The investigator studies the non-equilibrium statistical physics aspects of large spatially extended systems, in particular, nonlinear dispersive wave turbulence. He aims to go beyond the traditional weak-turbulence regime to include the dynamics of turbulence of coherent excitations induced by strong nonlinearity, including intermittent wave collapses, in the interaction of resonant waves. The non-equilibrium statistical physics of wave turbulence is studied from two new perspectives: (1) Fluctuation Theorems: These new theorems have provoked much recent activity for many physical systems. Here the investigator considers whether Fluctuation Theorems hold for non-equilibrium wave turbulence and studies related far-from-equilibrium issues, such as (i) the universality of Fluctuation Theorems in wave turbulence, (ii) the relation to large-deviation theory, (iii) the dynamical consequences of effective temperatures, and (iv) the implications of Fluctuation Theorems for phase-mixing and dephasing processes at the onset of wave turbulence. (2) The Maximum-Entropy Principle: Previously, wave turbulence has been examined using this principle for equilibrium states only. Here the investigator aims (i) to include the consequences of the maximum-entropy principle for wave turbulence flux dynamics, when applied to the weakly nonlinear regime, in which the weak-turbulence often arises, and (ii) to further examine the applicability of the maximum-entropy principle to wave turbulence far from equilibrium. The project requires synergistic applications of theoretical concepts and techniques that are derived from statistical physics, stochastic processes, dynamical systems, computational science, and asymptotic analysis in modern applied mathematics. The topics are theoretically important for providing a more complete description of fluctuations in the dynamics of wave turbulence from near-equilibrium to far-from-equilibrium. The results derived from these investigations could provide new mathematical formulations of nonlinear dispersive wave turbulence.
The investigator uses new theoretical approaches to study nonlinear dispersive wave turbulence, which is one of the most challenging theoretical problems. This work broadens the scope of wave turbulence from non-equilibrium statistical physics and extends the applicability of physical principles of non-equilibrium statistical mechanics to wave turbulence, which arises, for example, in nonlinear optics, acoustic waves, plasmas, superfluid helium and the Bose-Einstein condensation, capillary and gravity waves on the ocean surface, internal waves in the ocean. Theoretical insights derived from this work may shed light on turbulence-induced complexity, such as in the atmosphere and ocean dynamics, or in the transport of chemicals in a turbulent environment.
