Collective charge transport is studied in one-and two-dimensional arrays of small normal-metal dots separated by tunnel barriers. At temperatures well below the charging energy of a dot, disorder leads to a threshold for conduction which grows linearly with the size of the array. For short-ranged interactions, one of the correlation length exponents near threshold is found from a novel argument based on interface growth. The dynamical exponent for the current above threshold is also predicted analytically, and the requirements for its experimental observation are described.Typeset Using REVTEX 1

A simple model that describes traffic flow in two dimensions is studied. A sharp jamming transition is found that separates between the low density dynamical phase in which all cars move at maximal speed and the high density jammed phase in which they are all stuck. Self organization effects in both phases are studied and discussed.Typeset Using REVTEX

The nature of the zero temperature ordering transition in the three dimensional Gaussian random field Ising magnet is studied numerically, aided by scaling analyses. Various numerical calculations are used to consistently infer the location of the transition to a high precision. A variety of boundary conditions are imposed on large samples to study the order of the transition and the number of states in the large volume limit. In the ferromagnetic phase, where the domain walls have fractal dimension ds = 2, the scaling of the roughness of the domain walls, w ∼ L ζ , is consistent with the theoretical prediction ζ = 2/3. As the randomness is increased through the transition, the probability distribution of the interfacial tension of domain walls scales in a manner that is clearly consistent with a single second order transition. At the critical point, the fractal dimensions of domain walls and the fractal dimension of the outer surface of spin clusters are investigated: there are at least two distinct physically important fractal dimensions that describe domain walls. These dimensions are argued to be related by scaling to combinations of the energy scaling exponent, θ, which determines the violation of hyperscaling, the correlation length exponent ν, and the magnetization exponent β. The value β = 0.017 ± 0.005 computed from finite size scaling of the magnetization is very nearly zero: this estimate is supported by the study of the spin cluster size distribution at criticality. The variation of configurations in the interior of a sample with boundary conditions is consistent with the hypothesis that there is a single transition separating the disordered phase with one ground state from the ordered phase with two ground states. The array of results, including values for several exponents, are shown to be consistent with a scaling picture and a geometric description of the influence of boundary conditions on the spins. The details of the algorithm used and its implementation are also described.

Analytic results are presented for the dynamic behavior of sliding charge-density waves (CDW's) and related extended nonlinear systems with randomness. It is shown that, in the limit of long times, a sliding configuration approaches a unique solution. In CDW models, the velocity of this asymptotic solution is periodic in time. These results explain previous numerical observations, simplify further analysis and simulation, and have direct experimental implications.PACS numbers: 71.45.LrThere are many physical systems, including interfaces in random media, flux lattices in type-II superconductors, and charge-density waves (CDW's), where many degrees of freedom interact strongly in a random environment. A common problem in such systems is determining the response to an external drive, e.g., current or electric field; this is the problem of collective transport in systems with quenched randomness [1]. A general difficulty in treating random systems is the existence of many metastable solutions, which can complicate both analysis and numerical computations. However, in some systems exhibiting collective transport, the dynamics, though still complex, is simpler than might be expected. I report here analytic results that explain this behavior, under certain conditions, using CDW transport as an example system and summarizing the extension to other systems below.An incommensurate charge-density wave in a solid can be modeled as an elastic medium that is subject to both spatially varying pinning forces, due to impurities, and a uniform external force, due to an electric field [2-4]. If thermal noise can be neglected, the possible dynamical behaviors of CDW's can be sharply divided into two types: pinned and sliding. For small drive fields, the impurities pin the CDW in one of many static configurations. If the field is then increased above a threshold value, the CDW slides with a nonzero average velocity, thereby contributing to the electric current. The equations of motion for the CDW are nonlinear and describe an extended system with quenched randomness. It therefore would not be surprising for the CDW to exhibit some sort of turbulent behavior in the sliding state, or, at least, that there would be an aperiodic attractor or multiple attractors for the CDW dynamics.However, as I show in this Letter for a broad class of models describing CDW's and related systems, sliding configurations approach, at long times, a solution that is unique up to time translation. Also, the transition between pinned and sliding states is nonhysteretic. These results are generally applicable when the equations of motion are first order in time, phase distortions are described by a single component, and the elastic force between phases on neighboring sites increases with the phase gradient (i.e., the interaction potential is convex). For the periodic pinning potential of the CDW model, the CDW sliding state has a particularly simple temporal behavior, with the CDW velocity at each point being periodic in time, though the spatial behavior is qu...

We present the results of molecular dynamic simulations of a two-dimensional vortex array driven by a uniform current through random pinning centers at zero temperature. We identify two types of flow of the driven array near the depinning threshold. For weak disorder the flux array contains few dislocation and moves via correlated displacements of patches of vortices in a crinkle motion. As the disorder strength increases, we observe a crossover to a spatially inhomogeneous regime of plastic flow, with a very defective vortex array and a channel-like structure of the flowing regions. The two regimes are characterized by qualitatively different spatial distribution of vortex velocities. In the crinkle regime the distribution of vortex velocities near threshold has a single maximum that shifts to larger velocities as the driving force is increased. In the plastic regime the distribution of vortex velocities near threshold has a clear bimodal structure that persists upon time-averaging the individual velocities. The bimodal structure of the velocity distribution reflects the coexistence of pinned and flowing regions and is proposed as a quantitative signature of plastic flow.