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A. Iomin

Publications and source records attributed to A. Iomin.

At least 19 recordsLinked to original sources
arXiv2021

Backbone diffusion and first-passage dynamics in a comb structure with confining branches under stochastic resetting

We study the diffusive motion of a test particle in a two-dimensional comb structure consisting of a main backbone channel with continuously distributed side branches, in the presence of stochastic Markovian resetting to the initial position of the particle. We assume that the motion along the infinitely long branches is biased by a confining potential. The crossover to the steady state is quantified in terms of a large deviation function, which is derived for the first time for comb structures in present paper. We show that the relaxation region is demarcated by a nonlinear "light-cone" beyond which the system is evolving in time. We also investigate the first-passage times along the backbone and calculate the mean first-passage time and optimal resetting rate.

cond-mat.stat-mech↗
arXiv2021

Anomalous diffusion in umbrella comb

Anomalous transport in a circular comb is considered. The circular motion takes place for a fixed radius, while radii are continuously distributed along the circle. Two scenarios of the anomalous transport, related to the reflecting and periodic angular boundary conditions, are studied. The first scenario with the reflection boundary conditions for the circular diffusion corresponds to the conformal mapping of a 2D comb Fokker-Planck equation on the circular comb. This topologically constraint motion is named umbrella comb model. In this case, the reflecting boundary conditions are imposed on the circular (rotator) motion, while the radial motion corresponds to geometric Brownian motion with vanishing to zero boundary conditions on infinity. The radial diffusion is described by the log-normal distribution, which corresponds to exponentially fast motion with the mean squared displacement (MSD) of the order of $e^t$. The second scenario corresponds to the circular diffusion with periodic boundary conditions and the outward radial diffusion with vanishing to zero boundary conditions at infinity. In this case the radial motion corresponds to normal diffusion. The circular motion in both scenarios is a superposition of cosine functions that results in the stationary Bernoulli polynomials for the probability distributions.

cond-mat.dis-nn↗
arXiv2016

Subdiffusion in classical and quantum nonlinear Schrödinger equations with disorder

The review is concerned with the nonlinear Schrödinger equation (NLSE) in the presence of disorder. Disorder leads to localization in the form of the localized Anderson modes (AM), while nonlinearity is responsible for the interaction between the AMs and transport. The dynamics of an initially localized wave packets are concerned in both classical and quantum cases. In both cases, there is a subdiffusive spreading, which is explained in the framework of a continuous time random walk (CTRW), and it is shown that subdiffusion is due to the transitions between those AMs, which are strongly overlapped. This overlapping being a common feature of both classical and quantum dynamics, leads to the clustering with an effective trapping of the wave packet inside each cluster. Therefore, the dynamics of the wave packet corresponds to the CTRW, where the basic mechanism of subdiffusion is an entrapping of the wave packet with delay, or waiting, times distributed by the power law $w(t)\sim 1/t^{1+α}$, where $α$ is the transport exponent. It is obtained that $α=1/3$ for the classical NLSE and $α=1/2$ for the quantum NLSE.

nlin.CD↗
arXiv2015

Destruction of ultra-slow diffusion in a three dimensional cylindrical comb structure

We present a rigorous result on ultra-slow diffusion by solving a Fokker-Planck equation, which describes anomalous transport in a three dimensional (3D) comb. This 3D cylindrical comb consists of a cylinder of discs threaten on a backbone. It is shown that the ultra-slow contaminant spreading along the backbone is described by the mean squared displacement (MSD) of the order of $\ln (t)$. This phenomenon takes place only for normal two dimensional diffusion inside the infinite secondary branches (discs). When the secondary branches have finite boundaries, the ultra-slow motion is a transient process and the asymptotic behavior is normal diffusion. In another example, when anomalous diffusion takes place in the secondary branches, a destruction of ultra-slow (logarithmic) diffusion takes place as well. As the result, one observes "enhanced" subdiffusion with the MSD $\sim t^{1-α}\ln t$, where $0<α<1$.

cond-mat.dis-nn↗
arXiv2015

Levy flights in a box

It is shown that a quantum Lévy process in a box leads to a problem involving topological constraints in space, and its treatment in the framework of the path integral formalism with the Lévy measure is suggested. The eigenvalue problem for the infinite potential well is properly defined and solved. An analytical expression for the evolution operator is obtained in the path integral presentation, and the path integral takes the correct limit of the local quantum mechanics with topological constraints. An example of the Lévy process in oscillating walls is also considered in the adiabatic approximation.

quant-ph↗
arXiv2015

Electro-chemical manifestation of nanoplasmonics in fractal media

Electrodynamics of composite materials with fractal geometry is studied in the framework of fractional calculus. This consideration establishes a link between fractal geometry of the media and fractional integro-differentiation. The photoconductivity in the vicinity of the electrode-electrolyte fractal interface is studied. The methods of fractional calculus are employed to obtain an analytical expression for the giant local enhancement of the optical electric field inside the fractal composite structure at the condition of the surface plasmon excitation. This approach makes it possible to explain experimental data on photoconductivity in the nano-electrochemistry.

cond-mat.mtrl-sci↗
arXiv2015

Continuous Time Random Walk and Migration Proliferation Dichotomy

A theory of fractional kinetics of glial cancer cells is presented. A role of the migration-proliferation dichotomy in the fractional cancer cell dynamics in the outer-invasive zone is discussed an explained in the framework of a continuous time random walk. The main suggested model is based on a construction of a 3D comb model, where the migration-proliferation dichotomy becomes naturally apparent and the outer-invasive zone of glioma cancer is considered as a fractal composite with a fractal dimension $\frD<3$.

q-bio.CB↗
arXiv2015

Actin polymerization front propagation in a comb-reaction system

Anomalous transport and reaction dynamics are considered by providing the theoretical grounds for the possible experimental realization of actin polymerization in comb-like geometry. Two limiting regimes are recovered, depending on the concentration of reagents (magnesium and actin). These are both the failure of the reaction front propagation and a finite speed corresponding to the Fisher-KPP long time asymptotic regime.

cond-mat.soft↗
arXiv2014

Comb models for transport along spiny dendrites

This chapter is a contribution in the "Handbook of Applications of Chaos Theory" ed. by Prof. Christos H Skiadas. The chapter is organized as follows. First we study the statistical properties of combs and explain how to reduce the effect of teeth on the movement along the backbone as a waiting time distribution between consecutive jumps. Second, we justify an employment of a comb-like structure as a paradigm for further exploration of a spiny dendrite. In particular, we show how a comb-like structure can sustain the phenomenon of the anomalous diffusion, reaction-diffusion and Lévy walks. Finally, we illustrate how the same models can be also useful to deal with the mechanism of ta translocation wave / translocation waves of CaMKII and its propagation failure. We also present a brief introduction to the fractional integro-differentiation in appendix at the end of the chapter.

q-bio.NC↗
arXiv2014

Maximum therapeutic effect of glioma treatment by radio-frequency electric field

An influence of a radio-frequency electric field on glioma - brain cancer development is considered. A specific task emerging here is whether this new medical technology is effective against invasive cells with a high motility, when switching between migrating and proliferating phenotypes takes place. This therapeutic effect is studied in the framework of a continuous time random walk. It is shown that the migration proliferation dichotomy of cancer cells leads to the weakening of the electric field treatment.

q-bio.CB↗
arXiv2014

Topology of delocalization in the nonlinear Anderson model and anomalous diffusion on finite clusters

This study is concerned with destruction of Anderson localization by a nonlinearity of the power-law type. We suggest using a nonlinear Schrödinger model with random potential on a lattice that quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. For super-quadratic nonlinearity the borderline spreading corresponds to diffusion processes on finite clusters. We have proposed an analytical method to predict and explain such transport processes. Our method uses a topological approximation of the nonlinear Anderson model and, if the exponent of the power nonlinearity is either integer or half-integer, will yield the wanted value of the transport exponent via a triangulation procedure in an Euclidean mapping space. A kinetic picture of the transport arising from these investigations uses a fractional extension of the diffusion equation to fractional derivatives over the time, signifying non-Markovian dynamics with algebraically decaying time correlations.

cond-mat.stat-mech↗
arXiv2012

Localization-delocalization transition on a separatrix system of nonlinear Schrodinger equation with disorder

Localization-delocalization transition in a discrete Anderson nonlinear Schrödinger equation with disorder is shown to be a critical phenomenon $-$ similar to a percolation transition on a disordered lattice, with the nonlinearity parameter thought as the control parameter. In vicinity of the critical point the spreading of the wave field is subdiffusive in the limit $t\rightarrow+\infty$. The second moment grows with time as a powerlaw $\propto t^α$, with $α$ exactly 1/3. This critical spreading finds its significance in some connection with the general problem of transport along separatrices of dynamical systems with many degrees of freedom and is mathematically related with a description in terms fractional derivative equations. Above the delocalization point, with the criticality effects stepping aside, we find that the transport is subdiffusive with $α= 2/5$ consistently with the results from previous investigations. A threshold for unlimited spreading is calculated exactly by mapping the transport problem on a Cayley tree.

cond-mat.dis-nn↗
arXiv2012

A toy model of fractal glioma development under RF electric field treatment

A toy model for glioma treatment by a radio frequency electric field is suggested. This low-intensity, intermediate-frequency alternating electric field is known as the tumor-treating-field (TTF). In the framework of this model the efficiency of this TTF is estimated, and the interplay between the TTF and the migration-proliferation dichotomy of cancer cells is considered. The model is based on a modification of a comb model for cancer cells, where the migration-proliferation dichotomy becomes naturally apparent. Considering glioma cancer as a fractal dielectric composite of cancer cells and normal tissue cells, a new effective mechanism of glioma treatment is suggested in the form of a giant enhancement of the TTF. This leads to the irreversible electroporation that may be an effective non-invasive method of treating brain cancer.

q-bio.CB↗
arXiv2010

Generalized Lyapunov Exponent and Transmission Statistics in One-dimensional Gaussian Correlated Potentials

Distribution of the transmission coefficient T of a long system with a correlated Gaussian disorder is studied analytically and numerically in terms of the generalized Lyapunov exponent (LE) and the cumulants of lnT. The effect of the disorder correlations on these quantities is considered in weak, moderate and strong disorder for different models of correlation. Scaling relations between the cumulants of lnT are obtained. The cumulants are treated analytically within the semiclassical approximation in strong disorder, and numerically for an arbitrary strength of the disorder. A small correlation scale approximation is developed for calculation of the generalized LE in a general correlated disorder. An essential effect of the disorder correlations on the transmission statistics is found. In particular, obtained relations between the cumulants and between them and the generalized LE show that, beyond weak disorder, transmission fluctuations and deviation of their distribution from the log-normal form (in a long but finite system) are greatly enhanced due to the disorder correlations. Parametric dependence of these effects upon the correlation scale is presented.

cond-mat.dis-nn↗
arXiv2009

Dynamics of wave packets for the nonlinear Schroedinger equation with a random potential

The dynamics of an initially localized Anderson mode is studied in the framework of the nonlinear Schroedinger equation in the presence of disorder. It is shown that the dynamics can be described in the framework of the Liouville operator. An analytical expression for a wave function of the initial time dynamics is found by a perturbation approach. As follows from a perturbative solution the initially localized wave function remains localized. At asymptotically large times the dynamics can be described qualitatively in the framework of a phenomenological probabilistic approach by means of a probability distribution function. It is shown that the probability distribution function may be governed by the fractional Fokker-Planck equation and corresponds to subdiffusion.

cond-mat.stat-mech↗