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

研究者研究了大型空间扩展系统的非平衡统计物理方面，特别是非线性色散波湍流。他的目标是超越传统的弱湍流状态，包括在共振波的相互作用中由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。波浪湍流的非平衡统计物理从两个新的角度进行了研究：(1)涨落定理：这些新定理最近引起了许多物理系统的活跃。在这里，研究者考虑涨落定理是否适用于非平衡波湍流，并研究了与非平衡波湍流相关的问题，例如(i)涨落定理在波湍流中的普遍性，（ii）与大偏差理论的关系，（iii）有效温度的动力学后果，以及（iv）涨落定理对波湍流开始时的相位混合和脱相过程的含义。(2)最大熵原理：以前，波浪湍流已被检查使用该原理的平衡状态。在这里，研究者的目的是(i)包括最大熵原理对波浪湍流通量动力学的影响，当应用于弱非线性状态时，其中经常出现弱湍流，以及（ii）进一步检查最大熵原理对远离平衡的波浪湍流的适用性。该项目需要协同应用来自统计物理、随机过程、动力系统、计算科学和现代应用数学中的渐近分析的理论概念和技术。这些主题在理论上是重要的，为波浪湍流从接近平衡到远离平衡的动力学波动提供更完整的描述。这些研究结果可以为非线性色散波湍流提供新的数学公式。研究人员采用新的理论方法来研究非线性色散波湍流，这是最具挑战性的理论问题之一。这项工作扩大了非平衡统计物理学的波动湍流的范围，扩展了非平衡统计力学的物理原理对波动湍流的适用性，例如，在非线性光学、声波、等离子体、超流氦和玻色-爱因斯坦凝聚、海洋表面的毛细管波和重力波、海洋内波等领域。从这项工作中获得的理论见解可能会揭示湍流引起的复杂性，例如在大气和海洋动力学中，或者在湍流环境中化学物质的运输中。

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.