Oyeon Kum

Time-Reversible Continuum Mechanics

Levesque and Verlet developed a time-reversible and “bit-reversible” computational leapfrog algorithm. Their algorithm uses integer arithmetic and is exactly time reversible to the last computational bit describing the particle coordinates. We generalize their idea, developed for atomistic molecular dynamics, to smoothed-particle continuum mechanics. In the special case of a two-dimensional isentropic ideal gas, these two approaches, one microscopic and the other macroscopic, are isomorphic. In the more general nonadiabatic case, but still without dissipative terms, our continuum extension of the leapfrog scheme remains stable and also exhibits the exact time and bit reversibility associated with Levesque and Verlets atomistic approach.

Accurate symplectic integrators via random sampling

We develop a random‐sampling method for finding accurate symplectic integrators which best match the exact trajectory of a one‐dimensional harmonic oscillator. We recover several well‐known algorithms. We demonstrate the usefulness of the random sampling method by finding and validating a new integrator, applying it to the classical many‐body problem.

Microscopic Time-Reversibility and Macroscopic Irreversibility — Still a Paradox?

Microscopic time reversibility and macroscopic irreversibility are a paradoxical combination. This was first observed by J. Loschmidt in 1876 and was explained, for conservative systems, by L. Boltzmann the following year. Both these features are also present in modern simulations of classic many-body systems in steady nonequilibrium states. We illustrate them here for the simplest possible models, a continuous one-dimensional model of field-driven diffusion, the so-called driven Lorentz gas or Galton Board, and an ergodic time reversible dissipative map.

Monte Carlo calculations of free energy in the solid phase

The method of direct Monte Carlo measurement of free energy in the solid phase developed by Jhung and Jhung (J. Chem. Phys. 87, 5403 (1987)] has been applied to the inverse power potential systems and Lennard‐Jones system. The calculated results show that the method provides an accurate and practical means for the calculation of the solid‐phase Helmholtz free energy.

VIBRATIONAL PROPERTIES OF SMALL TWO-DIMENSIONAL CLASSICAL CRYSTALS

Recent computer simulations have stressed the dependence of transport properties on boundary conditions in two dimensions, where fluctuations and boundary conditions are equally important effects of order N1/2. Elastically isotropic harmonic crystals provide a test case in which these two effects can be studied precisely without sacrificing realism. We investigate the boundary dependence of spatial fluctuations in two‐dimensional crystals. Our results confirm the expected boundary independence of the extensive vibrational entropy. We find also that clamped crystal boundaries significantly alter the rate of divergence of the root‐mean‐square (rms) displacement with crystal size, but do not alter the [logarithmic] functional form, which is known to dominate vibrational fluctuations in periodic two‐dimensional crystals.