RUI: Diverse Manifolds in Random Media

RUI：随机媒体中的多样化流形

• 批准号: 9528071
• 负责人: Timothy Halpin-Healy
• 金额: $ 8.13万
• 依托单位: Barnard College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-02-01 至 2000-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9528071&HistoricalAwards=false
• 关键词: RUI; Diverse; Manifolds; Random; Media

9528071 Halpin -Healy This project involves scaling properties in random media involving interplay between thermal fluctuations and disorder induced roughening. The specific problems are directed polymers in random media (DPRM) and impurity-pinned domain walls in magnets. The global optimization problem in DPRM is similar in exhibiting an ultrametric tree structure to the problems in river basin deltas, capillary blood vessel networks and neuronal arrays in the brain. A Cole- Hopf transformation of the DPRM relates it to dynamic scaling problem in noisy Burgers equation, the latter relevant to the statistical mechanical properties of a far- from-equilibrium driven lattice gas. %%% This project is to study the common properties of a variety of problems by (a) focusing on the problem of directed polymers in a random media and (b) demonstrating the mathematical equivalence between this problem and others such as river basin deltas, capillary blood vessel networks and neuronal arrays in the brain. ***

9528071 HALPIN -HEALY这个项目涉及在随机介质中缩放特性，涉及热波动和疾病引起的粗糙性之间的相互作用。 特定问题是在随机介质（DPRM）中的定向聚合物和磁铁中的杂质小域壁。 DPRM中的全球优化问题在表现出与大脑中河流三角洲，毛细血管血管网络和神经元阵列的问题的超级树结构时相似。 DPRM的Cole-Hopf转换将其与嘈杂的汉堡方程中的动态缩放问题有关，后者与远程驱动的晶格气体的统计机械性能相关。 该项目是通过（a）在随机培养基中关注定向聚合物的问题的各种问题的共同特性，以及（b）证明该问题与其他问题（例如河流盆地三角洲，毛细血管血管网络和大脑中的神经元阵列）之间的数学等效性。 ***