Systems far from equilibrium: relaxation processes and steady-state properties

远离平衡的系统：弛豫过程和稳态特性

• 批准号: 1606814
• 负责人: Michel Pleimling
• 金额: $ 29万
• 依托单位: Virginia Polytechnic Institute and State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-06-01 至 2021-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1606814&HistoricalAwards=false
• 关键词: Systems; far; equilibrium; relaxation; processes

NONTECHNICAL SUMMARYThis award supports theoretical research and education toward developing a theory of systems far from the unchanging and familiar state of equilibrium. Nonequilibrium phenomena are omnipresent and range from weather patterns to life itself. For systems that are out of equilibrium two complementary aspects, both equally relevant, can be distinguished. These are stationary states, wherein the system will remain if not pushed from the outside, and the relaxation towards these stationary states. Gaining a better understanding of both the stationary properties and the relaxation processes are needed in order to fully understand the world around us, and to develop new ways to use these processes for tailoring the properties of various systems of interest, ranging from novel materials to biological systems and ecosystems. The study of systems far from equilibrium poses many challenges, both on the fundamental and on the practical level. Whereas there is a well-established theoretical framework for equilibrium systems, a similar comprehensive framework for non-equilibrium systems and processes remains elusive. This project aims at exploiting a variety of analytical and numerical techniques to advance understanding of non-equilibrium phenomena. The project covers both fundamental and applied aspects. One important activity focuses on the investigation of the stability of food webs to various perturbations, as for example species extinction, species migration or seasonal changes. Related to this is the question of ecomanagement and the targeted intervention in predator-prey systems in order to achieve specific goals, as for example maintaining biodiversity or removing a detrimental species. Another activity investigates the relaxation properties in model systems used to describe synchronization phenomena in biology. This investigation will allow to explore possible relationships between physical and biological aging.The project is designed so that both undergraduate and graduate students can learn and contribute in a substantial and meaningful way. This training through research approach allows to involve students at every level in cutting-edge research projects.TECHNICAL SUMMARYThis award supports theoretical research and education toward developing a theory of systems far from equilibrium. Non-equilibrium processes in nature and in human activities, such as making and processing materials, abound, and a unifying theoretical description of non-equilibrium interacting many-body systems remains elusive. The study of specific model systems can lead to progress in understanding systems far from equilibrium through revealing universal properties, using the large toolbox of numerical and analytical methods provided by statistical physics. The PI will combine advanced analytical and numerical techniques to address fundamental questions and potential applications of systems far from equilibrium through three different research thrusts. The first research thrust focuses on directed spin models that are prototypical examples of system that evolve to the equilibrium Boltzmann-Gibbs distribution even though detailed balance is violated due to the irreversibility of the dynamics. Preliminary results for the two-dimensional directed Ising model show that in the low temperature phase directedness yields a remarkable acceleration of the dynamics, manifested by a change in the value of the dynamical exponent. The research on directed spin models, addresses both fundamental aspects, such as change in dynamic properties due to irreversibility, and applied aspects, such as algorithmic tools to accelerate convergence to equilibrium. New insights into the properties of systems that violate detailed balance but fulfill the weaker condition of global balance are expected to result. For some classes of systems, directed models have the potential to become an algorithmic tool to accelerate convergence to equilibrium, which could have impact on many disciplines. The second research thrust proposes to investigate relaxation processes and the responses to perturbations in many-species systems. Food webs, discussed in the context of population dynamics, allow to gain insights into generic issues related to biodiversity and species extinction. Many of these food webs exhibit remarkable space-time patterns in a spatial setting that warrant an in-depth characterization. The PI plans (1) to study the stability of an ecological system, more specifically its response to perturbations, both small and large, and how it relaxes to the steady state, and (2) to investigate the control of an ecology, for example in order to assure biodiversity and avoid species extinction. Optimal control theory will be exploited as an analytical tool for understanding targeted interventions in predator-prey systems. This study is expected to yield valuable insights into the ecomanagement of non-trivial food webs. The third research thrust is devoted to the study of physical aging in coupled classical rotators. Coupled classical rotators and related systems present a class of systems with dynamic properties reminiscent of spin glasses. The PI will study the aging properties of these systems, investigate their responses to perturbations, and explore the existence of memory and rejuvenation effects. This study of coupled oscillators and related systems, with known biological applications, will provide an opportunity to explore possible relationships between physical and biological aging.Due to the ubiquity of non-equilibrium processes in nature, this research project may have impact beyond the boundaries of condensed matter physics. Gaining a better understanding of transient and steady-state properties in systems amenable to an in-depth investigation using the large toolbox of statistical physics should contribute to the development of a more general theory that describes systems far from equilibrium. This project is designed so that both undergraduate and graduate students can learn and contribute in a substantial and meaningful way. This training through research approach allows to involve students at every level in cutting-edge research projects.

该奖项支持理论研究和教育，以发展远离不变和熟悉的平衡状态的系统理论。非平衡现象无所不在，范围从天气模式到生命本身。对于失去平衡的系统，可以区分出两个互补的方面，它们都同样相关。这些都是定态，如果系统没有从外部被推，系统会保持不变，松弛到这些定态。为了充分了解我们周围的世界，需要更好地理解静止特性和松弛过程，并开发新的方法来使用这些过程来定制各种感兴趣的系统的特性，从新材料到生物系统和生态系统。对远离平衡的系统的研究在基础和实践层面上都提出了许多挑战。虽然平衡系统有一个完善的理论框架，但非平衡系统和过程的类似综合框架仍然难以捉摸。该项目旨在利用各种分析和数值技术来促进对非平衡现象的理解。该项目涵盖基础和应用两个方面。一项重要的活动集中于调查食物网在各种扰动下的稳定性，例如物种灭绝、物种迁移或季节变化。与此相关的是生态管理问题和对捕食者-猎物系统进行有针对性的干预，以实现具体目标，例如维持生物多样性或消除有害物种。另一项活动是研究用于描述生物学同步现象的模型系统中的松弛特性。这项研究将有助于探索生理衰老和生物衰老之间可能存在的关系。该项目旨在使本科生和研究生都能以实质性和有意义的方式学习和贡献。这种通过研究方法进行的培训允许学生参与各个层次的前沿研究项目。该奖项支持理论研究和教育，以发展远离均衡的系统理论。自然界和人类活动中的非平衡过程，如制造和加工材料，比比皆是，而非平衡相互作用的多体系统的统一理论描述仍然难以捉摸。利用统计物理学提供的大量数值和分析方法，通过揭示普遍性质，对特定模型系统的研究可以在理解远离平衡的系统方面取得进展。PI将结合先进的分析和数值技术，通过三个不同的研究重点来解决远离平衡的系统的基本问题和潜在应用。第一个研究重点是定向自旋模型，这是系统进化到平衡玻尔兹曼-吉布斯分布的典型例子，即使由于动力学的不可逆性而破坏了详细的平衡。二维定向Ising模型的初步结果表明，在低温阶段，定向性产生了显著的动力学加速，表现为动力指数值的变化。对定向自旋模型的研究涉及两个基本方面，例如由于不可逆性而导致的动态特性的变化，以及应用方面，例如加速收敛到平衡的算法工具。预计将产生对违反详细平衡但满足全局平衡较弱条件的系统性质的新见解。对于某些类型的系统，定向模型有可能成为加速收敛到平衡的算法工具，这可能对许多学科产生影响。第二个研究重点是研究多物种系统中的松弛过程和对扰动的响应。在种群动态的背景下讨论食物网，可以深入了解与生物多样性和物种灭绝有关的一般问题。这些食物网中的许多在空间设置中表现出非凡的时空模式，值得深入表征。PI计划(1)研究生态系统的稳定性，更具体地说，它对大小扰动的反应，以及它是如何松弛到稳定状态的；(2)研究对生态系统的控制，例如，为了确保生物多样性和避免物种灭绝。最优控制理论将被用作理解捕食者-猎物系统中有针对性干预的分析工具。这项研究有望为非琐碎食物网的生态管理提供有价值的见解。第三个研究重点是耦合经典旋转体的物理老化研究。耦合经典旋转体及其相关系统是一类具有类似自旋玻璃动力学性质的系统。PI将研究这些系统的老化特性，调查它们对扰动的反应，并探索记忆和返老还童效应的存在。这项耦合振荡器和相关系统的研究，具有已知的生物学应用，将为探索物理和生物衰老之间可能的关系提供机会。由于自然界中非平衡过程的普遍存在，本研究项目的影响可能超出凝聚态物理的边界。更好地理解系统中的瞬态和稳态特性，可以使用统计物理的大工具箱进行深入研究，这将有助于发展描述远离平衡的系统的更一般的理论。该项目旨在使本科生和研究生都能以实质性和有意义的方式学习和贡献。这种通过研究方法进行的培训允许学生参与各个层次的前沿研究项目。