Microscopic and Macroscopic Rayleigh-Benard Flows : Continuum and Particle Simulations, Turbulence, Fluctuations, Time Reversibility, and Lyapunov Instability

We discuss the irreversibility, nonlocality, and fluctuations, as well as the Lyapunov and hydrodynamic instabilities characterizing atomistic, smooth-particle, and finite-difference solutions of the two-dimensional Rayleigh-B\'enard problem. To speed up the numerical analysis we control the time-dependence of the Rayleigh number so as to include many distinct flow morphologies in a single simulation. The relatively simple nature of these computational algorithms and the richness of the results they can yield make such studies and their interpretation particularly well suited to graduate-level research.