Capacity and Transport in Contrast Composite Structures: Asymptotic Analysis and Applications

Is it possible to apply a network model to composites with conical inclusions?

How does the energy pass through contrast composites?

Devoted to the analysis of transport problems for systems of densely packed, high-contrast composite materials, Capacity and Transport in Contrast Composite Structures: Asymptotic Analysis and Applications answers questions such as these and presents new and modified asymptotic methods for real-world applications in composite materials development.

A mathematical discussion of phenomena related to natural sciences and engineering, this book covers historical developments and new progress in mathematical calculations, computer techniques, finite element computer programs, and presentation of results of numerical computations.

The "transport problem"—which is described with scalar linear elliptic equations—implies problems of thermoconductivity, diffusion, and electrostatics. To address this "problem," the authors cover asymptotic analysis of partial differential equations, material science, and the analysis of effective properties of electroceramics. Providing numerical calculations of modern composite materials that take into account nonlinear effects, the book also:


Presents results of numerical analysis, demonstrating specific properties of distributions of local fields in high-contrast composite structures and systems of closely placed bodies


Assesses whether total flux, energy, and capacity exhaust characteristics of the original continuum model


Illustrates the expansion of the method for systems of bodies to highly filled contrast composites


This text addresses the problem of loss of high-contrast composites, as well as transport and elastic properties of thin layers that cover or join solid bodies. The material presented will be particularly useful for applied mathematicians interested in new methods, and engineers dealing with prospective materials and design methods.

A.A. Kolpakov works in the Department of Mathematics and Mechanics at Novosibirsk State University, Russia and Université de Fribourg, Fribourg Pérolles, Switzerland. A.G. Kolpakov works as Marie Curie Fellow at Università degli Studi di Cassino, Italy and Siberian State University of Telecommunications and Informatics, Russia.

IDEAS AND METHODS OF ASYMPTOTIC ANALYSIS AS APPLIED TO TRANSPORT IN COMPOSITE STRUCTURES
Effective properties of composite materials and the homogenization theory
Transport properties of periodic arrays of densely packed bodies
Disordered media with piecewise characteristics and random collections of bodies
Capacity of a system of bodies


NUMERICAL ANALYSIS OF LOCAL FIELDS IN A SYSTEM OF CLOSELY PLACED BODIES
Numerical analysis of two-dimensional periodic problem
Numerical analysis of three-dimensional periodic problem
The energy concentration and energy localization phenomena
Which physical field demonstrates localization most strongly?
Numerical analysis of potential of bodies in a system of closely placed bodies with finite element method and network model
Energy channels in non-periodic systems of disks


ASYMPTOTIC BEHAVIOR OF CAPACITY OF A SYSTEM OF CLOSELY PLACED BODIES. TAMM SHIELDING. NETWORK APPROXIMATION
Problem of capacity of a system of bodies
Formulation of the problem and definitions
Heuristic network model
Proof of the principle theorems
Completion of proof of the theorems
Some consequences of the theorems about NL zones and network approximation
Capacity of a pair of bodies dependent on shape


NETWORK APPROXIMATION FOR POTENTIALS OF CLOSELY PLACED BODIES
Formulation of the problem of approximation of potentials of bodies
Proof of the network approximation theorem for potentials
The speed of convergence of potentials for a system of circular disks


ANALYSIS OF TRANSPORT PROPERTIES OF HIGHLY FILLED CONTRAST COMPOSITES USING THE NETWORK APPROXIMATION METHOD
Modification of the network approximation method as applied to particle-filled composite materials
Numerical analysis of transport properties of highly filled disordered composite material with network model


EFFECTIVE TUNABILITY OF HIGH-CONTRAST COMPOSITES
Nonlinear characteristics of composite materials
Homogenization procedure for nonlinear electrostatic problem
Tunability of laminated composite
Tunability amplification factor of composite
Numerical design of composites possessing high tunability amplification factor
The problem of maximum value for the homogenized tunability amplification factor
What determines the effective characteristics of composites?
The difference between design problems of tunable composites in the cases of weak and strong fields
Numerical analysis of tunability of composite in strong fields


EFFECTIVE LOSS OF HIGH-CONTRAST COMPOSITES
Effective loss of particle-filled composite
Effective loss of laminated composite material


TRANSPORT AND ELASTIC PROPERTIES OF THIN LAYERS
Asymptotic of first boundary-value problem for elliptic equation in a region with a thin cover
Elastic bodies with thin underbodies layer (glued bodies)