Totally asymmetric exclusion process fed by using a non-Poissonian clock.

In this article we consider the one-dimensional totally asymmetric open-boundary exclusion process fed by a process with power-law-distributed waiting times. More specifically, we use a modified Pareto distribution to define the jump rate for jumps into the system. We then characterize the propagation of fluctuations through the system by kinetic Monte Carlo simulations and by numerical evaluation of the steady-state partition function.

Accelerated transport and growth with symmetrized dynamics.

In this paper we consider a model of accelerated dynamics with the rules modified from those of the recently proposed [Dong et al., Phys. Rev. Lett. 109, 130602 (2012)] accelerated exclusion process (AEP) such that particle-vacancy symmetry is restored to facilitate a mapping to a solid-on-solid growth model in 1+1 dimensions. In addition to kicking a particle ahead of the moving particle, as in the AEP, in our model another particle from behind is drawn, provided it is within the "distance of interaction" denoted by ℓ(max). We call our model the doubly accelerated exclusion process (DAEP). We observe accelerated transport and interface growth and widening of the cluster size distribution for cluster sizes above ℓ(max), when compared with the ordinary totally asymmetric exclusion process (TASEP). We also characterize the difference between the TASEP, AEP, and DAEP by computing a "staggered" order parameter, which reveals the local order in the steady state. This order in part explains the behavior of the particle current as a function of density. The differences of the steady states are also reflected by the behavior of the temporal and spatial correlation functions in the interface picture.

Single-layer metal-on-metal islands driven by strong time-dependent forces.

Nonlinear transport properties of single-layer metal-on-metal islands driven with strong static and time-dependent forces are studied. We apply a semiempirical lattice model and use master-equation and kinetic Monte Carlo simulation methods to compute observables such as the velocity and the diffusion coefficient. Two types of time-dependent driving are considered: a pulsed rotated field and an alternating field with a zero net force (electrophoretic ratchet). Small islands up to 12 atoms were studied in detail with the master-equation method and larger ones with simulations. Results are presented mainly for a parametrization of Cu on Cu(001) surface, which has been the main system of interest in several previous studies. The main results are that the pulsed field can increase the current in both diagonal and axis direction when compared to static field, and there exists a current inversion in the electrophoretic ratchet. Both of these phenomena are a consequence of the coupling of the internal dynamics of the island with its transport. In addition to the previously discovered "magic size"effect for islands in equilibrium, a strong odd-even effect was found for islands driven far out of equilibrium. Master-equation computations revealed nonmonotonous behavior for the leading relaxation constant and effective Arrhenius parameters. Using cycle optimization methods, typical island transport mechanisms are identified for small islands.

Characteristics of the polymer transport in ratchet systems.

Molecules with complex internal structure in time-dependent periodic potentials are studied by using short Rubinstein-Duke model polymers as an example. We extend our earlier work on transport in stochastically varying potentials to cover also deterministic potential switching mechanisms, energetic efficiency, and nonuniform charge distributions. We also use currents in the nonequilibrium steady state to identify the dominating mechanisms that lead to polymer transportation and analyze the evolution of the macroscopic state (e.g., total and head-to-head lengths) of the polymers. Several numerical methods are used to solve the master equations and nonlinear optimization problems. The dominating transport mechanisms are found via graph optimization methods. The results show that small changes in the molecule structure and the environment variables can lead to large increases of the drift. The drift and the coherence can be amplified by using deterministic flashing potentials and customized polymer charge distributions. Identifying the dominating transport mechanism by graph analysis tools is found to give insight in how the molecule is transported by the ratchet effect.

Finite-size effects in dynamics of zero-range processes.

The finite-size effects prominent in zero-range processes exhibiting a condensation transition are studied by using continuous-time Monte Carlo simulations. We observe that, well above the thermodynamic critical point, both static and dynamic properties display fluidlike behavior up to a density ρc(L), which is the finite-size counterpart of the critical density ρc=ρc(L→∞). We determine this density from the crossover behavior of the average size of the largest cluster. We then show that several dynamical characteristics undergo a qualitative change at this density. In particular, the size distribution of the largest cluster at the moment of relocation, the persistence properties of the largest cluster, and the correlations in its motion are studied.

Diffusion between evolving interfaces.

Diffusion in an evolving environment is studied by continuous-time Monte Carlo simulations. Diffusion is modeled by continuous-time random walkers on a lattice, in a dynamic environment provided by bubbles between two one-dimensional interfaces driven symmetrically towards each other. For one-dimensional random walkers constrained by the interfaces, the bubble size distribution dominates diffusion. For two-dimensional random walkers, it is also controlled by the topography and dynamics of the interfaces. The results of the one-dimensional case are recovered in the limit where the interfaces are strongly driven. Even with simple hard-core repulsion between the interfaces and the particles, diffusion is found to depend strongly on the details of the dynamical rules of particles close to the interfaces.

Polymer dynamics in time-dependent periodic potentials.

The dynamics of a discrete polymer in time-dependent external potentials is studied with the master equation approach. We consider both stochastic and deterministic switching mechanisms for the potential states and give the essential equations for computing the stationary-state properties of molecules with internal structure in time-dependent periodic potentials on a lattice. As an example, we consider standard and modified Rubinstein-Duke polymers and calculate their mean drift and effective diffusion coefficient in the two-state nonsymmetric flashing potential and symmetric traveling potential. Rich nonlinear behavior of these observables is found. By varying the polymer length, we find current inversions caused by the rebound effect that is only present for molecules with internal structure. These results depend strongly on the polymer type. We also notice increased transport coherence for longer polymers.

Roughness of two nonintersecting one-dimensional interfaces.

The dynamics of two spatially discrete one-dimensional single-step model interfaces with a noncrossing constraint is studied in both nonsymmetric propagating and symmetric relaxing cases. We consider possible scaling scenarios and study a few special cases by using continuous-time Monte Carlo simulations. The roughness of the interfaces is observed to be nonmonotonic as a function of time, and in the stationary state it is nonmonotonic also as a function of the strength of the effective force driving the interfaces against each other. This is related on the one hand to the reduction of the available configuration space and on the other hand to the ability of the interfaces to conform to each other.