Discrete Networks and Singular Phenomena in Heterogeneous Media

点击翻译按钮获取中文摘要

NovikovDMS-0604600 The investigator studies thermal, elastic and othereffective properties of high-contrast two-phase particulatecomposites where concentration of inclusions in the matrix ishigh. He uses their fundamental property: the dominantcontribution to the rate of thermal dissipation, elastic energyand other bulk properties comes from the areas between closelyspaced particles. This allows to develop Discrete NetworkApproximations to effective properties of a composite. The maingoal of the project is to develop rigorous mathematicalfoundations for these approximations. The investigator studiesthe concept of a Perforated Composite as the key step in hisanalysis. This concept allows to develop the discrete networkmethod into an effective and attractive tool for analysis andapplications. He applies this concept to determine effectiveelastic properties of particulate composites, conductivity ofstrongly nonlinear composites, and rate of viscous dissipation inhighly concentrated suspensions. The investigator studies a class of heterogeneous media suchas ocean flows, oil-bearing sands, particle-reinforced andfiber-reinforced composites, mud and blood among others. Thesemedia are ubiquitous and characterization of their properties isparamount for development of new technologies and materials. Experimental studies of many such media are impossible orprohibitively expensive. Computational studies of such mediaoften are beyond our current capabilities. The investigatorcharacterizes analytically these media as networks, which allowsdeveloping reliable and effective reduced models amenable tofurther analysis and numerical simulations. Such models help toassess thermal and elastic properties of ceramics/polymercomposites, augmented transport of plasma proteins in blood, andthe spreading of pollutants in ocean.