Collaborative Research-Smoluchowski Equations: Analysis of Dynamics, Singularities and Statistics in Complex Fluid-Particle Mixtures.

协作研究-Smoluchowski 方程：复杂流体-粒子混合物中的动力学、奇异性和统计分析。

• 批准号: 0504099
• 负责人: Yannis Kevrekidis
• 金额: $ 5万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-09-01 至 2008-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0504099&HistoricalAwards=false
• 关键词: Collaborative; Research; Smoluchowski; Equations; Analysis

In this collaborative project, the investigators study theinteraction between fluids and particle distributions. Theyexamine the nonlinear Smoluchowski equations with both passive andactive interaction with an ambient fluid. The specific goals are:a study of the transition to nematic states in the highconcentration limit, effects of shear, complex dynamics and modesof coupling. Particular attention is given to the activeinteractions with fluids, singularity formation, the stabilizationof high concentration suspensions, and the dissipation effects dueto the insertions. Many biological and artificial materials are involved inprocesses in which melts or fluid flows carry inserted particles. The orientation of the particles and their overall distributioninfluence the physical and chemical properties of the mixture. The investigators carry out a mathematical study of models of suchmixtures. The goals are to describe qualitatively the patternsformed by the particles, which of these patterns are stable, whatare the conditions for the creation of discontinuities in thepatterns, and what are the energetics and bulk physical propertiesassociated with them. Better understanding of the effects ofsmall-scale nonequilibrium dynamics on large-scale transport incomplex particle-fuid systems, such as the viscous polymersuspensions considered here, is important in chemistry, biology,and engineering.

在这个协作项目中，研究人员研究了流体和粒子分布之间的相互作用。 他们将非线性Smoluchowski方程与环境流体具有被动和活性相互作用。 具体目标是：在高浓度极限，剪切，复杂动力学和耦合模态的效果下向列的过渡的研究。 特别注意与流体，奇异性形成，高浓度悬浮液的稳定和耗散效果插入插入的影响。 许多生物学和人造材料涉及熔融或流体流带有插入的颗粒的过程。颗粒的方向及其整体分布，即混合物的物理和化学特性。研究人员对这种混合模型进行了数学研究。 目标是定性地描述粒子形成的模式，这些模式中的哪种模式稳定，在体系中创造不连续性的条件以及与之相关的能量和散装物理属性是什么。 更好地理解small尺度非平衡动力学对此处考虑的大规模传输粒子粒子捕集系统的影响，例如粘性聚合物求解系统，在化学，生物学和工程中很重要。