Scaling dynamics and stability in extended physical systems

扩展物理系统中的扩展动力学和稳定性

基本信息

批准号：
0905723
负责人：
Robert Pego
金额：
$ 27.72万
依托单位：
Carnegie-Mellon University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2009
资助国家：
美国
起止时间：
2009-09-01 至 2014-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=0905723&HistoricalAwards=false
关键词：
Scaling dynamics stability extended physical

项目摘要

PegoDMS-0905723 The focus of this work is on understanding stable dynamicalbehavior in complex nonlinear systems. A variety of phenomenaare investigated in models of strong physical interest,especially: dynamic scaling in models of aggregation andcoarsening (coagulation equations with input, simplified graingrowth models in metallurgy, ballistic aggregation with softcollisions); the robustness of coherent structures in nonlinearfield theories (in particular, spectral stability for exactsolitary water waves); and stability analysis for incompressibleviscous fluids in light of recent progress on boundary conditionsfor pressure (addressing domains with corners, coupling tomagnetism and stress relaxation, and the zero-viscosity limit). Work on dynamic scaling in particular aims to further developideas that connect dynamical systems methods with infinitedivisibility theory in probability. Progress in this program leads to improved mathematicalmethods for understanding how coherent behavior emerges incomplex nonlinear systems. The particular models to be studiedmathematically are of fundamental scientific interest, relevantto materials science at the nanoscale, aerosol physics (models ofsmog, soot, and smoke), population genetics, physical chemistry,and other fields. The work on fluid boundaries should lead toimprovements in the numerical modeling of small-scale flows, withconsequences for studying small flying and swimming objects,blood flow, and engineered microfluidic systems, for example.

PEGODMS-0905723这项工作的重点是了解复杂的非线性系统中稳定的动态行为。在强烈的身体兴趣模型中研究了各种现象，尤其是：聚集和填充模型中的动态缩放（具有输入，简化的冶金，弹道聚合中具有软弹片的凝血方程）；非线性场理论中相干结构的鲁棒性（特别是，精确水波的光谱稳定性）；根据边界条件的最新进展，对不可压缩的液体进行了稳定分析（解决域，拐角处，耦合的阶数和压力放松以及零粘度限制）。特别是在动态缩放方面的工作是旨在进一步开发动态系统方法与概率无限可见性理论联系起来。该程序的进展会导致改进的数学方法，以了解连贯行为如何出现不复杂的非线性系统。在纳米级，气溶胶物理学（SMOG，烟灰和烟雾的模型），种群遗传学，物理化学和其他领域的材料科学方面，要研究的特定模型具有基本的科学兴趣，与材料科学相关。例如，关于流体边界的工作应导致小尺度流的数值建模中的toimprovement，并以研究小型飞行和游泳对象，血流和工程的微流体系统的原因。