Discrete Networks and Singular Phenomena in Heterogeneous Media

研究者研究了高对比的两相颗粒复合材料的热、弹性和其他有效性能，其中基体中夹杂物浓度高。他利用了它们的基本性质：对热耗散率、弹性能和其他体积性质的主要贡献来自于间隔紧密的粒子之间的区域。这允许对复合材料的有效特性开发离散网络近似。该项目的主要目标是为这些近似建立严格的数学基础。研究者研究穿孔复合材料的概念是他分析的关键步骤。这一概念允许将离散网络方法发展成为一种有效和有吸引力的分析和应用工具。他将这一概念应用于确定颗粒复合材料的有效弹性特性、强非线性复合材料的导电性以及高浓度悬浮液的粘性耗散率。研究者研究了一类非均质介质，如海洋流体、含油砂、颗粒增强和纤维增强复合材料、泥浆和血液等。这些介质无处不在，其特性的表征对于新技术和新材料的开发至关重要。对许多这样的介质进行实验研究是不可能的，或者是非常昂贵的。对这种媒介的计算研究往往超出了我们目前的能力。研究人员分析表征这些媒体作为网络，这允许开发可靠和有效的简化模型适用于进一步的分析和数值模拟。这些模型有助于评估陶瓷/聚合物复合材料的热弹性特性，血液中血浆蛋白的增强运输以及海洋中污染物的扩散。

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.