Diffusionssimulationen

Diffusionssimulationen are computer-based experiments designed to model the spreading of particles, energy, or information through a medium over time. The term is most common in German-speaking scientific literature and refers to the numerical implementation of stochastic differential equations that describe random motion governed by diffusion processes. Typical simulations include Monte Carlo methods, Brownian dynamics, and lattice-based random walk models.

In physics and materials science, diffusion simulations help predict how atoms migrate within solids, how gases permeate membranes, or how heat diffuses through composite materials. In chemistry, they are used to study reaction–diffusion systems such as pattern formation in chemical gardens or the spread of catalysts in porous media. Biologists employ diffusion models to understand the transport of signaling molecules across cellular membranes or the migration of cells in tissue engineering. In finance, analogous diffusion models, like the Black–Scholes equation, are simulated to price options and assess risk under stochastic market dynamics.

Key algorithms in diffusion simulations include the Euler–Maruyama method for solving stochastic differential equations and the Metropolis–Hastings algorithm for sampling equilibrium states. Adaptive time stepping, parallel computing, and GPU acceleration are often integrated to handle the large scale of realistic systems. Validation against analytical solutions or experimental data such as neutron scattering profiles or fluorescence recovery after photobleaching ensures model fidelity.

Diffusionssimulationen are crucial for predicting material behavior, designing pharmaceuticals, optimizing industrial processes, and understanding natural phenomena, thereby bridging theoretical models with practical applications.