Driven lattice gas with nearest-neighbor exclusion: shear-like drive

Abstract

We present Monte Carlo simulations of the lattice gas with nearest-neighbor exclusion and Kawasaki (hopping) dynamics, under the influence of a nonuniform drive, on the square lattice.The drive, which favors motion along the +x and inhibits motion in the opposite direction, varies linearly with y, mimicking the velocity profile of laminar flow between parallel plates with distinct velocities. We study two drive configurations and associated boundary conditions: (1) a linear drive profile, with rigid walls at the layers with zero and maximum bias, and (2) a symmetric (piecewise linear) profile with periodic boundaries. The transition to a sublattice-ordered phase occurs at a density of about 0.298, lower than in equilibrium (ρ c ≃ 0.37), but somewhat higher than in the uniformly driven case at maximal bias (ρ c ≃ 0.272). For smaller global densities (ρ ≤ 0.33), particles tend to accumulate in the low-drive region. Above this density we observe a surprising reversal in the density profile, with particles migrating to the high-drive region and forming structures similar to force chains in granular systems.

Particle redistribution and slow decay of correlations in hard-core fluids on a half-driven ladder

“…The redistribution found here is qualitatively similar to that observed in the twodimensional driven NNE lattice gas with a linear drive profile [10], but here the effects are much weaker, and migration to the driven lane is not accompanied by jamming, as it is in the two-dimensional system. The density difference observed in the one-dimensional system is relatively small, on the order of 1% or less of the total density; in the two-dimensional system this difference can reach 25%.…”

Failure of steady-state thermodynamics in nonuniform driven lattice gases

“…Migration to regions of zero or weaker drive was noted (for low densities) in Ref. [27], in which the NNE model is subject to a drive which varies linearly with position j in the direction perpendicular to the drive. In Ref.…”

“…Migration to regions of zero or weaker drive was noted (for low densities) in [24], in which the NNE model is subject to a drive which varies linearly with position j in the direction perpendicular to the drive. In [25] a NNE model on a two-lane ring (one driven, the other undriven) was found to exhibit particle migration to the undriven region for smaller global densities, and migration in the opposite sense for ρ > 0.3.…”

Entropy Production from the Master Equation for Driven Lattice Gases

“…Monte Carlo simulations have used tens of thousands [32] to a million sites [33] on square lattices. Even on the less-studied triangular and hexagonal lattices, Monte Carlo simulations have used thousands of sites [20] Simulation results for large systems are highly valuable.…”

“…However, because transition matrices are large the full spectrum was not calculated for the systems reported in this work. Rather, the master equation was integrated as a set of coupled differential equations, using Burkardt's C++ version of RKF45 [32]. The Runge-Kutta-Felhberg method with local extrapolation offers good stability and accuracy and low memory requirements [33] The method requires a relatively large number of matrix-vector multiplications.…”