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

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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.