Applications of Non-Equilibrium Statistical Physics to Collective Phenomena in Materials and Complex Systems

技术概要该奖项支持非平衡统计物理学的基本问题及其在基本自然过程（如磁系统的粗化）和社会力量驱动的现象（如意见传播、技术创新和时尚）中的应用的理论研究和教育。PI旨在加深对伊辛模型粗化的理解。 虽然这个范式系统已经研究，PI的最近的研究发现，相当令人惊讶的是，在三维的粗化动力学不符合传统的图片幂律域增长。 相反，系统陷入了一个拓扑复杂的状态，由两个高度相互渗透的域组成，弛豫时间与系统大小呈指数关系。 这个系统的长时间性质显示出各种令人困惑的特征，PI将通过大规模模拟，标度参数以及拓扑学和微分几何的技术相结合来研究。在二维伊辛模型中，PI将利用最近与连续渗流理论的联系来阐明长时间状态的拓扑结构。 在这里，单相畴可以组织成各种绕组编号的条带。 PI的目的是计算条纹状态的概率，并根据缠绕数对跨越域进行广泛的分类。 他还将研究在理想化的几何结构中，相反排列的自旋畴之间的单一界面的演变，例如在单个角上的演变。 在二维中，这个系统可以映射到一个排斥过程，PI将使用它来求解界面形状。 这种方法将被扩展到具有更长距离相互作用的伊辛系统的未探索的情况下，其中隐藏着令人惊讶的特征。 与排斥过程的联系也导致PI探索关于额外排斥相互作用的作用的开放性问题。PI还将研究原型社会动力学模型，其中强化起着决定性作用。 强化意味着代理在实际改变其状态之前需要来自交互伙伴的多个提示。 这一新的属性对随后的动态产生了深远的影响。 对于社会强化的投票者模型，在平均场极限下有令人惊讶的快速动态，而在格点网络上有令人惊讶的缓慢动态。 后者的起源似乎是一个有效的表面张力之间的界面上的对立意见域。对于创新，强化延迟其启动。 当一项创新在某种程度上被放弃时，其结果就是一种短暂的时尚。 采用时尚的人口比例经历了一个突然的转变，作为放弃率的函数，PI将通过分析和数字来探索。PI将研究时尚如何在空间分散的人群中传播。 反常的特征出现在一个“阴燃”的过渡期，这个过渡期将时尚在全球范围内传播的政权与时尚迅速消失的政权分开。 NONTECHNICAL SUMMARY该奖项支持理论研究和教育，以了解远离稳态平衡的系统。 非平衡态统计物理学关注的是包含许多相互作用的元素或粒子的演化系统。 对于处于平衡状态的系统，存在着决定其详细物理性质的全局原理。 然而，当一个系统失去平衡时，无论是通过暴露于不断变化的外部条件，还是通过增加或提取能量或质量，对演化的理解仍然没有很好的表征。一个典型的例子是磁性系统，它最初处于高温，没有磁化，并且在微观水平上没有表现出磁性的空间组织，并突然冷却到低于磁性转变温度。 从最初的无序，竞争区域的磁秩序自发地增长，形成一个粗糙的马赛克域。 PI试图了解这个域马赛克的几何形状和动力学，以及有序域之间的界面特性。 虽然这个经典问题以前已经研究过，但PI的初步结果表明，三维系统包含许多当前理论所没有预料到的惊喜。 PI还旨在研究一系列动态的社会过程时，强化起着至关重要的作用。 强化意味着单个代理在实际改变其状态之前必须经历来自相邻代理的多次提示。 强化导致非常不同的进化现象相比的情况下，一个代理改变状态后，一个单一的遭遇与相邻的代理。 这种强化机制的效果将被探索的人口中的意见演变的动态，以及不可逆转的创新和短暂的时尚的传播。 强化效应对时尚至关重要，因为这一特征控制着时尚是否会迅速消失，几乎不被注意到，或者在逐渐消失之前广泛传播。

TECHNICAL SUMMARYThis award supports theoretical research and education on fundamental issues of non-equilibrium statistical physics and their applications to basic natural processes, such as the coarsening of magnetic systems, and to phenomena driven by social forces, such as the spread of opinions, technological innovations, and fads.The PI aims to deepen understanding of the coarsening of the Ising model. While this paradigmatic system has been studied, the PI's recent research has found, quite surprisingly, that coarsening dynamics in three dimensions does not conform to the conventional picture of power-law domain growth. Instead, the system gets stuck in a topologically complex state that consists of two highly interpenetrating domains, with the relaxation time scaling exponentially with the system size. The long-time properties of this system display a variety of puzzling features that the PI will to investigate by a combination of large-scale simulations, scaling arguments, and techniques from topology and differential geometry.In the two-dimensional Ising model, the PI will exploit a recent connection with continuum percolation theory developed to elucidate the topology of long-time states. Here single-phase domains can organize into stripes of various winding numbers. The PI aims to calculate the probabilities of stripe state and to broadly categorize spanning domains according to the winding numbers. He will also investigate the evolution of single interfaces between oppositely-aligned spin domains in idealized geometries, such the evolution at a single corner. In two dimensions, this system can be mapped onto an exclusion process, an equivalence that the PI will use to solve the interface shape. This approach will be extended to the unexplored case of Ising systems with longer-range interactions, where surprising features appear to lurk. The connection to exclusion processes also leads the PI to explore open questions about the role of additional repulsive interactions.The PI will also investigate prototypical social dynamics models in which reinforcement plays a decisive role. Reinforcement means that an agent requires multiple prompts from interaction partners before actually changing its state. This new attribute has a profound effect on the ensuing dynamics. For the socially-reinforced voter model, there is surprisingly fast dynamics in the mean-field limit and anomalously slow dynamics on lattice networks. The origin of the latter appears to be an effective surface tension at the interface between opposite-opinion domains.For innovations, reinforcement delays its onset. When an innovation is abandoned at some rate, the outcome is a transient fad. The population fraction that adopts the fad undergoes a sudden transition as function of the abandonment rate that the PI will explore analytically and numerically. The PI will study how a fad spreads through a spatially dispersed population. Anomalous features arise at a "smoldering" transition that separates a regime where the fad spreads globally from a regime where a fad quickly disappears. Contact with empirical data will be made where possible.NONTECHNICAL SUMMARYThis award supports theoretical research and education to understand systems that are far from the steady state of equilibrium. Non-equilibrium statistical physics is concerned with evolving systems that contain many interacting elements or particles. For systems in equilibrium, there exist global principles that determine their detailed physical properties. However, when a system is out of equilibrium, either by exposing it to changing external conditions or by adding or extracting energy or mass, the understanding of the evolution is still not well characterized.A prototypical example is a magnetic system that is initially at high-temperature where it is not magnetized and shows no spatial organization of magnetism at a microscopic level, and is suddenly cooled to below the transition temperature to magnetism. From the initial disorder, competing regions of magnetic order spontaneously grow to form a coarsening mosaic of domains. The PI seeks to understand the geometry and dynamics of this domain mosaic, as well as the properties of the interface between ordered domains. Although this classic problem has been studied before, the PI's preliminary results show that the three-dimensional system contains many surprises that are not anticipated in current theories. The PI also aims to study a range of dynamic social processes when reinforcement plays an essential role. Reinforcement means that an individual agent must experience multiple prompts from neighboring agents before actually changing its state. Reinforcement leads to very different evolutionary phenomena compared to the case where an agent changes state after a single encounter with a neighboring agent. The effect of this reinforcement mechanism will be explored for both the dynamics of opinion evolution in a population, as well as the spread of irreversible innovations and transient fads. The effect of reinforcement is crucial for fads, because this feature controls whether a fad can quickly fizzle out and barely be noticed or can become widespread before gradually disappearing.