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

该奖项支持关于非平衡统计物理学基本问题的理论研究和教育，以及它们在基本自然过程中的应用，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。PI旨在加深对伊辛模型粗化的理解。当这个范例系统被研究时，PI最近的研究发现，相当令人惊讶的是，三维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互穿域组成的拓扑复杂状态，松弛时间随系统大小呈指数级增长。该系统的长期特性显示了各种令人困惑的特征，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将利用最近与连续统渗透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圈数的条纹。PI的目的是计算条纹状态的概率，并根据圈数对跨越域进行广义分类。他还将研究理想几何中相反排列的自旋域之间的单界面的演变，例如单个角的演变。在二维中，这个系统可以映射到一个不相容过程，PI将使用这个等价来求解界面形状。这种方法将被扩展到具有更远距离相互作用的未探索的伊辛系统中，在那里，令人惊讶的特征似乎潜伏着。与排斥过程的联系也导致PI探索关于额外排斥相互作用作用的开放问题。PI还将研究强化起决定性作用的典型社会动力学模型。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次提示。这个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，在平均场极限上有惊人的快速动态，而在晶格网络上有异常缓慢的动态。后者的起源似乎是对立意见领域之间界面上的有效表面张力。对于创新，强化延迟了它的开始。当一项创新在某种程度上被放弃时，其结果只是昙花一现。采用这种时尚的人口比例作为放弃率的函数经历了一个突然的转变，PI将对其进行分析和数值研究。PI将研究一种时尚如何在空间分散的人群中传播。反常的特征出现在“阴燃”过渡时期，这种过渡将一个风尚在全球蔓延的政权与一个风尚迅速消失的政权分开。在可能的情况下，将与经验数据联系。该奖项支持理论研究和教育，以了解远离平衡稳定状态的系统。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，存在决定其详细物理性质的全局原理。然而，当一个系统处于非平衡状态时，无论是通过使其暴露于不断变化的外部条件下，还是通过增加或提取能量或质量，对演化的理解仍然没有很好地表征。一个典型的例子是一个磁系统，它最初处于高温状态，在微观水平上没有磁化，也没有显示出磁性的空间组织，然后突然冷却到低于磁性的转变温度。从最初的无序，磁有序的竞争区域自发地生长，形成一个粗糙的马赛克域。PI试图理解这种域镶嵌的几何和动力学，以及有序域之间界面的属性。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，三维系统包含了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改变其状态之前必须经历来自相邻代理的多次提示。与单个智能体与相邻智能体相遇后改变状态的情况相比，强化导致的进化现象非常不同。这种强化机制的影响将被探讨在一个群体的意见演变的动态，以及不可逆转的创新和短暂的时尚的传播。强化效应对流行趋势至关重要，因为这一特性控制着流行趋势是迅速消失，几乎不被注意到，还是在逐渐消失之前变得广泛。

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.