Instability of an inverse problem for the stationary radiative transport near the diffusion limit

In this work, we study the instability of an inverse problem of radiative transport equation with angularly averaged measurement near the diffusion limit, i.e. the normalized mean free path (the Knudsen number) 0 < \eps \ll 1. It is well-known that there is a transition of stability from H\"{o}lder type to logarithmic type with \eps\to 0, the theory of this transition of stability is still an open problem. In this study, we show the transition of stability by establishing the balance of two different regimes depending on the relative sizes of \eps and the perturbation in measurements. When \eps is sufficiently small, we obtain exponential instability, which stands for the diffusive regime, and otherwise we obtain H\"{o}lder instability instead, which stands for the transport regime.Comment: 20 page

Fundamental Solutions in Plane Problem for Anisotropic Elastic Medium Under Moving Oscillating Source

In present article we consider the problems of concentrated point force which is moving with constant velocity and oscillating with cyclic frequency in unbounded homogeneous anisotropic elastic two-dimensional medium. The properties of plane waves and their phase, slowness and ray or group velocity curves for 2D problem in moving coordinate system are described. By using the Fourier integral transform techniques and established the properties of the plane waves, the explicit representation of the elastodynamic Green's tensor is obtained for all types of source motion as a sum of the integrals over the finite interval. The dynamic components of the Green's tensor are extracted. The stationary phase method is applied to derive an asymptotic approximation of the far wave field. The simple formulae for Poynting energy flux vectors for moving and fixed observers are presented too. It is noted that in the far zones the cylindrical waves are separated under kinematics and energy. It is shown that the motion bring some differences in the far field properties. They are modification of the wave propagation zones and their number, fast and slow waves appearance under trans- and superseismic motion and so on.Comment: 19 pages, Proceeding of the Conference "Advanced Problems in Mechanics", Russia, St.Petersburg (Repino), June 22-July 2, 200

On the Measurement of the Helicity of Intergalactic Magnetic Fields Using Ultra-High-Energy Cosmic Rays

The origin of the first magnetic fields in the Universe is a standing problem in cosmology. Intergalactic magnetic fields (IGMFs) may be an untapped window to the primeval Universe, providing further constrains on magnetogenesis. We demonstrate the feasibility of using ultra-high-energy cosmic rays (UHECRs) to constrain the helicity of IGMFs by performing simulations of cosmic-ray propagation in simple magnetic field configurations. We show that the first harmonic moments of the arrival distribution of UHECRs may be used to measure the absolute value of the helicity and its sign.Comment: 25 pages, 11 figures; published versio

Effects of anisotropy in geostrophic turbulence

The Boussinesq model of convection in a flat layer with heating from below is considered. We analyze the effects of anisotropy caused by rapid rotation in physical and wave spaces and demonstrate the suppression of energy transfer by rotation. We also examine the structure of the wave triangle in nonlinear interaction. The range of parameters is adapted to the models of convection in the geodynamo

Large-scale anisotropy in scalar turbulence

The effect of anisotropy on the statistics of a passive tracer transported by a turbulent flow is investigated. We show that under broad conditions an arbitrarily small amount of anisotropy propagates to the large scales where it eventually dominates the structure of the concentration field. This result is obtained analytically in the framework of an exactly solvable model and confirmed by numerical simulations of scalar transport in two-dimensional turbulence

Self-induced and induced transparencies of two-dimensional and three- dimensional superlattices

The phenomenon of transparency in two-dimensional and three-dimensional superlattices is analyzed on the basis of the Boltzmann equation with a collision term encompassing three distinct scattering mechanisms (elastic, inelastic and electron-electron) in terms of three corresponding distinct relaxation times. On this basis, we show that electron heating in the plane perpendicular to the current direction drastically changes the conditions for the occurrence of self-induced transparency in the superlattice. In particular, it leads to an additional modulation of the current amplitudes excited by an applied biharmonic electric field with harmonic components polarized in orthogonal directions. Furthermore, we show that self-induced transparency and dynamic localization are different phenomena with different physical origins, displaced in time from each other, and, in general, they arise at different electric fields.Comment: to appear in Physical Review