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The paper reviews briefly elements from our work on the solution of various field induced, time independent or time dependent many electron problems, which has been developed and carried out within state and property specific frameworks.…
The properties of cosmic shock waves are studied through numerical simulations in two cosmological scenarios (SCDM and LCDM). The scaling relations for the average radius and velocity associated with the accretion shocks are somewhat…
We show that the model of discrete spaces that we have proposed in previous contributions gives a comprehensive and detailed interpretation of the properties of the standard model of particles. Moreover the model also suggests the possible…
On simple example is shown that a model of mechanically extended source of radiation in classical electrodynamics indeed has some problems with radiation reaction force. So one cannot, in general case, state, that the present situation with…
We study arc spaces and jet schemes of generic determinantal varieties. Using the natural group action, we decompose the arc spaces into orbits, and analyze their structure. This allows us to compute the number of irreducible components of…
We examine the dynamics of accelerating normal shocks in stratified planar atmospheres, providing accurate fitting formulae for the scaling index relating shock velocity to the initial density and for the post-shock acceleration factor as…
We provide a new class of interior solutions for anisotropic stars admitting conformal motion. The Einstein's field equations in this construction are solved for specific choices of the density/mass functions. We analyze the behavior of the…
The existence of gauge pathologies associated with the Bona-Masso family of generalized harmonic slicing conditions is proven for the case of simple 1+1 relativity. It is shown that these gauge pathologies are true shocks in the sense that…
Strong discontinuities in solutions of the gas dynamic equations under isentropic conditions, i.e., with continuity of entropy at the discontinuity, are examined. Solutions for a standard shock wave with continuity of energy at the…
We discuss the formation of stochastic fractals and multifractals using the kinetic equation of fragmentation approach. We also discuss the potential application of this sequential breaking and attempt to explain how nature creats fractals.
The observational evidence for dark matter on progressively larger cosmic scales is reviewed in a rather pedagogical fashion. Although the emphasis is on dark matter in galaxies and in clusters of galaxies, its cosmological evidence as well…
Black holes are among the most extreme objects that can be found in the Universe and an ideal laboratory for testing fundamental physics. This article will briefly review the basic properties of black holes as expected from general…
The contributions of different radiation mechanisms to the diffuse gamma-ray emission of the galactic disk are studied in a broad energy region from X-rays to very high energy gamma rays.
In this article we study a system of eikonal equations. Our aim is to isolate the solutions which minimise the discontinuity set of the gradient.
We introduce an original approach to geometric calculus in which we define derivatives and integrals on functions which depend on extended bodies in space--that is, paths, surfaces, and volumes etc. Though this theory remains to be fully…
We consider general reaction diffusion systems posed on rectangular lattices in two or more spatial dimensions. We show that travelling wave solutions to such systems that propagate in rational directions are nonlinearly stable under small…
We numerically investigate momentum diffusion rates for the pulse kicked rotor across the quantum to classical transition as the dynamics are made more macroscopic by increasing the total system action. For initial and late time rates we…
We discuss a semi-analytical solution of the transport equation for electrons at a non-relativistic shock in the presence of synchrotron energy losses. We calculate the spectrum of accelerated (test) particles at any point upstream and…
The nonlinear propagation of low-frequency circularly polarized waves in a magnetized dusty plasma is analyzed. It is found that wave steepening and shock formation can take place due to the presence of nonlinear quantum vacuum effects,…
Collisionless shocks, that is shocks mediated by electromagnetic processes, are customary in space physics and in astrophysics. They are to be found in a great variety of objects and environments: magnetospheric and heliospheric shocks,…