Thermal transport in the long-range interactions Fermi-Pasta-Ulam model with weak interface

We investigate the thermal transport properties of a one-dimensional long-range Fermi-Pasta-Ulam (β-FPU) model with the inclusion of a weak interface. The system comprises two nonlinear long-range FPU chains connected via a linear weak interface. The weak interface is modeled using linear harmonic interactions. The equations of motion were simulated using molecular dynamics , enabling the calculation of thermal transport quantities, including heat flux J, thermal conductivity κ, and the local temperature distribution T i . Furthermore, an analysis of finite-size effects was conducted. Our analysis reveals distinct thermal transport behaviors governed by a critical value of δ, which marks a transition in the heat flux and thermal conductivity . This critical δ depends on the coupling strength of the interface k int ; for instance, δ=5.0 is observed when k int =0.1. This threshold delineates two regimes of thermal conductivity : monotonic growth for δ<δ c and stabilization for δ>δ c . Notably, for a system without an interface, thermal conductivity peaks at δ=2.0. On the other hand, we also observed a scaling behavior of the heat flux J∝k int , which is consistent with previous studies. To elucidate the underlying mechanisms of this behavior, we calculate the mean standard deviation σ of the local heat fluxes J i , which provides a consistent explanation for the observed critical phenomena in both heat flux and thermal conductivity .