Random number generators a la Boltzmann

Abstract

In the last few decades, simulations of stochastic processes have gained prominence in many elds of science and engineering. These simulations rely on Random Number generators (RNGs), routines that produce seemingly random sequence of numbers. Currently two paradigms exist for building RNGs | extracting noise from physical devices and complicated mathematical constructs based mostly on number theory. In this thesis we show that a synergy of these two paradigms, that a simulation of a stochastic process can in fact form the basis of an RNG. We illustrate this via simulating gas molecules which follow a collectively chaotic motion. This thesis also shows that various numerical schemes that can solve for hydrodynamics at a mesoscopic level generate random sequences of numbers. We propose a new algorithm with these concepts as foundation that can generate Gaussian and exponential random numbers orders-of-magnitude faster than existing methods. By employing this algorithm we simulate reaction-di usion problem and binary gas mixtures modeled at a mesoscopic level. vii