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.
