Can Disorder Induce a Finite Thermal Conductivity in 1D Lattices?

We study heat conduction in one-dimensional mass-disordered harmonic and anharmonic lattices. It is found that the thermal conductivity kappa of the disordered anharmonic lattice is finite at low temperature, whereas it diverges as kappa approximately N0.43 at high temperature. Moreover, we demonstrate that a unique nonequilibrium stationary state in the disordered harmonic lattice does not exist at all.     

Size Dependent Heat Conduction in One-Dimensional Diatomic Lattices

We study the size dependency of heat conduction in one-dimensional diatomic FPU-β lattices and establish that for low dimensional material,contribution from optical phonons is found more effective to the thermal conductivity and enhance heat transport in the thermodynamic limit N →∞.For the finite size,thermal conductivity of 1D diatomic lattice is found to be lower than 1D monoatomic chain of the same size made up of the constituent particle of the diatomic chain.For the present 1D diatomic chain,obtained value of power divergent exponent of thermal conductivity0.428±0.001 and diffusion exponent 1.2723 lead to the conclusions that increase in the system size,increases the thermal conductivity and existence of anomalous energy diffusion.Existing numerical data supports our findings.     

Heat Conduction in the α−β Fermi–Pasta–Ulam Chain

Recent simulation results on heat conduction in a one-dimensional chain with an asymmetric inter-particle interaction potential and no onsite potential found non-anomalous heat transport in accordance to Fourier’s law. This is a surprising result since it was long believed that heat conduction in one-dimensional systems is in general anomalous in the sense that the thermal conductivity diverges as the system size goes to infinity. In this paper we report on detailed numerical simulations of this problem to investigate the possibility of a finite temperature phase transition in this system. Our results indicate that the unexpected results for asymmetric potentials is a result of insufficient chain length, and does not represent the asymptotic behavior.     

高温超导直接冷却的氮化铝与无氧铜接触界面热阻的实验研究

氮化铝(AlN)具有高热导性、高电绝缘性,是超导二元电流引线热截流结构中常用的材料之一。根据稳态导热法建立低温真空实验装置,实验研究了超导冷却系统热截流结构中,界面温度和接触压力对AlN块材与无氧铜(OFHC-Cu)块材间接触界面热阻的影响。在实验温度(90K-210K)和压力(0.273MPa-0.985MPa)条件下,AlN/OFHC-Cu接触界面热阻随接触压力的提高而降低,而当界面温度上升时界面热阻由于热载子热运动的强化而降低,温度较高时,接触界面热阻随压力变化的速率趋缓。低温下AlN/OFHC-Cu间的接触界面热阻是直接冷却超导系统的设计和超导系统的热稳定性方面必需解决的问题。     

Anharmonic Excitations,Time Correlations and Electric Conductivity

We study the influence of anharmonic mechanical excitations of a classical ionic lattice on its electric properties. First, to illustrate salient features, we investigate a simple model, an one‐dimensional (1D) system consisting of ten semiclassical electrons embedded in a lattice or a ring with ten ions interacting with exponentially repulsive interactions. The lattice is embedded in a thermal bath. The behavior of the velocity autocorrelation function and the dynamic structure factor of the system are analyzed. We show that in this model the nonlinear excitations lead to long lasting time correlations and, correspondingly, to an increase of the conductivity in a narrow temperature region, where the excitations are supersonic soliton‐like. In the second part we consider the quantum statistics of general ion‐electron systems with arbitrary dimension and express ‐ following linear response transport theory ‐ the quantum‐mechanical conductivity by means of equilibrium time correlation functions. Within the relaxation time approach an expression for the effective collision frequency is derived in Born approximation, which takes into account quantum effects and dynamic effects of the ion motion through the dynamic structure factor of the lattice and the quantum dynamics of the electrons. An evaluation of the influenec of solitons predicts for 1D‐lattices a conductivity increase in the temperature region where most thermal solitons are excited, similar as shown in the classical Drude‐Lorentz‐Kubo framework. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

From compact point defects to extended structures in silicon

We show that in contrast to the 1d Frenkel-Kontorova (FK) chain known to obey the Fourier law of heat conduction and several 2d models which show logarithmic dependence of conductivity on system size, a scalar 2d FK lattice with commensurate structure exhibits anomalous heat conduction, whose thermal conductivity displays a power law behavior. The dependence of thermal gradient on bulk temperature and noise correlation is critically analyzed. A dynamical contribution to conductivity when the system attains a nonequilibrium steady state of thermal conduction has been identified.     

Phonon-mediated heat dissipation in a monatomic lattice: case study on Ni

The recently introduced analytical model for the heat current autocorrelation function of a crystal with a monatomic lattice [Evteev et al., Phil. Mag. 94 (2014) p. 731 and 94 (2014) p. 3992] is employed in conjunction with the Green–Kubo formalism to investigate in detail the results of an equilibrium molecular dynamics calculations of the temperature dependence of the lattice thermal conductivity and phonon dynamics in f.c.c. Ni. Only the contribution to the lattice thermal conductivity determined by the phonon–phonon scattering processes is considered, while the contribution due to phonon–electron scattering processes is intentionally ignored. Nonetheless, during comparison of our data with experiment an estimation of the second contribution is made. Furthermore, by comparing the results obtained for f.c.c. Ni model to those for other models of elemental crystals with the f.c.c. lattice, we give an estimation of the scaling relations of the lattice thermal conductivity with other lattice properties such as the coefficient of thermal expansion and the bulk modulus. Moreover, within the framework of linear response theory and the fluctuation-dissipation theorem, we extend our analysis in this paper into the frequency domain to predict the power spectra of equilibrium fluctuations associated with the phonon-mediated heat dissipation in a monatomic lattice. The practical importance of the analytical treatment lies in the fact that it has the potential to be used in the future to efficiently decode the generic information on the lattice thermal conductivity and phonon dynamics from a power spectrum of the acoustic excitations in a monatomic crystal measured by a spectroscopic technique in the frequency range of about 1–20 THz.     

Normal heat conduction in a chain with a weak interparticle anharmonic potential

We analytically study heat conduction in a chain with an interparticle interaction V(x)= lambda[1-cos(x)] and harmonic on-site potential. We start with each site of the system connected to a Langevin heat bath, and investigate the case of small coupling for the interior sites in order to understand the behavior of the system with thermal reservoirs at the boundaries only. We study, in a perturbative analysis, the heat current in the steady state of the one-dimensional system with a weak interparticle potential. We obtain an expression for the thermal conductivity, compare the low and high temperature regimes, and show that, as we turn off the couplings with the interior heat baths, there is a "phase transition": Fourier's law holds only at high temperatures.     

Experimental and theoretical studies on high-temperature thermal properties of fibrous insulation

In the present paper, an experimental apparatus has been developed to measure heat transfer through high-alumina fibrous insulation for thermal protection system. Effective thermal conductivities of the fibrous insulation were measured over a wide range of temperature (300-973 K) and pressure (10⁻²-10⁵ Pa) using the developed apparatus. The specific heat and the transmittance spectra in the wavelength range of 2.5-25 μm were also measured. The spectral extinction coefficients and Rosseland mean extinction coefficients were obtained from transmittance data at various temperatures to investigate the radiative heat transfer in fibrous insulation. A one-dimensional finite volume numerical model combined radiation and conduction heat transfer was developed to predict the behavior of the effective thermal conductivity of the fibrous insulation at various temperatures and pressures. The two-flux approximation was used to model the radiation heat transfer through the insulation. The experimentally measured specific heat and Rosseland mean extinction coefficients were used in the numerical heat transfer model to calculate the effective thermal conductivity. The average deviation between the numerical results for different values of albedo of scattering and the experimental results was investigated. The numerical results for ω=1 and experimental data were compared. It was found that the calculated values corresponded with the experimental values within an average of 13.5 percent. Numerical results were consistent with experimental results through the environmental conditions under examination.     

Heat conduction in a one-dimensional gas of elastically colliding particles of unequal masses

We study the nonequilibrium state of heat conduction in a one-dimensional system of hard point particles of unequal masses interacting through elastic collisions. A BBGKY-type formulation is presented and some exact results are obtained from it. Extensive numerical simulations for the two-mass problem indicate that, even for arbitrarily small mass differences, a nontrivial steady state is obtained. This state exhibits local thermal equilibrium and has a temperature profile as predicted by kinetic theory. The temperature jumps typically seen in such studies are shown to be finite-size effects. The thermal conductivity appears to have a very slow divergence with system size, different from that seen in most other systems.     

Computer Simulation Study of Thermal Conduction in 1D Chains of Anharmonic Oscillators

In this work thermal conduction in one-dimensional(1D) chains of anharmonic oscillators are studied using computer simulation.The temperature profile,heat flux and thermal conductivity are investigated for chain length N = 100,200,400,800 and 1600.In the computer simulation anharmonicity is introduced due to Fermi-Pasta-Ulam-β(FPU-β) model.For substrate interaction,an onsite potential due to Frenkel-Kontorova(FK) model has been used.Numerical simulations demonstrate that temperature gradient scales behave as N-1 linearly with the relation J = 0.1765/N.For the thermal conductivity K,KN to N obey the linear relation of the type KN = 0.8805N.It is shown that thermal transport is dependent on phonon-phonon interaction as well as phonon-lattice interaction.The thermal conductivity increases linearly with increase inanharmonicity and predicts relation κ = 0.133 + 0.804β.It is also concluded that for higher value of the strength of the onsite potential system tends to a thermal insulator.     

Energy Transport in Weakly Anharmonic Chains

We investigate the energy transport in a one-dimensional lattice of oscillators with a harmonic nearest neighbor coupling and a harmonic plus quartic on-site potential. As numerically observed for particular coupling parameters before, and confirmed by our study, such chains satisfy Fourier’s law: a chain of length N coupled to thermal reservoirs at both ends has an average steady state energy current proportional to 1/N. On the theoretical level we employ the Peierls transport equation for phonons and note that beyond a mere exchange of labels it admits nondegenerate phonon collisions. These collisions are responsible for a finite heat conductivity. The predictions of kinetic theory are compared with molecular dynamics simulations. In the range of weak anharmonicity, respectively low temperatures, reasonable agreement is observed.     

Heat conduction in one-dimensional systems with hard-point interparticle interactions

Results of extensive and accurate numerical studies on heat transfer in a system of particles with unequal masses, interacting through hard-point potentials with two types of symmetry, are reported. The particles are confined in a one-dimensional box with fixed ends coupled to heat reservoirs at different temperatures. The study aims to throw light upon recent controversial results on thermal conductivity in one-dimensional systems. When the particles interact through elastic hard-point collisions (a standard asymmetric case), the system is shown to have always infinite (anomalous) thermal conductivity as follows from the Prosen-Campbell theorem.     

含有格点势的一维Fibonacci链热传导性质的研究

用传输矩阵的方法,研究了格点势(on-site势)对一维Fibonacci链的热传导性质(透射系数、Lyapunov指数及热导率κ)的影响.研究结果表明:当固定原子质量比和力作用常数比时,随着格点势的增大,低频区域的透射系数减小,对应的Lyapunov指数增大,透射谱向高频方向移动.同时,格点势越大,同样大小的体系对应的κ越小,当格点势足够大时,κ会趋近零.在热导率κ对振动频率ω²作图中,κ呈现台阶式缓慢上升的趋势,且在高频     

有限温度下一维Hubbard模型的化学势泛函理论研究

通过数值方法求解了有限温度下一维均匀Hubbard模型的热力学Bethe-ansatz方程组,得到了在给定温度和相互作用强度情况下,比热c、磁化率χ和压缩比κ随化学势μ的变化图像.基于有限温度下一维均匀Hubbard模型的精确解,利用化学势(μ)-泛函理论研究了一维谐振势下的非均匀Hubbard模型,给出了金属态和Mott绝缘态下不同温度情况时局域粒子密度n_i和局域压缩比_κi随格点的变化情况.     

The effect of temperature-dependent thermal conductivity in heat transfer simulations of frozen biomaterials

The thermal conductivity value of pure water ice is inversely proportional to the temperature and decreases about 5-fold as the temperature increases from the liquid nitrogen boiling temperature (77 K to the freezing point of pure water. The temperature dependency of the thermal conductivity is typically overlooked in bioheat transfer simulations. A closed-form solution of the one-dimensional temperature distribution in frozen water and blood is presented in this study, based on a new thermal conductivity model. Results indicate that temperatures are overestimated up to 38K, and heat fluxes through the frozen region boundaries are underestimated by a factor of 2, when the temperature dependency of the thermal conductivity is neglected.     

热动力学问题的数值计算

 对含热传导的流体动力学方程组，用有限元方法进行数值求解。采用傅里叶热传导计算热流、用热流连续条件计算单元间接触面的温度、用三角形传热法计算体单元表面的热流，考虑各向同性弹塑性流体材料模型、三项式物态方程和导热系数与状态的相关性，给出了傅里叶热传导、接触传热、热应力应变效应、以及混合物冲击压缩特性等算例。对混合物冲击温度的数值模拟表明，小颗粒混合物在冲击压缩过程中，颗粒间的温度有差别、稍有波动，并随时间趋向于一致，以至热平衡。     

Lattice bosons in a quasi-disordered environment

In this paper, we study non-interacting bosons in a quasi-disordered one-dimensional optical lattice in a harmonic potential. We consider the case of deterministic quasi-disorder produced by an Aubry–André potential. Using exact diagonalization, we investigate both the zero temperature and the finite temperature properties. We investigate the localization properties by using an entanglement measure. We find that the extreme sensitivity of the localization properties to the number of lattice sites in finite size closed chains disappear in open chains. This feature continues to be present in the presence of a harmonic confining potential. The quasi-disorder is found to strongly reduce the Bose–Einstein condensation temperature and the condensate fraction in open chains. The low temperature thermal depletion rate of the condensate fraction increases considerably with increasing quasi-disorder strength. We also find that the critical quasi-disorder strength required for localization increases with increasing strength of the harmonic potential. Further, we find that the low temperature condensate fraction undergoes a sharp drop to 0.5 in the localization transition region. The temperature dependence of the specific heat is found to be only marginally affected by the quasi-disorder.     

Phonon relaxation and heat conduction in one-dimensional Fermiben Pastaben Ulam β lattices by molecular dynamics simulations

The phonon relaxation and heat conduction in one-dimensional Fermi-Pasta-Ulam (FPU) β lattices are studied by using molecular dynamics simulations. The phonon relaxation rate, which dominates the length dependence of the FPU β lattice, is first calculated from the energy autocorrelation function for different modes at various temperatures through equilibrium molecular dynamics simulations. We find that the relaxation rate as a function of wave number k is proportional to k^1.688, which leads to a N^0.41 divergence of the thermal conductivity in the framework of Green-Kubo relation. This is also in good agreement with the data obtained by non-equilibrium molecular dynamics simulations which estimate the length dependence exponent of the thermal conductivity as 0.415. Our results confirm the N^2/5 divergence in one-dimensional FPU β lattices. The effects of the heat flux on the thermal conductivity are also studied by imposing different temperature differences on the two ends of the lattices. We find that the thermal conductivity is insensitive to the heat flux under our simulation conditions. It implies that the linear response theory is applicable towards the heat conduction in one-dimensional FPU β lattices.     

计算导热系数的新公式

在传统的一维传热模型下导热系数的计算公式误差较大.本文通过建立试样内部的三维传热模型,更为科学地考虑了侧壁散热的影响,推导出了计算导热系数的新公式.以橡胶为研究材料进行实验,证明了新公式的合理性.引入影响因子P来衡量侧壁散热对系统的影响程度,分析得到P值随着试样厚度增加而增大.