RUI: Extremal Paths in Complex Systems

RUI：复杂系统中的极值路径

• 批准号: 0083204
• 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: 2000
• 资助国家: 美国
• 起止时间: 2000-07-15 至 2004-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0083204&HistoricalAwards=false
• 关键词: RUI; Extremal; Paths; Complex; Systems

0083204Halpin-HealyThis grant for Research at an Undergraduate Institution (RUI) provides support for theoretical research on the statistical mechanics of directed polymers in random media (DPRM) and domain-walls in impurity-stricken magnets. Because of common technical aspects, the DPRM has been christened a baby-version of the spin-glass problem. As such, the T=0 DPRM is a matter of global optimization, exhibiting an ultrametric tree structure reminiscent of those found in river delta basins, capillary blood vessel networks, and neuronal arrays in the brain. A Hopf-Cole transformation maps the DPRM to the far-from-equilibrium dynamics of Kardar-Parisi-Zhang (KPZ) stochastic growth models. A final payoff follows from the blood relation of KPZ and noisy Burgers equations, the latter relevant to nonequilibrium kinetics of driven lattice gases. An important goal at hand is further exploration of this rich KPZ triumvirate: DPRM, kinetic roughening, and driven lattice gases. With the DPRM becoming a classic problem of ill-condensed matter, however, future research will focus on diverse, general issues concerning geometric complexity, including scaling of extremal trajectories and networks in geomorphology, evolutionary biology, and other multidisciplinary statistical mechanics contexts.%%%This grant for Research at an Undergraduate Institution (RUI) provides support for theoretical research on the statistical mechanics of directed polymers in random media (DPRM) and domain-walls in impurity-stricken magnets. These statistical models have far-reaching applications in addition to their intrinsic fundamental interest. The research involves extensive undergraduate participation.***

0083204HALPIN-HEALYTHIS在本科机构（RUI）的研究赠款（RUI）提供了关于随机培养基（DPRM）中定向聚合物统计力学的理论研究的支持，而杂质 - 刺激磁铁中的域壁和域壁。 由于具有共同的技术方面，DPRM被命名为旋转玻璃问题的婴儿。 因此，t = 0 dprm是全球优化的问题，它表现出一种超规模的树结构，让人联想到大脑中河流盆地，毛细血管血管网络和神经元阵列中发现的。 HOPF-Cole转换将DPRM映射到Kardar-Parisi-Zhang（KPZ）随机生长模型的远距离平衡动力学。 最终的回报来自KPZ和嘈杂的汉堡方程的血液关系，后者与驱动晶格气体的非平衡动力学有关。 一个重要的目标是进一步探索这种富含KPZ的Triumvirate：DPRM，动力学粗糙和驱动的晶格气体。 然而，随着DPRM成为不符合条件的物质的经典问题，未来的研究将集中在多样化的，有关几何复杂性的一般问题上，包括对地貌学，进化生物学的极端轨迹和网络的规模缩放，进化生物学以及其他多学科统计学机制。 （DPRM）和域壁中有杂质的磁铁。 这些统计模型除了其内在的基本兴趣外，还具有深远的应用。 该研究涉及广泛的本科参与。***