79 research outputs found
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
- …