Biomedical subjects

Sergei Fedotov

Publications and source records attributed to Sergei Fedotov.

11 recordsLinked to original sources

PubMed2006

Stochastic dynamo model for subcritical transition.

The effects of stochastic perturbations in a nonlinear alpha Omega-dynamo model are investigated. By using transformation of variables we identify a "slow" variable that determines the global evolution of the non-normal alpha Omega-dynamo system in the subcritical case. We apply an adiabatic elimination procedure to derive a closed stochastic differential equation for the slow variable for which the dynamics is determined along one of the eigenvectors of the full system. We derive the corresponding Fokker-Planck equation and show that the generation of a large scale magnetic field can be regarded as a first-order phase transition. We show that the an advantage of the reduced system is that we have explicit expressions for both the stochastic and deterministic potentials. We also obtain the stationary solution of the Fokker-Planck equation and show that an increase in the intensity of the multiplicative noise leads to qualitative changes in the stationary probability density function. The latter can be interpreted as a noise-induced phase transition. By a numerical simulation of the stochastic galactic dynamo model, we show that the qualitative behavior of the "empirical" stationary pdf of the slow variable is accurately predicted by the stationary pdf of the reduced system.

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PubMed2005

Stochastic mixing model with power law decay of variance.

A stochastic mixing model based on the law of large numbers is presented that describes the decay of the variance of a conserved scalar in decaying turbulence as a power law, sigma2(c) proportional t(-alpha). A general Lagrangian mixing process is modeled by a stochastic difference equation where the mixing frequency and the ambient concentration are random processes. The mixing parameter lambda is introduced as a coefficient in the mixing frequency in order to account for initial length-scale ratio of the velocity and scalar field and other physical dependencies. We derive a nonlinear integral equation for the probability density function (pdf) of a conserved scalar that describes the relaxation of an arbitrary initial distribution to a delta-function. Numerical studies of this equation are conducted, and it is shown that lambda has a distinct influence on the decay rate of the scalar. Results obtained from the model for the evolution of the pdf are in a good agreement with direct numerical simulation (DNS) data.

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PubMed2004

Analysis of fronts in reaction-dispersal processes.

The existence of traveling wave front solutions with a minimum speed selected for reaction-dispersal processes is studied. We obtain a general existence condition in terms of the waiting time and dispersal distance probability distribution functions and we detail this result for situations of ecological interest. In particular, when particles disperse according to jumps of short length and any waiting time probability distribution function, we show that the minimum speed selection for traveling wave fronts is not always possible, so the waiting time and the dispersal distance distributions cannot be arbitrarily chosen.

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PubMed2004

Waves in a reaction-transport system with memory, long-range interactions, and transmutations.

We develop a theory of wave propagation into an unstable state for a system of integral equations with memory, long-range interactions, and transmutations. In particular we use continuous-time random walk theory to describe the transport and transmutation processes. We use a hyperbolic scaling and Hamilton-Jacobi formalism to derive formulas for the speed of propagation of the traveling wave generated by the system in the long-time large-distance limit. Our theory is valid for arbitrary waiting-time, jump-length and, transmutation probability density functions and the propagation speed can generally be found numerically. However, we illustrate our theory by considering an example where analytic results are possible--that is, for a system of Markovian reaction-transport equations. We derive formulas to determine the propagation speed in both the so-called weakly coupled and strongly coupled cases.

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PubMed2004

Front propagation in reaction-dispersal models with finite jump speed.

The continuous-time random walk and the Hamilton-Jacobi method are used to reach analytical expressions for the speed of traveling fronts in reaction-dispersal models. In this work the waiting time and jump length are assumed to be coupled random variables. The jump length for any jump is selected according to the waiting time at the end of the previous jump, and in consequence jumps of finite speed are performed. We study the effect of finite jump speed of the particles on the speed of the traveling fronts and find that in the parabolic and hyperbolic limits it can exceed the jump speed of the particles. We report analytical expressions for different probability distribution functions. Finally, we introduce the possibility that several particle speeds are allowed, so different dispersal mechanisms can be considered simultaneously.

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PubMed2003

Non-normal and stochastic amplification of magnetic energy in the turbulent dynamo: subcritical case.

Our attention focuses on the stochastic dynamo equation with non-normal operator that gives an insight into the role of stochastics and non-normality in magnetic field generation. The main point of this Brief Report is a discussion of the generation of a large-scale magnetic field that cannot be explained by traditional linear eigenvalue analysis. The main result is a discovery of nonlinear deterministic instability and growth of finite magnetic field fluctuations in alpha beta dynamo theory. We present a simple stochastic model for the thin-disk axisymmetric alpha Omega dynamo involving three factors: (a) non-normality generated by differential rotation, (b) nonlinearity reflecting how the magnetic field affects the turbulent dynamo coefficients, and (c) stochastic perturbations. We show that even for the subcritical case (all eigenvalues are negative), there are three possible mechanisms for the generation of magnetic field. The first mechanism is a deterministic one that describes an interplay between transient growth and nonlinear saturation of the turbulent alpha effect and diffusivity. It turns out that the trivial state is nonlinearly unstable to small but finite initial perturbations. The second and third are stochastic mechanisms that account for the interaction of non-normal effect generated by differential rotation with random additive and multiplicative fluctuations.

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PubMed2003

Speed of reaction-diffusion fronts in spatially heterogeneous media.

The front speed problem for nonuniform reaction rate and diffusion coefficient is studied by using singular perturbation analysis, the geometric approach of Hamilton-Jacobi dynamics, and the local speed approach. Exact and perturbed expressions for the front speed are obtained in the limit of large times. For linear and fractal heterogeneities, the analytic results have been compared with numerical results exhibiting a good agreement. Finally we reach a general expression for the speed of the front in the case of smooth and weak heterogeneities.

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PubMed2002

Stochastic analysis of a non-normal dynamical system mimicking a laminar-to-turbulent subcritical transition.

The effects of stochastic perturbations on a non-normal dynamical system mimicking a laminar-to-turbulent subcritical transition are investigated both analytically and numerically. It is found that a nonlinear dynamical system with non-normal transient linear growth is very sensitive to the presence of weak random perturbations. The effect of non-normality on the exit probability from the zero fixed point is analyzed numerically for small values of the noise intensity parameter. It is found that an increase in the intensity of the noise, or a decrease of the non-normality parameter leads to qualitative changes in the behavior of the trajectories that can be interpreted as noise-induced phase transitions. By using the Itô formula and the adiabatic elimination procedure a stochastic equation governing the slow evolution of the energy of the non-normal system is derived.

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PubMed2002

Continuous-time random walks and traveling fronts.

We present a geometric approach to the problem of propagating fronts into an unstable state, valid for an arbitrary continuous-time random walk with a Fisher-Kolmogorov-Petrovski-Piskunov growth/reaction rate. We derive an integral Hamilton-Jacobi type equation for the action functional determining the position of reaction front and its speed. Our method does not rely on the explicit derivation of a differential equation for the density of particles. In particular, we obtain an explicit formula for the propagation speed for the case of anomalous transport involving non-Markovian random processes.

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PubMed2002

Non-Markovian random processes and traveling fronts in a reaction-transport system with memory and long-range interactions.

The problem of finding the propagation rate for traveling waves in reaction-transport systems with memory and long-range interactions has been considered. Our approach makes use of the generalized master equation with logistic growth, hyperbolic scaling, and Hamilton-Jacobi theory. We consider the case when the waiting-time distribution for the underlying microscopic random walk is modeled by the family of gamma distributions, which in turn leads to non-Markovian random processes and corresponding memory effects on mesoscopic scales. We derive formulas that enable us to determine the front propagation rate and understand how the memory and long-range interactions influence the propagation rate for traveling fronts. Several examples involving the Gaussian and discrete distributions for jump densities are presented.

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PubMed2002

Memory effects in a turbulent dynamo: generation and propagation of a large-scale magnetic field.

We are concerned with large-scale magnetic-field dynamo generation and propagation of magnetic fronts in turbulent electrically conducting fluids. An effective equation for the large-scale magnetic field is developed here that takes into account the finite correlation times of the turbulent flow. This equation involves the memory integrals corresponding to the dynamo source term describing the alpha effect and turbulent transport of magnetic field. We find that the memory effects can drastically change the dynamo growth rate, in particular, nonlocal turbulent transport might increase the growth rate several times compared to the conventional gradient transport expression. Moreover, the integral turbulent transport term leads to a large decrease of the speed of magnetic front propagation.

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