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Biomedical subjects

I M Sokolov

Publications and source records attributed to I M Sokolov.

At least 19 recordsLinked to original sources
PubMed2003

Cyclization of a polymer: first-passage problem for a non-Markovian process.

We discuss a closure of a polymer chain released from a state with given end-to-end distance. Considering the situation as a first passage problem for a non-Markovian process, we express the survival probability through the three-time distribution of the end-to-end distance and evaluate it numerically by solving a Volterra equation. We also show how the Wilemski-Fixmann approximation emerges within this scheme and discuss its geometrical nature.

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PubMed2002

Geography in a scale-free network model.

We offer an example of a network model with a power-law degree distribution, P(k) approximately k(-alpha), for nodes, but which nevertheless has a well-defined geography and a nonzero threshold percolation probability for alpha>2, the range of real-world contact networks. This is different from p(c)=0 for alpha<3 results for the original well-mixed scale-free networks. In our lattice-based scale-free network, individuals link to nearby neighbors on a lattice. Even considerable additional small-world links do not change our conclusion of nonzero thresholds. When applied to disease propagation, these results suggest that random immunization may be more successful in controlling human epidemics than previously suggested if there is geographical clustering.

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PubMed2002

Retarding subdiffusion and accelerating superdiffusion governed by distributed-order fractional diffusion equations.

We propose diffusionlike equations with time and space fractional derivatives of the distributed order for the kinetic description of anomalous diffusion and relaxation phenomena, whose diffusion exponent varies with time and which, correspondingly, cannot be viewed as self-affine random processes possessing a unique Hurst exponent. We prove the positivity of the solutions of the proposed equations and establish their relation to the continuous-time random walk theory. We show that the distributed-order time fractional diffusion equation describes the subdiffusion random process that is subordinated to the Wiener process and whose diffusion exponent decreases in time (retarding subdiffusion). This process may lead to superslow diffusion, with the mean square displacement growing logarithmically in time. We also demonstrate that the distributed-order space fractional diffusion equation describes superdiffusion phenomena with the diffusion exponent increasing in time (accelerating superdiffusion).

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PubMed2002

Solutions of a class of non-Markovian Fokker-Planck equations.

We show that a formal solution of a rather general non-Markovian Fokker-Planck equation can be represented in a form of an integral decomposition and thus can be expressed through the solution of the Markovian equation with the same Fokker-Planck operator. This allows us to classify memory kernels into safe ones, for which the solution is always a probability density, and dangerous ones, when this is not guaranteed. The first situation describes random processes subordinated to a Wiener process, while the second one typically corresponds to random processes showing a strong ballistic component. In this case the non-Markovian Fokker-Planck equation is only valid in a restricted range of parameters, initial and boundary conditions.

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PubMed2002

Evolving networks with disadvantaged long-range connections.

We consider a growing network, whose growth algorithm is based on the preferential attachment typical for scale-free constructions, but where the long-range bonds are disadvantaged. Thus, the probability of getting connected to a site at distance d is proportional to d(-alpha), where alpha is a tunable parameter of the model. We show that the properties of the networks grown with alpha<1 are close to those of the genuine scale-free construction, while for alpha>1 the structure of the network is quite different. Thus, in this regime, the node degree distribution is no longer a power law, and it is well represented by a stretched exponential. On the other hand, the small-world property of the growing networks is preserved at all values of alpha.

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PubMed2002

Relative dispersion in fully developed turbulence: the Richardson's law and intermittency corrections.

Relative dispersion in fully developed turbulence is investigated by means of direct numerical simulations. Lagrangian statistics is found to be compatible with Richardson description although small systematic deviations are found. The value of the Richardson constant is estimated as C2 approximately equal to 0.55, in a close agreement with recent experimental findings [S. Ott and J. Mann, J. Fluid Mech. 422, 207 (2000)]. By means of exit-time statistics it is shown that the deviations from Richardson's law are a consequence of Eulerian intermittency. The measured Lagrangian scaling exponents require a set of Eulerian structure function exponents zeta(p) which are remarkably close to standard ones known for fully developed turbulence.

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PubMed2001

Do strange kinetics imply unusual thermodynamics?

We introduce a fractional Fokker-Planck equation (FFPE) for Lévy flights in the presence of an external field. The equation is derived within the framework of the subordination of random processes which leads to Lévy flights. It is shown that the coexistence of anomalous transport and a potential displays a regular exponential relaxation toward the Boltzmann equilibrium distribution. The properties of the Lévy-flight FFPE derived here are compared with earlier findings for a subdiffusive FFPE. The latter is characterized by a nonexponential Mittag-Leffler relaxation to the Boltzmann distribution. In both cases, which describe strange kinetics, the Boltzmann equilibrium is reached, and modifications of the Boltzmann thermodynamics are not required.

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PubMed2001

Disorder and plasticity in the fragmentation of coatings.

Using a one-dimensional model that takes into account ideal plasticity of the surface layer, we investigate the fragmentation of thin coatings under uniaxial tension. The coating is modeled as a chain of plastically deforming elements that are connected via leaf springs to a uniformly stretched substrate. Each coating element can only withstand a maximum elongation, which is randomly distributed. From simulations of the fragmentation process we find that the average crack spacing scales with applied strain epsilon, i.e., proportional to epsilon(-kappa). Simulations and analytical arguments show that the scaling exponent kappa depends on the disorder parameters of the model.

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PubMed2001

Directed particle diffusion under "burnt bridges" conditions.

We study random walks on a one-dimensional lattice that contains weak connections, so-called "bridges." Each time the walker crosses the bridge from the left or attempts to cross it from the right, the bridge may be destroyed with probability p; this restricts the particle's motion and directs it. Our model, which incorporates asymmetric aspects in an otherwise symmetric hopping mechanism, is very akin to "Brownian ratchets" and to front propagation in autocatalytic A+B-->2A reactions. The analysis of the model and Monte Carlo simulations show that for large p the velocity of the directed motion is extremely sensitive to the distribution of bridges, whereas for small p the velocity can be understood based on a mean-field analysis. The single-particle model advanced by us here allows an almost quantitative understanding of the front's position in the A+B-->2A many-particle reaction.

Biophysics↗
PubMed2001

Thermodynamics and fractional Fokker-Planck equations.

The relaxation to equilibrium in many systems that show strange kinetics is described by fractional Fokker-Planck equations (FFPEs). These can be considered as phenomenological equations of linear nonequilibrium theory. We show that the FFPEs describe a system whose noise in equilibrium fulfills the Nyquist theorem. Moreover, we show that for subdiffusive dynamics, the solutions of the corresponding FFPEs are probability densities for all cases in which the solutions of the normal Fokker-Planck equation (with the same Fokker-Planck operator and with the same initial and boundary conditions) exist. The solutions of the FFPEs for superdiffusive dynamics are not always probability densities. This fact means only that the corresponding kinetic coefficients are incompatible with each other and with the initial conditions.

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PubMed2001

Irreversible and reversible modes of operation of deterministic ratchets.

We discuss a problem of optimization of the energetic efficiency of a simple rocked ratchet. We concentrate on a low-temperature case in which the particle's motion in a ratchet potential is deterministic. We show that the energetic efficiency of a ratchet working adiabatically is bounded from above by a value depending on the form of ratchet potential. The ratchets with strongly asymmetric potentials can achieve ideal efficiency of unity without approaching reversibility. On the other hand we show that for any form of the ratchet potential a set of time protocols of the outer force exists under which the operation is reversible and the ideal value of efficiency eta=1 is also achieved. The mode of operation of the ratchet is still quasistatic but not adiabatic. The high values of efficiency can be preserved even under elevated temperatures.

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PubMed2000

Lévy flights from a continuous-time process.

Lévy flight dynamics can stem from simple random walks in a system whose operational time (number of steps n) typically grows superlinearly with physical time t. Thus this process is a kind of continuous-time random walk (CTRW), dual to the typical Scher-Montroll model, in which n grows sublinearly with t. Models in which Lévy flights emerge due to a temporal subordination allow one easily to discuss the response of a random walker to a weak outer force, which is shown to be nonlinear. On the other hand, the relaxation of an ensemble of such walkers in a harmonic potential follows a simple exponential pattern, and leads to a normal Boltzmann distribution. Mixed models, describing normal CTRW's in superlinear operational time and Lévy flights under the operational time of subdiffusive CTRW's lead to a paradoxical diffusive behavior, similar to the one found in transport on polymer chains. The relaxation to the Boltzmann distribution in such models is slow, and asymptotically follows a power law.

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PubMed1999

Dispersion of passive particles by a quasi-two-dimensional turbulent flow.

Using the experimental data of Paret and Tabeling [Phys. Rev. Lett. 79, 4162 (1997)] we consider in detail the dispersion of particle pairs by a two-dimensional turbulent flow and its relation to the kinematic properties of the velocity field. We show that the mean square separation of a pair of particles is governed by rather rare, extreme events and that the majority of initially close pairs are not dispersed by the flow. Another manifestation of the same effect is the fact that the dispersion of an initially dense cluster is not the result of homogeneously spreading the particles within the whole system. Instead it proceeds through a splitting into smaller but also dense clusters. The statistical nature of this effect is discussed.

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PubMed1999

Relation between the probability density and other properties of a stationary random process.

We consider the Pope-Ching differential equation [Phys. Fluids A 5, 1529 (1993)] connecting the probability density p(x)(x) of a stationary, homogeneous stochastic process x(t) and the conditional moments of its squared velocity and acceleration. We show that the solution of the Pope-Ching equation can be expressed as n(x) , where n(x) is the mean number of crossings of the x level per unit time and is the mean inverse velocity of crossing. This result shows that the probability density at x is fully determined by a one-point measurement of crossing velocities, and does not imply knowledge of the x(t) behavior outside of the infinitesimally narrow window near x.

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PubMed1999

Reversible fluctuation rectifier.

The analysis of a Feynman's ratchet system [J. M. R. Parrondo and P. Español, Am. J. Phys. 64, 1125 (1996)] and of its electrical counterpart, a diode engine [I. M. Sokolov, Europhys. Lett. 44, 278 (1998)] has shown that "fluctuation rectifiers" consisting of a nonlinear element (ratchet, diode) and a linear element (vane, resistor) kept at different temperatures always show efficiency smaller than the Carnot value, thus indicating the irreversible mode of operation. We show that this irreversibility is not intrinsic for a system in simultaneous contact with two heat baths at different temperatures and that a fluctuation rectifier can work reversibly. This is illustrated by a model with two diodes switched in opposite directions, where the Carnot efficiency is achieved when backward resistivity of the diodes tends to infinity.

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PubMed1999

Two-particle dispersion by correlated random velocity fields.

We consider the two-particle dispersion in a velocity field, where the relative two-point velocity scales according to v(2)(r) proportional, variantr(alpha) and the corresponding correlation time scales as tau(r) proportional r(beta). We show that for alpha/2+beta<1 the diffusion approximation holds, and the increase in the interparticle distances is governed by the distance-dependent diffusion coefficient K(r) proportional r(alpha+beta). The possible regimes outside of the validity of diffusion approximation are discussed. The Kolmogorov scaling in turbulent flow alpha=beta=2/3 corresponds to a borderline situation. The experimental data for this case suggest that the separation regime is probably ballistic.

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PubMed1996

Statistical features in the lakes-straits model and the influence of hernias.

We evaluate numerically the mobility of DNA chains under field-inversion gel electrophoresis (FIGE) conditions in the framework of the lakes-straits model introduced by Zimm (Phys. Rev. Lett. 1988, 61, 2965-2968; J. Phys. Chem. 1991, 94, 2197-2206). We extend the model by allowing both simple and also multiple-branched hernias; this is achieved by arranging the data structure used in the algorithm so that each fragment in a lake can be treated separately. We show that the existence of hernias allows the probe to migrate faster and that with hernias the mobility minimum in FIGE shifts to smaller field periods. These effects occur only if the electric field is strong enough. We also discuss the influence of the model's parameters on the mobility.

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