Anomalous Transport In Brownian Thermal Controller

Utilizing thermal energy has been a challenge for existence and continuable de-velopment of mankind.Up to now,how to collect wasted these thermal energy is still a research hot spot.With the development of nanotechnology,the technology of thermal controller is more and more mature,and its thermal controller plays an important role in collecting heat energy.In this thesis,the research background,re-search status,research significance and related theoretical knowledge of anomalous transport in Brownian thermal controller are described.This thesis expounds the background,current situation and significance of the research on abnormal trans-port in Brownian thermal controller.Through theoretical analysis and numerical simulation,the abnormal transport of the Brownian thermal controller under sym-metrical and asymmetric conditions is studied.The results of this discussion shall be as follows:1.In this thesis,under the description of Langevin equation,a simulation method between two correlated colored noises is proposed,and the correlation functions of two colored noises with different autocorrelation times are derived theoretically.Firstly,starting from the two-dimensional Markov Langevin equation,it is proved that the two-dimensional Markov Langevin equation can replace the one-dimensional stochastic system with colored noise.Since the correlation functions of two white noises with different correlation times have been widely used,the correlation func-tions of two colored noises with different correlation times need to be further studied.With the help of two white noise correlation functions,we discuss what kind of ex-pression the correlation function of two colored noises with different correlation time should satisfy.In the theoretical derivation,we find two correlation functions of colored noise with different correlation time.The correlation function between two colored noises with different correlation time is verified by numerical simulation.2.We have investigated the thermal transports of the Brownian thermal con-trol device(BTCD).Through calculating numerically its thermal current,it is found that there exist three types of abnormal transport phenomena in the system:ther-mal rectification,unidirectional negative differential thermal resistance(NDTR)and bidirectional NDTR.These are caused completely by the spatially periodic forces of the BTCD.As amplitudes and frequencies of the spatial forces of the system take smaller values,the thermal current is directly proportional to the normalized temperature difference,and the system exhibits a normal transport.Their further increments can enhance nonlinearity of the BTCD,which gives rise to the abnor-mal transport of the system.If symmetry of the BTCD is broken,a unidirectional NDTR effect appears;if not,a bidirectional NDTR effect does.For the greater spatial amplitudes,the thermal current of the system can be hampered or cut of-f effectively.Thus,adjusting the amplitudes and frequencies of the spatial forces of the BTCD can make it be a thermal rectifier or a thermal on–off.Of course,the coupling constant and the averaged environmental reference temperature also influence on them to some degree.These findings have an important significance for understanding operating mechanisms through which some nano-scale machines and organisms usually work under environments of constant temperatures.3.The influence of inertial mass on Brownian thermal controller is studied in the case of the underdamped.The results indicate that:There are three abnor-mal transport phenomena in the system:thermal rectification,current reversal and NDTR effect.When the inertial mass is smaller,the thermal current in Brownian thermal controller is almost zero.With the increase of inertial mass,the thermal current appears slowly in the system,the thermal current to the negative direction is greatly hampered to a large degree,yet the thermal current to positive direction can be passed smoothly through the Brownian thermal controller.This is a typi-cal thermal rectification phenomenon.In this case,adjusting the inertial mass can switch the thermal control current.If the Brownian thermal controller system is symmetric,there are two phenomena:current reversal and NDTR.When the iner-tial mass m_i(i=1,2)?1,the current reversal phenomenon appears in the system,and the inertial mass regulation can effectively control the operation of Brownian heat controller;When the inertial mass m_i(i=1,2)>1,the NDTR effect appears in the system,This is due to the symmetry breaking caused by the inertial mass in the system.If the Brownian thermal controller system is asymmetric,the NDTR will also appear in the system.Therefore,adjusting the inertial mass of Brownian thermal controller system can play the role of thermal rectifier or thermal switch,and also provide some theoretical basis for the design of thermal controller.