Relaxation and Aging Processes out of Equilibrium

该奖项是根据《2009年美国复苏和再投资法案》(公法111-5)资助的。技术摘要该奖项支持远离均衡、缓慢发展的系统的理论研究和教育。PI的目的是推广他提出的一个理论框架，该框架适用于那些根据详细的平衡违反动力学而演化并因此松弛到非平衡稳态的系统。PI的框架基于局部尺度不变性的概念。沿着这些思路取得的进展将从根本上加强对放松和衰老的理解。结合先进的分析和数值技术，PI将探索松弛和老化过程的几个新方面，包括：1.反应扩散系统中的老化和波动。尽管可逆化学反应具有慢动力学的特点，但其老化机制尚未被详细研究。建立一个关于衰老的预测理论将是非常可取的。此外，这样的过程是非常通用的，对于任何系统参数值都会发生。因此，为了验证这一理论的预测，用真实系统进行实验应该是相对容易的。此外，对不可逆反应扩散系统中涨落的拟议研究将对真正不平衡系统的一般性质产生新的见解。生长过程中的老化。对生长过程中老化现象的研究是最近才开始的，仅涉及线性朗之万方程。为了描述超越线性近似有效性的过程，PI建议研究与非线性朗之万方程相关的老化现象，例如Kardar-Parisi-Zhang方程。一种描述老化系统的新方法。最近发现的非平衡物理问题和弦理论问题之间的映射开启了PI建议探索的一种新颖而未知的方法。这一方法，加上对PI成功的局部标度不变性理论的预期推广，为描述大类老化系统提供了令人兴奋的统一理论框架的可能性。通过研究进行培训是本提案的中心教育方面。该项目使本科生和研究生都能以一种实质性和有意义的方式做出贡献。学生将有充分的机会精通各种分析和数值技术，包括在最先进的高性能计算机上进行并行计算。非技术总结该奖项广泛支持处于远离平衡状态的多粒子系统的理论研究和教育。非平衡系统和过程无处不在，涵盖了从材料生长到呈现有趣空间模式的化学系统到维持生命的过程的广泛现象。PI的目的是通过发展一种理论方法来描述处于非平衡状态的系统如何随时间转变为非平衡状态，而不是平衡状态，从而促进我们对非平衡系统的理解。这将有助于我们理解玻璃等材料以及化学和其他系统中发生的松弛和老化过程。通过研究进行培训是本提案的核心教育方面。该项目使本科生和研究生都能以一种实质性和有意义的方式做出贡献。学生将有充分的机会精通各种分析和数值技术，包括在最先进的高性能计算机上进行并行计算。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).TECHNICAL SUMMARY This award supports theoretical research and education in systems far from equilibrium that evolve with slow dynamics. The PI aims to generalize a theoretical framework that he has proposed to systems that evolve according to a detailed balance violating dynamics and that therefore relax toward nonequilibrium steady states. The PI's framework is based on the notion of local scale invariance. Progress along these lines would enhance understanding of relaxation and aging at a fundamental level. Combining advanced analytical and numerical techniques, the PI will explore several novel aspects of relaxation and aging processes, including:1. Aging and fluctuations in reaction-diffusion systems. Even though reversible chemical reactions are known to be characterized by slow dynamics, their aging regime has not yet been studied in detail. Building a predictive theory of aging would be highly desirable. Moreover, such processes are quite generic, occurring for any value of the system parameters. Thus, it should be relatively easy to set up experiments with real systems in order to verify the predictions from this theory. In addition, the proposed study of fluctuations in irreversible reaction-diffusion systems will yield new insights into the generic properties of truly out-of-equilibrium systems.2. Aging in growth processes. The study of aging phenomena in growth processes began quite recently, and has addressed only linear Langevin equations. To describe processes beyond the validity of linear approximations, the PI proposes to investigate aging phenomena associated with nonlinear Langevin equations, as, e.g., the Kardar-Parisi-Zhang equation.3. A novel approach for the description of aging systems. A recently uncovered mapping between nonequilibrium physics problems and string theoretical problems opens a novel and uncharted approach that the PI proposes to explore. This approach, together with anticipated generalizations of the PI's successful theory of local scale invariance, offers the exciting possibility of a unifying theoretical framework for the description of wide classes of aging systems.Training through research is the central educational aspect of the present proposal. The project allows both undergraduate and graduate students can contribute in a substantial and meaningful way. The students will have ample opportunities to become proficient in various analytical and numerical techniques, including parallel computing on state-of-the-art high performance computers.NONTECHNICAL SUMMARYThis award supports theoretical research and education broadly on many-particle systems that in states far from equilibrium. Nonequilibrium systems and processes are ubiquitous and encompass a wide range of phenomena from materials growth to chemical systems that exhibit interesting spatial patterns to the processes that sustain life. The PI aims to advance our understanding of systems that are out of equilibrium by developing a theoretical approach to describe how a system in a nonequilbrium state transforms to a nonequilbrium state, as opposed to an equilibrium state, with time. This will contribute to our understanding of relaxation and aging processes that occur in materials, such as glasses, as well as chemical and other systems. Training through research is the central educational aspect of the present proposal. The project allows both undergraduate and graduate students can contribute in a substantial and meaningful way. The students will have ample opportunities to become proficient in various analytical and numerical techniques, including parallel computing on state-of-the-art high performance computers.