Frenkel-Kontorova晶格热传导中的随机动力学行为

发布时间：2018-06-13 06:25

本文选题：FK晶格 + 热传导　；参考：《昆明理工大学》2016年博士论文

【摘要】：能源节约与利用一直是人们关注的一个焦点问题,如何收集浪费的热能逐渐成为一个新的研究热点。相比于简谐晶格,非线性Frenkel-Kontorova (FK)晶格由于具有非线性周期作用势,使得它在噪声的作用下表现出许多与简谐晶格不同的随机动力学行为。非线性晶格作为热传导的重要媒质,它处于非平衡态的随机动力学行为是热能控制与利用的理论基础。本课题使用理论分析与数值计算相结合的方法,研究了FK晶格系统在热传导过程中出现的双向负微分热阻、随机共振和热流反转等反常传输行为,并使用随机动力学和晶格动力学理论解释了这些特征动力学行为的发生条件和潜在物理机制。本课题的研究不仅为非线性晶格随机动力学提供了理论基础,还对热能的控制和利用以及热器件研制提供了非常好的参考,具有重要的实际意义。本文工作主要由以下几部分组成：1.研究了耦合位移对FK晶格热流传输的影响。研究结果表明：当系统在对称情况下,耦合位移可以增大系统热流、合适的耦合位移取值能够使热流达到最大；当系统处于非对称情况时,耦合位移可以增强负微分热阻效应、对热整流起着开关的作用。2.研究了FK晶格热传导中所出现的双向负微分热阻现象,并对其物理机制进行了解释和说明。研究结果表明：当系统在对称情况下,合适的周期作用势振幅取值将会使FK晶格在热流传输过程中出现双向负微分热阻现象；若系统处于非对称情况,此时调节系统一端的周期作用势振幅取值,双向负微分热阻像便会逐渐变为单向负微分热阻现象；除此之外,所出现的双向负微分热阻现象也与参数晶格周期的取值有关,随着晶格周期取值的增大,双向负微分热阻现象会逐渐减弱,直到消失。同时,通过利用随机动力学中的定态几率分布函数,对负微分热阻现象的物理机制进行了揭示。3.对高斯色噪声如何影响FK晶格的热流传输进行了研究。研究结果表明：当系统在对称情况下时,系统的热流和热传导率都会随着色噪声自关联率的增大而增大；当系统在非对称情况下,FK晶格在热传导过程中的负微分热阻现象只有在特定自关联率取值的情况下才会出现；若对系统左右两部分取不同的晶格周期,当色噪声的自关联率取值较小时,系统在热传导过程中也会出现负微分热阻现象,而此时在高斯白噪声驱动下系统则不会出现负微分热阻现象；最后对色噪声作用下FK晶格在热传导过程中出现的双向负微分热阻现象进行了研究,发现晶格周期和色噪声自关联率的取值是决定其能否出现双向负微分热阻现象的两个重要因素。4.结合随机动力学中随机共振的基本理论,当系统在没有温差的情况下,研究了FK晶格在热传导过程中所出现的随机共振和热流反转现象。数值模拟结果表明：在周期作用力和噪声的共同作用下,系统在热传导过程中会出现随机共振现象,而共振频率的大小主要由噪声的强度所决定；当系统的晶格周期取值较小时,通过调节周期作用力驱动频率的大小,系统在热传导过程中会同时出现随机共振和热流反转现象,而出现随机共振和反转热流的峰值大小主要与噪声强度、晶格周期、周期作用势的振幅值等动力学参数有关。
[Abstract]:Energy conservation and utilization have always been a focus of attention. How to collect waste heat energy has gradually become a new research focus. Compared to a simple harmonic lattice, the nonlinear Frenkel-Kontorova (FK) lattice, because of its nonlinear periodic action potential, makes it different from the simple harmonic lattice under the effect of noise. The nonlinear lattice is an important medium for heat conduction, and the stochastic dynamic behavior in the nonequilibrium state is the theoretical basis for the control and utilization of heat energy. This subject uses the method of theoretical analysis and numerical calculation to study the bidirectional negative differential thermal resistance, random resonance, and resonance in the heat conduction of the FK lattice system. The conditions and potential physical mechanisms of these characteristics are explained by the theory of random dynamics and lattice dynamics. The study not only provides a theoretical basis for the nonlinear lattice stochastic dynamics, but also provides a non - thermal energy control and utilization as well as the development of thermal devices. The work of this paper is of great practical significance. The work of this paper is mainly composed of the following parts: 1. the effect of coupling displacement on the heat flow transmission of FK lattice is studied. The results show that when the system is symmetrical, the coupling displacement can increase the heat flow of the system, and the suitable coupling displacement can make the heat flux reach the maximum; In an asymmetric case, the coupling displacement can enhance the negative differential thermal resistance effect, and the effect of the heat rectifying switch on the FK lattice heat conduction is studied by.2., and its physical mechanism is explained and explained. The amplitude values will result in a two-way negative differential thermal resistance in the FK lattice during the heat flow transmission. If the system is in an asymmetric case, the amplitude of the periodic action potential at one end of the regulation system is obtained, and the bi-directional negative differential thermal resistance will gradually become a one-way negative differential thermal resistance phenomenon; in addition, the phenomenon of bidirectional negative differential thermal resistance appears also. It is related to the value of the lattice period of the parameter. With the increase of the lattice period, the bi-directional negative differential thermal resistance will gradually weaken and disappear. At the same time, by using the stationary probability distribution function in the stochastic dynamics, the physical mechanism of the negative differential thermal resistance phenomenon is uncovering how the Gauss color noise affects the heat flow of the FK lattice. The results show that the heat flow and thermal conductivity of the system increase with the increase of the autocorrelation rate of the color noise when the system is symmetrical, and the negative differential thermal resistance of the FK lattice in the process of heat conduction will only appear when the system is unsymmetrical. If the different lattice period of the two parts of the system is taken, the system will also have negative differential thermal resistance during the heat conduction process when the value of the autocorrelation rate of the color noise is small. At this time, the system will not appear negative differential thermal resistance under the Gauss white noise drive. Finally, the lattice of FK appears in the heat conduction process under the effect of color noise. The phenomenon of bi-directional negative differential thermal resistance is studied. It is found that the value of the lattice period and the autocorrelation of color noise is the two important factor determining whether it can appear the phenomenon of bidirectional negative differential thermal resistance, the basic theory of random resonance in.4. combined with stochastic dynamics. When the system has no temperature difference, the FK lattice is studied during the heat conduction process. The results of the stochastic resonance and heat flux inversion show that the stochastic resonance phenomenon occurs during the heat conduction process under the joint action of the periodic force and the noise, and the resonance frequency is mainly determined by the intensity of the noise. At the same time, random resonance and heat flux reversal will occur simultaneously in the process of heat conduction, while the peak value of random resonance and reverse heat flow is mainly related to the dynamic parameters such as the noise intensity, the lattice period and the amplitude of the periodic action potential.
【学位授予单位】：昆明理工大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TK124

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