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Inhomogeneous Exclusion Processes With Extended Objects: The Effect Of Defect Locations, J. J. Dong, Beate Schmittmann, R. K. P. Zia
Inhomogeneous Exclusion Processes With Extended Objects: The Effect Of Defect Locations, J. J. Dong, Beate Schmittmann, R. K. P. Zia
Beate Schmittmann
We study the effects of local inhomogeneities, i.e., slow sites of hopping rate q<1, in a totally asymmetric simple exclusion process for particles of size ℓ⩾1 (in units of the lattice spacing). We compare the simulation results of ℓ=1 and ℓ>1 and notice that the existence of local defects has qualitatively similar effects on the steady state. We focus on the stationary current as well as the density profiles. If there is only a single slow site in the system, we observe a significant dependence of the current on the location of the slow site for both ℓ=1 and ℓ>1 cases. When two slow sites are introduced, more intriguing phenomena emerge, e.g., dramatic decreases in the current when the two are close together. In addition, …
Power Spectra Of The Total Occupancy In The Totally Asymmetric Simple Exclusion Process, D. `A. Adams, R. K. P. Zia, Beate Schmittmann
Power Spectra Of The Total Occupancy In The Totally Asymmetric Simple Exclusion Process, D. `A. Adams, R. K. P. Zia, Beate Schmittmann
Beate Schmittmann
As a solvable and broadly applicable model system, the totally asymmetric exclusion process enjoys iconic status in the theory of nonequilibrium phase transitions. Here, we focus on the time dependence of the total number of particles on a 1-dimensional open lattice and its power spectrum. Using both Monte Carlo simulations and analytic methods, we explore its behavior in different characteristic regimes. In the maximal current phase and on the coexistence line (between high and low density phases), the power spectrum displays algebraic decay, with exponents −1.62 and −2.00, respectively. Deep within the high and low density phases, we find pronounced …
Controlling Surface Morphologies By Time-Delayed Feedback, M. Block, Beate Schmittmann, E. Schöll
Controlling Surface Morphologies By Time-Delayed Feedback, M. Block, Beate Schmittmann, E. Schöll
Beate Schmittmann
We propose a method to control the roughness of a growing surface via a time-delayed feedback scheme. The method is very general and can be applied to a wide range of nonequilibrium growth phenomena, from solid-state epitaxy to tumor growth. Possible experimental realizations are suggested. As an illustration, we consider the Kardar-Parisi-Zhang equation [Phys. Rev. Lett. 56, 889 (1986)] in 1+1 dimensions and show that the effective growth exponent of the surface width can be stabilized at any desired value in the interval [0.25, 0.33], for a significant length of time.
Coarsening Of “Clouds” And Dynamic Scaling In A Far-From-Equilibrium Model System, D. A. Adams, Beate Schmittmann, R. K. P. Zia
Coarsening Of “Clouds” And Dynamic Scaling In A Far-From-Equilibrium Model System, D. A. Adams, Beate Schmittmann, R. K. P. Zia
Beate Schmittmann
A two-dimensional lattice gas of two species, driven in opposite directions by an external force, undergoes a jamming transition if the filling fraction is sufficiently high. Using Monte Carlo simulations, we investigate the growth of these jams (‘‘clouds’’), as the system approaches a nonequilibrium steady state from a disordered initial state. We monitor the dynamic structure factor S(kx,ky;t) and find that the kx=0 component exhibits dynamic scaling, of the form S(0,ky;t)=tβS̃ (kytα). Over a significant range of times, we observe excellent data collapse with α=1/2 and β=1. The effects of varying filling fraction and driving force are discussed.