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High-rate Deformation of Condensed Matter Followed by Self-Organization on the Mesoscale

Tatiana A. Khantuleva


The purpose of the paper is to demonstrate the advantages of the developed self-consistent non-local approach to the description of processes in condensed matter far from local thermodynamic equilibrium and new opportunities for understanding and practical use of such phenomena as self-organization, multi-scale energy exchange and turbulence. This interdisciplinary approach, based on rigorous results obtained in non-equilibrium statistical mechanics with the use of feedback control laws, offers a universal mathematical apparatus for describing processes beyond the applicability of generally accepted theoretical models. Application of the methods developed in the control theory to describe high-rate processes in complex systems allows not only a prediction of the system properties under the action of external forces, but also to control them. The mathematical model of a highly non-equilibrium process makes it possible to describe a gradual transition from elastic compression of a medium through self-organization of turbulent structures in it to the establishment of a hydrodynamic flow, taking into account a complex of relaxation effects. Of greatest interest among the obtained results may be the solution of the problem on the propagation of a shock-induced pulse in a condensed medium, which is accompanied by the formation of new medium structures on the mesoscale.

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