Long-Time Asymptotics for the Defocusing Integrable Discrete Nonlinear Schr\"odinger Equation II

We investigate the long-time asymptotics for the defocusing integrable discrete nonlinear Schr\"odinger equation. If $|n|<2t$, we have decaying oscillation of order $O(t^{-1/2})$ as was proved in our previous paper. Near $|n|=2t$, the behavior is decaying oscillation of order $O(t^{-1/3})$ and the coefficient of the leading term is expressed by the Painlev\'e II function. In $|n|>2t$, the solution decays more rapidly than any negative power of $n$

Thermal analysis of turbulent flow of a supercritical fluid

The influence of the large variation of thermodynamics and transport properties near the pseudocritical temperature on the heat transfer coefficient of supercritical fluid in turbulent flow was studied. The formation of the characteristics peak in the heat transfer coefficient vs. bulk temperature curve is described, and the necessity of the fluid element at pseudocritical temperature located in the buffer layer is discussed