Discrete Networks and Singular Phenomena in Heterogeneous Media

Novikov

DMS-0604600

The investigator studies thermal, elastic and other

effective properties of high-contrast two-phase particulate

composites where concentration of inclusions in the matrix is

high. He uses their fundamental property: the dominant

contribution to the rate of thermal dissipation, elastic energy

and other bulk properties comes from the areas between closely

spaced particles. This allows to develop Discrete Network

Approximations to effective properties of a composite. The main

goal of the project is to develop rigorous mathematical

foundations for these approximations. The investigator studies

the concept of a Perforated Composite as the key step in his

analysis. This concept allows to develop the discrete network

method into an effective and attractive tool for analysis and

applications. He applies this concept to determine effective

elastic properties of particulate composites, conductivity of

strongly nonlinear composites, and rate of viscous dissipation in

highly concentrated suspensions.

The investigator studies a class of heterogeneous media such

as ocean flows, oil-bearing sands, particle-reinforced and

fiber-reinforced composites, mud and blood among others. These

media are ubiquitous and characterization of their properties is

paramount for development of new technologies and materials.

Experimental studies of many such media are impossible or

prohibitively expensive. Computational studies of such media

often are beyond our current capabilities. The investigator

characterizes analytically these media as networks, which allows

developing reliable and effective reduced models amenable to

further analysis and numerical simulations. Such models help to

assess thermal and elastic properties of ceramics/polymer

composites, augmented transport of plasma proteins in blood, and

the spreading of pollutants in ocean.