MCAIM Graduate Seminar Seminar

Wave Turbulence is a non-equilibrium statistical system of randomly interacting waves. Kinetic equations of Wave Turbulence describe the evolution of wave energy in Fourier space. In this talk, we begin by introducing the basic idea of Wave Turbulence formalism and making a summary of the work done for the alpha-Fermi-Pasta-Ulam system, and figure out that there is no rigorous proof for the kinetic equation and the resulting timescale. We then derive the kinetic equation for the six-wave Interactions in the alpha-Fermi-Pasta-Ulam system with N = 16, 32, and 64 masses, which has a slightly different model whose four-wave resonances cannot be removed by any nondivergent canonical transformations compared to the common six-wave Hamiltonian system, following the formal steps. Speaker(s): Boyang Wu (University of Michigan)