29 research outputs found
Scaling of Reaction Zones in the A+B->0 Diffusion-Limited Reaction
We study reaction zones in three different versions of the A+B->0 system. For
a steady state formed by opposing currents of A and B particles we derive
scaling behavior via renormalization group analysis. By use of a previously
developed analogy, these results are extended to the time-dependent case of an
initially segregated system. We also consider an initially mixed system, which
forms reaction zones for dimension d<4. In this case an extension of the
steady-state analogy gives scaling results characterized by new exponents.Comment: 4 pages, REVTeX 3.0 with epsf, 2 uuencoded postscript figures
appended, OUTP-94-33
Kinetics of A+B--->0 with Driven Diffusive Motion
We study the kinetics of two-species annihilation, A+B--->0, when all
particles undergo strictly biased motion in the same direction and with an
excluded volume repulsion between same species particles. It was recently shown
that the density in this system decays as t^{-1/3}, compared to t^{-1/4}
density decay in A+B--->0 with isotropic diffusion and either with or without
the hard-core repulsion. We suggest a relatively simple explanation for this
t^{-1/3} decay based on the Burgers equation. Related properties associated
with the asymptotic distribution of reactants can also be accounted for within
this Burgers equation description.Comment: 11 pages, plain Tex, 8 figures. Hardcopy of figures available on
request from S
Renormalization Group Study of the A+B->0 Diffusion-Limited Reaction
The diffusion-limited reaction, with equal initial densities
, is studied by means of a field-theoretic renormalization
group formulation of the problem. For dimension an effective theory is
derived, from which the density and correlation functions can be calculated. We
find the density decays in time as a,b \sim C\sqrt{\D}(Dt)^{-d/4} for , with \D = n_0-C^\prime n_0^{d/2} + \dots, where is a universal
constant, and is non-universal. The calculation is extended to the
case of unequal diffusion constants , resulting in a new
amplitude but the same exponent. For a controlled calculation is not
possible, but a heuristic argument is presented that the results above give at
least the leading term in an expansion. Finally, we address
reaction zones formed in the steady-state by opposing currents of and
particles, and derive scaling properties.Comment: 17 pages, REVTeX, 13 compressed figures, included with epsf. Eq.
(6.12) corrected, and a moderate rewriting of the introduction. Accepted for
publication in J. Stat. Phy
Diffusion-Limited Annihilation with Initially Separated Reactants
A diffusion-limited annihilation process, A+B->0, with species initially
separated in space is investigated. A heuristic argument suggests the form of
the reaction rate in dimensions less or equal to the upper critical dimension
. Using this reaction rate we find that the width of the reaction front
grows as in one dimension and as in two
dimensions.Comment: 9 pages, Plain Te
Exact Solution of Two-Species Ballistic Annihilation with General Pair-Reaction Probability
The reaction process is modelled for ballistic reactants on an
infinite line with particle velocities and and initially
segregated conditions, i.e. all A particles to the left and all B particles to
the right of the origin. Previous, models of ballistic annihilation have
particles that always react on contact, i.e. pair-reaction probability .
The evolution of such systems are wholly determined by the initial distribution
of particles and therefore do not have a stochastic dynamics. However, in this
paper the generalisation is made to , allowing particles to pass through
each other without necessarily reacting. In this way, the A and B particle
domains overlap to form a fluctuating, finite-sized reaction zone where the
product C is created. Fluctuations are also included in the currents of A and B
particles entering the overlap region, thereby inducing a stochastic motion of
the reaction zone as a whole. These two types of fluctuations, in the reactions
and particle currents, are characterised by the `intrinsic reaction rate', seen
in a single system, and the `extrinsic reaction rate', seen in an average over
many systems. The intrinsic and extrinsic behaviours are examined and compared
to the case of isotropically diffusing reactants.Comment: 22 pages, 2 figures, typos correcte
Delocalization Transition of a Rough Adsorption-Reaction Interface
We introduce a new kinetic interface model suitable for simulating
adsorption-reaction processes which take place preferentially at surface
defects such as steps and vacancies. As the average interface velocity is taken
to zero, the self- affine interface with Kardar-Parisi-Zhang like scaling
behaviour undergoes a delocalization transition with critical exponents that
fall into a novel universality class. As the critical point is approached, the
interface becomes a multi-valued, multiply connected self-similar fractal set.
The scaling behaviour and critical exponents of the relevant correlation
functions are determined from Monte Carlo simulations and scaling arguments.Comment: 4 pages with 6 figures, new comment
Formation of Liesegang patterns: A spinodal decomposition scenario
Spinodal decomposition in the presence of a moving particle source is
proposed as a mechanism for the formation of Liesegang bands. This mechanism
yields a sequence of band positions x_n that obeys the spacing law
x_n~Q(1+p)^n. The dependence of the parameters p and Q on the initial
concentration of the reagents is determined and we find that the functional
form of p is in agreement with the experimentally observed Matalon-Packter law.Comment: RevTex, 4 pages, 4 eps figure
Cluster persistence in one-dimensional diffusion--limited cluster--cluster aggregation
The persistence probability, , of a cluster to remain unaggregated is
studied in cluster-cluster aggregation, when the diffusion coefficient of a
cluster depends on its size as . In the mean-field the
problem maps to the survival of three annihilating random walkers with
time-dependent noise correlations. For the motion of persistent
clusters becomes asymptotically irrelevant and the mean-field theory provides a
correct description. For the spatial fluctuations remain relevant
and the persistence probability is overestimated by the random walk theory. The
decay of persistence determines the small size tail of the cluster size
distribution. For the distribution is flat and, surprisingly,
independent of .Comment: 11 pages, 6 figures, RevTeX4, submitted to Phys. Rev.
Reaction Front in an A+B -> C Reaction-Subdiffusion Process
We study the reaction front for the process A+B -> C in which the reagents
move subdiffusively. Our theoretical description is based on a fractional
reaction-subdiffusion equation in which both the motion and the reaction terms
are affected by the subdiffusive character of the process. We design numerical
simulations to check our theoretical results, describing the simulations in
some detail because the rules necessarily differ in important respects from
those used in diffusive processes. Comparisons between theory and simulations
are on the whole favorable, with the most difficult quantities to capture being
those that involve very small numbers of particles. In particular, we analyze
the total number of product particles, the width of the depletion zone, the
production profile of product and its width, as well as the reactant
concentrations at the center of the reaction zone, all as a function of time.
We also analyze the shape of the product profile as a function of time, in
particular its unusual behavior at the center of the reaction zone