Stochastic Dynamics Behaviors In Thermal Conduction Of Frenkel-Kontorova Lattice

Saving and utilization of energy have been considered a hot issue and how to exploit these thermal energy will become more and more important. In the actions of noises, nonlinear Frenkel-Kontorova(FK) lattice exhibits a lot of stochastic dynamical behaviors due to their nonlinear potentials, different from those of harmonic lattices. Because the nonlinear lattices act as promising mediums, their stochastic dynamical behaviors in the non-equilibrium state play roles of basic theories in controlling and exploiting the thermal energy. In this paper, by means of combination of theoretical analysis and numerical calculations, we will investigate the characteristics of abnormal transports such as bidirectional negative differential thermal resistance, stochastic resonance and thermal reversal phenomenon in the thermal conduction of Frenkel-Kontorova(FK) lattice driven by noises. Besides, the conditions and intrinsic physical mechanisms of which will also be explained by using theories of stochastic dynamics and lattice dynamics. The results of the paper will not only provide with basic theory for stochastic dynamics of nonlinear lattices but also be of practical significance in controlling and exploiting thermal energy and fabricating thermal devices. The paper consists of the following parts.Firstly, effect of coupling displacement on thermal current of Frenkel-Kontorova (FK) lattices in the underdamped case is investigated by means of numerical calculations. The results indicate that:(i)As the system is symmetric, the coupling displacement can boost up its thermal current, and an optimal coupling displacement can make its thermal current be maximal, (ⅱ) As the system is asymmetric, the coupling displacement cannot only enhance negative differential thermal resistance(NDTR) effect but also regulate thermal rectifier of the system as a thermal switch.Secondlv, we discuss the bidirectional NDTR phenomenon that occurs in the thermal conduction of FK lattice. The results indicate that:(ⅰ)For appropriate on-site poten-tial, as the system is symmetric, a bidirectional negative differential thermal resistance (NDTR) phenomenon will appear. (ⅱ)If the symmetry of the system is broken slowly, the bidirectional NDTR effect is gradually converted into the unidirectional NDTR effect, (ⅱ-ⅰ)Besides, the bidirectional effect also depends on the period of the FK nonlinear lattices. As the lattice period is increased, the bidirectional NDTR effect becomes weaker and weaker. For the bigger lattice period, the bidirectional and unidirectional NDTR effects will all disappear. (Ⅳ)From a stochastic dynamics point of view, by means of analy-sis of the stationary probability distribution functions(SPDF)s of the atoms at several temperature difference, physical mechanism of the NDTR is found out.Thirdly, how the colored noise affects the thermal conduction of FK lattice has been discussed in detail. The results show that:(i)As the system is symmetric, the thermal current and heat conductivity becomes bigger with the increasement of association rate. (ⅱ)As the system is asymmetric, the NDTR phenomenon only exists in some specific values of association rate. (ⅲ)When the lattice has the same on-site potential and dif-ferent lattice period, NDTR phenomenon can also occur when with colored noise bath and it can not occur in the same conditions with white noise bath. (Ⅳ)The values of lattice period and association rate of the colored noise are two important factors which determines whether the bidirectional NDTR phenomenon of the thermal conduction of FK lattice.Finally, combining with the basic theory of stochastic dynamics, we observe the occurrence of stochastic resonance and thermal reversal phenomenon without thermal bias. The results indicate that:(ⅰ)There exists a certain value of the driving frequency at which the heat flux takes its maximum, indicating the occurrence of thermal stochastic resonance. Thermal stochastic resonance occurs when the driving frequency cooperates with the intensity of the noise, (ⅱ) When the lattice period is small, the heat flow can become directed and even can be reversed by suitably selecting the driving freauency. (ⅲ) The peak values of stochastic resonance and the reversed heat flux are determined by some dynamical parameters of the model, such as lattice period, the intensity of the noise, the amplitude value of on-site potential and so on.