Mechanics and Physics of Structured Media: Asymptotic and Integral Methods of Leonid Filshtinsky provides unique information on the macroscopic properties of various composite materials and the mathematical techniques key to understanding their physical behaviors. The book is centered around the arguably monumental work of Leonid Filshtinsky. His last works provide insight on fracture in electromagnetic-elastic systems alongside approaches for solving problems in mechanics of solid materials. Asymptotic methods, the method of complex potentials, wave mechanics, viscosity of suspensions, conductivity, vibration and buckling of functionally graded plates, and critical phenomena in various random systems are all covered at length.
Other sections cover boundary value problems in fracture mechanics, two-phase model methods for heterogeneous nanomaterials, and the propagation of acoustic, electromagnetic, and elastic waves in a one-dimensional periodic two-component material.
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Table of Contents
1. L.A. Filshtinsky's contribution to Applied Mathematics and Mechanics of Solids Vladimir Mityushev, Igor Andrianov, and Simon Gluzman
2. Cracks in two-dimensional magneto-electro-elastic medium D. Nosov, L.A. Filshtinskii, and V. Mityushev
3. Two-dimensional equations of magneto-electro-elasticity V. Mityushev, D. Nosov, and R. Wojnar
4. Hashin-Shtrikman assemblage of inhomogeneous spheres A. Cherkaev and V. Mityushev
5. Inverse conductivity problem for spherical particles Vladimir Mityushev, Natalia Rylko, Zhanat Zhunussova, and Yeskendyr Ashimov
6. Compatibility conditions: number of independent equations and boundary conditions I.V. Andrianov and H. Topol
7. Critical index for conductivity, elasticity, superconductivity. Results and methods Simon Gluzman
8. Double periodic bianalytic functions Piotr Drygas
9. The slowdown of group velocity in periodic waveguides Yuri A. Godin and Boris Vainberg
10. Some aspects of wave propagation in a fluid-loaded membrane J. Kaplunov, L. Prikazchikova, and S. Shamsi
11. Parametric vibrations of axially compressed functionally graded sandwich plates with a complex planform Kurpa Lidiya and Shmatko Tetyana
12. Application of volume integral equations for numerical calculation of local fields and effective properties of elastic composites S. Kanaun and A. Markov
13. A slipping zone model for a conducting interface crack in a piezoelectric bimaterial V. Loboda, A. Sheveleva, and O. Mykhail
14. Dependence of effective properties upon regular perturbations Matteo Dalla Riva, Paolo Luzzini, Paolo Musolino, and Roman Pukhtaievych
15. Riemann-Hilbert problems with coefficients in compact Lie groups G. Giorgadze and G. Khimshiashvili
16. When risks and uncertainties collide: quantum mechanical formulation of mathematical finance for arbitrage markets Simone Farinelli and Hideyuki Takada
17. Thermodynamics and stability of metallic nano-ensembles Michael Vigdorowitsch
18. Comparative analysis of local stresses in unidirectional and cross-reinforced composites A.G. Kolpakov and S.I. Rakin
19. Statistical theory of structures with extended defects V.I. Yukalov and E.P. Yukalova
20. Effective conductivity of 2D composites and circle packing approximations Roman Czapla and Wojciech Nawalaniec
21. Asymptotic homogenization approach applied to Cosserat heterogeneous media Victor Yanes, Federico J. Sabina, Yoanh Espinosa-Almeyda, Jose A. Otero, and Reinaldo Rodr�guez-Ramos
Authors
Igor Andrianov Professor Emeritus, RWTH Aachen University, Germany. Igor V. Andrianov is Professor Emeritus, RWTH Aachen University. He is the author or co-author of 14 books and more than 300 papers in peer-reviewed journals. He has presented papers at more than 150 international conferences and seminars and also supervised 21 PhD. Students. His research interests include mechanics of solids, mechanics of composite materials, nonlinear dynamics, and asymptotic methods. Simon Gluzman Independent Researcher, Toronto, Canada. Simon Gluzman is presently an Independent Researcher (Toronto, Canada) and formerly a Research Associate at PSU in Applied Mathematics. He is interested in Re-summation methods in theory of random and regular composites and the method of self-similar and rational approximants. Vladimir Mityushev Institute of Mathematics, Faculty of Computer Science and Telecommunications, Cracow University of Technology, Krak�w, Poland. Vladimir Mityushev is the Professor of Cracow University of Technology, a leader of the research group www.materialica.plus. He is interested in mathematical modeling and computer simulations, Industrial mathematics and boundary value problems and their applications..
