Shock Propagation in dilute inelastic and elastic media[HBNI Th174]

Abstract

A system that is in thermal equilibrium or in a non-equilibrium steady state, when slightly perturbed, relaxes to its stationary state with time. For small perturbations, the relaxation may be studied within linear response theory. However, when the perturbation is strong, the system is taken far from the stationary state, and the response becomes difficult to study. A special class of a strong perturbation is one when the perturbation is localized in space, either as a single impact or continuous in time. When the perturbation is localized in space, then a shock wave may result if the flow velocity is much larger than the speed of sound in the medium. Such situations arise in many di↵erent physical phenomena. Examples include atomic explosion, supernova remnants, crater formation, viscous fingering, etc. In this thesis, we study shock propagation in both an elastic medium (dilute gas) and an inelastic medium (granular material).