Mathematical Modeling of Shock-Wave Processes in Condensed Matter From Statistical Thermodynamics to Control Theory

This book offers an interdisciplinary theoretical approach based on non-equilibrium statistical thermodynamics and control theory for mathematically modeling shock-induced out-of-equilibrium processes in condensed matter. The book comprises two parts. The first half of the book establishes the theoretical approach, reviewing fundamentals of non-equilibrium statistical thermodynamics and control theory of adaptive systems. The latter half applies the presented approach to a problem on shock-induced plane wave propagation in condensed matter. The result successfully reproduces the observed feature of waveform propagation in experiments, which conventional continuous mechanics cannot access. Further, the consequent stress–strain relationships derived with relaxation and inertia effect in elastic–plastic transition determines material properties in transient regimes.

Tatiana Aleksandrovna Khantuleva is a professor at Saint Petersburg State University. Her research is primarily concerned with non-equilibrium phenomena and complex systems and their mathematical modeling. She received her Ph.D. degree in fluid and plasma mechanics from the State Institute of Mathematics and Mechanics, Saint Petersburg, Russia, in 1977. She joined Saint Petersburg State University as an associate professor in 1999 and was promoted to her current position in 2007. She received certificates of honor from Saint Petersburg State University and the Russian Academy of Science in 2007, 2010, and 2017.

She currently focuses on the problems related to modeling transient and shock-induced processes, out-of-equilibrium thermodynamic evolution, and synergetic effects at a mesoscopic scale and on developing several new original special courses of lectures for graduate students.