Transition scattering in stochastically inhomogeneous media

When a physical object (“a source”) without its own eigenfrequency moves through an acoustically homogeneous medium, the only possible form of acoustic radiation is the emission of Mach shock waves, which appear when the source velocity surpasses sonic speed. In nonhomogeneous media, in nonstationary media, or in the neighborhood of such media, the source motion is accompanied by the so-called “transition” radiation (diffraction or scattering), which has place even when the source moves with subsonic velocity. Key features pertaining to the formation of the acoustical transition scattering in media with fluctuating acoustical parameters are established. To analytically study the effect, the Green's function method formulated in terms of functional derivatives is used. The relationship between the wave number and frequency, k=k(ω), for acoustic waves is found. The results serve to determine the phasing conditions necessary for opening the transition scattering and Cherenkov radiation channel and to establish the physical explanation for the phenomenon—scattering (transformation) on inhomogeneities of the accompanied source field; i.e., formation of radiation appears when the attached field readjusts back to the equilibrium state after being deformed while passing through the fluctuations of the medium

Hypothesis about Enrichment of Solar System

Despite significant progress in the understanding of galactic nucleosynthesis and its influence on the solar system neighborhood, challenges remain in the understanding of enrichment of the solar system itself. Based on the detailed review of multi-disciplinary literature, we propose a scenario that an event of nucleogenesis -- not nucleosynthesis (from lower nucleon numbers A to higher A) but nuclear-fission (from higher A to lower A) -- occurred in the inner part of the solar system at one of the stages of its evolution. We propose a feasible mechanism of implementation of such event. The occurrence of such event could help explain the puzzles in yet-unresolved isotopic abundances, certain meteoritic anomalies, as well as peculiarities in the solar system's composition and planetary structure. We also discuss experimental data and available results from existing models (in several relevant sub-fields) that provide support and/or appear consistent with the hypothesis.Comment: 73 pages, 31 figures. arXiv admin note: text overlap with arXiv:1610.07202, arXiv:1109.3432, arXiv:1302.6530 by other author

Non polynomial conservation law densities generated by the symmetry operators in some hydrodynamical models

New extra series of conserved densities for the polytropic gas model and nonlinear elasticity equation are obtained without any references to the recursion operator or to the Lax operator formalism. Our method based on the utilization of the symmetry operators and allows us to obtain the densities of arbitrary homogenuity dimensions. The nonpolynomial densities with logarithmics behaviour are presented as an example. The special attention is paid for the singular case $(\gamma=1)$ for which we found new non homogenious solutions expressed in terms of the elementary functions.Comment: 11 pages, 1 figur

Tsunami generation by ocean floor rupture front propagation: Hamiltonian description

The Hamiltonian method is applied to the problem of tsunami generation caused by a propagating rupture front and deformation of the ocean floor. The method establishes an alternative framework for analyzing the tsunami generation process and produces analytical expressions for the power and directivity of tsunami radiation (in the far-field) for two illustrative cases, with constant and gradually varying speeds of rupture front propagation

Constrained Reductions of 2D dispersionless Toda Hierarchy, Hamiltonian Structure and Interface Dynamics

Finite-dimensional reductions of the 2D dispersionless Toda hierarchy, constrained by the ``string equation'' are studied. These include solutions determined by polynomial, rational or logarithmic functions, which are of interest in relation to the ``Laplacian growth'' problem governing interface dynamics. The consistency of such reductions is proved, and the Hamiltonian structure of the reduced dynamics is derived. The Poisson structure of the rationally reduced dispersionless Toda hierarchies is also derivedComment: 18 pages LaTex, accepted to J.Math.Phys, Significantly updated version of the previous submissio

Some estimates on the space scales of vortex pairs emitted from river mouths

International audienceTwo-dimensional vortex pairs are frequently observed in geophysical conditions, for example, in a shelf zone of the ocean near river mouths. The main aims of the work are to estimate the space scales of such vortex structures, to analyze possible scenarios of vortex pair motion and to give the qualitative classification of their trajectories. We discuss some features of the motion of strong localized vorticity concentrations in a given flow in the presence of boundaries. The analyses are made in the framework of a 2D point vortex mo-del with an open polygonal boundary. Estimations are made for the characteristic parameters of dipole vortex structures emitted from river mouths into the open ocean