First-Passage and Non-Equilibrium Dynamics of Many-Body Systems

非技术总结该奖项支持“非平衡统计力学”中的理论和计算研究，以及教育和研究培训活动。非平衡统计力学是描述材料消耗能量、不可逆地从一种形式变化到另一种形式、或在受到扰动后松弛到最终状态的科学分支。正如静态物质有不同的相(如水和冰)一样，动力物质也有相。本项目的一部分将探索其中的一些阶段。其中一个关键工具是首次通过问题，指的是在一个受到随机性冲击的系统中发生的第一次事情，例如一块钢材断裂。首次穿越问题在凝聚态和材料物理学中比比皆是。除了材料断裂导致的失效外，还包括聚合物在表面上的运动，化学物质在多孔介质中的渗流，以及热或电流通过无序材料。PI和他的团队将开发新的理论来理解复杂的首次通过现象。首次通过理论在工程、金融和生物学中的具体应用包括预测电网故障、细菌菌落灭绝，以及设计一个系统来储存足够的太阳能来满足社区过冬的需求。PI将分析有关电网性能和太阳能通量的现有数据集，以帮助制定和验证他开发的非平衡统计力学中的理论想法。对首次通过概率的准确预测可能会对太阳能生产的使用产生政策影响，因为材料创新降低了成本。PI为圣达菲研究所的教育和培训计划做出了贡献，并是最近两本关于首次通过时间及其应用的书籍的作者。技术和平衡统计力学很大程度上被理解；另一方面，到目前为止，还没有关于远离平衡的材料和现象的全面理论。这个项目开发了与活动物质相关的非平衡统计力学的三个相关领域的工具和想法：随机破产问题、排除过程和社会动力学。在随机破产问题中，目标是了解一个动态过程如何到达一个结束状态，并优化随机策略以预防或促进这种结束状态。这些理论问题可以用细菌菌落灭绝或电网故障等术语来表述。PI的团队将应用首次通过过程的丰富经验来研究与这一理论相关的基本问题。完全不对称简单排斥过程(TASEP)被称为非平衡统计力学的伊辛模型。最初被引入来模拟核糖体翻译的TASEP也被用来描述车辆交通和其他活跃的、流动的物质的例子。就像平衡统计力学解释静态物质的相一样，TASEP也有丰富的动态相图。本项目将研究连接几何图形中的TASEP。这项研究将确定相位、涨落、密度分布和冲击波的存在作为输入和输出速率的函数。社会动力学模型提供了一个描述多体相互作用的一般框架，其中相互作用的拓扑结构比平均场或近邻更复杂。该项目的一个应用是在流行病期间传播感染，因为社交网络中的个人通过限制互动来适应。国际和平协会将于2020年11月共同组织一次会议，主题是“相互作用的传染病的动力学”。类似的自适应网络想法，以分级投票者模型的形式，可以应用于在社交媒体上传播信息或错误信息。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

NONTECHNICAL SUMMARYThis award supports theoretical and computational research, as well as educational and research training activities, in "non-equilibrium statistical mechanics," the branch of science that describes materials expending energy, changing irreversibly from one form to another, or relaxing toward a final state after being perturbed. Just as static matter has different phases (e.g., water and ice), so dynamical materials also have phases. Part of this project will explore some of these phases. One of the key tools is the first-passage problem, referring to the first time something happens, e.g., a piece of steel fails, in a system buffeted by randomness. First-passage problems abound in condensed-matter and materials physics. In addition to materials failure due to fracture, examples include the motion of polymers on a surface, percolation of chemicals in a porous medium, and the passage of heat or electrical current through a disordered material. The PI and his team will develop new theories to understand complex first-passage phenomena.Concrete applications of first-passage theory to engineering, finance, and biology include predicting failure of an electrical grid, extinction of a bacterial colony, and design of a system to store enough solar power to fulfill the needs of a community through the winter. The PI will analyze available datasets about electrical grid performance and about solar energy fluxes to help formulate and validate the theoretical ideas in non-equilibrium statistical mechanics he develops. Accurate prediction of first-passage probabilities could have policy implications for the use of solar-energy production as materials innovations have driven down the costs. The PI contributes to the educational and training programs at the Santa Fe Institute and is the author of two recent books about first-passage times and their applications.TECHNICAL SUMMARYEquilibrium statistical mechanics is largely understood; on the other hand, there is, so far, no comprehensive theory of materials and phenomena far from equilibrium. This project develops tools and ideas in three related areas of non-equilibrium statistical mechanics relevant to active matter: stochastic ruin problems, exclusion processes, and social dynamics. In stochastic-ruin problems, the goals are to understand how a dynamical process reaches an end state and to optimize stochastic strategies to forestall or promote such end states. These theoretical problems can be framed in terms such as the extinction of a bacterial colony or failure of the power grid. The PI's team will apply extensive experience with first-passage processes to investigate basic questions associated with this theory.The totally asymmetric simple exclusion process (TASEP) has been called the Ising model of non-equilibrium statistical mechanics. Originally introduced to model ribosomal translation, TASEP has also been used to describe vehicular traffic and other examples of active, flowing matter. Just as equilibrium statistical mechanics elucidates the phases of static matter, so TASEP has a rich dynamical phase diagram. This project will investigate TASEP in a junction geometry. The research will determine phases, fluctuations, density profiles, and the presence of shock waves as functions of input and output rates.Social-dynamics models provide a general framework for describing many-body interactions where the interaction topology is more complicated than mean-field or near-neighbor. One application in this project is to the spread of infection during an epidemic, as individuals in a social network adapt by limiting interactions. The PI is co-organizing a conference for November 2020 on "Dynamics of Interacting Contagions." Similar adaptive-network ideas in the form of the ranked-voter model can be applied to the spread of information or misinformation on social media.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.