step === 0).slice(0, particleCount);
}
} else {
// Need more particles - use cached as base and add more
const additionalCount = particleCount - baseCount;
const additional = this.generateOrbitalParticlesInternal(n, l, m, additionalCount);
return [...cached, ...additional];
}
}
// Not in cache, generate normally
return null;
}
/**
* Convert spherical coordinates to Cartesian
* @param {number} r - Radius
* @param {number} theta - Polar angle (0 to π)
* @param {number} phi - Azimuthal angle (0 to 2π)
* @returns {{x: number, y: number, z: number}}
*/
sphericalToCartesian(r, theta, phi) {
const x = r * Math.sin(theta) * Math.cos(phi);
const y = r * Math.sin(theta) * Math.sin(phi);
const z = r * Math.cos(theta);
return { x, y, z };
}
/**
* Sample radius using CDF (Cumulative Distribution Function) sampling
* This is more efficient and accurate than rejection sampling
* @param {number} n - Principal quantum number
* @param {number} l - Azimuthal quantum number
* @param {number} resolution - Number of samples for CDF (default 1000)
* @returns {number} Sampled radius
*/
sampleRadius(n, l, resolution = 1000) {
// Maximum radius to sample (most probability within ~3n² Bohr radii)
const maxR = 3 * n * n * CONSTANTS.BOHR_RADIUS;
// Minimum radius to avoid singularities at origin
const minR = 0.01 * CONSTANTS.BOHR_RADIUS;
// Build CDF array
const cdf = [];
let sum = 0;
for (let i = 0; i < resolution; i++) {
// Start from minR instead of 0 to avoid origin
const r = minR + (i / resolution) * (maxR - minR);
// Radial probability: P(r) = r² |R(n,l,r)|²
const R = this.quantumEngine.radialWaveFunction(n, l, r);
const prob = r * r * R * R;
sum += prob;
cdf.push(sum);
}
// Check if sum is valid
if (sum === 0 || !isFinite(sum)) {
console.warn(`Invalid CDF sum for radius sampling: ${sum}`);
return maxR / 2;
}
// Normalize CDF
for (let i = 0; i < cdf.length; i++) {
cdf[i] /= sum;
}
// Sample from CDF
const rand = Math.random();
for (let i = 0; i < cdf.length; i++) {
if (rand <= cdf[i]) {
return minR + (i / resolution) * (maxR - minR);
}
}
return maxR;
}
/**
* Sample theta (polar angle) using CDF sampling
* @param {number} l - Azimuthal quantum number
* @param {number} m - Magnetic quantum number
* @param {number} resolution - Number of samples for CDF (default 500)
* @returns {number} Sampled theta
*/
sampleTheta(l, m, resolution = 500) {
// Build CDF array for theta
const cdf = [];
let sum = 0;
// Small epsilon to avoid exact 0 and PI
const epsilon = 0.001;
for (let i = 0; i < resolution; i++) {
// Map to range [epsilon, PI - epsilon] to avoid poles
const theta = epsilon + (i / resolution) * (CONSTANTS.PI - 2 * epsilon);
// For theta distribution, we need to integrate over phi
// |Y(l,m,θ,φ)|² integrated over φ gives us the theta-only distribution
// For real spherical harmonics, the phi integral gives a constant factor
const absM = Math.abs(m);
const legendre = window.legendrePolynomial(l, absM, Math.cos(theta));
const prob = legendre * legendre * Math.sin(theta); // sin(theta) is the Jacobian
sum += prob;
cdf.push(sum);
}
// Check if sum is valid
if (sum === 0 || !isFinite(sum)) {
console.warn(`Invalid CDF sum for theta sampling: ${sum}`);
return CONSTANTS.PI / 2; // Return equator
}
// Normalize CDF
for (let i = 0; i < cdf.length; i++) {
cdf[i] /= sum;
}
// Sample from CDF
const rand = Math.random();
for (let i = 0; i < cdf.length; i++) {
if (rand <= cdf[i]) {
return epsilon + (i / resolution) * (CONSTANTS.PI - 2 * epsilon);
}
}
return CONSTANTS.PI / 2;
}
/**
* Sample phi (azimuthal angle) using CDF sampling
* For orbitals with m != 0, phi distribution depends on cos²(m*phi) or sin²(m*phi)
* @param {number} m - Magnetic quantum number
* @param {number} resolution - Number of samples for CDF (default 500)
* @returns {number} Sampled phi
*/
samplePhi(m, resolution = 500) {
// For m = 0, phi is uniformly distributed
if (m === 0) {
return Math.random() * CONSTANTS.TWO_PI;
}
// For m != 0, we need to sample according to the phi distribution
// Real spherical harmonics:
// m > 0: proportional to cos²(m*phi)
// m < 0: proportional to sin²(|m|*phi)
const cdf = [];
let sum = 0;
const absM = Math.abs(m);
for (let i = 0; i < resolution; i++) {
const phi = (i / resolution) * CONSTANTS.TWO_PI;
let prob;
if (m > 0) {
// cos²(m*phi) distribution
const val = Math.cos(m * phi);
prob = val * val;
} else {
// sin²(|m|*phi) distribution
const val = Math.sin(absM * phi);
prob = val * val;
}
sum += prob;
cdf.push(sum);
}
// Check if sum is valid
if (sum === 0 || !isFinite(sum)) {
console.warn(`Invalid CDF sum for phi sampling: ${sum}`);
return Math.random() * CONSTANTS.TWO_PI;
}
// Normalize CDF
for (let i = 0; i < cdf.length; i++) {
cdf[i] /= sum;
}
// Sample from CDF
const rand = Math.random();
for (let i = 0; i < cdf.length; i++) {
if (rand <= cdf[i]) {
return (i / resolution) * CONSTANTS.TWO_PI;
}
}
return CONSTANTS.TWO_PI / 2;
}
/**
* Generate particle positions for an orbital using CDF sampling
* @param {number} n - Principal quantum number
* @param {number} l - Azimuthal quantum number
* @param {number} m - Magnetic quantum number
* @param {number} particleCount - Number of particles to generate
* @returns {Array<{position: {x, y, z}, probability: number}>}
*/
generateOrbitalParticles(n, l, m, particleCount) {
validateQuantumNumbers(n, l, m);
const count = Math.max(CONSTANTS.MIN_PARTICLE_COUNT,
Math.min(particleCount, CONSTANTS.MAX_PARTICLE_COUNT));
console.log(`Generating ${count} particles for orbital (${n},${l},${m})`);
// Try to get from cache first
const cachedParticles = this.getParticlesFromCache(n, l, m, count);
if (cachedParticles) {
console.log(`Returned ${cachedParticles.length} particles from cache`);
return cachedParticles;
}
// Not in cache, generate normally
return this.generateOrbitalParticlesInternal(n, l, m, count);
}
/**
* Internal method to generate particles (used when cache miss)
* @param {number} n - Principal quantum number
* @param {number} l - Azimuthal quantum number
* @param {number} m - Magnetic quantum number
* @param {number} count - Number of particles to generate
* @returns {Array<{position: {x, y, z}, probability: number}>}
*/
generateOrbitalParticlesInternal(n, l, m, count) {
const particles = [];
// Pre-calculate some particles to find max probability for normalization
const sampleSize = Math.min(100, count);
let maxProb = 0;
for (let i = 0; i < sampleSize; i++) {
const r = this.sampleRadius(n, l);
const theta = this.sampleTheta(l, m);
const phi = this.samplePhi(m);
const prob = this.quantumEngine.probabilityDensity(n, l, m, r, theta, phi);
if (prob > maxProb) maxProb = prob;
}
// Generate all particles
for (let i = 0; i < count; i++) {
// Sample spherical coordinates using CDF
const r = this.sampleRadius(n, l);
const theta = this.sampleTheta(l, m);
const phi = this.samplePhi(m);
// Convert to Cartesian coordinates with scaling
const cartesian = this.sphericalToCartesian(
r * CONSTANTS.SCALE_FACTOR,
theta,
phi
);
// Calculate probability density for color coding
const probability = this.quantumEngine.probabilityDensity(n, l, m, r, theta, phi);
particles.push({
position: cartesian,
probability: maxProb > 0 ? probability / maxProb : 0
});
}
console.log(`Generated ${particles.length} particles successfully`);
return particles;
}
}
// Make class available globally
window.ParticleSampler = ParticleSampler;
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