Chapters authored
Application of Onsager and Prigozhin Variational Principles of Nonequilibrium Thermodynamics to Obtain MHD-Equation Dissipative System in Drift Approximation
Electromagnetic phenomena in plasma are easier to describe in terms of fields, expressing the electric current through the rotor of the magnetic field. But the approach that ignores the corpuscular aspect of the electric current, as noted by H. Alfven, does not allow describing many processes in space plasma. Indeed, relying on the concept of continuity, it is impossible in the mechanics of continuous media to take into account the fluctuations of hydrodynamic functions formed due to the molecular structure of the medium. At the hydrodynamic level of description, taking into account the structure leads to the Langevin equation. Therefore, to describe processes in a magnetized plasma, it is of certain interest to obtain MHD equations in the drift approximation not from the Vlasov equations, but based on the principles of Onsager and Prigogine, combined by Gyarmati into one variational principle and obtaining a one-liquid plasma model in the drift approximation. Fluctuations are taken into account by introducing an additional term in the expression for pressure, written in the drift approximation, which is similar to the postulation of the Langevin source for describing Brownian motion. The obtained fluctuating-dissipative system differs from the reversible one-liquid approximation of the two adiabatic invariants of Chu, Goldberger, Low.
Part of the book: Magnetosphere and Solar Winds, Humans and Communication
Investigation of the Dynamics of the Seismic Regime in the Kamchatka Region Based on the Combination of Methods of Nonequilibrium Thermodynamics and the Axiomatic Method of Kolmogorov A.N.
In the presented chapter, the preparation of an earthquake on the example of the Kronotsky event that occurred on 1997-12-05 with a magnitude Mc = 7.7 is considered from the standpoint of nonequilibrium thermodynamics, in which the evolution of systems is due to self-organization processes. With this approach, the lithosphere is an open nonlinear system in which, due to internal dissipation and the coordinated interaction of its elements, a self-organization process can occur, leading the system to a critical state. In this case, the scales of the connection between different parts of the nonlinear structure change, that is, the scales of temporal and spatial correlation change. However, the methods of seismological monitoring of the stress-strain geoenvironment can be expanded if, for its study, the method of calculating the probability distribution of earthquakes for various random events is used, based on the axiomatic approach of Kolmogorov A.N., applied to the catalog of Kamchatka earthquakes. This makes it possible to follow the dynamics of correlated spatial and temporal changes in the probability distribution of random variables for weak earthquakes preceding a strong event using probabilistic methods.
Part of the book: Earthquakes