Pattern Formation in Non-equilibrium Systems: Self-organization and Stochasticity

[01:17 . 93]该奖项支持图案形成的理论和计算研究，并将其应用于物理、化学和生物问题。研究的重点包括模式成核、自组织簇态和界面动力学中的随机性。PI的目的是应用数值和分析相结合的方法来解决模式成核问题。模式成核是指在具有多稳定性的系统中由波动效应产生的模式。研究工作将包括应用程序。直接感兴趣的是随机通道打开自发产生的细胞内钙波。群集行为发生在相互作用的多粒子系统中，远离任何简单的平衡状态。从微生物菌落到人类行人交通，在广泛的不同系统中发现了由群集引起的自组织结构。将为这些过程设计连续方程，目的是更好地理解允许的参数范围和不稳定机制。模型计算的结果将与现实世界的数据进行比较，这些数据部分是通过与动物群集、交通模式和变形虫聚集等领域的领先专家合作获得的。PI还将继续研究随机性如何影响界面动力学。努力将集中于扩展两种可能性，即可激系统中的脉冲逆射和噪声引起的扩散不稳定性。PI旨在找到一种解析方法，并找到这些异常噪声效应发生的充分必要条件。一项新的努力计划应用于感染传播过程中的噪音效应。该奖项还通过将研究成果纳入模式形成课程和编写模式形成教科书来支持教育。该奖项支持非平衡过程物理学的理论和计算研究，特别是在扩展系统中空间模式的出现。这项研究将在一定程度上利用过去十年来该领域的巨大进步，对各种复杂系统的行为做出关键的、重要的预测。这项工作将集中在波动如何影响具有共存动态状态的系统中模式的形成，理解相互作用的自推进粒子的自组织特性，以及更好地表征噪声敏感界面发生的条件。这项工作的结果将为物理、化学和生物系统的广泛具体应用提供基础。PI将重点研究随机通道打开、动物聚集、交通模式、阿米巴原虫聚集和感染传播等因素对细胞内钙波的自发产生。该奖项还通过将研究成果纳入模式形成课程和编写模式形成教科书来支持教育

0101793LevineThis award supports theoretical and computational research on pattern formation with applications to physical, chemical, and biological problems. The focus of the research includes pattern nucleation, self-organized flocking states, and stochasticity in interface dynamics. The PI aims to apply a combined numerical and analytical approach to the problem of pattern nucleation. Pattern nucleation refers to the creation of patterns by fluctuation effects in systems exhibiting multistability. The research effort will include applications. Of immediate interest is the spontaneous creation of intracellular calcium waves by stochastic channel openings. Flocking behavior occurs in interacting multiparticle systems away from any simple equilibrium state. Self-organized structures arising from flocking have been found in a wide range of diverse systems from microorganism colonies to human pedestrian traffic. Continuum equations will be devised for these processes with an aim to better understand allowed parameter ranges and instability mechanisms. Results from model calculations will be compared to real-world data obtained in part through collaboration with leading experts in the fields of animal flocking, traffic patterns, and amoeba aggregation. The PI will also continue his studies of how stochasticity influences interface dynamics. Efforts will focus on extending two possibilities, pulse backfiring in excitable systems and noise-induced diffusive instabilities. The PI aims to find an analytic approach and to find necessary and sufficient conditions for the occurrence of these anomalous noise effects. A new effort is planned on an application to noise effects during infection spreading. This award also supports education through research results that are incorporated into a course on pattern formation and through the preparation of a textbook on pattern formation.%%%This award supports theoretical and computational research on the physics of non-equilibrium processes, especially in the emergence of spatial patterns in extended systems. The research will in part, capitalize on tremendous advances in the field over the past decade to make critical and nontrivial predictions regarding the behavior of a wide variety of complex systems. The work will focus on how fluctuations influence the formation of patterns in systems with coexisting dynamical states, on understanding the self-organizing properties of interacting self-propelled particles, and on better characterizing the conditions under which noise-sensitive interfaces occur.Results of this work will provide a foundation for a wide range of specific applications to physical, chemical, and biological systems. The PI will focus on the spontaneous creation of intracellular calcium waves by stochastic channel openings, animal flocking, traffic patterns, amoeba aggregation, and infection spreading. This award also supports education through research results that are incorporated into a course on pattern formation and through the preparation of a textbook on pattern formation.***