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

技术摘要该奖项支持非平衡统计物理基本问题的理论研究和教育及其在基本自然过程（例如磁系统的粗化）以及社会力量驱动的现象（例如观点传播、技术创新和时尚）中的应用。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被研究过，但 PI 最近的研究令人惊讶地发现，三个维度的粗化动力学并不符合幂律域增长的传统图景。 相反，系统陷入由两个高度相互渗透的域组成的拓扑复杂状态，弛豫时间随着系统规模呈指数级增长。 该系统的长期特性显示出各种令人费解的特征，PI 将通过大规模模拟、缩放参数以及拓扑和微分几何技术的组合来研究这些特征。在二维伊辛模型中，PI 将利用最近与连续介质渗流理论的联系，该理论旨在阐明长期状态的拓扑。 这里，单相域可以组织成各种绕组数的条带。 PI 旨在计算条带状态的概率，并根据缠绕数对跨越域进行广泛分类。 他还将研究理想化几何形状中相反排列的自旋域之间的单个界面的演化，例如单个角的演化。 在二维中，该系统可以映射到排除过程，这是 PI 将用来求解界面形状的等效过程。 这种方法将扩展到具有远距离相互作用的伊辛系统的未探索案例，其中似乎潜藏着令人惊讶的特征。 与排斥过程的联系也导致 PI 探索有关额外排斥性相互作用的作用的开放性问题。PI 还将研究典型的社会动力学模型，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交互伙伴的多次提示。 这个新属性对随后的动态产生深远的影响。 对于社会强化选民模型，平均场极限具有令人惊讶的快速动态，而晶格网络则具有异常缓慢的动态。 后者的起源似乎是相反意见领域之间界面上的有效表面张力。对于创新而言，强化会延迟其发生。 当一项创新在一定程度上被放弃时，其结果就是昙花一现。 采用时尚的人口比例会随着放弃率的函数而经历突然的转变，PI 将通过分析和数值方式探索这一点。 PI 将研究时尚如何在空间分散的人群中传播。 异常特征出现在“闷烧”过渡中，这种过渡将时尚在全球传播的政权与时尚迅速消失的政权分开。 将尽可能接触经验数据。非技术摘要该奖项支持理论研究和教育，以了解远离稳定平衡状态的系统。 非平衡统计物理学涉及包含许多相互作用的元素或粒子的演化系统。 对于平衡系统，存在确定其详细物理特性的全局原理。 然而，当一个系统失去平衡时，无论是通过将其暴露在不断变化的外部条件下，还是通过添加或提取能量或质量，对演化的理解仍然没有得到很好的表征。一个典型的例子是一个磁系统，它最初处于高温，没有被磁化，在微观水平上没有显示出磁性的空间组织，然后突然冷却到磁性转变温度以下。 从最初的无序开始，磁序的竞争区域自发生长，形成粗化的磁畴镶嵌体。 PI 试图了解这种域镶嵌的几何形状和动力学，以及有序域之间的界面的属性。 尽管这个经典问题之前已经被研究过，但 PI 的初步结果表明，三维系统包含许多当前理论没有预料到的惊喜。 PI 还旨在研究强化发挥重要作用时的一系列动态社会过程。 强化意味着单个智能体在实际改变其状态之前必须经历来自相邻智能体的多次提示。 与智能体在与相邻智能体单次遭遇后改变状态的情况相比，强化会导致非常不同的进化现象。 我们将探讨这种强化机制对群体中舆论演变的动态以及不可逆转的创新和短暂时尚的传播的影响。 强化的效果对于时尚来说至关重要，因为这一特征决定了时尚是否会很快消失而几乎不被注意到，或者在逐渐消失之前会变得广泛传播。

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.