Computational Physics

// Computational Physics Framework class ComputationalPhysics { constructor() { this.particles = []; this.fields = []; this.boundaries = []; this.time = 0; this.dt = 0.01; } // Molecular dynamics simulation molecularDynamics(particles, forces, timeStep, totalTime) { const simulation = { particles: particles, forces: forces, timeStep: timeStep, totalTime: totalTime, trajectory: [], energy: [], temperature: [] }; for (let t = 0; t < totalTime; t += timeStep) { // Calculate forces const currentForces = this.calculateForces(particles, forces); // Update positions and velocities particles.forEach(particle => { particle.velocity += currentForces[particle.id] * timeStep / particle.mass; particle.position += particle.velocity * timeStep; }); // Store trajectory simulation.trajectory.push(particles.map(p => ({...p}))); simulation.energy.push(this.calculateTotalEnergy(particles)); simulation.temperature.push(this.calculateTemperature(particles)); } return simulation; } // Monte Carlo simulation monteCarlo(system, temperature, steps) { const simulation = { system: system, temperature: temperature, steps: steps, energy: [], acceptance: 0 }; for (let step = 0; step < steps; step++) { // Generate random move const move = this.generateRandomMove(system); // Calculate energy change const deltaE = this.calculateEnergyChange(system, move); // Accept or reject move if (deltaE < 0 || Math.random() < Math.exp(-deltaE / temperature)) { this.applyMove(system, move); simulation.acceptance++; } simulation.energy.push(this.calculateTotalEnergy(system)); } return simulation; } // Finite difference method finiteDifference(equation, boundary, grid, timeStep) { const solution = { equation: equation, boundary: boundary, grid: grid, timeStep: timeStep, field: [], time: 0 }; // Initialize field solution.field = this.initializeField(grid, boundary); // Time evolution for (let t = 0; t < 1000; t++) { solution.field = this.updateField(solution.field, equation, timeStep); solution.time += timeStep; } return solution; } // Quantum Monte Carlo quantumMonteCarlo(wavefunction, hamiltonian, steps) { const simulation = { wavefunction: wavefunction, hamiltonian: hamiltonian, steps: steps, energy: [], variance: [] }; for (let step = 0; step < steps; step++) { // Sample configuration const config = this.sampleConfiguration(wavefunction); // Calculate local energy const localEnergy = this.calculateLocalEnergy(config, hamiltonian); // Update wavefunction this.updateWavefunction(wavefunction, config, localEnergy); simulation.energy.push(localEnergy); simulation.variance.push(this.calculateVariance(simulation.energy)); } return simulation; } }