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.