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Maxwell Distribution Simulation

What is Maxwell Distribution?

The Maxwell-Boltzmann distribution describes the distribution of speeds of particles in a gas at thermal equilibrium. This simulation demonstrates how particle collisions lead to a statistical distribution of velocities, showing:

• Particle collisions: Particles repel each other when they get too close
• Velocity distribution: The histogram on the right shows how particle speeds are distributed
• Boundary interactions: Particles bounce off the walls of the container
• Gravity: Optional gravitational force can be applied

Controls:

• ⏯️ Playback: Reverse time direction, Pause/Resume, increase/decrease simulation speed (×2, ÷2)
• ⚙️ dt (Time Step): Adjust precision - Reset, ×2, ×10, ÷2, ÷10. Smaller dt = more accurate but slower
• ⚛️ Particles:
  • Count: Number of particles (0-10000)
  • Layout: Grid (ordered) or Random placement
  • Radius: Particle size
  • Zero velocity: Start particles with zero initial velocity
• 🌍 Gravity: Enable and set X/Y components (default Y=60 for downward gravity)
• ⚙️ Integration Method:
  • Euler (Semi-Implicit): Fast, good for most cases, stable
  • Runge-Kutta 4 (RK4): More accurate, better for complex dynamics, slower
  • Verlet: Best energy conservation, ideal for long simulations, symplectic
• 💥 Collision Model:
  • Elastic (Spring): Particles repel with spring-like forces, energy conserved (default)
  • Inelastic (Damped): Damped spring forces, energy dissipates over time
  • Hard Body: Instantaneous impulse-based collisions, perfect momentum transfer, no overlap
• 🔄 Actions: Restart simulation, Show Help
• 👋 HotHand: Click on canvas to create a particle manipulator. Click and drag to move particles, click again to release

Status Bar:

• Left side: Legend showing particle types (Normal, Under Force, HotHand)
• Right side: Real-time statistics:
  • Particles: Current particle count
  • Time Step: Current dt value
  • Kinetic Energy: Total kinetic energy (0.5 × m × v²)
  • Potential Energy: Total potential energy from particle compressions
  • Total Energy: Sum of kinetic + potential energy

Histogram Panel:

• The right panel shows the Maxwell velocity distribution histogram with 20 bars
• Each bar represents a speed range (shown as "min-max") and its width indicates how many particles have speeds in that range
• Statistics below the histogram show kinetic energy, min/max speeds, mean speed, mean quadratic speed, temperature, and FPS

Tips:

• Start with default settings (256 particles, Euler, Elastic) to see the Maxwell distribution emerge
• Watch the histogram evolve as particles collide and exchange energy
• Enable gravity (Y=60) to see how it affects the velocity distribution
• Use HotHand to push particles around and observe how the distribution changes
• Try different integration methods: Euler for speed, RK4 for accuracy, Verlet for energy conservation
• Hard Body collisions work best with RK4 or Verlet integration - particles won't stick to boundaries
• Watch the energy statistics - in Elastic mode with Verlet, total energy should remain relatively constant
• Adjust dt for faster (larger dt, less accurate) or slower (smaller dt, more accurate) simulations
• Use "Zero velocity" checkbox to start particles at rest, then watch them accelerate due to collisions
• Increase particle count to see a smoother Maxwell distribution

(c) kusaku 2001 - Maxwell Distribution Simulation
No rights reserved - Modernized for modern browsers