2,704 research outputs found
Exact shock measures and steady-state selection in a driven diffusive system with two conserved densities
We study driven 1d lattice gas models with two types of particles and nearest
neighbor hopping. We find the most general case when there is a shock solution
with a product measure which has a density-profile of a step function for both
densities. The position of the shock performs a biased random walk. We
calculate the microscopic hopping rates of the shock. We also construct the
hydrodynamic limit of the model and solve the resulting hyperbolic system of
conservation laws. In case of open boundaries the selected steady state is
given in terms of the boundary densities.Comment: 12 pages, 4 figure
Phase transition in the two-component symmetric exclusion process with open boundaries
We consider single-file diffusion in an open system with two species of
particles. At the boundaries we assume different reservoir densities which
drive the system into a non-equilibrium steady state. As a model we use an
one-dimensional two-component simple symmetric exclusion process with two
different hopping rates and open boundaries. For investigating the
dynamics in the hydrodynamic limit we derive a system of coupled non-linear
diffusion equations for the coarse-grained particle densities. The relaxation
of the initial density profile is analyzed by numerical integration. Exact
analytical expressions are obtained for the self-diffusion coefficients, which
turns out to be length-dependent, and for the stationary solution. In the
steady state we find a discontinuous boundary-induced phase transition as the
total exterior density gradient between the system boundaries is varied. At one
boundary a boundary layer develops inside which the current flows against the
local density gradient. Generically the width of the boundary layer and the
bulk density profiles do not depend on the two hopping rates. At the phase
transition line, however, the individual density profiles depend strongly on
the ratio . Dynamic Monte Carlo simulation confirm our theoretical
predictions.Comment: 26 pages, 6 figure
Bethe ansatz and current distribution for the TASEP with particle-dependent hopping rates
Using the Bethe ansatz we obtain in a determinant form the exact solution of
the master equation for the conditional probabilities of the totally asymmetric
exclusion process with particle-dependent hopping rates on Z. From this we
derive a determinant expression for the time-integrated current for a
step-function initial state.Comment: 14 page
Phase Coexistence in Driven One Dimensional Transport
We study a one-dimensional totally asymmetric exclusion process with random
particle attachments and detachments in the bulk. The resulting dynamics leads
to unexpected stationary regimes for large but finite systems. Such regimes are
characterized by a phase coexistence of low and high density regions separated
by domain walls. We use a mean-field approach to interpret the numerical
results obtained by Monte-Carlo simulations and we predict the phase diagram of
this non-conserved dynamics in the thermodynamic limit.Comment: 4 pages, 3 figures. Accepted for publication on Phys. Rev. Let
Infinite reflections of shock fronts in driven diffusive systems with two species
Interaction of a domain wall with boundaries of a system is studied for a
class of stochastic driven particle models. Reflection maps are introduced for
the description of this process. We show that, generically, a domain wall
reflects infinitely many times from the boundaries before a stationary state
can be reached. This is in an evident contrast with one-species models where
the stationary density is attained after just one reflection.Comment: 11 pages, 8 eps figs, to appearin JPhysA 01.200
Bethe ansatz solution of zero-range process with nonuniform stationary state
The eigenfunctions and eigenvalues of the master-equation for zero range
process with totally asymmetric dynamics on a ring are found exactly using the
Bethe ansatz weighted with the stationary weights of particle configurations.
The Bethe ansatz applicability requires the rates of hopping of particles out
of a site to be the -numbers . This is a generalization of the rates
of hopping of noninteracting particles equal to the occupation number of a
site of departure. The noninteracting case can be restored in the limit . The limiting cases of the model for correspond to the totally
asymmetric exclusion process, and the drop-push model respectively. We analyze
the partition function of the model and apply the Bethe ansatz to evaluate the
generating function of the total distance travelled by particles at large time
in the scaling limit. In case of non-zero interaction, , the
generating function has the universal scaling form specific for the
Kardar-Parizi-Zhang universality class.Comment: 7 pages, Revtex4, mistypes correcte
Hydrodynamics of the zero-range process in the condensation regime
We argue that the coarse-grained dynamics of the zero-range process in the
condensation regime can be described by an extension of the standard
hydrodynamic equation obtained from Eulerian scaling even though the system is
not locally stationary. Our result is supported by Monte Carlo simulations.Comment: 14 pages, 3 figures. v2: Minor alteration
Amplication of Molecular Traffic Control in catalytic grains with novel channel topology design
We investigate the conditions for reactivity enhancement of catalytic processes in porous solids by the use of molecular traffic control (MTC). With dynamic Monte-Carlo simulations and continuous-time master equation theory applied to the high concentration regime, we obtain a quantitative description of the MTC effect for a network of intersecting single-file channels in a wide range of grain parameters and for optimal external operating conditions. Implementing the concept of MTC in models with specially designed alternating bimodal channels, we find the efficiency ratio (compared with a topologically and structurally similar reference system without MTC) to be enhanced with increasing grain diameter, a property verified for the first time for a MTC system. Even for short intersection channels, MTC leads to a reactivity enhancement of up to approximately 65%. This suggests that MTC may significantly enhance the efficiency of a catalytic process for small as well as large porous particles with a suitably chosen binary channel topology
Shocks in asymmetric simple exclusion processes of interacting particles
In this paper, we study shocks and related transitions in asymmetric simple
exclusion processes of particles with nearest neighbor interactions. We
consider two kinds of inter-particle interactions. In one case, the
particle-hole symmetry is broken due to the interaction. In the other case,
particles have an effective repulsion due to which the particle-current-density
drops down near the half filling. These interacting particles move on a one
dimensional lattice which is open at both the ends with injection of particles
at one end and withdrawal of particles at the other. In addition to this, there
are possibilities of attachments or detachments of particles to or from the
lattice with certain rates. The hydrodynamic equation that involves the exact
particle current-density of the particle conserving system and additional terms
taking care of the attachment-detachment kinetics is studied using the
techniques of boundary layer analysis.Comment: 10 pages, 8 figure
On U_q(SU(2))-symmetric Driven Diffusion
We study analytically a model where particles with a hard-core repulsion
diffuse on a finite one-dimensional lattice with space-dependent, asymmetric
hopping rates. The system dynamics are given by the
\mbox{U[SU(2)]}-symmetric Hamiltonian of a generalized anisotropic
Heisenberg antiferromagnet. Exploiting this symmetry we derive exact
expressions for various correlation functions. We discuss the density profile
and the two-point function and compute the correlation length as well
as the correlation time . The dynamics of the density and the
correlations are shown to be governed by the energy gaps of a one-particle
system. For large systems and depend only on the asymmetry. For
small asymmetry one finds indicating a dynamical exponent
as for symmetric diffusion.Comment: 10 pages, LATE
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