170 research outputs found
Single-Species Reactions on a Random Catalytic Chain
We present an exact solution for a catalytically-activated annihilation A + A
\to 0 reaction taking place on a one-dimensional chain in which some segments
(placed at random, with mean concentration p) possess special, catalytic
properties. Annihilation reaction takes place, as soon as any two A particles
land from the reservoir onto two vacant sites at the extremities of the
catalytic segment, or when any A particle lands onto a vacant site on a
catalytic segment while the site at the other extremity of this segment is
already occupied by another A particle. We find that the disorder-average
pressure per site of such a chain is given by , where is the
Langmuir adsorption pressure, (z being the activity and \beta^{-1} - the
temperature), while is the reaction-induced contribution, which
can be expressed, under appropriate change of notations, as the Lyapunov
exponent for the product of 2 \times 2 random matrices, obtained exactly by
Derrida and Hilhorst (J. Phys. A {\bf 16}, 2641 (1983)). Explicit asymptotic
formulae for the particle mean density and the compressibility are also
presented.Comment: AMSTeX, 17 pages, 1 figure, submitted to J. Phys.
Kinetic description of diffusion-limited reactions in random catalytic media
We study the kinetics of bimolecular, catalytically-activated reactions
(CARs) in d-dimensions. The elementary reaction act between reactants takes
place only when these meet in the vicinity of a catalytic site; such sites are
assumed to be immobile and randomly distributed in space. For CARs we develop a
kinetic formalism, based on Collins-Kimball-type ideas; within this formalism
we obtain explicit expressions for the effective reaction rates and for the
decay of the reactants' concentrations.Comment: 15 pages, Latex, two figures, to appear in J. Chem. Phy
Scaling Model of Annihilation-Diffusion Kinetics for Charged Particles with Long-Range Interactions
We propose the general scaling model for the diffusio n-annihilation reaction
with long-range power-law i
nteractions. The presented scaling arguments lead to the finding of three
different regimes, dep ending on the space dimensionality d and the long-range
force power e xponent n. The obtained kinetic phase diagram agrees well with
existing simulation data and approximate theoretical results.Comment: RevTEX, 7 pages, no figures, accepted to Physical Review
Influence of auto-organization and fluctuation effects on the kinetics of a monomer-monomer catalytic scheme
We study analytically kinetics of an elementary bimolecular reaction scheme
of the Langmuir-Hinshelwood type taking place on a d-dimensional catalytic
substrate. We propose a general approach which takes into account explicitly
the influence of spatial correlations on the time evolution of particles mean
densities and allows for the analytical analysis. In terms of this approach we
recover some of known results concerning the time evolution of particles mean
densities and establish several new ones.Comment: Latex, 25 pages, one figure, submitted to J. Chem. Phy
Intermittent random walks for an optimal search strategy: One-dimensional case
We study the search kinetics of an immobile target by a concentration of
randomly moving searchers. The object of the study is to optimize the
probability of detection within the constraints of our model. The target is
hidden on a one-dimensional lattice in the sense that searchers have no a
priori information about where it is, and may detect it only upon encounter.
The searchers perform random walks in discrete time n=0,1,2, ..., N, where N is
the maximal time the search process is allowed to run. With probability \alpha
the searchers step on a nearest-neighbour, and with probability (1-\alpha) they
leave the lattice and stay off until they land back on the lattice at a fixed
distance L away from the departure point. The random walk is thus intermittent.
We calculate the probability P_N that the target remains undetected up to the
maximal search time N, and seek to minimize this probability. We find that P_N
is a non-monotonic function of \alpha, and show that there is an optimal choice
\alpha_{opt}(N) of \alpha well within the intermittent regime, 0 <
\alpha_{opt}(N) < 1, whereby P_N can be orders of magnitude smaller compared to
the "pure" random walk cases \alpha =0 and \alpha = 1.Comment: 19 pages, 5 figures; submitted to Journal of Physics: Condensed
Matter; special issue on Chemical Kinetics Beyond the Textbook: Fluctuations,
Many-Particle Effects and Anomalous Dynamics, eds. K.Lindenberg, G.Oshanin
and M.Tachiy
Microscopic Model of Charge Carrier Transfer in Complex Media
We present a microscopic model of a charge carrier transfer under an action
of a constant electric field in a complex medium. Generalizing previous
theoretical approaches, we model the dynamical environment hindering the
carrier motion by dynamic percolation, i.e., as a medium comprising particles
which move randomly on a simple cubic lattice, constrained by hard-core
exclusion, and may spontaneously annihilate and re-appear at some prescribed
rates. We determine analytically the density profiles of the "environment"
particles, as seen from the stationary moving charge carrier, and calculate its
terminal velocity as the function of the applied field and other system
parameters. We realize that for sufficiently small external fields the force
exerted on the carrier by the "environment" particles shows a viscous-like
behavior and define an analog of the Stokes formula for such dynamic
percolative environments. The corresponding friction coefficient is also
derived.Comment: appearing in Chem. Phys. Special Issue on Molecular Charge Transfer
in Condensed Media - from Physics and Chemistry to Biology and
Nano-Engineering, edited by A.Kornyshev (Imperial College London), M.Newton
(Brookhaven Natl Lab) and J.Ulstrup (Technical University of Denmark
Spreading of a Macroscopic Lattice Gas
We present a simple mechanical model for dynamic wetting phenomena. Metallic
balls spread along a periodically corrugated surface simulating molecules of
liquid advancing along a solid substrate. A vertical stack of balls mimics a
liquid droplet. Stochastic motion of the balls, driven by mechanical vibration
of the corrugated surface, induces diffusional motion. Simple theoretical
estimates are introduced and agree with the results of the analog experiments,
with numerical simulation, and with experimental data for microscopic spreading
dynamics.Comment: 19 pages, LaTeX, 9 Postscript figures, to be published in Phy. Rev. E
(September,1966
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