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Full Description
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.
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 Rodríguez-Ramos
