兰州大学机构库 >物理科学与技术学院
一维微观粒子模型热传导及相关问题的研究
Alternative TitleHeat conduction and related problem of one-dimensional particle model
李海彬
Thesis Advisor汪映海
2002-05-12
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name博士
Keyword热传导 傅里叶定律
Abstract非平衡态向平衡态趋近的过程是一不可逆过程。热传导作为一种输运过程,体现了这种宏观不可逆特性。傅里叶定律(Fourier)是决定热传导的宏观规律。从微观的、可逆的牛顿动力学的角度讨论热传导问题成为一个引起广泛注意的课题。目前的研究重点集中在一维微观模型的热传导问题:具有什么样的动力特征的哈密顿系统具有符合于傅里叶定律的热传导。本文的研究也是基于这样的前提。我们发现在一维离散的 模型的热传导性质是依赖于温度的。在高温区域呈现出的正常热传导归因于伫立呼吸子(standing breather)的激发,而移动呼吸子(mobile breather)和声子(phonon)则对应于发散的和类似简谐振子模型的热传导行为。双势阱作用势存在的一维模型中存在有序和无序结构。不同的结构会导致不同的热传导行为。无序结构不会导致正常的热传导,而是发散的热传导行为。对于一维双原子气体模型的研究表明,热传导系数是发散的, ,这证明了文献[P.L. Garrido et.al, Phy. Rev. Lett. 86,5486 (2001)]中得到的结果是不正确的。最后,对一维 模型推广得到多链 模型。准二维结构可以由新定义的hull function 来描述,也显示了解析破缺相变。Depinning force 和应用于摩擦的研究显示了体积、结构因素对静摩擦力的影响。
Other AbstractThe relaxing process of nonequilibrium state into equilibrium state is irreversible in macroscopic scale. The heat conduction is one of the typical irreversible process which is ruled by Fourier law. To understand the microscopic origin of macroscopic heat conduction law in term of determined reversible Newton dynamic has been a challenging problem in nonlinear and statistical physics. The study of one-dimensional system focus on the problem that what Hamilton system can obey the Fourier law and what can lead to diffusive behavior of energy. In this thesis, we find that in one-dimensional discrete model, the heat conduction is dependent on the temperature. Normal heat conduction, divergent heat conduction and the heat conduction alike harmonic chain occur in different temperature region due to the different kind of excitation(standing breather, mobile breather and phonon). Order、disorder structure exist in one-dimensional lattice with double-well interaction potential. Heat conduction in disorder structure is against Fourier law with heat conductivity divergent like . The heat conduction of this model experiences the transitions accompanying with the order-disorder transition when temperature increases. The studies of one-dimensional diatomic gas model, including the calculation of heat conductivity by Fourier law and by Green-Kubo formula, show that the heat conduction is not normal, which is opposite to the result in ref [P.L. Garrido et.al, Phy. Rev. Lett. 86,5486 (2001)]. At last, we extend the Frenkel-Kontorova into multi-chain F-K model. The ground state of multi-chain F-K model shows the quasi-two-dimensional structure describing by the new defined hull function which also presents the analyticity breaking transition. The study of depinning force and its application in friction show the structure effect on the static friction.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/229105
Collection物理科学与技术学院
Recommended Citation
GB/T 7714
李海彬. 一维微观粒子模型热传导及相关问题的研究[D]. 兰州. 兰州大学,2002.
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