10,987 research outputs found
Three-Species Diffusion-Limited Reaction with Continuous Density-Decay Exponents
We introduce a model of three-species two-particle diffusion-limited
reactions A+B -> A or B, B+C -> B or C, and C+A -> C or A, with three
persistence parameters (survival probabilities in reaction) of the hopping
particle. We consider isotropic and anisotropic diffusion (hopping with a
drift) in 1d. We find that the particle density decays as a power-law for
certain choices of the persistence parameter values. In the anisotropic case,
on one symmetric line in the parameter space, the decay exponent is
monotonically varying between the values close to 1/3 and 1/2. On another, less
symmetric line, the exponent is constant. For most parameter values, the
density does not follow a power-law. We also calculated various characteristic
exponents for the distance of nearest particles and domain structure. Our
results support the recently proposed possibility that 1d diffusion-limited
reactions with a drift do not fall within a limited number of distinct
universality classes.Comment: 12 pages in plain LaTeX and four Postscript files with figure
The Reaction-Diffusion Front for in One Dimension
We study theoretically and numerically the steady state diffusion controlled
reaction , where currents of and particles
are applied at opposite boundaries. For a reaction rate , and equal
diffusion constants , we find that when the
reaction front is well described by mean field theory. However, for , the front acquires a Gaussian profile - a result of
noise induced wandering of the reaction front center. We make a theoretical
prediction for this profile which is in good agreement with simulation.
Finally, we investigate the intrinsic (non-wandering) front width and find
results consistent with scaling and field theoretic predictions.Comment: 11 pages, revtex, 4 separate PostScript figure
Does hardcore interaction change absorbing type critical phenomena?
It has been generally believed that hardcore interaction is irrelevant to
absorbing type critical phenomena because the particle density is so low near
an absorbing phase transition. We study the effect of hardcore interaction on
the N species branching annihilating random walks with two offspring and report
that hardcore interaction drastically changes the absorbing type critical
phenomena in a nontrivial way. Through Langevin equation type approach, we
predict analytically the values of the scaling exponents, in one dimension for all N > 1. Direct numerical
simulations confirm our prediction. When the diffusion coefficients for
different species are not identical, and vary
continuously with the ratios between the coefficients.Comment: 4 pages, 1 figur
Life and Death at the Edge of a Windy Cliff
The survival probability of a particle diffusing in the two dimensional
domain near a ``windy cliff'' at is investigated. The particle dies
upon reaching the edge of the cliff. In addition to diffusion, the particle is
influenced by a steady ``wind shear'' with velocity , \ie, no average bias either toward or away from the cliff.
For this semi-infinite system, the particle survival probability decays with
time as , compared to in the absence of wind. Scaling
descriptions are developed to elucidate this behavior, as well as the survival
probability within a semi-infinite strip of finite width with particle
absorption at . The behavior in the strip geometry can be described in
terms of Taylor diffusion, an approach which accounts for the crossover to the
decay when the width of the strip diverges. Supporting numerical
simulations of our analytical results are presented.Comment: 13 pages, plain TeX, 5 figures available upon request to SR
(submitted to J. Stat. Phys.
Theory of Branching and Annihilating Random Walks
A systematic theory for the diffusion--limited reaction processes and is developed. Fluctuations are taken into account via
the field--theoretic dynamical renormalization group. For even the mean
field rate equation, which predicts only an active phase, remains qualitatively
correct near dimensions; but below a nontrivial
transition to an inactive phase governed by power law behavior appears. For
odd there is a dynamic phase transition for any which is described
by the directed percolation universality class.Comment: 4 pages, revtex, no figures; final version with slight changes, now
accepted for publication in Phys. Rev. Let
Refined Simulations of the Reaction Front for Diffusion-Limited Two-Species Annihilation in One Dimension
Extensive simulations are performed of the diffusion-limited reaction
AB in one dimension, with initially separated reagents. The reaction
rate profile, and the probability distributions of the separation and midpoint
of the nearest-neighbour pair of A and B particles, are all shown to exhibit
dynamic scaling, independently of the presence of fluctuations in the initial
state and of an exclusion principle in the model. The data is consistent with
all lengthscales behaving as as . Evidence of
multiscaling, found by other authors, is discussed in the light of these
findings.Comment: Resubmitted as TeX rather than Postscript file. RevTeX version 3.0,
10 pages with 16 Encapsulated Postscript figures (need epsf). University of
Geneva preprint UGVA/DPT 1994/10-85
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