633 research outputs found
Exact correlations in a single file system with a driven tracer
We study the effect of a single driven tracer particle in a bath of other
particles performing the random average process on an infinite line using a
stochastic hydrodynamics approach. We consider arbitrary fixed as well as
random initial conditions and compute the two-point correlations. For quenched
uniform and annealed steady state initial conditions we show that in the large
time limit the fluctuations and the correlations of the positions of the
particles grow subdiffusively as and have well defined scaling forms
under proper rescaling of the labels. We compute the corresponding scaling
functions exactly for these specific initial configurations and verify them
numerically. We also consider a non translationally invariant initial condition
with linearly increasing gaps where we show that the fluctuations and
correlations grow superdiffusively as at large times.Comment: 7 pages, 4 figures, supplementary material appended. To appear in EP
Zone clearance in an infinite TASEP with a step initial condition
The TASEP is a paradigmatic model of out-of-equilibrium statistical physics,
for which many quantities have been computed, either exactly or by approximate
methods. In this work we study two new kinds of observables that have some
relevance in biological or traffic models. They represent the probability for a
given clearance zone of the lattice to be empty (for the first time) at a given
time, starting from a step density profile. Exact expressions are obtained for
single-time quantities, while more involved history-dependent observables are
studied by Monte Carlo simulation, and partially predicted by a
phenomenological approach
Wake-mediated interaction between driven particles crossing a perpendicular flow
Diagonal or chevron patterns are known to spontaneously emerge at the
intersection of two perpendicular flows of self-propelled particles, e.g.
pedestrians. The instability responsible for this pattern formation has been
studied in previous work in the context of a mean-field approach. Here we
investigate the microscopic mechanism yielding to this pattern. We present a
lattice model study of the wake created by a particle crossing a perpendicular
flow and show how this wake can localize other particles traveling in the same
direction as a result of an effective interaction mediated by the perpendicular
flow. The use of a semi-deterministic model allows us to characterize
analytically the effective interaction between two particles.Comment: 23 pages, 8 figures. To appear in J. Stat. Mec
Two dimensional outflows for cellular automata with shuffle updates
In this paper, we explore the two-dimensional behavior of cellular automata
with shuffle updates. As a test case, we consider the evacuation of a square
room by pedestrians modeled by a cellular automaton model with a static floor
field. Shuffle updates are characterized by a variable associated to each
particle and called phase, that can be interpreted as the phase in the step
cycle in the frame of pedestrian flows. Here we also introduce a dynamics for
these phases, in order to modify the properties of the model. We investigate in
particular the crossover between low- and high-density regimes that occurs when
the density of pedestrians increases, the dependency of the outflow in the
strength of the floor field, and the shape of the queue in front of the exit.
Eventually we discuss the relevance of these results for pedestrians.Comment: 20 pages, 5 figures. v2: 16 pages, 5 figures; changed the title,
abstract and structure of the paper. v3: minor change
Crossing pedestrian traffic flows,diagonal stripe pattern, and chevron effect
We study two perpendicular intersecting flows of pedestrians. The latter are
represented either by moving hard core particles of two types, eastbound
(\symbp) and northbound (\symbm), or by two density fields, \rhop_t(\brr)
and \rhom_t(\brr). Each flow takes place on a lattice strip of width so
that the intersection is an square. We investigate the spontaneous
formation, observed experimentally and in simulations, of a diagonal pattern of
stripes in which alternatingly one of the two particle types dominates. By a
linear stability analysis of the field equations we show how this pattern
formation comes about. We focus on the observation, reported recently, that the
striped pattern actually consists of chevrons rather than straight lines. We
demonstrate that this `chevron effect' occurs both in particle simulations with
various different update schemes and in field simulations. We quantify the
effect in terms of the chevron angle and determine its
dependency on the parameters governing the boundary conditions.Comment: 36 pages, 22 figure
Exact domain wall theory for deterministic TASEP with parallel update
Domain wall theory (DWT) has proved to be a powerful tool for the analysis of
one-dimensional transport processes. A simple version of it was found very
accurate for the Totally Asymmetric Simple Exclusion Process (TASEP) with
random sequential update. However, a general implementation of DWT is still
missing in the case of updates with less fluctuations, which are often more
relevant for applications. Here we develop an exact DWT for TASEP with parallel
update and deterministic (p=1) bulk motion. Remarkably, the dynamics of this
system can be described by the motion of a domain wall not only on the
coarse-grained level but also exactly on the microscopic scale for arbitrary
system size. All properties of this TASEP, time-dependent and stationary, are
shown to follow from the solution of a bivariate master equation whose
variables are not only the position but also the velocity of the domain wall.
In the continuum limit this exactly soluble model then allows us to perform a
first principle derivation of a Fokker-Planck equation for the position of the
wall. The diffusion constant appearing in this equation differs from the one
obtained with the traditional `simple' DWT.Comment: 5 pages, 4 figure
Continuous and first-order jamming transition in crossing pedestrian traffic flows
After reviewing the main results obtained within a model for the intersection
of two perpendicular flows of pedestrians, we present a new finding: the
changeover of the jamming transition from continuous to first order when the
size of the intersection area increases.Comment: 14 pages, 9 figure
Exact gap statistics for the random average process on a ring with a tracer
We study statistics of the gaps in Random Average Process (RAP) on a ring
with particles hopping symmetrically, except one tracer particle which could be
driven. These particles hop either to the left or to the right by a random
fraction of the space available till next particle in the respective
directions. The random fraction is chosen from a distribution
. For non-driven tracer, when satisfies a necessary and
sufficient condition, the stationary joint distribution of the gaps between
successive particles takes an universal form that is factorized except for a
global constraint. Some interesting explicit forms of are found which
satisfy this condition. In case of driven tracer, the system reaches a
current-carrying steady state where such factorization does not hold.
Analytical progress has been made in the thermodynamic limit, where we computed
the single site mass distribution inside the bulk. We have also computed the
two point gap-gap correlation exactly in that limit. Numerical simulations
support our analytical results.Comment: 19 pages, 6 figure
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