64 research outputs found
Annihilating random walks in one-dimensional disordered media
We study diffusion-limited pair annihilation on one-dimensional
lattices with inhomogeneous nearest neighbour hopping in the limit of infinite
reaction rate. We obtain a simple exact expression for the particle
concentration of the many-particle system in terms of the
conditional probabilities for a single random walker in a dual
medium. For some disordered systems with an initially randomly filled lattice
this leads asymptotically to for the
disorder-averaged particle density. We also obtain interesting exact relations
for single-particle conditional probabilities in random media related by
duality, such as random-barrier and random-trap systems. For some specific
random barrier systems the Smoluchovsky approach to diffusion-limited
annihilation turns out to fail.Comment: LaTeX, 2 eps-figures, to be published in PR
Single-Particle Diffusion-Coefficient on Surfaces with Ehrlich-Schwoebel-Barriers
The diffusion coefficient of single particles in the presence of
Ehrlich-Schwoebel barriers (ESB)is considered. An exact expression is given for
the diffusion coefficient on linear chains with random arrangements of ESB. The
results are extended to surfaces having ESB with uniform extension in one or
both directions. All results are verified by Monte Carlo simulations.Comment: 11 pages, LaTeX2e, 6 eps-figure
Dynamic regimes of fluids simulated by multiparticle-collision dynamics
We investigate the hydrodynamic properties of a fluid simulated with a
mesoscopic solvent model. Two distinct regimes are identified, the `particle
regime' in which the dynamics is gas-like, and the `collective regime' where
the dynamics is fluid-like. This behavior can be characterized by the Schmidt
number, which measures the ratio between viscous and diffusive transport.
Analytical expressions for the tracer diffusion coefficient, which have been
derived on the basis of a molecular-chaos assumption, are found to describe the
simulation data very well in the particle regime, but important deviations are
found in the collective regime. These deviations are due to hydrodynamic
correlations. The model is then extended in order to investigate self-diffusion
in colloidal dispersions. We study first the transport properties of heavy
point-like particles in the mesoscopic solvent, as a function of their mass and
number density. Second, we introduce excluded-volume interactions among the
colloidal particles and determine the dependence of the diffusion coefficient
on the colloidal volume fraction for different solvent mean-free paths. In the
collective regime, the results are found to be in good agreement with previous
theoretical predictions based on Stokes hydrodynamics and the Smoluchowski
equation.Comment: 15 pages, 15 figure
A Numerical Model for Brownian Particles Fluctuating in Incompressible Fluids
We present a numerical method that consistently implements thermal
fluctuations and hydrodynamic interactions to the motion of Brownian particles
dispersed in incompressible host fluids. In this method, the thermal
fluctuations are introduced as random forces acting on the Brownian particles.
The hydrodynamic interactions are introduced by directly resolving the fluid
motions with the particle motion as a boundary condition to be satisfied. The
validity of the method has been examined carefully by comparing the present
numerical results with the fluctuation-dissipation theorem whose analytical
form is known for dispersions of a single spherical particle. Simulations are
then performed for more complicated systems, such as a dispersion composed of
many spherical particles and a single polymeric chain in a solvent.Comment: 6 pages, 8 figure
Diffusion with rearranging traps
A model for diffusion on a cubic lattice with a random distribution of traps
is developed. The traps are redistributed at certain time intervals. Such
models are useful for describing systems showing dynamic disorder, such as
ion-conducting polymers. In the present model the traps are infinite, unlike an
earlier version with finite traps, this model has a percolation threshold. For
the infinite trap version a simple analytical calculation is possible and the
results agree qualitatively with simulation.Comment: Latex, five figure
Branching and annihilating Levy flights
We consider a system of particles undergoing the branching and annihilating
reactions A -> (m+1)A and A + A -> 0, with m even. The particles move via
long-range Levy flights, where the probability of moving a distance r decays as
r^{-d-sigma}. We analyze this system of branching and annihilating Levy flights
(BALF) using field theoretic renormalization group techniques close to the
upper critical dimension d_c=sigma, with sigma<2. These results are then
compared with Monte-Carlo simulations in d=1. For sigma close to unity in d=1,
the critical point for the transition from an absorbing to an active phase
occurs at zero branching. However, for sigma bigger than about 3/2 in d=1, the
critical branching rate moves smoothly away from zero with increasing sigma,
and the transition lies in a different universality class, inaccessible to
controlled perturbative expansions. We measure the exponents in both
universality classes and examine their behavior as a function of sigma.Comment: 9 pages, 4 figure
The one-dimensional contact process: duality and renormalisation
We study the one-dimensional contact process in its quantum version using a
recently proposed real space renormalisation technique for stochastic
many-particle systems. Exploiting the duality and other properties of the
model, we can apply the method for cells with up to 37 sites. After suitable
extrapolation, we obtain exponent estimates which are comparable in accuracy
with the best known in the literature.Comment: 15 page
A Method of Intervals for the Study of Diffusion-Limited Annihilation, A + A --> 0
We introduce a method of intervals for the analysis of diffusion-limited
annihilation, A+A -> 0, on the line. The method leads to manageable diffusion
equations whose interpretation is intuitively clear. As an example, we treat
the following cases: (a) annihilation in the infinite line and in infinite
(discrete) chains; (b) annihilation with input of single particles, adjacent
particle pairs, and particle pairs separated by a given distance; (c)
annihilation, A+A -> 0, along with the birth reaction A -> 3A, on finite rings,
with and without diffusion.Comment: RevTeX, 13 pages, 4 figures, 1 table. References Added, and some
other minor changes, to conform with final for
Surface Critical Behavior in Systems with Non-Equilibrium Phase Transitions
We study the surface critical behavior of branching-annihilating random walks
with an even number of offspring (BARW) and directed percolation (DP) using a
variety of theoretical techniques. Above the upper critical dimensions d_c,
with d_c=4 (DP) and d_c=2 (BARW), we use mean field theory to analyze the
surface phase diagrams using the standard classification into ordinary,
special, surface, and extraordinary transitions. For the case of BARW, at or
below the upper critical dimension, we use field theoretic methods to study the
effects of fluctuations. As in the bulk, the field theory suffers from
technical difficulties associated with the presence of a second critical
dimension. However, we are still able to analyze the phase diagrams for BARW in
d=1,2, which turn out to be very different from their mean field analog.
Furthermore, for the case of BARW only (and not for DP), we find two
independent surface beta_1 exponents in d=1, arising from two distinct
definitions of the order parameter. Using an exact duality transformation on a
lattice BARW model in d=1, we uncover a relationship between these two surface
beta_1 exponents at the ordinary and special transitions. Many of our
predictions are supported using Monte-Carlo simulations of two different models
belonging to the BARW universality class.Comment: 19 pages, 12 figures, minor additions, 1 reference adde
Lattice Boltzmann simulations of soft matter systems
This article concerns numerical simulations of the dynamics of particles
immersed in a continuum solvent. As prototypical systems, we consider colloidal
dispersions of spherical particles and solutions of uncharged polymers. After a
brief explanation of the concept of hydrodynamic interactions, we give a
general overview over the various simulation methods that have been developed
to cope with the resulting computational problems. We then focus on the
approach we have developed, which couples a system of particles to a lattice
Boltzmann model representing the solvent degrees of freedom. The standard D3Q19
lattice Boltzmann model is derived and explained in depth, followed by a
detailed discussion of complementary methods for the coupling of solvent and
solute. Colloidal dispersions are best described in terms of extended particles
with appropriate boundary conditions at the surfaces, while particles with
internal degrees of freedom are easier to simulate as an arrangement of mass
points with frictional coupling to the solvent. In both cases, particular care
has been taken to simulate thermal fluctuations in a consistent way. The
usefulness of this methodology is illustrated by studies from our own research,
where the dynamics of colloidal and polymeric systems has been investigated in
both equilibrium and nonequilibrium situations.Comment: Review article, submitted to Advances in Polymer Science. 16 figures,
76 page
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