NSF-BSF: Fluctuation phenomena out of equilibrium

该奖项支持基础研究和教育，旨在描述相互作用实体的大型集合中集体行为的出现。虽然系统中单个组件的行为可能难以绘制（由于混沌的经典运动或固有的量子不确定性），但大量的集体行为可以更容易预测，例如，尽管气体分子随机运动，声波的弥散。这是通过统计物理工具实现的，统计物理工具可以对分子的随机运动进行系统平均，以描述相关密度演化的有效场论。在描述处于平衡状态的物理系统时，这种方法从不确定的粒子运动到接近确定的集体行为进行平均，其广泛的实用性表明它适用于更广泛的实体类别。本研究探讨了复杂实体的集体行为，特别是在非平衡系统中的一些例子。(i)活性物质的新兴领域涉及实体的集体运动，如细菌、人工自动力纳米机器人，甚至是鸟群或鱼群，它们单独消耗和耗散能量。尽管在个体层面上具有随机性，但相互作用导致了集体的迷人协调运动。我们发现，这种远距离的协调可能会被媒介内部的障碍，甚至是边缘的混乱所破坏。研究小组将探索无序和边界在活性物质相中的作用。待研究的现象包括杂质造成的长期破坏，以及被动旁观者在活跃物质流动中徘徊。（二）在基本层面上，活性物质元素和“平衡物质”中的原子之间的一个关键区别是，能量的消耗建立了一个自然的时间箭头。相反，人们无法区分平衡气体粒子向前或向后运动的轨迹。有趣的是，从“活性物质”的行为中获得的见解可以在物理学的其他领域进行探索，例如在光子和辐射的背景下，例如传热。该团队正在研究基于辐射的热机的可行性，这种热机类似于通过不对称边界产生的棘轮效应施加在活性物质中的非平衡力。（iii）生命系统是非平衡的缩影，它消耗的能量不仅用于移动，而且用于生长和繁殖，呈现出其他值得探索的现象。例如，当细菌膜或肿瘤扩展到新的空间时，其组成由扩张前沿的成功祖先主导。这在前面的形状和竞争的细菌变体之间建立了联系。研究小组将对在竞争变体的生长和扩展过程中可能出现的薄膜形状进行分类。这项研究活动与PI的研讨会和课程紧密结合，PI通过出版的教科书和网页向广泛的科学界传播。这项研究跨越了学科界限，在从应用数学到免疫学的各个领域都有潜在的影响。技术概述涨落，无论是量子涨落、热涨落还是非平衡涨落，都是各种物理现象的原因或标志。将描述平衡波动的概念和数学工具推广到非平衡现象领域是一项长期的努力。本研究旨在量化不同背景下的非平衡波动。具体目标包括：(i)活性物质的新兴领域涉及消耗能量移动的实体的集体行为。通过系统的能量流产生新的集体相和波动，并不总是用平衡物质的场论来描述。研究项目将探讨无序和边界（静态或移动）对活性物质的作用。要探索的现象包括长期的相关性和力，以及包裹体的异常动力学。(2)无时间反转对称装置中的量子电动力学现象与活性物质具有共同特征。特别是，我们将探索利用棘轮效应产生力的辐射热机的可行性，以及在破坏电磁互反的设置中违反牛顿第三定律的力。（三）不断增长的人口为探索新出现的现象提供了另一个场所。一组研究项目涉及对竞争物种生长和扩张过程中产生的膜的形态进行分类。另一组涉及由于突变或外部条件而具有时变繁殖率的种群的动力学。本研究项目将采用数值与分析相结合的方法进行研究。典型的起点是一个简化的元素模型，遵循简化但可细化的规则。在分析方面，目标是将模型粗化到连续体描述的水平，然后应用场论方法来表征相位和波动。数值任务将是实现简化的规则和描述紧急行为，以对比或支持理论。描述非平衡状态下波动的概率分布一直是统计物理学的一个长期探索，最近在几个方面取得了显著进展。然而，活性物质中的力的谜题，以及生长中的细菌前沿的固定，只是几个项目中的两个例子，这些项目指向了潜在现象的复杂性，这是本研究旨在解开的。人力资源的教育和发展具有重要的更广泛的影响：研究活动与通过教科书和网页接触到广泛科学界的PI的研讨会和课程密切结合。该组过去的学生和博士后是学术和研究社区的生产性成员。这项研究跨越了学科界限，在从应用数学到免疫学的各个领域都有潜在的影响。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

NONTECHNICAL SUMMARYThis award supports basic research and education aimed at characterizing emergence of collective behaviors in large assemblies of interacting entities. While actions of individual components of a system may be difficult to chart (due to chaotic classical motion or inherent quantum uncertainty), the collective behavior of a large number can be easier to predict, for example the dispersion of sound waves despite random movements of gas molecules. This is made possible by the tools of statistical physics that enable systematic averaging over stochastic motions of molecules, to describe effective field theories for evolution of relevant densities. The extensive utility of this approach, averaging from uncertain motions of particles to near deterministic collective behavior, in describing physical systems in equilibrium, suggests its applicability to broader class of entities. Some examples of collective behaviors of complex entities, especially in systems out of equilibrium, are explored in this research. (i) The emerging field of active matter is concerned with collective motions of entities, such as bacteria, artificial self-powered nanobots, of even flocks of birds or school of fish, that individually consume and dissipate energy. Despite stochasticity at the individual level, interactions lead to fascinating coordinated motions of the collective. We have found that such long-range coordination can be disrupted by obstacles within the medium, or even disorder at its edges. The research team will explore the roles of disorder and boundaries on phases of active matter. Phenomena to be studied include the long-reach of disruptions caused by impurities, and the wanderings of passive bystanders caught in the flow of active matter.(ii) At a basic level, a key difference between elements of active matter and atoms in “equilibrium matter,” is that consumption of energy sets up a natural arrow of time. In contrast, one cannot distinguish between movies of equilibrium gas particles running forward or backward. Interestingly, insights gained from behavior of “active matter” can be explored in other domains of physics, such as in the context of photons and radiation, for example, heat transfer. The team is investigating the feasibility of heat engines based on radiation, with similarity to non-equilibrium forces exerted in active matter through the ratchet effect arising from asymmetric boundaries.(iii) Living systems, the epitome of non-equilibrium, consume energy not only to move, but to grow and reproduce, presenting other phenomena to explore. For example, as a bacterial film, or a tumor expands into new space, its composition is dominated by successful ancestors at the expansion front. This sets up a connection between the shape of the front, and the competing bacterial variants. The research team will classify possible shapes of films that may appear during growth and expansion of competing variants. This research activity is closely incorporated in seminars and courses of the PI which through his published textbooks and web-pages reach a broad scientific community. This research crosses disciplinary boundaries and has potential impact in diverse areas from applied mathematics to immunology.TECHNICAL SUMMARYFluctuations, whether of quantum, thermal, or non-equilibrium origin, are cause or signature of various physical phenomena. Generalizing concepts and mathematical tools characterizing equilibrium fluctuations to the realm of non-equilibrium phenomena has been a long-running endeavor. This research aims at quantifying out of equilibrium fluctuations in diverse contexts. Specific goals include:(i) The emerging field of active matter is concerned with collective behaviors of entities that consume energy to move. The current of energy through the system yields novel collective phases and fluctuations, not always describable with field theories of equilibrium matter. The research projects will explore the roles of disorder and boundaries (static or mobile) on active matter. Phenomena to be explored include long-ranged correlations and force, and anomalous dynamics of inclusions.(ii) Quantum electrodynamic phenomena in setups without time reversal symmetry share common features with active matter. In particular, we shall explore the feasibility of a radiative heat engine that utilizes a ratchet effect to generate force, and forces that violate Newton’s third law in setups that break electromagnetic reciprocity.(iii) Growing populations provide yet another venue for exploration of emergent phenomena. One set of research projects pertain to classifying morphologies of films arising during growth and expansion of competing species. Another set deals with dynamics of populations with time-varying reproduction rate due to mutations or external conditions.The projects in this research will be studied through a combination of numerical and analytical methods. The typical starting point would be a simplified model of elements following simplified but refine-able rules. On the analytic front, the goal would be to coarse-grain the model to the level of a continuum description, and to then apply methods of field theory to characterize phases and fluctuations. The numerical task would be to implement the simplified rules and characterize the emergent behaviors, in contrast or support to the theory.Characterizing probability distributions underlying fluctuations in nonequilibrium settings has been a long-standing quest in statistical physics, with notable recent progress on several fronts. Yet, puzzles of force in active matter, and fixation in growing bacterial fronts are but two examples amongst several projects pointing to complexity of the underlying phenomena, which this research aims to unravel.Education and development of human resources are an essential broader impact: The research activity is closely incorporated in seminars and courses of the PI which through textbooks and web-pages reach a broad scientific community. Past students and postdocs of the group are productive members of academic and research communities. This research crosses disciplinary boundaries and has potential impact in diverse areas from applied mathematics to immunology.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.