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G Oshanin

Publications and source records attributed to G Oshanin.

At least 19 recordsLinked to original sources
PubMed2003

Equilibrium properties of a monomer-monomer catalytic reaction on a one-dimensional chain.

We study the equilibrium properties of a lattice-gas model of an A+B-->0 catalytic reaction on a one-dimensional chain in contact with a reservoir for the particles. The particles of species A and B are in thermal contact with their vapor phases acting as reservoirs, i.e., they may adsorb onto empty lattice sites and may desorb from the lattice. If adsorbed A and B particles appear at neighboring lattice sites, they instantaneously react and both desorb. For this model of a catalytic reaction in the adsorption-controlled limit, we derive analytically the expression of the pressure and present exact results for the mean densities of particles and for the compressibilities of the adsorbate as a function of the chemical potentials of the two species.

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PubMed2003

Pascal principle for diffusion-controlled trapping reactions.

In this paper, we analyze the long-time behavior of the survival probability P(A)(t) of an A particle, that performs lattice random walk in the presence of randomly moving traps B. We show that for both perfect and imperfect trapping reactions, for arbitrary spatial dimension d and for a rather general class of random walks, P(A)(t) is less than or equal to the survival probability of an immobile target A in the presence of randomly moving traps.

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PubMed2003

Adsorption of reactive particles on a random catalytic chain: an exact solution.

We study equilibrium properties of a catalytically activated annihilation A+A-->0 reaction taking place on a one-dimensional chain of length N (N--> infinity ) 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 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. Noncatalytic segments are inert with respect to reaction and here two adsorbed A particles harmlessly coexist. For both "annealed" and "quenched" disorder in placement of the catalytic segments, we calculate exactly the disorder-averaged pressure per site. Explicit asymptotic formulas for the particle mean density and the compressibility are also presented.

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PubMed2002

Trapping reactions with randomly moving traps: exact asymptotic results for compact exploration.

In a recent paper, Bray and Blythe have shown that the survival probability P(A)(t) of an A particle diffusing with a diffusion coefficient D(A) in a one-dimensional system with diffusive traps B is independent of D(A) in the asymptotic limit t--> infinity and coincides with the survival probability of an immobile target in the presence of diffusive traps. Here, we show that this remarkable behavior has a more general range of validity and holds for systems of an arbitrary dimension d, integer or fractal, provided that the traps are "compactly exploring" the space, i.e., the "fractal" dimension d(w) of traps' trajectories is greater than d. For the marginal case when d(w)=d, as exemplified here by conventional diffusion in two-dimensional systems, the decay form is determined up to a numerical factor in the characteristic decay time.

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PubMed2002

Defect-induced perturbations of atomic monolayers on solid surfaces.

We study long-range morphological changes in atomic monolayers on solid substrates induced by different types of defects; e.g., by monoatomic steps in the surface, or by the tip of an atomic force microscope (AFM), placed at some distance above the substrate. Representing the monolayer in terms of a suitably extended Frenkel-Kontorova-type model, we calculate the defect-induced density profiles for several possible geometries. In case of an AFM tip, we also determine the extra force exerted on the tip due to the tip-induced dehomogenization of the monolayer.

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PubMed2002

Ultraslow vacancy-mediated tracer diffusion in two dimensions: the Einstein relation verified.

We study the dynamics of a charged tracer particle (TP) on a two-dimensional lattice, all sites of which except one (a vacancy) are filled with identical neutral, hard-core particles. The particles move randomly by exchanging their positions with the vacancy, subject to the hard-core exclusion. In the case when the charged TP experiences a bias due to external electric field E (which favors its jumps in the preferential direction), we determine exactly the limiting probability distribution of the TP position in terms of appropriate scaling variables and the leading large-n (n being the discrete time) behavior of the TP mean displacement X(n); the latter is shown to obey an anomalous, logarithmic law /X(n)/=alpha(0)(/E/)ln(n). Comparing our results with earlier predictions by Brummelhuis and Hilhorst [J. Stat. Phys. 53, 249 (1988)] for the TP diffusivity D(n) in the unbiased case, we infer that the Einstein relation mu(n)=betaD(n) between the TP diffusivity and the mobility mu(n)=lim(/E/-->0)(/X(n)///E/n) holds in the leading n order, despite the fact that both D(n) and mu(n) are not constant but vanish as n--> infinity. We also generalize our approach to the situation with very small but finite vacancy concentration rho(v), in which case we find a ballistic-type law /X(n)/=pi(alpha)(0)(/E/)rho(v)n. We demonstrate that here, again, both D(n) and mu(n), calculated in the linear in rho(v) approximation, do obey the Einstein relation.

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PubMed2001

Atomic slide puzzle: self-diffusion of an impure atom.

In a series of recent papers [Phys. Rev. Lett. 86, 1562 (2001); Nature (London) 408, 665 (2000)] van Gastel and co-workers have presented what may be the first experimental evidence, based on a series of scanning tunnel microscope images, that impure, Indium atoms, embedded into the first, close-packed layer of a Cu(001) surface, are not localized but make concerted, long excursions. Such excursions occur due to continuous reshuffling of the surface following the position exchanges of both impure and host Cu atoms with the naturally occurring surface vacancies. van Gastel and co-workers have also formulated an original lattice-gas type model with asymmetric exchange probabilities, whose numerical solution is in a good agreement with the experimental data. In this paper we propose an exact lattice solution of several versions of this model.

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PubMed2001

Influence of auto-organization and fluctuations on the kinetics of a monomer-monomer catalytic scheme.

We study analytically the 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 that takes into account explicitly the influence of spatial correlations on the time evolution of the mean particle density. With this approach, we recover some known results concerning the time evolution of the mean particle density and establish others.

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PubMed2000

Stokes formula and density perturbances for driven tracer diffusion in an adsorbed monolayer

We study the intrinsic friction of monolayers adsorbed on solid surfaces from a gas phase or vapor. Within the framework of the Langmuir model of delocalized adsorption, we calculate the resistance offered by the mobile adsorbate's particles to some impure tracer molecule, whose diffusive random motion is biased by a constant external force. We find that for sufficiently small driving forces the force exerted on the tracer shows viscouslike behavior. We derive then the analog of the Stokes formula for two-dimensional adsorbates, calculate the corresponding friction coefficient, and determine the stationary particle distribution in the monolayer as seen from the driven impurity.

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PubMed2000

Kinetics of stochastically gated diffusion-limited reactions and geometry of random walk trajectories

In this paper we study the kinetics of diffusion-limited, pseudo-first-order A+B-->B reactions in situations in which the particles' intrinsic reactivities are not constant but vary randomly in time. That is, we suppose that the particles are bearing "gates" which fluctuate in time, randomly and independently of each other, between two states-an active state, when the reaction may take place between A and B particles appearing in close contact; and a blocked state, when the reaction is completely inhibited. We focus here on two customary limiting cases of pseudo-first-order reactions-the so-called target annihilation and the Rosenstock trapping model-and consider four different particular models, such that the A particle can be either mobile or immobile or gated or ungated, and ungated or gated B particles can be fixed at random positions or move randomly. All models are formulated on a d-dimensional regular lattice, and we suppose that the mobile species perform independent, homogeneous, discrete-time lattice random walks. The model involving a single, immobile, ungated target A and a concentration of mobile, gated B particles is solved exactly. For the remaining three models we determine exactly, in the form of rigorous lower and upper bounds showing the same N dependence, the large-N asymptotical behavior of the probability that the A particle survives until the Nth step. We also realize that for all four models studied here the A particle survival probability can be interpreted as the moment generating function of some functionals of random walk trajectories, such as, e. g., the number of self-intersections, the number of sites visited exactly a given number of times, the "residence time" on a random array of lattice sites, etc. Our results thus apply to the asymptotic behavior of corresponding generating functions which are not known as yet.

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PubMed2000

Generalized model for dynamic percolation

We study the dynamics of a carrier, which performs a biased motion under the influence of an external field E-->, in an environment which is modeled by dynamic percolation and created by hard-core particles. The particles move randomly on a simple cubic lattice, constrained by hard-core exclusion, and they spontaneously annihilate and reappear at some prescribed rates. We determine the density profiles of the "environment" particles, as seen from the stationary moving carrier, and calculate its terminal velocity V(c) as the function of the applied field and other system parameters. For sufficiently small driving forces the force exerted on the carrier by the "environment" particles shows a viscouslike behavior. An analog Stokes formula for such dynamic percolative environments and the corresponding friction coefficient are derived. We show that the density profile of the environment particles is strongly inhomogeneous: In front of the stationary moving carrier the density is higher than the average density rho(s), while past the carrier the local density is lower than rho(s).

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