100 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
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
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
Kinetics of diffusion-limited catalytically-activated reactions: An extension of the Wilemski-Fixman approach
We study kinetics of diffusion-limited catalytically-activated
reactions taking place in three dimensional systems, in which an annihilation
of diffusive particles by diffusive traps may happen only if the
encounter of an with any of the s happens within a special catalytic
subvolumen, these subvolumens being immobile and uniformly distributed within
the reaction bath. Suitably extending the classical approach of Wilemski and
Fixman (G. Wilemski and M. Fixman, J. Chem. Phys. \textbf{58}:4009, 1973) to
such three-molecular diffusion-limited reactions, we calculate analytically an
effective reaction constant and show that it comprises several terms associated
with the residence and joint residence times of Brownian paths in finite
domains. The effective reaction constant exhibits a non-trivial dependence on
the reaction radii, the mean density of catalytic subvolumens and particles'
diffusion coefficients. Finally, we discuss the fluctuation-induced kinetic
behavior in such systems.Comment: To appear in J. Chem. Phy
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