arXiv subjects

Alexander Iomin

Publications and source records attributed to Alexander Iomin.

39 records · Page 3Linked to original sources

arXiv2007

The Localization Length of Stationary States in the Nonlinear Schreodinger Equation

For the nonlinear Schreodinger equation (NLSE), in presence of disorder, exponentially localized stationary states are found. In the present Letter it is demonstrated analytically that the localization length is typically independent of the strength of the nonlinearity and is identical to the one found for the corresponding linear equation. The analysis makes use of the correspondence between the stationary NLSE and the Langevin equation as well as of the resulting Fokker-Planck equation. The calculations are performed for the ``white noise'' random potential and an exact expression for the exponential growth of the eigenstates is obtained analytically. It is argued that the main conclusions are robust.

cond-mat.dis-nn↗

arXiv2006

Migration and proliferation dichotomy in tumor cell invasion

We propose a two-component reaction-transport model for the migration-proliferation dichotomy in the spreading of tumor cells. By using a continuous time random walk (CTRW) we formulate a system of the balance equations for the cancer cells of two phenotypes with random switching between cell proliferation and migration. The transport process is formulated in terms of the CTRW with an arbitrary waiting time distribution law. Proliferation is modeled by a standard logistic growth. We apply hyperbolic scaling and Hamilton-Jacobi formalism to determine the overall rate of tumor cell invasion. In particular, we take into account both normal diffusion and anomalous transport (subdiffusion) in order to show that the standard diffusion approximation for migration leads to overestimation of the overall cancer spreading rate.

q-bio.CB↗

arXiv2006

Regimes of stability of accelerator modes

The phase diagram of a simple area-preserving map, which was motivated by the quantum dynamics of cold atoms, is explored analytically and numerically. Periodic orbits of a given winding ratio are found to exist within wedge-shaped regions in the phase diagrams, which are analogous to the Arnol'd tongues which have been extensively studied for a variety of dynamical systems, mostly dissipative ones. A rich variety of bifurcations of various types are observed, as well as period doubling cascades. Stability of periodic orbits is analyzed in detail.

quant-ph↗