Three Lectures: Nemd, Spam, and Shockwaves

TL;DR

This paper explores three interconnected topics—NEMD, SPAM, and shockwaves—highlighting their roles in simulating and understanding nonequilibrium phenomena in molecular and continuum systems, with implications for graduate research.

Contribution

It introduces the SPAM particle method for continuum problems, applies it to shockwave analysis, and demonstrates its effectiveness in revealing tensor temperature and stress responses.

Findings

SPAM simplifies continuum problem solving by using ordinary differential equations.

Application of SPAM to shockwaves reveals tensor temperature and delayed stress response.

The study demonstrates the dynamic instability of shockwaves in dense fluids.

Abstract

We discuss three related subjects well suited to graduate research. The first, Nonequilibrium molecular dynamics or "NEMD", makes possible the simulation of atomistic systems driven by external fields, subject to dynamic constraints, and thermostated so as to yield stationary nonequilibrium states. The second subject, Smooth Particle Applied Mechanics or "SPAM", provides a particle method, resembling molecular dynamics, but designed to solve continuum problems. The numerical work is simplified because the SPAM particles obey ordinary, rather than partial, differential equations. The interpolation method used with SPAM is a powerful interpretive tool converting point particle variables to twice-differentiable field variables. This interpolation method is vital to the study and understanding of the third research topic we discuss, strong shockwaves in dense fluids. Such shockwaves exhibit stationary far-from-equilibrium states obtained with purely reversible Hamiltonian mechanics. The SPAM interpolation method, applied to this molecular dynamics problem, clearly demonstrates both the tensor character of kinetic temperature and the time-delayed response of stress and heat flux to the strain rate and temperature gradients. The dynamic Lyapunov instability of the shockwave problem can be analyzed in a variety of ways, both with and without symmetry in time. These three subjects suggest many topics suitable for graduate research in nonlinear nonequilibrium problems.