Currently, I’m working on the following projects.

Connections of nano-scale heat transport problems to continues SPDEs

From full molecular dynamics setup, we derive reduced models in different orders that are able to capture the statistics of CG variables, using a projection formalism. The reduced dynamics coincides with a semi-discretized SPDE, and we show that the reduced models actually converge to continues linear/nonlinear SPDEs as the spacing goes to zero.

The derivation of fluctuating energy transport models from molecular dynamics

Energy transport equations are derived directly from full molecular dynamics models as a coarse-grained description. This derivation yields a stochastic dynamics model for the spatially averaged energy. We discuss the approximation of the memory term, along with the approximation of the random force using both additive and multiplicative noises, to ensure that the correct statistics of the solution.

Various types of temperature boundary conditions and the associated boundary heat flux

For thermal systems resting in heat bathes at different temperatures, traditional approach to simulate the temperature gradient always indicates obvious temperature jumps and provides difficulties in computing thermal conductivities. In this work, we investigate the origin of the temperature boundary slip of one-dimensional chain model as well as appropriate parameter selections to minimize such boundary jumps.

Asymptotic Behavior of the Kernel Function in the Generalized Langevin Equation

We present some estimates for the memory kernel in the generalized Langevin equation, derived from the Mori-Zwanzig projection formalism. The memory kernel in the corresponding Langevin equation can be explicitly expressed in a matrix form. Our analysis focuses on the decay properties, both spatially and temporally, aiming at a power-law behavior.