Physics Resources & Documentation

Technical documentation, equations, and computational methods for understanding granular materials simulation in interactive applications.

Mathematical Framework

Discrete Element Method (DEM)

The core of our particle simulation relies on the Discrete Element Method, where each sand grain is treated as a rigid body with specific properties. The fundamental equations governing particle motion are:

Newton's Second Law for Particles:

Translation: mi dvi/dt = Σ Fij + Fg
Rotation: Iii/dt = Σ Tij
Where mi is particle mass, vi is velocity, Fij represents contact forces, Fg is gravitational force, Ii is moment of inertia, ωi is angular velocity, and Tij represents torques.

Contact Force Models

Particle interactions are modeled using Hertz-Mindlin contact theory, accounting for both normal and tangential forces:

Normal Contact Force:

Fn = (4/3) E* √(R*) δn3/2 - γn vn

Tangential Contact Force:

Ft = min(μ|Fn|, |8G* √(R*δn) δt + γt vt|)

WebGL Implementation

🔢 Parallel Processing

GPU-accelerated particle updates using WebGL compute shaders for handling thousands of simultaneous calculations.

Performance: ~50,000 particles at 60 FPS on modern hardware

🎯 Spatial Hashing

Efficient neighbor detection using uniform grid spatial partitioning reduces collision detection complexity from O(n²) to O(n).

Grid size: Dynamic based on average particle radius

⚡ Time Integration

Velocity-Verlet integration scheme ensures numerical stability while maintaining energy conservation in the system.

Timestep: Adaptive based on maximum particle velocity

🌊 Fluid Coupling

Hybrid approach combining DEM with simplified fluid dynamics for realistic avalanche and flow behaviors.

Method: Lattice Boltzmann Method (LBM) approximation

System Parameters

Material Properties

  • Density: 2650 kg/m³ (quartz sand)
  • Young's Modulus: 70 GPa
  • Poisson's Ratio: 0.3
  • Friction Coefficient: 0.5-0.8
  • Restitution: 0.1-0.3

Simulation Settings

  • Particle Count: 10,000-50,000
  • Timestep: 1e-5 to 1e-4 seconds
  • Gravity: 9.81 m/s²
  • Grid Resolution: 64x64x32
  • Contact Detection: R-tree spatial index

Performance Metrics

  • Target FPS: 60 Hz
  • GPU Memory: ~200 MB
  • CPU Usage: <15% single core
  • WebGL Version: 2.0 required
  • Browser Support: Chrome 80+, Firefox 75+

Research Applications

Beyond gaming, this physics simulation platform has potential applications in various research domains:

🏗️ Geotechnical Engineering

Understanding soil behavior, landslide mechanics, and foundation stability through interactive particle simulations. The platform can model different soil types by adjusting particle properties and interaction parameters.

Applications: Slope stability analysis, earthquake soil liquefaction, retaining wall design

🔬 Materials Science

Investigating powder processing, pharmaceutical tablet formation, and ceramic sintering through granular flow visualization. Particle size distribution and shape effects can be studied interactively.

Applications: Powder mixing, compaction processes, segregation phenomena

🎓 Educational Physics

Interactive demonstration of fundamental physics concepts including conservation laws, energy transfer, and statistical mechanics through hands-on particle manipulation.

Applications: University physics courses, graduate research training, public science outreach

Future Development

This platform represents an ongoing exploration of how advanced physics simulation can be made accessible through web technologies. Future enhancements may include additional particle interaction models, extended material property libraries, and integration with educational curricula.

We are committed to maintaining scientific accuracy while continuously improving performance and user experience. The codebase follows established computational physics practices and leverages modern web standards for optimal cross-platform compatibility.

Explore the Simulation

Experience these physics principles firsthand through our interactive particle simulation platform.