Non-homogeneous random walks, subdiffusive migration of cells and anomalous chemotaxis

This paper is concerned with a non-homogeneous in space and non-local in time random walk model for anomalous subdiffusive transport of cells. Starting with a Markov model involving a structured probability density function, we derive the non-local in time master equation and fractional equation for the probability of cell position. We show the structural instability of fractional subdiffusive equation with respect to the partial variations of anomalous exponent. We find the criteria under which the anomalous aggregation of cells takes place in the semi-infinite domain.Comment: 18 pages, accepted for publicatio

On eigenfunction approximations for typical non-self-adjoint Schroedinger operators

We construct efficient approximations for the eigenfunctions of non-self-adjoint Schroedinger operators in one dimension. The same ideas also apply to the study of resonances of self-adjoint Schroedinger operators which have dilation analytic potentials. In spite of the fact that such eigenfunctions can have surprisingly complicated structures with multiple local maxima, we show that a suitable adaptation of the JWKB method is able to provide accurate lobal approximations to them.Comment: 17 pages, 11 figure

Creation of electron-positron plasma with superstrong laser field

We present a short review of recent progress in studying QED effects of interaction of ultra-relativistic laser pulses with vacuum and $e^-e^+$ plasma. The development of laser technologies promises very rapid growth of laser intensities in close future already. Two exawatt class facilities (ELI and XCELS, Russia) in Europe are already in the planning stage. Realization of these projects will make available a laser of intensity $\sim 10^{26}$W/cm$^2$ or even higher. Therefore, discussion of nonlinear optical effects in vacuum are becoming urgent for experimentalists and are currently gaining much attention. We show that, in spite of the fact that the respective field strength is still essentially less than $E_S=m^2c^3/e\hbar=1.32\cdot 10^{16}$V/cm, the nonlinear vacuum effects will be accessible for observation at ELI and XCELS facilities. The most promissory for observation is the effect of pair creation by laser pulse in vacuum. It is shown, that at intensities $\sim 5\cdot 10^{25}$W/cm$^2$, creation even of a single pair is accompanied by development of an avalanchelike QED cascade. There exists an important distinctive feature of the laser-induced cascades, as compared with the air showers arising due to primary cosmic ray entering the atmosphere. In our case the laser field plays not only the role of a target (similar to a nucleus in the case of air showers). It is responsible also for acceleration of slow particles. It is shown that the effect of pair creation imposes a natural limit for attainable laser intensity. Apparently, the field strength $E\sim E_S$ is not accessible for pair creating electromagnetic field at all.Comment: To be published in digest "IZEST Scientific Case" in EPJ ST early 201

Projections of potential luminosity improvement for low-energy RHIC operation with electron cooling

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