ABSTRACT
This chapter starts with a numerical solution of heat equation using a leapfrog (time-stepping) algorithm. It develops simulations for three stochastic processes: random walks, diffusion-limited aggregation, and deposition of particles onto a surface. The chapter presents some problems on the thermal behavior of magnetic materials, starting with a simple search for the roots of the equation relating magnetization to temperature. It also presents the Ising model and the Metropolis algorithm that simulates thermal equilibrium. The Metropolis algorithm is a technique for computing the Monte Carlo calculation of averages that accurately simulates the fluctuations occurring during thermal equilibrium. Continued application of the Metropolis algorithm generates the statistical fluctuations about equilibrium from which are deduced thermodynamic quantities. The chapter concludes with molecular dynamics (MD), a big subject with a variety of research-level codes often used in physics and chemistry.
