Long-Time Behavior of Velocity Autocorrelation Function for Interacting Particles in a Two-Dimensional Disordered System

The long-time behavior of the velocity autocorrelation function (VACF) is investigated by the molecular dynamics simulation of a two-dimensional system which has both a many-body interaction and a random potential. With strengthening the random potential by increasing the density of impurities, a crossover behavior of the VACF is observed from a positive tail, which is proportional to t^{-1}, to a negative tail, proportional to -t^{-2}. The latter tail exists even when the density of particles is the same order as the density of impurities. The behavior of the VACF in a nonequilibrium steady state is also studied. In the linear response regime the behavior is similar to that in the equilibrium state, whereas it changes drastically in the nonlinear response regime.Comment: 12 pages, 5 figure

Theory of Second and Higher Order Stochastic Processes

This paper presents a general approach to linear stochastic processes driven by various random noises. Mathematically, such processes are described by linear stochastic differential equations of arbitrary order (the simplest non-trivial example is $\ddot x = R(t)$, where $R(t)$ is not a Gaussian white noise). The stochastic process is discretized into $n$ time-steps, all possible realizations are summed up and the continuum limit is taken. This procedure often yields closed form formulas for the joint probability distributions. Completely worked out examples include all Gaussian random forces and a large class of Markovian (non-Gaussian) forces. This approach is also useful for deriving Fokker-Planck equations for the probability distribution functions. This is worked out for Gaussian noises and for the Markovian dichotomous noise.Comment: 35 pages, PlainTex, accepted for publication in Phys Rev. E

Liquid-Solid Phase Transition of the System with Two particles in a Rectangular Box

We study the statistical properties of two hard spheres in a two dimensional rectangular box. In this system, the relation like Van der Waals equation loop is obtained between the width of the box and the pressure working on side walls. The auto-correlation function of each particle's position is calculated numerically. By this calculation near the critical width, the time at which the correlation become zero gets longer according to the increase of the height of the box. Moreover, fast and slow relaxation processes like $\alpha$ and $\beta$ relaxations observed in supper cooled liquid are observed when the height of the box is sufficiently large. These relaxation processes are discussed with the probability distribution of relative position of two particles.Comment: 6 figure

Stacking Entropy of Hard Sphere Crystals

Classical hard spheres crystallize at equilibrium at high enough density. Crystals made up of stackings of 2-dimensional hexagonal close-packed layers (e.g. fcc, hcp, etc.) differ in entropy by only about $10^{-3}k_B$ per sphere (all configurations are degenerate in energy). To readily resolve and study these small entropy differences, we have implemented two different multicanonical Monte Carlo algorithms that allow direct equilibration between crystals with different stacking sequences. Recent work had demonstrated that the fcc stacking has higher entropy than the hcp stacking. We have studied other stackings to demonstrate that the fcc stacking does indeed have the highest entropy of ALL possible stackings. The entropic interactions we could detect involve three, four and (although with less statistical certainty) five consecutive layers of spheres. These interlayer entropic interactions fall off in strength with increasing distance, as expected; this fall-off appears to be much slower near the melting density than at the maximum (close-packing) density. At maximum density the entropy difference between fcc and hcp stackings is $0.00115 +/- 0.00004 k_B$ per sphere, which is roughly 30% higher than the same quantity measured near the melting transition.Comment: 15 page

Free energies of crystalline solids: a lattice-switch Monte Carlo method

We present a method for the direct evaluation of the difference between the free energies of two crystalline structures, of different symmetry. The method rests on a Monte Carlo procedure which allows one to sample along a path, through atomic-displacement-space, leading from one structure to the other by way of an intervening transformation that switches one set of lattice vectors for another. The configurations of both structures can thus be sampled within a single Monte Carlo process, and the difference between their free energies evaluated directly from the ratio of the measured probabilities of each. The method is used to determine the difference between the free energies of the fcc and hcp crystalline phases of a system of hard spheres.Comment: 5 pages Revtex, 3 figure

Effect of boundary conditions on diffusion in two-dimensional granular gases

We analyze the influence of boundary conditions on numerical simulations of the diffusive properties of a two dimensional granular gas. We show in particular that periodic boundary conditions introduce unphysical correlations in time which cause the coefficient of diffusion to be strongly dependent on the system size. On the other hand, in large enough systems with hard walls at the boundaries, diffusion is found to be independent of the system size. We compare the results obtained in this case with Langevin theory for an elastic gas. Good agreement is found. We then calculate the relaxation time and the influence of the mass for a particle of radius $R_s$ in a sea of particles of radius $R_b$. As granular gases are dissipative, we also study the influence of an external random force on the diffusion process in a forced dissipative system. In particular, we analyze differences in the mean square velocity and displacement between the elastic and inelastic cases.Comment: 15 figures eps figures, include

Intermediate energy Coulomb excitation as a probe of nuclear structure at radioactive beam facilities

The effects of retardation in the Coulomb excitation of radioactive nuclei in intermediate energy collisions (Elab ~100 MeV/nucleon) are investigated. We show that the excitation cross sections of low-lying states in 11Be, {38,40,42}S and {44,46}Ar projectiles incident on gold and lead targets are modified by as much as 20% due to these effects. The angular distributions of decaying gamma-rays are also appreciably modified.Comment: 21 pages, 3 figures, Phys. Rev. C, in pres

Evaluation of a present-day climate simulation with a new coupled atmosphere-ocean model GENMOM

We present a new, non-flux corrected AOGCM, GENMOM, that combines the GENESIS version 3 atmospheric GCM (Global Environmental and Ecological Simulation of Interactive Systems) and MOM2 (Modular Ocean Model version 2) nominally at T31 resolution. We evaluate GENMOM by comparison with reanalysis products (e.g., NCEP2) and three models used in the IPCC AR4 assessment. GENMOM produces a global temperature bias of 0.6 °C. Atmospheric features such as the jet stream structure and major semi-permanent sea level pressure centers are well simulated as is the mean planetary-scale wind structure that is needed to produce the correct position of stormtracks. Most ocean surface currents are reproduced except where they are not resolvable at T31 resolution. Overall, GENMOM captures reasonably well the observed gradients and spatial distributions of annual surface temperature and precipitation and the simulations are on par with other AOGCMs. Deficiencies in the GENMOM simulations include a warm bias in the surface temperature over the southern oceans, a split in the ITCZ and weaker-than-observed overturning circulation

Coulomb corrected eikonal description of the breakup of halo nuclei

The eikonal description of breakup reactions diverges because of the Coulomb interaction between the projectile and the target. This divergence is due to the adiabatic, or sudden, approximation usually made, which is incompatible with the infinite range of the Coulomb interaction. A correction for this divergence is analysed by comparison with the Dynamical Eikonal Approximation, which is derived without the adiabatic approximation. The correction consists in replacing the first-order term of the eikonal Coulomb phase by the first-order of the perturbation theory. This allows taking into account both nuclear and Coulomb interactions on the same footing within the computationally efficient eikonal model. Excellent results are found for the dissociation of 11Be on lead at 69 MeV/nucleon. This Coulomb Corrected Eikonal approximation provides a competitive alternative to more elaborate reaction models for investigating breakup of three-body projectiles at intermediate and high energies.Comment: 19 pages, 9 figures, accepted for publication in Phys. Rev.