Time-Reversible Random Number Generators : Solution of Our Challenge by Federico Ricci-Tersenghi

Nearly all the evolution equations of physics are time-reversible, in the sense that a movie of the solution, played backwards, would obey exactly the same differential equations as the original forward solution. By way of contrast, stochastic approaches are typically not time-reversible, though they could be made so by the simple expedient of storing their underlying pseudorandom numbers in an array. Here we illustrate the notion of time-reversible random number generators. In Version 1 we offered a suitable reward for the first arXiv response furnishing a reversed version of an only slightly-more-complicated pseudorandom number generator. Here we include Professor Ricci-Tersenghi's prize-winning reversed version as described in his arXiv:1305.1805 contribution: "The Solution to the Challenge in `Time-Reversible Random Number Generators' by Wm. G. Hoover and Carol G. Hoover".Comment: Seven pages with a single Figure, dedicated to the memories of our late colleague Ian Snoo

Three Lectures: Nemd, Spam, and Shockwaves

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.Comment: 40 pages, with 21 figures, as presented at the Granada Seminar on the Foundations of Nonequilibrium Statistical Physics, 13-17 September, as three lecture

Smooth-Particle Phase Stability with density and density-gradient potentials

Stable fluid and solid particle phases are essential to the simulation of continuum fluids and solids using Smooth Particle Applied Mechanics. We show that density-dependent potentials, such as Phi=(1/2)Sum (rho-rho_0)^2, along with their corresponding constitutive relations, provide a simple means for characterizing fluids and that a special stabilization potential, Phi=(1/2)Sum (delrho)^2, not only stabilizes crystalline solid phases (or meshes) but also provides a surface tension which is missing in the usual density-dependent-potential approach. We illustrate these ideas for two-dimensional square, triangular, and hexagonal lattices.Comment: 10 pages, 5 figure