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

技术总结该奖项支持关于非平衡统计物理的基本问题及其在基本自然过程中的应用的理论研究和教育，如磁系统的粗化，以及由社会力量驱动的现象，如观点的传播、技术创新和时尚。该奖项旨在加深对伊辛模型粗化的理解。虽然已经研究了这个范例系统，但PI最近的研究发现，非常令人惊讶的是，三维中的粗化动力学并不符合传统的幂函数域增长的图景。相反，系统陷入了一种复杂的拓扑状态，它由两个高度互穿的区域组成，松弛时间随系统大小呈指数增长。这个系统的长时间特性显示出许多令人费解的特征，PI将结合大规模模拟、标度论证以及拓扑学和微分几何的技术进行研究。在二维Ising模型中，PI将利用最近发展起来的连续介质渗流理论来解释长时间态的拓扑。在这里，单相区可以组织成不同缠绕数的条纹。PI的目的是计算条带状态的概率，并根据缠绕数对跨域进行广泛的分类。他还将研究理想化几何中相对排列的自旋域之间的单一界面的演化，例如在单个角落的演化。在两个维度上，这个系统可以映射到一个排除过程，PI将使用这种等价性来解决界面形状。这种方法将扩展到伊辛系统的未知情况，这种系统具有更远距离的相互作用，其中似乎潜藏着令人惊讶的特征。与排斥过程的联系也使PI探索关于额外排斥相互作用的作用的开放问题。PI还将研究强化在其中起决定性作用的典型社会动力学模型。强化意味着，在实际更改其状态之前，代理需要来自交互伙伴的多个提示。这一新属性对随后的动态产生了深远的影响。对于社会强化的选民模型，平均场极限有令人惊讶的快速动力学，而格子网络有异常缓慢的动力学。后者的起源似乎是相反意见域之间的交界处的有效表面张力。对于创新，加固延迟了它的开始。当一项创新以某种速度被放弃时，结果是短暂的时尚。采用FAD的人口比例经历了一个突然的转变，这是PI将分析和数值研究的遗弃率的函数。PI将研究一种时尚如何在空间分散的人群中传播。反常特征出现在一种“阴燃”的过渡时期，这种过渡将一种时尚在全球蔓延的政权与一种时尚迅速消失的政权区分开来。尽可能地接触经验数据。非技术总结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，存在着确定其详细物理性质的全球原则。然而，当一个系统失去平衡时，无论是通过暴露在变化的外部条件下，还是通过增加或提取能量或质量，对演化的理解仍然不是很好。一个典型的例子是一个磁系统，它最初处于高温，在那里它没有磁化，在微观水平上没有显示出磁的空间组织，然后突然冷却到低于向磁性的转变温度。从最初的无序开始，磁序的竞争区域自发地增长，形成一个粗化的磁畴马赛克。PI试图了解这种区域镶嵌的几何和动力学，以及有序区域之间界面的属性。尽管这一经典问题以前已经被研究过，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。强化意味着单个代理在实际更改其状态之前必须经历来自邻近代理的多个提示。与代理人在与邻近代理人相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。这一强化机制的作用将在群体中的意见演变动态以及不可逆转的创新和短暂时尚的传播中进行探索。加固的效果对时尚至关重要，因为这一特征控制着一种时尚是会迅速消失，几乎不会被注意到，还是会在逐渐消失之前变得普遍。

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.