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 研究了基体中夹杂物浓度较高的高对比度两相颗粒复合材料的热性能、弹性性能和其它有效性能。 他利用了它们的基本性质：对热耗散率、弹性能和其他整体性质的主要贡献来自于密集粒子之间的区域。 这允许开发离散网络逼近复合材料的有效性能。 该项目的主要目标是为这些近似建立严格的数学基础。 研究者研究了穿孔复合材料的概念，并将其作为分析的关键步骤。 这一概念使离散网络方法发展成为一种有效的和有吸引力的分析和应用工具。 他应用这一概念来确定颗粒复合材料的有效弹性，强非线性复合材料的导电性，以及高浓度悬浮液中的粘性耗散率。 研究人员研究了一类非均匀介质，如海洋流动，含油砂，颗粒增强和纤维增强复合材料，泥浆和血液等。 这些介质是无处不在的和表征其属性是至关重要的新技术和材料的发展。对许多这样的介质进行实验研究是不可能的，或者是昂贵得令人望而却步。 对这种媒体的计算研究往往超出了我们目前的能力。 该分析器将这些介质分析为网络，从而允许开发可靠和有效的简化模型，以进行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性能和弹性性能，血液中血浆蛋白的增强运输以及海洋中污染物的传播。