Convective heat conduction and diffusion in one-dimensional hydrodynamics

The impurity concentration in localized structures is described on the basis of analytic solutions of model equations for convective diffusion in the one-dimensional hydrodynamic approximation without pressure. The simplicity of the derivation of the analytic results depends on the ratio of the kinetic coefficients of the liquid (the Prandtl numbers). For the same kinetic coefficients, any time-dependent problem can be reduced to problems for the conventional heat conduction equation. For integer Prandtl numbers the problem of time-dependent convective diffusion in the flow field of a uniformly moving shock wave likewise reduces to problems for the heat conduction equation. Relations are established between problems whose Prandtl numbers differ by an integer. Various representations of the Green’s functions for the equations of convective diffusion are analyzed. For integer Prandtl numbers they can be expressed in terms of error functions. The asymptotic character of the solutions depends strongly on the satisfaction of global conservation laws. For global conservation of the impurity mass, coalescence of shock waves corresponds to merging of impurity solitons, i.e., clustering. Zh. éksp. Teor. Fiz. 116, 1616–1629 (November 1999)     

Anomalous heat conduction in one-dimensional momentum-conserving systems

We show that for one-dimensional fluids the thermal conductivity generically diverges with system size L as L(1/3), as a result of momentum conservation. Our results are consistent with the largest-scale numerical studies of two-component hard-particle systems. We suggest explanations for the apparent disagreement with studies on Fermi-Pasta-Ulam chains.     

Anomalous heat conduction and anomalous diffusion in one-dimensional systems

We establish a connection between anomalous heat conduction and anomalous diffusion in one-dimensional systems. It is shown that if the mean square of the displacement of the particle is =2Dt(alpha)(01) implies anomalous heat conduction with a divergent thermal conductivity (beta>0). More interestingly, subdiffusion (alpha<1) implies anomalous heat conduction with a convergent thermal conductivity (beta<0), and, consequently, the system is a thermal insulator in the thermodynamic limit. Existing numerical data support our results.     

Anomalous energy diffusion and heat conduction in one-dimensional system

We propose a new concept, the centre of energy, to study energy diffusion and heat conduction in one-dimensional hard-point model. For diatom model, we find an anomalous energy diffusion as $\langle x^2 \rangle\sim t^\beta$ with $\beta=1.33$, which is independent of initial condition and mass rate. The present model can be viewed as the model composed by independent quasi-particles, the centre of energy. In this way, heat current can be calculated. Based on theory of dynamic billiard, the divergent exponent of heat conductivity is estimated to be $\alpha=0.33$, which is confirmed by a simple numerical calculation.     

Current progress on heat conduction in one-dimensional gas channels

We give a brief review of the past development of model studies on one-dimensional heat conduction. Particularly, we describe recent achievements on the study of heat conduction in one-dimensional gas models including the hard-point gas model and billiard gas channel. For a one-dimensional gas of elastically colliding particles of unequal masses, heat conduction is anomalous due to momentum conservation, and the divergence exponent of heat conductivity is estimated as α≈0.33 in k ∼ L ^α . Moreover, in billiard gas models, it is found that exponent instability is not necessary for normal heat conduction. The connection between heat conductivity and diffusion is investigated. Some new progress is reported. A recently proposed model with a quantized degree of freedom to study the heat transport in quasi-one dimensional systems is illustrated in which three distinct temperature regimes of heat conductivity are manifested. The establishment of local thermal equilibrium (LTE) in homogeneous and heterogeneous systems is also discussed. Finally, we give a summary with an outlook for further study about the problem of heat conduction.     

Simple one-dimensional model of heat conduction which obeys Fourier's law.

We present the computer simulation results of a chain of hard-point particles with alternating masses interacting on its extremes with two thermal baths at different temperatures. We found that the system obeys Fourier's law at the thermodynamic limit. This result is against the actual belief that one-dimensional systems with momentum conservative dynamics and nonzero pressure have infinite thermal conductivity. It seems that thermal resistivity occurs in our system due to a cooperative behavior in which light particles tend to absorb much more energy than the heavier ones.     

Theory of a quasi-one-dimensional band-conductor

Following the very recent experiments on the Pt-complex based one-dimensional (1-d) conductors we present a microscopic theory of a 1-d band conductor which explicitly shows how the giant Kohn anomaly in a higher-temperature metallic state can be the precursor of a second-order phase transition to a lower-temperature insulating phase, the electronic energy gap of which is of the BCS type.     

Thermal conduction of one-dimensional carbon nanomaterials and nanoarchitectures

This review summarizes the current studies of the thermal transport properties of one-dimensional(1D) carbon nanomaterials and nanoarchitectures. Considering different hybridization states of carbon, emphases are laid on a variety of 1D carbon nanomaterials, such as diamond nanothreads, penta-graphene nanotubes, supernanotubes, and carbyne. Based on experimental measurements and simulation/calculation results, we discuss the dependence of the thermal conductivity of these 1D carbon nanomaterials on a wide range of factors, including the size effect, temperature influence, strain effect, and others. This review provides an overall understanding of the thermal transport properties of 1D carbon nanomaterials and nanoarchitectures, which paves the way for effective thermal management at nanoscale.     

阻尼作用下一维体系热传导性质的研究

利用分子动力学方法，研究了阻尼对一维体系热传导性质的影响.研究结果表明，当体系的可积性因阻尼的引入而被破坏时，在一维谐振子晶格体系中也能够形成线性的温度分布.弱阻尼对非可积体系的温度分布和热导率的影响是一种微扰，而对于可积体系是一种性态的改变.在强阻尼条件下，由于体系能量的过度耗散，体系中呈现出凹形的温度分布和收敛的热导率. 关键词： 非线性动力学 一维体系 能量传输 阻尼     

Transition from a one-dimensional to a quasi-one-dimensional state in interacting quantum wires

Upon increasing the electron density in a quantum wire, the one-dimensional electron system undergoes a transition to a quasi-one-dimensional state. In the absence of interactions between electrons, this corresponds to filling up the second subband of transverse quantization, and there are two gapless excitation modes above the transition. On the other hand, strongly interacting one-dimensional electrons form a Wigner crystal, and the transition corresponds to it splitting into two chains (zigzag crystal). We show that the soft mode driving the transition to the zigzag state is gapped, and only one gapless mode exists above the transition. Furthermore, we establish that in the vicinity of the transition already arbitrarily weak interactions open a gap in the second mode. We then argue that only one gapless mode exists near the transition at any interaction strength.     

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.     

Effect of impurities on the heat capacity of quasi-one-dimensional conductors

The low-temperature heat capacity of a quasi-one-dimensional conductor in the Luttinger liquid state is studied for conductors with a charge density wave and without it. It is shown that pinning of the Luttinger liquid leads to localization of spins and a strong effect of the magnetic field on the thermodynamics of samples resembling the effect observed in recent experiments. We believe that this indicates the possibility of the formation of a Luttinger liquid in quasi-one-dimensional crystals.

     

A model of heat conduction

We construct a model of a chain of atoms coupled at its ends to two reservoirs at different temperatures. In a weak coupling limit the atoms obey a stochastic evolution law and have an equilibrium state with a uniform temperature gradient along the chain.     

Coupling heat conduction and radiative transfer

A method to compute combined heat conduction and radiative transfer in a semitransparent medium is proposed. The heat equation is solved by an implicit finite-difference scheme and the radiation is simulated using a ray-tracing method. Stability and convergence for the coupling of both methods is shown. The crucial point for ray-tracing as well as for discrete-ordinate methods is the selection of the transfer directions and their associated weights. Using a model problem different direction sets proposed in the literature are compared with respect to their accuracy and the computational effort.