In memory of Arkady Viktorovich Kryazhimskiy (1949-2014)

The article is devoted to the description of Academician Arkady Kryazhimskiy's life path. The facts of the scientific biography of Acad. Kryazhimskiy are presented with the emphasis on his outstanding contribution into the theory of dynamic inversion, the theory of differential games, and control theory. His personal talents in different spheres are also marked out

Mathematical modeling of bulk and directional crystallization with the moving phase transition layer

This paper is devoted to the mathematical modeling of a combined effect of directional and bulk crystallization in a phase transition layer with allowance for nucleation and evolution of newly born particles. We consider two models with and without fluctuations in crystal growth velocities, which are analytically solved using the saddle-point technique. The particle-size distribution function, solid-phase fraction in a supercooled two-phase layer, its thickness and permeability, solidification velocity, and desupercooling kinetics are defined. This solution enables us to characterize the mushy layer composition. We show that the region adjacent to the liquid phase is almost free of crystals and has a constant temperature gradient. Crystals undergo intense growth leading to fast mushy layer desupercooling in the middle of a two-phase region. The mushy region adjacent to the solid material is filled with the growing solid-phase structures and is almost desupercooled. © 2021 The Authors. Mathematical Methods in the Applied Sciences published by John Wiley & Sons, Ltd.Russian Science Foundation, RSF: 21-79-10012The authors gratefully acknowledge financial support from the Russian Science Foundation (project no. 21-79-10012). Open Access funding enabled and organized by Projekt DEAL

Wave-induced loss of ultra-relativistic electrons in the Van Allen radiation belts.

The dipole configuration of the Earth's magnetic field allows for the trapping of highly energetic particles, which form the radiation belts. Although significant advances have been made in understanding the acceleration mechanisms in the radiation belts, the loss processes remain poorly understood. Unique observations on 17 January 2013 provide detailed information throughout the belts on the energy spectrum and pitch angle (angle between the velocity of a particle and the magnetic field) distribution of electrons up to ultra-relativistic energies. Here we show that although relativistic electrons are enhanced, ultra-relativistic electrons become depleted and distributions of particles show very clear telltale signatures of electromagnetic ion cyclotron wave-induced loss. Comparisons between observations and modelling of the evolution of the electron flux and pitch angle show that electromagnetic ion cyclotron waves provide the dominant loss mechanism at ultra-relativistic energies and produce a profound dropout of the ultra-relativistic radiation belt fluxes

Phenomenology of Quantum Gravity and its Possible Role in Neutrino Anomalies

New phenomenological models of Quantum Gravity have suggested that a Lorentz-Invariant discrete spacetime structure may become manifest through a nonstandard coupling of matter fields and spacetime curvature. On the other hand, there is strong experimental evidence suggesting that neutrino oscillations cannot be described by simply considering neutrinos as massive particles. In this manuscript we motivate and construct one particular phenomenological model of Quantum Gravity that could account for the so-called neutrino anomalies.Comment: For the proceedings of "Relativity and Gravitation: 100 Years after Einstein in Prague" (June 2012, Prague

The effect of spontaneous collapses on neutrino oscillations

We compute the effect of collapse models on neutrino oscillations. The effect of the collapse is to modify the evolution of the `spatial' part of the wave function, which indirectly amounts to a change on the flavor components. In many respects, this phenomenon is similar to neutrino propagation through matter. For the analysis we use the mass proportional CSL model, and perform the calculation to second order perturbation theory. As we will show, the CSL prediction is very small - mainly due to the very small mass of neutrinos - and practically undetectable.Comment: 24 pages, RevTeX. Updated versio