The establishment of the foundation of molecular nonlinear acoustics and the resolution of mass, momentum and energy transports in microscales

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It is important to investigate the mass, momentum, and energy transports for the understanding of nonlinear and nonequilibrium phenomena in fluid mechanics. To establish the foundation of the theory that addresses the abovementioned topics, i.e., molecular nonlinear acoustics, we have carried out several theoretical and numerical studies : (1) Asymptotic analysis of nonlinear resonant gas oscillation based on the Boltzmann equation. (2) Molecular dynamics study of equilibrium and nonequilibrium states of nano-droplet surrounded by its vapor. (3) Analysis of the effect of evaporation/condensation on the sound reflecting and transmitting a vapor-liquid interface.