  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.
