Near-and-Far-from-Equilibrium Statistical Physics of Nonlinear Dispersive Waves

非线性色散波的近平衡和远平衡统计物理

• 批准号: 0507901
• 负责人: David Cai
• 金额: --
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-08-15 至 2009-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0507901&HistoricalAwards=false
• 关键词: Near; Far; Equilibrium; Statistical; Physics

The investigator studies the non-equilibrium statisticalphysics aspects of large spatially extended systems, inparticular, nonlinear dispersive wave turbulence. He aims to gobeyond the traditional weak-turbulence regime to include thedynamics of turbulence of coherent excitations induced by strongnonlinearity, including intermittent wave collapses, in theinteraction of resonant waves. The non-equilibrium statisticalphysics of wave turbulence is studied from two new perspectives: (1) Fluctuation Theorems: These new theorems have provoked muchrecent activity for many physical systems. Here the investigatorconsiders whether Fluctuation Theorems hold for non-equilibriumwave turbulence and studies related far-from-equilibrium issues,such as (i) the universality of Fluctuation Theorems in waveturbulence, (ii) the relation to large-deviation theory, (iii) thedynamical consequences of effective temperatures, and (iv) theimplications of Fluctuation Theorems for phase-mixing anddephasing processes at the onset of wave turbulence. (2) The Maximum-Entropy Principle: Previously, wave turbulencehas been examined using this principle for equilibrium statesonly. Here the investigator aims (i) to include the consequencesof the maximum-entropy principle for wave turbulence fluxdynamics, when applied to the weakly nonlinear regime, in whichthe weak-turbulence often arises, and (ii) to further examine theapplicability of the maximum-entropy principle to wave turbulencefar from equilibrium. The project requires synergisticapplications of theoretical concepts and techniques that arederived from statistical physics, stochastic processes, dynamicalsystems, computational science, and asymptotic analysis in modernapplied mathematics. The topics are theoretically important forproviding a more complete description of fluctuations in thedynamics of wave turbulence from near-equilibrium tofar-from-equilibrium. The results derived from theseinvestigations could provide new mathematical formulations ofnonlinear dispersive wave turbulence. The investigator uses new theoretical approaches to studynonlinear dispersive wave turbulence, which is one of the mostchallenging theoretical problems. This work broadens the scope ofwave turbulence from non-equilibrium statistical physics andextends the applicability of physical principles ofnon-equilibrium statistical mechanics to wave turbulence, whicharises, for example, in nonlinear optics, acoustic waves, plasmas,superfluid helium and the Bose-Einstein condensation, capillaryand gravity waves on the ocean surface, internal waves in theocean. Theoretical insights derived from this work may shed lighton turbulence-induced complexity, such as in the atmosphere andocean dynamics, or in the transport of chemicals in a turbulentenvironment.

研究员研究大型空间扩展系统的非平衡物理学方面，特别是非线性色散波湍流。 他的目标是超越传统的弱湍流制度，包括强非线性引起的相干激发的湍流动力学，包括间歇性波崩溃，在共振波的相互作用。 本文从两个新的角度研究了波动湍流的非平衡物理学：（1）涨落定理：这些新的定理在许多物理系统中引起了很大的兴趣。 本文讨论了涨落定理是否适用于非平衡波湍流，并研究了与之相关的远离平衡的问题，如（i）涨落定理在波湍流中的普适性，（ii）与大偏差理论的关系，（iii）有效温度的动力学结果，（iv）涨落定理对波湍流开始时相混合和失相过程的影响。 (2)最大熵原理：以前，波的连续性只在平衡态下使用这一原理进行了研究。 在这里，研究者的目的是（i）包括最大熵原理的波动湍流通量动力学的后果，当应用到弱非线性制度，其中弱湍流经常出现，和（ii）进一步检查的适用性的最大熵原理的波动湍流远离平衡。 该项目需要协同应用的理论概念和技术，是来自统计物理，随机过程，dynamicalsystems，计算科学，和渐近分析在现代应用数学。 这一课题对于更完整地描述波动湍流动力学从近平衡到远离平衡的波动具有重要的理论意义。 这些研究结果可为非线性色散波湍流提供新的数学模型。 非线性色散波湍流是最具挑战性的理论问题之一，研究者采用新的理论方法对其进行了研究。 这一工作拓宽了非平衡统计物理中波动湍流的研究范围，将非平衡统计力学的物理原理扩展到波动湍流中，如非线性光学、声波、等离子体、超流氦和玻色-爱因斯坦凝聚、海洋表面的毛细波和重力波、海洋内波等。 从这项工作中获得的理论见解可能会摆脱光致发光引起的复杂性，如在大气中的动力学，或在运输的化学物质在一个发光。