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Properties of the one-dimensional totally asymmetric simple exclusion process (TASEP), and their connection with the dynamical scaling of moving interfaces described by a Kardar-Parisi-Zhang equation are investigated. With periodic boundary conditions, scaling of interface widths (the latter defined via a discrete occupation-number-to-height mapping), gives… (More)

We consider the one-dimensional totally asymmetric simple exclusion process (TASEP) with position-dependent hopping rates. The problem is solved, in a mean-field adiabatic approximation, for a general (smooth) form of spatial rate variation. Numerical simulations of systems with hopping rates varying linearly against position (constant rate gradient), for… (More)

We discuss the application of wavelet transforms to a critical interface model which is known to provide a good description of Barkhausen noise in soft ferromagnets. The two-dimensional version of the model (one-dimensional interface) is considered, mainly in the adiabatic limit of very slow driving. On length scales shorter than a crossover length (which… (More)

We study the dynamical evolution toward steady state of the stochastic nonequilibrium model known as the totally asymmetric simple exclusion process, in both uniform and nonuniform (staggered) one-dimensional systems with open boundaries. Domain-wall theory and numerical simulations are used and, where pertinent, their results are compared to existing… (More)

We present a mean-field theory for the dynamics of driven flow with exclusion in graphenelike structures, and numerically check its predictions. We treat first a specific combination of bond transmissivity rates, where mean field predicts, and numerics to a large extent confirms, that the sublattice structure characteristic of honeycomb networks becomes… (More)

Numerical transfer-matrix methods are used to discuss the shape of the phase diagram, in field-temperature parameter space, of two-dimensional honeycomb-lattice Ising spin-1/2 magnets, with antiferromagnetic couplings along at least one lattice axis, in a uniform external field. Both the order and universality class of the underlying phase transition are… (More)

We study driven flow with exclusion in graphenelike structures. The totally asymmetric simple exclusion process (TASEP), a well-known model in its strictly one-dimensional (chain) version, is generalized to cylinder (nanotube) and ribbon (nanoribbon) geometries. A mean-field theoretical description is given for very narrow ribbons ("necklaces") and… (More)

We consider fluctuations of steady-state current activity, and of its dynamic counterpart, the local current, for the one-dimensional totally asymmetric simple exclusion process. The cumulants of the integrated activity behave similarly to those of the local current, except that they do not capture the anomalous scaling behavior in the maximal-current phase… (More)

We consider steady-state current activity statistics for the one-dimensional totally asymmetric simple exclusion process. With the help of the known operator algebra (for general open boundary conditions), as well as general probabilistic concepts (for the periodic case), we derive and evaluate closed-form expressions for the lowest three moments of the… (More)

Transfer-matrix methods, with the help of finite-size scaling and conformal invariance concepts, are used to investigate the critical behavior of two-dimensional square-lattice Ising spin-1/2 systems with first- and second-neighbor interactions, both antiferromagnetic, in a uniform external field. On the critical curve separating collinearly ordered and… (More)