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Igor M. Sokolov

Publications and source records attributed to Igor M. Sokolov.

85 records · Page 5Linked to original sources
arXiv2010

On the relation between event-based and time-based current statistics

Current statistics can be calculated in various ways. Event-based approaches use the statistics of the number of events occuring during a given time. Time-based approaches use the statistics of the time needed to reach a given number of events. By analyzing normal as well as anomalous statistics of nonequilibrium currents through a two level system in contact with two different reservoirs, we investigate the conditions under which these different statistics do or do not yield identical predictions. We rely on the continuous time random walk formulation introduced in our earlier work [Phys. Rev. E 77, 051119 (2008)].

cond-mat.stat-mech↗
arXiv2010

Kramers escape driven by fractional Brownian motion

We investigate the Kramers escape from a potential well of a test particle driven by fractional Gaussian noise with Hurst exponent 0<H<1. From a numerical analysis we demonstrate the exponential distribution of escape times from the well and analyze in detail the dependence of the mean escape time as function of H and the particle diffusivity D. We observe different behavior for the subdiffusive (antipersistent) and superdiffusive (persistent) domains. In particular we find that the escape becomes increasingly faster for decreasing values of H, consistent with previous findings on the first passage behavior. Approximate analytical calculations are shown to support the numerically observed dependencies.

cond-mat.stat-mech↗
arXiv2008

Bulk-mediated surface diffusion on a cylinder: propagators and crossovers

We consider the effective surface motion of a particle that freely diffuses in the bulk and intermittently binds to that surface. From an exact approach we derive various regimes of the effective surface motion characterized by physical rates for binding/unbinding and the bulk diffusivity. We obtain a transient regime of superdiffusion and, in particular, a saturation regime characteristic for the cylindrical geometry. This saturation, however, in a finite system is not terminal but eventually turns over to normal surface diffusion. The first passage behavior of particles to the cylinder surface is derived. Consequences for actual systems are discussed.

cond-mat.stat-mech↗
arXiv2008

Ecological Complex Systems

Main aim of this topical issue is to report recent advances in noisy nonequilibrium processes useful to describe the dynamics of ecological systems and to address the mechanisms of spatio-temporal pattern formation in ecology both from the experimental and theoretical points of view. This is in order to understand the dynamical behaviour of ecological complex systems through the interplay between nonlinearity, noise, random and periodic environmental interactions. Discovering the microscopic rules and the local interactions which lead to the emergence of specific global patterns or global dynamical behaviour and the noises role in the nonlinear dynamics is an important, key aspect to understand and then to model ecological complex systems.

physics.bio-ph↗
arXiv2008

Front propagation in A+B -> 2A reaction under subdiffusion

We consider an irreversible autocatalytic conversion reaction A+B -> 2A under subdiffusion described by continuous time random walks. The reactants' transformations take place independently on their motion and are described by constant rates. The analog of this reaction in the case of normal diffusion is described by the Fisher-Kolmogorov-Petrovskii-Piskunov (FKPP) equation leading to the existence of a nonzero minimal front propagation velocity which is really attained by the front in its stable motion. We show that for subdiffusion this minimal propagation velocity is zero, which suggests propagation failure.

cond-mat.stat-mech↗
arXiv2007

Stationary spatial structures in reaction-subdiffusion

We discuss stationary concentrations of reactants in an A + B -> 0 reaction under subdiffusion and show that they are described by stationary reaction-diffusion equations with a nonlinear diffusion term. We consider stationary profiles of reactants' concentrations and of reaction zones in a flat subdiffusive medium fed by reactants of both types on its both sides (a subdiffusive gel reactor). The behavior of the concentrations and of the reaction intensity in subdiffusion differs strikingly from those in simple diffusion. The most important differences correspond to the existence of accumulation and depletion zones close to the boundaries and to non-monotonous behavior of the reaction intensity with respect to the strength of the minor source. The implications of these results for other situations are also discussed.

cond-mat.stat-mech↗
arXiv2007

Fractal Properties of Anomalous Diffusion in Intermittent Maps

An intermittent nonlinear map generating subdiffusion is investigated. Computer simulations show that the generalized diffusion coefficient of this map has a fractal, discontinuous dependence on control parameters. An amended continuous time random walk theory well approximates the coarse behavior of this quantity in terms of a continuous function. This theory also reproduces a full suppression of the strength of diffusion, which occurs at the dynamical phase transition from one type of diffusive behavior to another. Similarly, the probability density function of this map exhibits a nontrivial fine structure while its coarse functional form is governed by a time fractional diffusion equation. A more detailed understanding of the irregular structure of the generalized diffusion coefficient is provided by an anomalous Taylor-Green-Kubo formula establishing a relation to de Rham-type fractal functions.

nlin.CD↗
arXiv2006

Diffusion mechanisms of localised knots along a polymer

We consider the diffusive motion of a localized knot along a linear polymer chain. In particular, we derive the mean diffusion time of the knot before it escapes from the chain once it gets close to one of the chain ends. Self-reptation of the entire chain between either end and the knot position, during which the knot is provided with free volume, leads to an L^3 scaling of diffusion time; for sufficiently long chains, subdiffusion will enhance this time even more. Conversely, we propose local ``breathing'', i.e., local conformational rearrangement inside the knot region (KR) and its immediate neighbourhood, as additional mechanism. The contribution of KR-breathing to the diffusion time scales only quadratically, L^2, speeding up the knot escape considerably and guaranteeing finite knot mobility even for very long chains.

cond-mat.soft↗
arXiv2005

First passage time of N excluded volume particles on a line

Motivated by recent single molecule studies of proteins sliding on a DNA molecule, we explore the targeting dynamics of N particles ("proteins") sliding diffusively along a line ("DNA") in search of their target site (specific target sequence). At lower particle densities, one observes an expected reduction of the mean first passage time proportional to 1/N**2, with corrections at higher concentrations. We explicitly take adsorption and desorption effects, to and from the DNA, into account. For this general case, we also consider finite size effects, when the continuum approximation based on the number density of particles, breaks down. Moreover, we address the first passage time problem of a tagged particle diffusing among other particles.

cond-mat.stat-mech↗
arXiv2004

Lévy flights as subordination process: first passage times

We obtain the first passage time density for a Lévy flight random process from a subordination scheme. By this method, we infer the asymptotic behavior directly from the Brownian solution and the Sparre Andersen theorem, avoiding explicit reference to the fractional diffusion equation. Our results corroborate recent findings for Markovian Lévy flights and generalize to broad waiting times.

cond-mat.stat-mech↗
arXiv2002

Towards deterministic equations for Levy walks: the fractional material derivative

Levy walks are random processes with an underlying spatiotemporal coupling. This coupling penalizes long jumps, and therefore Levy walks give a proper stochastic description for a particle's motion with broad jump length distribution. We derive a generalized dynamical formulation for Levy walks in which the fractional equivalent of the material derivative occurs. Our approach will be useful for the dynamical formulation of Levy walks in an external force field or in phase space for which the description in terms of the continuous time random walk or its corresponding generalized master equation are less well suited.

cond-mat.stat-mech↗
arXiv2001

Fractional Klein-Kramers equation for superdiffusive transport: normal versus anomalous time evolution in a differential L{é}vy walk model

We introduce a fractional Klein-Kramers equation which describes sub-ballistic superdiffusion in phase space in the presence of a space-dependent external force field. This equation defines the differential L{é}vy walk model whose solution is shown to be non-negative. In the velocity coordinate, the probability density relaxes in Mittag-Leffler fashion towards the Maxwell distribution whereas in the space coordinate, no stationary solution exists and the temporal evolution of moments exhibits a competition between Brownian and anomalous contributions.

cond-mat.stat-mech↗