Random number generators and the Metropolis algorithm: application to various problems in physics and mechanics as an introduction to computational physics

摘要

We present known and new applications of pseudo random numbers and of the Metropolis algorithm to phenomena of physical and mechanical interest, such as the search of simple clusters isomers with interactive visualization, or vehicle motion planning. The progression towards complicated problems was used with first-year graduate students who wrote most of the programs presented here. We argue that the use of pseudo random numbers in simulation and extrema research programs in teaching numerical methods in physics allows one to get quick programs and physically meaningful and demonstrative results without recurring to the advanced numerical analysis methods.