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.