Stationary uphill currents in locally perturbed Zero Range Processes

Uphill currents are observed when mass diffuses in the direction of the density gradient. We study this phenomenon in stationary conditions in the framework of locally perturbed 1D Zero Range Processes (ZRP). We show that the onset of currents flowing from the reservoir with smaller density to the one with larger density can be caused by a local asymmetry in the hopping rates on a single site at the center of the lattice. For fixed injection rates at the boundaries, we prove that a suitable tuning of the asymmetry in the bulk may induce uphill diffusion at arbitrarily large, finite volumes. We also deduce heuristically the hydrodynamic behavior of the model and connect the local asymmetry characterizing the ZRP dynamics to a matching condition relevant for the macroscopic problem

Effects of communication efficiency and exit capacity on fundamental diagrams for pedestrian motion in an obscure tunnel|a particle system approach

Fundamental diagrams describing the relation between pedestrians speed and density are key points in understanding pedestrian dynamics. Experimental data evidence the onset of complex behaviors in which the velocity decreases with the density and different logistic regimes are identified. This paper addresses the issue of pedestrians transport and of fundamental diagrams for a scenario involving the motion of pedestrians escaping from an obscure tunnel. % via a simple one--dimensional particle system model. We capture the effects of the communication efficiency and the exit capacity by means of two thresholds controlling the rate at which particles (walkers, pedestrians) move on the lattice. Using a particle system model, we show that in absence of limitation in communication among pedestrians we reproduce with good accuracy the standard fundamental diagrams, whose basic behaviors can be interpreted in terms of the exit capacity limitation. When the effect of a limited communication ability is considered, then interesting non--intuitive phenomena occur. Particularly, we shed light on the loss of monotonicity of the typical speed--density curves, revealing the existence of a pedestrians density optimizing the escape. We study both the discrete particle dynamics as well as the corresponding hydrodynamic limit (a porous medium equation and a transport (continuity) equation). We also point out the dependence of the effective transport coefficients on the two thresholds -- the essence of the microstructure information

Uphill migration in coupled driven particle systems

In particle systems subject to a nonuniform drive, particle migration is observed from the driven to the non--driven region and vice--versa, depending on details of the hopping dynamics, leading to apparent violations of Fick's law and of steady--state thermodynamics. We propose and discuss a very basic model in the framework of independent random walkers on a pair of rings, one of which features biased hopping rates, in which this phenomenon is observed and fully explained.Comment: 8 pages, 10 figure

Transport in quantum multi-barrier systems as random walks on a lattice

A quantum finite multi-barrier system, with a periodic potential, is considered and exact expressions for its plane wave amplitudes are obtained using the Transfer Matrix method [10]. This quantum model is then associated with a stochastic process of independent random walks on a lattice, by properly relating the wave amplitudes with the hopping probabilities of the particles moving on the lattice and with the injection rates from external particle reservoirs. Analytical and numerical results prove that the stationary density profile of the particle system overlaps with the quantum mass density profile of the stationary Schrodinger equation, when the parameters of the two models are suitably matched. The equivalence between the quantum model and a stochastic particle system would mainly be fruitful in a disordered setup. Indeed, we also show, here, that this connection, analytically proven to hold for periodic barriers, holds even when the width of the barriers and the distance between barriers are randomly chosen