Models and Asymptotics of Non-equilibrium Steady States in Driven Diffusive Systems

驱动扩散系统中非平衡稳态的模型和渐近

• 批准号: 1212167
• 负责人: Nicholas Ercolani
• 金额: $ 22.6万
• 依托单位: University of Arizona
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-01 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1212167&HistoricalAwards=false
• 关键词: Models; Asymptotics; Non; equilibrium; Steady

This award will support the analysis of non-equilibrium steady states (NESS) in driven diffusive systems. Physical systems of interest in this general class are typically modeled either deterministically by diffusive nonlinear evolution equations or stochastically by certain types of Markov processes. The NESS referred to here differ from the equilibria of linear dynamics or the invariant measures of detailed balance in that the non-equilibrium steady states exhibit phase separation (often driven by boundary dynamics), spontaneous symmetry breaking and/or long range correlations away from critical transitions. Specific contexts to be explored include the strong bending regime of striped pattern formation, spatial random partitions, and random matrix ensembles. Non-equilibrium steady states are typical for a number of physical systems and models, including defect condensation in pattern forming systems driven far from threshold, classical molecule formation, a system of interacting Bose particles, shaken granular gasses, infinite allele models, network formation by preferential attachment or rewiring, stochastic growth models and two-dimensional quantum gravity. The award will support research approaches on the behavior of such systems that uses deterministic (non-random) as well as stochastic (random) techniques.

该奖项将支持对驱动扩散系统中非平衡稳态（NESS）的分析。通常，该通用类中感兴趣的物理系统通常通过扩散的非线性进化方程或随机地通过某些类型的马尔可夫过程来确定性地建模。这里提到的NES与线性动力学的平衡或详细平衡的不变度量不同，因为非平衡稳态表现出相位的分离（通常由边界动力学驱动），自发对称性破坏和/或远距离相关性远离关键过渡。要探索的特定上下文包括条纹图案形成的强弯曲状态，空间随机分区和随机矩阵合奏。非平衡稳态是许多物理系统和模型的典型特征，包括远离阈值的模式形成系统中的缺陷凝结，经典分子形成，一种相互作用的卵石颗粒的系统，摇摆的颗粒状气体，无限等位基因模型，网络模型，通过优惠的附着或重新固定的生长模型和二维量和两二光量。该奖项将支持有关使用确定性（非随机）以及随机（随机）技术的系统行为的研究方法。