Exponential decay of spatial correlation in driven diffusive system: A universal feature of macroscopic homogeneous state

Short-range and long-range correlations in driven dense colloidal mixtures in narrow pores

The system of a driven dense colloid mixture in a tube with diameter comparable to particle size is modeled by a generalization of the asymmetric simple exclusion process (ASEP) model. The generalization goes in two directions: relaxing the exclusion constraint by allowing several (but few) particles on a site and by considering two species of particles, which differ in size and transport coefficients. We calculate the nearest-neighbor correlations using a variant of the Kirkwood approximation and show by comparison with numerical simulations that the approximation provides quite accurate results. However, for long-range correlations, we show that the Kirkwood approximation is useless, as it predicts exponential decay of the density-density correlation function with distance, while simulation data indicate that the decay is algebraic. For the one-component system, we show that the decay is governed by a power law with universal exponent close to 2. In the two-component system, the correlation function behaves in a more complicated manner: Its sign oscillates but the envelope decays again very slowly and the decay is compatible with a power law with an exponent somewhat lower than 2. Therefore, our generalization of the ASEP belongs to a different universality class from the ensemble of generalized ASEP models which are mappable to zero-range processes.

Two-lane totally asymmetric simple exclusion process with extended Langmuir kinetics

Multilane totally asymmetric simple exclusion processes with interactions between the lanes have recently been investigated actively. This paper proposes a two-lane model with extended Langmuir kinetics on a periodic lattice. Both bidirectional and unidirectional flows are investigated. In our model, the hopping, attachment, and detachment rates vary depending on the state of the corresponding site in the other lane. We obtain a theoretical expression for the global density of the system in the steady state from three kinds of mean-field analyses [(1×1)-, (2×1)-, and (2×2)-cluster cases]. We verify that the (2×2)-cluster mean-field analysis reproduces the differences between the two directional flows and approximates well the results of computer simulations for some cases. We observe that (2×1)-cluster mean-field analyses are already good approximations of the simulation results for unidirectional flows; on the other hand, the accuracy of the approximations much improves by (2×2)-cluster one for bidirectional flows. We explain the phenomena in a qualitative manner by a simple analysis of correlations. We expect these findings to give informative suggestions for actual traffic systems.

Analytical and simulation studies of driven diffusive system with asymmetric heterogeneous interactions

Totally asymmetric simple exclusion process (namely, TASEP) is one of the most vital driven diffusive systems, which depicts stochastic dynamics of self-driven particles unidirectional updating along one-dimensional discrete lattices controlled by hard-core exclusions. Different with pre-existing results, driven diffusive system composed by multiple TASEPs with asymmetric heterogeneous interactions under two-dimensional periodic boundaries is investigated. By using detailed balance principle, particle configurations are extensively studied to obtain universal laws of characteristic order parameters of such stochastic dynamic system. By performing analytical analyses and Monte-Carlo simulations, local densities are found to be monotone increase with global density and spatially homogeneous to site locations. Oppositely, local currents are found to be non-monotonically increasing against global density and proportional to forward rate. Additionally, by calculating different cases of topologies, changing transition rates are found to have greater effects on particle configurations in adjacent subsystems. By intuitively comparing with pre-existing results, the improvement of our work also shows that introducing and considering totally heterogeneous interactions can improve the total current in such multiple TASEPs and optimize the overall transport of such driven-diffusive system. Our research will be helpful to understand microscopic dynamics and non-equilibrium dynamical behaviors of interacting particle systems.

Theoretical analysis and simulation for a facilitated asymmetric exclusion process

Driven diffusive systems are important models in nonequilibrium state statistical mechanics. This paper studies an asymmetric exclusion process model with nearest rear neighbor interactions associated with energy. The exact flux expression of the model is obtained by a cluster mean-field method. Based on the flux expression, the properties of the fundamental diagram have been investigated in detail. To probe the energy's influence on the coarsening process of the system, Monte Carlo simulations are carried out to acquire the monotonic phase boundary in energy-density space. Above the phase boundary, the system is inhomogeneous and the normalized residence distribution p(s) is nonmonotonically decreasing. Under the phase boundary, the system is homogeneous and p(s) is monotonically decreasing. Further study comparatively shows that the system has turned into a microscopic inhomogeneous state from a homogeneous state before the system current arrives at maximum, if nearest rear neighbor interactions are strong. Our findings offer insights to deeply understand the dynamic features of nonequilibrium state systems.