發(fā)布時(shí)間：2018-06-13 06:25

  本文選題：FK晶格 + 熱傳導(dǎo)��； 參考：《昆明理工大學(xué)》2016年博士論文

【摘要】：能源節(jié)約與利用一直是人們關(guān)注的一個(gè)焦點(diǎn)問題,如何收集浪費(fèi)的熱能逐漸成為一個(gè)新的研究熱點(diǎn)。相比于簡諧晶格,非線性Frenkel-Kontorova (FK)晶格由于具有非線性周期作用勢,使得它在噪聲的作用下表現(xiàn)出許多與簡諧晶格不同的隨機(jī)動(dòng)力學(xué)行為。非線性晶格作為熱傳導(dǎo)的重要媒質(zhì),它處于非平衡態(tài)的隨機(jī)動(dòng)力學(xué)行為是熱能控制與利用的理論基礎(chǔ)。本課題使用理論分析與數(shù)值計(jì)算相結(jié)合的方法,研究了FK晶格系統(tǒng)在熱傳導(dǎo)過程中出現(xiàn)的雙向負(fù)微分熱阻、隨機(jī)共振和熱流反轉(zhuǎn)等反常傳輸行為,并使用隨機(jī)動(dòng)力學(xué)和晶格動(dòng)力學(xué)理論解釋了這些特征動(dòng)力學(xué)行為的發(fā)生條件和潛在物理機(jī)制。本課題的研究不僅為非線性晶格隨機(jī)動(dòng)力學(xué)提供了理論基礎(chǔ),還對熱能的控制和利用以及熱器件研制提供了非常好的參考,具有重要的實(shí)際意義。本文工作主要由以下幾部分組成：1.研究了耦合位移對FK晶格熱流傳輸?shù)挠绊�。研究結(jié)果表明：當(dāng)系統(tǒng)在對稱情況下,耦合位移可以增大系統(tǒng)熱流、合適的耦合位移取值能夠使熱流達(dá)到最大；當(dāng)系統(tǒng)處于非對稱情況時(shí),耦合位移可以增強(qiáng)負(fù)微分熱阻效應(yīng)、對熱整流起著開關(guān)的作用。2.研究了FK晶格熱傳導(dǎo)中所出現(xiàn)的雙向負(fù)微分熱阻現(xiàn)象,并對其物理機(jī)制進(jìn)行了解釋和說明。研究結(jié)果表明：當(dāng)系統(tǒng)在對稱情況下,合適的周期作用勢振幅取值將會使FK晶格在熱流傳輸過程中出現(xiàn)雙向負(fù)微分熱阻現(xiàn)象；若系統(tǒng)處于非對稱情況,此時(shí)調(diào)節(jié)系統(tǒng)一端的周期作用勢振幅取值,雙向負(fù)微分熱阻像便會逐漸變?yōu)閱蜗蜇?fù)微分熱阻現(xiàn)象；除此之外,所出現(xiàn)的雙向負(fù)微分熱阻現(xiàn)象也與參數(shù)晶格周期的取值有關(guān),隨著晶格周期取值的增大,雙向負(fù)微分熱阻現(xiàn)象會逐漸減弱,直到消失。同時(shí),通過利用隨機(jī)動(dòng)力學(xué)中的定態(tài)幾率分布函數(shù),對負(fù)微分熱阻現(xiàn)象的物理機(jī)制進(jìn)行了揭示。3.對高斯色噪聲如何影響FK晶格的熱流傳輸進(jìn)行了研究。研究結(jié)果表明：當(dāng)系統(tǒng)在對稱情況下時(shí),系統(tǒng)的熱流和熱傳導(dǎo)率都會隨著色噪聲自關(guān)聯(lián)率的增大而增大；當(dāng)系統(tǒng)在非對稱情況下,FK晶格在熱傳導(dǎo)過程中的負(fù)微分熱阻現(xiàn)象只有在特定自關(guān)聯(lián)率取值的情況下才會出現(xiàn)；若對系統(tǒng)左右兩部分取不同的晶格周期,當(dāng)色噪聲的自關(guān)聯(lián)率取值較小時(shí),系統(tǒng)在熱傳導(dǎo)過程中也會出現(xiàn)負(fù)微分熱阻現(xiàn)象,而此時(shí)在高斯白噪聲驅(qū)動(dòng)下系統(tǒng)則不會出現(xiàn)負(fù)微分熱阻現(xiàn)象；最后對色噪聲作用下FK晶格在熱傳導(dǎo)過程中出現(xiàn)的雙向負(fù)微分熱阻現(xiàn)象進(jìn)行了研究,發(fā)現(xiàn)晶格周期和色噪聲自關(guān)聯(lián)率的取值是決定其能否出現(xiàn)雙向負(fù)微分熱阻現(xiàn)象的兩個(gè)重要因素。4.結(jié)合隨機(jī)動(dòng)力學(xué)中隨機(jī)共振的基本理論,當(dāng)系統(tǒng)在沒有溫差的情況下,研究了FK晶格在熱傳導(dǎo)過程中所出現(xiàn)的隨機(jī)共振和熱流反轉(zhuǎn)現(xiàn)象。數(shù)值模擬結(jié)果表明：在周期作用力和噪聲的共同作用下,系統(tǒng)在熱傳導(dǎo)過程中會出現(xiàn)隨機(jī)共振現(xiàn)象,而共振頻率的大小主要由噪聲的強(qiáng)度所決定；當(dāng)系統(tǒng)的晶格周期取值較小時(shí),通過調(diào)節(jié)周期作用力驅(qū)動(dòng)頻率的大小,系統(tǒng)在熱傳導(dǎo)過程中會同時(shí)出現(xiàn)隨機(jī)共振和熱流反轉(zhuǎn)現(xiàn)象,而出現(xiàn)隨機(jī)共振和反轉(zhuǎn)熱流的峰值大小主要與噪聲強(qiáng)度、晶格周期、周期作用勢的振幅值等動(dòng)力學(xué)參數(shù)有關(guān)。
[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.
【學(xué)位授予單位】：昆明理工大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：TK124

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本文編號：2013053