arXiv subjects

G. Oshanin

Publications and source records attributed to G. Oshanin.

At least 73 records · Page 4Linked to original sources

arXiv2003

Molecular motor with a build-in escapement device

We study dynamics of a classical particle in a one-dimensional potential, which is composed of two periodic components, that are time-independent, have equal amplitudes and periodicities. One of them is externally driven by a random force and thus performs a diffusive-type motion with respect to the other. We demonstrate that here, under certain conditions, the particle may move unidirectionally with a constant velocity, despite the fact that the random force averages out to zero. We show that the physical mechanism underlying such a phenomenon resembles the work of an escapement-type device in watches; upon reaching certain level, random fluctuations exercise a locking function creating the points of irreversibility in particle's trajectories such that the particle gets uncompensated displacements. Repeated (randomly) in each cycle, this process ultimately results in a random ballistic-type motion. In the overdamped limit, we work out simple analytical estimates for the particle's terminal velocity. Our analytical results are in a very good agreement with the Monte Carlo data.

cond-mat.stat-mech↗

arXiv2003

Intrinsic Friction of Monolayers Adsorbed on Solid Surfaces

We overview recent results on intrinsic frictional properties of adsorbed monolayers, composed of mobile hard-core particles undergoing continuous exchanges with a vapor phase. In terms of a dynamical master equation approach we determine the velocity of a biased impure molecule - the tracer particle (TP), constrained to move inside the adsorbed monolayer probing its frictional properties, define the frictional forces exerted by the monolayer on the TP, as well as the particles density distribution in the monolayer.

cond-mat.stat-mech↗

arXiv2003

Exactly Solvable Model of Monomer-Monomer Reactions on a Two-Dimensional Random Catalytic Substrate

We present an \textit{exactly solvable} model of a monomer-monomer $A + B \to \emptyset$ reaction on a 2D inhomogeneous, catalytic substrate and study the equilibrium properties of the two-species adsorbate. The substrate contains randomly placed catalytic bonds of mean density $q$ which connect neighboring adsorption sites. The interacting $A$ and $B$ (monomer) species undergo continuous exchanges with corresponding adjacent gaseous reservoirs. A reaction $A + B \to \emptyset$ takes place instantaneously if $A$ and $B$ particles occupy adsorption sites connected by a catalytic bond. We find that for the case of \textit{annealed} disorder in the placement of the catalytic bonds the reaction model under study can be mapped onto the general spin $S = 1$ (GS1) model. Here we concentrate on a particular case in which the model reduces to an exactly solvable Blume-Emery-Griffiths (BEG) model (T. Horiguchi, Phys. Lett. A {\bf 113}, 425 (1986); F.Y. Wu, Phys. Lett. A, {\bf 116}, 245 (1986)) and derive an exact expression for the disorder-averaged equilibrium pressure of the two-species adsorbate. We show that at equal partial vapor pressures of the $A$ and $B$ species this system exhibits a second-order phase transition which reflects a spontaneous symmetry breaking with large fluctuations and progressive coverage of the entire substrate by either one of the species.

cond-mat.mtrl-sci↗

arXiv2003

On the joint residence time of N independent two-dimensional Brownian motions

We study the behavior of several joint residence times of N independent Brownian particles in a disc of radius $R$ in two dimensions. We consider: (i) the time T_N(t) spent by all N particles simultaneously in the disc within the time interval [0,t]; (ii) the time T_N^{(m)}(t) which at least m out of N particles spend together in the disc within the time interval [0,t]; and (iii) the time {\tilde T}_N^{(m)}(t) which exactly m out of N particles spend together in the disc within the time interval [0,t]. We obtain very simple exact expressions for the expectations of these three residence times in the limit t\to\infty.

cond-mat.stat-mech↗

arXiv2003

Catalytic reactions with bulk-mediated excursions: Mixing fails to restore chemical equilibrium

In this paper we analyze the effect of the bulk-mediated excursions (BME) of reactive species on the long-time behavior of the catalytic Langmuir-Hinshelwood-like A + B \to 0 reactions in systems in which a catalytic plane (CP) is in contact with liquid phase, containg concentrations of reactive particles. Such BME result from repeated particles desorption from the CP, subsequent diffusion in the liquid phase and eventual readsorption on the CP away from the intial detachment point. This process which leads to an effective superdiffusive transport along the CP. We consider both "batch" reactions, in which all particles of reactive species were initially adsorbed onto the CP, and reactions followed by a steady inflow of particles onto the CP. We show that for "batch" reactions the BME provide an effective mixing channel and here the mean-field-type behavior emerges. On contrary, for reaction followed by a steady inflow of particles, we observe essential departures from the mean-field behavior and find that the mixing effect of the BME is insufficient to restore chemical equilibrium. We show that a steady-state is established as t \to \infty, in which the limiting value of the mean coverages of the CP depends on the particles' diffusion coefficient in the bulk liquid phase and the spatial distributions of adsorbed particles are strongly correlated. Moreover, we show that the relaxation to such a steady-state is described by a power-law function of time, in contrast to the exponential time-dependence describing the approach to equilibrium in perfectly stirred systems.

cond-mat.stat-mech↗

arXiv2003

Pascal Principle for Diffusion-Controlled Trapping Reactions

"All misfortune of man comes from the fact that he does not stay peacefully in his room", has once asserted Blaise Pascal. In the present paper we evoke this statement as the "Pascal principle" in regard to the problem of survival of an "A" particle, which performs a lattice random walk in presence of a concentration of randomly moving traps "B", and gets annihilated upon encounters with any of them. We prove here that at sufficiently large times for both perfect and imperfect trapping reactions, for arbitrary spatial dimension "d" and for a rather general class of random walks, the "A" particle survival probability is less than or equal to the survival probability of an immobile target in the presence of randomly moving traps.

cond-mat.stat-mech↗

arXiv2003

Exactly solvable model of reactions on a random catalytic chain

In this paper we study a catalytically-activated A + A \to 0 reaction taking place on a one-dimensional regular lattice which is brought in contact with a reservoir of A particles. The A particles have a hard-core and undergo continuous exchanges with the reservoir, adsorbing onto the lattice or desorbing back to the reservoir. Some lattice sites possess special, catalytic properties, which induce an immediate reaction between two neighboring A particles as soon as at least one of them lands onto a catalytic site. We consider three situations for the spatial placement of the catalytic sites: regular, annealed random and quenched random. For all these cases we derive exact results for the partition function, and the disorder-averaged pressure per lattice site. We also present exact asymptotic results for the particles' mean density and the system's compressibility. The model studied here furnishes another example of a 1D Ising-type system with random multisite interactions which admits an exact solution.

cond-mat.stat-mech↗

arXiv2003

Exactly solvable model of A + A \to 0 reactions on a heterogeneous catalytic chain

We present an exact solution describing equilibrium properties of the catalytically-activated A + A \to 0 reaction taking place on a one-dimensional lattice, where some of the sites possess special "catalytic" properties. The A particles undergo continuous exchanges with the vapor phase; two neighboring adsorbed As react when at least one of them resides on a catalytic site (CS). We consider three situations for the CS distribution: regular, annealed random and quenched random. For all three CS distribution types, we derive exact results for the disorder-averaged pressure and present exact asymptotic expressions for the particles' mean density. The model studied here furnishes another example of a 1D Ising-type system with random multi-site interactions which admits an exact solution.

cond-mat.stat-mech↗

arXiv2003

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 $A + B \to 0$ 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 function of the chemical potentials of the two species.

cond-mat.stat-mech↗

arXiv2002

Adsorption of Reactive Particles on a Random Catalytic Chain: An Exact Solution

We study equilibrium properties of a catalytically-activated annihilation $A + A \to 0$ reaction taking place on a one-dimensional chain of length $N$ ($N \to \infty$) 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. Non-catalytic 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-average pressure per site. Explicit asymptotic formulae for the particle mean density and the compressibility are also presented.

cond-mat.stat-mech↗

arXiv2002

Biased Tracer Diffusion in Hard-Core Lattice Gases: Some Notes on the Validity of the Einstein Relation

In this presentation we overview some recent results on biased tracer diffusion in lattice gases. We consider both models in which the gas particles density is explicitly conserved and situations in which the lattice gas particles undergo continuous exchanges with a reservoir, which case is appropriate, e.g., to adsorbed monolayers in contact with the vapor phase. For all these models we determine, in some cases exactly and in other ones - using a certain decoupling approximation, the mean displacement of a tracer particle (TP) driven by a constant external force in a dynamical background formed by the lattice gas particles whose transition rates are symmetric. Evaluating the TP mean displacement explicitly we are able to define the TP mobility, which allows us to demonstrate that the Einstein relation between the TP mobility and the diffusivity generally holds, despite the fact that in some cases diffusion is anomalous. For models treated within the framework of the decoupling approximation, our analytical results are confirmed by Monte Carlo simulations. Perturbance of the lattice gas particles distribution due to the presence of a biased TP and the form of the particle density profiles are also discussed.

cond-mat.stat-mech↗

arXiv2002

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 $P^{(quen)}$ per site of such a chain is given by $P^{(quen)} = P^{(lan)} + β^{-1} F$, where $P^{(lan)} = β^{-1} \ln(1+z)$ is the Langmuir adsorption pressure, (z being the activity and β^{-1} - the temperature), while $β^{-1} F$ 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.

cond-mat.stat-mech↗

arXiv2002

Trapping Reactions with Randomly Moving Traps: Exact Asymptotic Results for Compact Exploration

In a recent Letter Bray and Blythe have shown that the survival probability P(t) of an A particle diffusing with a diffusion coefficient D_A in a 1D system with diffusive traps B is independent of D_A in the asymptotic limit t \to \infty 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 dw of traps' trajectories is greater than d. For the marginal case when dw = d, as exemplified here by conventional diffusion in 2D systems, the decay form is determined up to a numerical factor in the characteristic decay time.

cond-mat.stat-mech↗

arXiv2002

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 de-homogenization of the monolayer.

cond-mat.soft↗

arXiv2002

Monolayer Spreading on a Chemically Heterogeneous Substrate

We study the spreading kinetics of a monolayer of hard-core particles on a semi-infinite, chemically heterogeneous solid substrate, one side of which is coupled to a particle reservoir. The substrate is modeled as a square lattice containing two types of sites -- ordinary ones and special, chemically active sites placed at random positions with mean concentration $α$. These special sites temporarily immobilize particles of the monolayer which then serve as impenetrable obstacles for the other particles. In terms of a mean-field-type theory, we show that the mean displacement $X_0(t)$ of the monolayer edge grows with time $t$ as $X_0(t) = \sqrt{2 D_α t \ln(4 D_α t/πa^2)}$, ($a$ being the lattice spacing). This time dependence is confirmed by numerical simulations; $D_α$ is obtained numerically for a wide range of values of the parameter $α$ and trapping times of the chemically active sites. We also study numerically the behavior of a stationary particle current in finite samples. The question of the influence of attractive particle-particle interactions on the spreading kinetics is also addressed.

cond-mat.stat-mech↗

arXiv2001

The Atomic Slide Puzzle: Self-Diffusion of an Impure Atom

In a series of recent papers van Gastel et al have presented first experimental evidence that impure, Indium atoms, embedded into the first layer of a Cu(001) surface, are not localized within the close-packed surface layers but make concerted, long excursions visualized in a series of STM images. Such excursions occur due to continuous reshuffling of the surface following the position exchanges of both impure and host atoms with the naturally occuring surface vacancies. Van Gastel et al 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.

cond-mat.stat-mech↗

arXiv2001

Propagation Dynamics of a Particle Phase in a Single-File Pore

We study propagation dynamics of a particle phase in a single-file pore connected to a reservoir of particles (bulk liquid phase). We show that the total mass $M(t)$ of particles entering the pore up to time $t$ grows as $M(t) = 2 m(J,ρ_F) \sqrt{D_0 t}$, where $D_0$ is the "bare" diffusion coefficient and the prefactor $m(J,ρ_F)$ is a non-trivial function of the reservoir density $ρ_F$ and the amplitude $J$ of attractive particle-particle interactions. Behavior of the dynamic density profiles is also discussed.

cond-mat.soft↗

arXiv2001

Intrinsic friction of adsorbed monolayers

In the present paper we overview our recent results on intrinsic frictional properties of adsorbed monolayers, composed of mobile hard-core particles undergoing continuous exchanges with a vapor phase. Within the framework of a dynamical master equation approach, describing the time evolution of the system, we determine in the most general form the terminal velocity of some biased impure molecule - the tracer particle (TP), constrained to move inside the adsorbed monolayer probing its frictional properties, define the frictional forces as well as the particles density distribution in the monolayer. Results for one-dimensional solid substrates, appropriate to adsorbtion on polymer chains, are compared against the Monte Carlo simulation data, which confirms our analytical predictions.

cond-mat.soft↗