6,606 research outputs found
Quantum regime of laser-matter interactions at extreme intensities
A survey of physical parameters and of a ladder of various regimes of
laser-matter interactions at extreme intensities is given. Special emphases is
made on three selected topics: (i) qualitative derivation of the scalings for
probability rates of the basic processes; (ii) self-sustained cascades (which
may dominate at the intensity levels attainable with next generation laser
facilities); and (iii) possibility of breaking down the Intense Field QED
approach for ultrarelativistic electrons and high-energy photons at certain
intensity level.Comment: To be published in the Proceedings of the Summer School "Quantum
Field Theory at the Limits: from Strong Fields to Heavy Quarks" (18-30 July
2016, BLTP, JINR, Dubna, Russia
Single integro-differential wave equation for L\'evy walk
The integro-differential wave equation for the probability density function
for a classical one-dimensional L\'evy walk with continuous sample paths has
been derived. This equation involves a classical wave operator together with
memory integrals describing the spatio-temporal coupling of the L\'evy walk. It
is valid for any running time PDF and it does not involve any long-time
large-scale approximations. It generalizes the well-known telegraph equation
obtained from the persistent random walk. Several non-Markovian cases are
considered when the particle's velocity alternates at the gamma and power-law
distributed random times.Comment: 5 page
Nonlinear subdiffusive fractional equations and aggregation phenomenon
In this article we address the problem of the nonlinear interaction of
subdiffusive particles. We introduce the random walk model in which statistical
characteristics of a random walker such as escape rate and jump distribution
depend on the mean field density of particles. We derive a set of nonlinear
subdiffusive fractional master equations and consider their diffusion
approximations. We show that these equations describe the transition from an
intermediate subdiffusive regime to asymptotically normal advection-diffusion
transport regime. This transition is governed by nonlinear tempering parameter
that generalizes the standard linear tempering. We illustrate the general
results through the use of the examples from cell and population biology. We
find that a nonuniform anomalous exponent has a strong influence on the
aggregation phenomenon.Comment: 10 page
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
Sub-diffusion in External Potential: Anomalous hiding behind Normal
We propose a model of sub-diffusion in which an external force is acting on a
particle at all times not only at the moment of jump. The implication of this
assumption is the dependence of the random trapping time on the force with the
dramatic change of particles behavior compared to the standard continuous time
random walk model. Constant force leads to the transition from non-ergodic
sub-diffusion to seemingly ergodic diffusive behavior. However, we show it
remains anomalous in a sense that the diffusion coefficient depends on the
force and the anomalous exponent. For the quadratic potential we find that the
anomalous exponent defines not only the speed of convergence but also the
stationary distribution which is different from standard Boltzmann equilibrium.Comment: 6 pages, 3 figure
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