Discrete Networks and Singular Phenomena in Heterogeneous Media

异构介质中的离散网络和奇异现象

• 批准号: 0604600
• 负责人: Alexei Novikov
• 金额: $ 11.65万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-06-01 至 2009-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0604600&HistoricalAwards=false
• 关键词: Discrete; Networks; Singular; Phenomena; Heterogeneous

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.

Novikovdms-0604600研究者研究了高对比度两相颗粒质体的热，弹性和眼源性特性，其中矩阵中的夹杂物浓度浓度。 他使用他们的基本特性：占主导地位的热量耗散速率，弹性能量和其他散装特性来自紧密空间颗粒之间的区域。 这允许将离散的网络应用开发为复合材料的有效属性。 该项目的元素是为这些近似值开发严格的数学基础。 研究人员Studiesthe穿孔复合材料作为Hisanalysis的关键步骤。 这个概念使开发离散网络的方法将其开发为有效而有吸引力的分析和应用工具。 他将此概念应用于确定颗粒复合材料的有效弹性特性，strongly非线性复合材料的电导率以及粘性耗散的速率过高的浓缩悬浮液。 研究人员研究了一类异质介质的诸如海洋流，含油的沙子，颗粒增强和纤维增强的复合材料，泥和血液等。 塞米亚无处不在，其性质的特征是开发新技术和材料的特性。许多此类媒体的实验研究是不可能的，昂贵的。 这种媒体的计算研究超出了我们当前的功能。 研究人员将这些媒体分析为网络，从而允许开发可靠有效的减少模型，可正便的Tofther分析和数值模拟。 这样的模型有助于陶瓷/多蛋白胶质材料的热和弹性特性，血浆中血浆蛋白在血液中的运输增强以及海洋中污染物的扩散。