Research On Nonlinear Lattice Anomalous Heat Conduction

The collection and utilization of heat has long been a hot issue in physics research,and especially the heat conduction at the molecular level has received much attention from scholars.The stochastic kinetic behavior of nonlinear lattices in nonequilibrium states is an important theoretical basis for the study.In this thesis,the anomalous transport behavior of the FK(Frenkel-Kontorova)lattice model and the FK-Φ~4 coupled lattice model in heat conduction is investigated using a combination of theoretical analysis and numerical simulations to elucidate the conditions for the anomalous heat conduction phenomenon and its intrinsic physical mechanism based on the stochastic kinetic theory.In the thesis,the heat transfer phenomena of the FK-FK(Frenkel-Kontorova)nonlinear lattice system are first investigated,and the results show that:1.the direction of the heat flux reverses as the driving frequency increases.2.there exists a value of the driving frequency that makes the heat flux reach a maximum when the temperature of one of the ends is adjusted periodically.3.the kinetic parameters of the model,such as the lattice period,coupling coefficient,field potential,etc.control the thermal phenomena,which indicates that the kinetic parameters are crucial for the development of thermal rectifier devices.Next,the thermal rectification phenomena appearing in the FK-Φ~4 coupled lattice model system are investigated.The left part of the model is the FK lattice chain,and the right part of the model is theΦ~4 lattice chain.The results show that:1.a significant thermal rectification effect is observed by applying a periodic force to the first atom at the left end;2.the thermal rectification effect is maximized by selecting appropriate parameter values;3.a single conduction of the thermal flux is achieved by applying a periodic force to the last atom at the right end.The numerical simulation results show that:under the joint action of the periodic force and noise,the system will appear in the heat conduction process,such as random resonance,heat flux reversal and thermal rectification and other anomalous heat conduction phenomena,while the peak size of the reversal heat flux and the effect of thermal rectification are mainly related to the lattice period,the amplitude value of the periodic potential,the coupling coefficient and other kinetic parameters.The research results will lay the theoretical foundation for the study of new types of nonlinear lattice systems,and will also provide the theoretical basis for the development and application of new types of thermoelectric power generation devices and rectification elements,and thus have practical value.