Non-Equilibrium Collective Phenomena

该奖项支持理论研究和教育，以调查凝聚态物质、生态和生物系统中的紧急现象，特别强调大脑。这些基础主题的培训也将有助于促进初级研究人员在物理、数学和生物科学领域的职业发展。总体目标是理解在有许多粒子或组件相互作用的系统中出现的现象。这些现象是协同作用的组成部分的反映，不同于与单个粒子或系统组成部分相关的属性。在铁磁性材料中，典型的例子是条形磁铁，磁性在低温下产生，在低温下，磁性的趋势压倒了热波动。然而，如果这种材料突然冷却到低温，铁磁性障碍就会出现，导致玻璃态的形成，而不是微观磁体在材料上的完美排列，从而导致铁磁性状态。这项研究的一个目标是确定磁性或玻璃性行为产生的条件。研究的一个主要焦点是密集网络的研究，其中链路的数量远远大于节点的数量。一个重要的例子是人类的大脑，它通常有1000亿个神经元和100万亿个连接。这些神经元的连接模式包含了丰富的局部图案，可能是大脑奇妙功能的基础。一个重要的目标是阐明这些迷人的结构。另一个重点是了解觅食对环境的消耗、觅食者对资源消耗的营养和资源增长对环境的补充之间的生态相互作用。一个重要的目标是确定在何种条件下觅食者和资源密度保持平衡，以及何时出现繁荣和萧条周期。该奖项还支持PI开发与统计物理相关主题的大规模开放在线课程的努力。该奖项支持理论研究和教育，涉及将非平衡统计物理技术应用于凝聚态物质、生态和生物系统中的紧急现象，重点是大脑。虽然表面上不同，但这些项目都依赖于共同的调查工具，包括主方程分析、缩放理论和大规模数值模拟。使用这些基本工具的培训也将有助于促进初级研究人员在物理、数学和生物科学领域的职业发展。第一个项目是了解不符合常规幂律粗化的动力学铁磁系统的动力学。这样的系统可能会陷入由多个“呼吸”域组成的复杂亚稳态。长期属性是受控的域合并——要么作为孤立的事件，要么作为宏观级联的一部分。由此产生的超低动力学类似于玻璃材料，应该为玻璃行为提供新的见解。第二个重点是密集网络，其中平均节点度随着节点数n的增加而增加。一个重要的例子是大脑。人类大脑通常有1000亿个神经元，每个神经元都与大约1000个其他神经元相连。大脑的结构连通性揭示了丰富的基序谱，其中小节点集紧密相连；这种结构可能是大脑奇妙功能的基础。这些和相关的特征，如固定大小的团密度中的多相变，将通过应用于密集网络的主方程来阐明。最后，研究了一种基于饥饿随机游走模型的觅食原则模型。在这里，觅食者一遇到食物就会吃掉它，从而消耗了当地的资源。此外，如果觅食者徘徊太久而没有遇到食物，它就会饿死。当再生和繁殖也被纳入其中时，一个更丰富的现象就出现了——动态可以是稳定的，也可以是振荡的，具有觅食者和资源的大规模空间组织。这些特征将通过利用第一通道和随机过程以及大规模模拟来阐明。该奖项还支持PI开发与统计物理相关主题的大规模开放在线课程的努力。

NONTECHNICAL SUMMARYThis award supports theoretical research and education to investigate emergent phenomena in condensed-matter, ecological, and biological systems, with a specific emphasis on the brain. Training in these fundamental topics will also help advance the careers of junior researchers in the physical, mathematical, and biological sciences. The overarching goal is to understand phenomena that emerge in systems with many particles or components that interact with each other. These phenomena are a reflection of the components acting in concert and are distinct from the properties associated from an individual particle or component of the system.In ferromagnetic materials, with the prototypical example being a bar magnet, magnetism arises at low temperatures, where the tendency for magnetism overwhelms thermal fluctuations. However, if such a material is suddenly cooled to low temperature, barriers to ferromagnetism arise, leading to the formation of a glassy state rather than the perfect alignment of microscopic magnets across the material which leads to the ferromagnetic state. A goal of the research is to determine the conditions under which magnetic or glassy behavior arises. A major focus of the research is the study of dense networks, in which the number of links is much larger than the number of nodes. An important example is the human brain, which typically has 100 billion neurons and 100 trillion connections. The connectivity patterns of these neurons contain a rich spectrum of local motifs that may underlie the wondrous functionality of the brain. An important goal is to elucidate these fascinating structures. Another focus is to understand the ecological interplay between depletion of an environment by foraging, the nourishment of the forager by resource consumption, and environmental replenishment by resource growth. An important aim is to determine the conditions under which the forager and resource densities remain in balance and when boom and bust cycles arise.This award also supports the PI's efforts to develop a massive open online course on topics related to statistical physics.TECHNICAL SUMMARYThis award supports theoretical research and education that involve applying the techniques of non-equilibrium statistical physics to emergent phenomena in condensed-matter, ecological, and biological systems, with a focus on the brain. While ostensibly disparate, these projects all rely on common investigative tools, including analysis of master equations, scaling theories, and large-scale numerical simulations. Training in using these essential tools will also help advance the careers of junior researchers in the physical, mathematical, and biological sciences.The first project is to understand the dynamics of kinetic ferromagnetic systems that do not conform to conventional power-law coarsening. Such systems may get stuck in complex metastable states that consist of multiple "breathing" domains. Long-time properties are controlled domain merging - either as isolated events or part of a macroscopic cascade. The resulting ultraslow dynamics resembles that of glassy materials and should provide new insights into glassy behavior.A second focus is dense networks in which the average node degree increases with the number of nodes N. An important example is the brain. Human brains typically have 100 billion neurons, each of which is connected to roughly 1000 other neurons. The structural connectivity of the brain reveals a rich spectrum of motifs in which small sets of nodes are densely interconnected; such structures may underlie the wondrous functionality of the brain. These and related features, such as multiple phase transitions in the density of fixed-size cliques will be elucidated by the master equation applied to dense networks.Finally, a principled model of foraging, which is based on the starving random walk model, will be investigated. Here the forager consumes food upon encountering it, thereby depleting the resource locally. Moreover, the forager starves if it wanders for too long without encountering food. When regeneration and reproduction are also incorporated, an even richer phenomenology arises - the dynamics can be steady or oscillatory, with a large-scale spatial organization of foragers and resources. These features will be elucidated by exploiting first-passage and stochastic processes and by large-scale simulations.This award also supports the PI's efforts to develop a massive open online course on topics related to statistical physics.