Transport in two dimensions. I the self-diffusion coefficient

The Mori formalism is used to study generalized transport coefficients in two dimensions. All finite multilinear products of the single particle density and momentum density comprise the set of the variables in the calculation of the self-diffusion coefficient. A self-consistent equation, which is a non-linear integral equation, is obtained for the leading asymptotic behavior of the generalized self-diffusion coefficient. An asymptotic solution is presented which for small wavevector (k) and frequency (s) behaves like $\text{In}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(s + k}{}^2\text{D)}{}^{\mathrm{?1}}$, where D has the dimensions of a diffusion coefficient. The mean square and mean fourth displacements of a tagged particle are also calculated. The long time behavior of the momentum correlation function exhibits a tail of the form $\text{[t}\text{In}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(t)]}{}^{\mathrm{?1}}$ whose coefficient is dependent of the intermolecular potential.     

Transport in two dimensions. III self-diffusion coefficient at low densities

The low density form of the generalized frequency (s) and wavevector (k) dependent self-diffusion coefficient D(k, s) is calculated, from which the low density forms of related quantities, e.g. the velocity autocorrelation function, are derived. Agreement is obtained with the low density kinetic theory results. A closed form expression for D(k, s) valid over a wide range of densities and times is also given, showing consistency between the asymptotic long time results, obtained previously, and the low density kinetic theory results.     

Electric conductivity of inhomogeneous two-component media in two dimensions

The electric conductivity is calculated for regular inhomogeneous two-component isotropic medium in which droplets of one phase with conductivity σ₂ are embedded in another, with conductivity σ₁. An expression is formulated that can be used in many different situations and is of particular relevance in the case where the relative proportion of the components is temperature-dependent and varies over a wide range. Behavior of the effective conductivity depends on the spatial arrangements and the shape of the inclusions.     

温度传感器在测定不良导体导热系数实验中的应用

将单片计算机与温度传感器结合用于导热系数测定仪中测量温度,改进后的导热系数测定仪结构紧凑,操作简单、读数方便.     

Exact diffusion coefficient of self-gravitating Brownian particles in two dimensions

We derive the exact expression of the diffusion coefficient of a self-gravitating Brownian gas in two dimensions. Our formula generalizes the usual Einstein relation for a free Brownian motion to the context of two-dimensional gravity. We show the existence of a critical temperature T_c at which the diffusion coefficient vanishes. For T < T_c, the diffusion coefficient is negative and the gas undergoes gravitational collapse. This leads to the formation of a Dirac peak concentrating the whole mass in a finite time. We also stress that the critical temperature T_c is different from the collapse temperature T_* at which the partition function diverges. These quantities differ by a factor 1-1/N where N is the number of particles in the system. We provide clear evidence of this difference by explicitly solving the case N = 2. We also mention the analogy with the chemotactic aggregation of bacteria in biology, the formation of “atoms” in a two-dimensional (2D) plasma and the formation of dipoles or “supervortices” in 2D point vortex dynamics.     

计算机辅助测量不良导体的导热系数

介绍了计算机数据采集及处理技术在不良导体导热系数测量实验中的应用及取得的结果．     

Transport properties of the disordered charged bose condensate in two dimensions

Analytical results for the frequency-dependent conductivity of a disordered two-dimensional interacting Bose condensate are presented. Charged and uncharged impurities are considered. We find that for weak disorder the condensate is a superfluid while for strong disorder it is an insulator (a Bose glass). At the superfluid-insulator transition point (at the critical boson densityN _c) the condensate exhibits metallic tranport properties. An loffe-Regel criterion for the transition point is derived. The conductivity at the transition point is of ordere ²/h (h is Planck's constant) and depends on the kind of disorder. For charged impurities (with impurity densityN _i) the conductivity (for a condensate of particles with charge 2e and forN _i=2N _c) at the transition point is given by _c =0.26x(2e)²/h. We discuss recent experiments on superconducting ultra-thin films and on high-T _c superconductors.     

Molecular-dynamics calculation of the thermal conductivity coefficient of the germanium single crystal

The thermal conductivity coefficient of the germanium crystal lattice has been calculated by molecular dynamics simulation. Calculations have been performed for both the perfect crystal lattice and the crystal lattice with defects such as monovacancies. For the perfect germanium single crystal, the dependence of the thermal conductivity coefficient on the lattice temperature has been obtained in the temperature range of 150–1000 K. The thermal conductivity coefficient of the germanium lattice has been calculated as a function of the monovacancy concentration.     

The Yukawa coupling of quantum fields in two dimensions. II

The Yukawa coupling in two dimensional space time is considered. A space outoff is introduced in the interaction termV, so that the renormalized HamiltonianH _ren is a rigorously defined bilinear form in the Fock Hilbert space. The main result is thatH _ren is positive provided the finite part of the renormalization terms are suitably chosen. As a consequence, the Schrödinger equation (i/t–H _ren)=0 can be solved.This work was supported in part by the National Science Foundation, GP — 6165.     

Difference equations in statistical mechanics. II. Solid-on-solid models in two dimensions

A review and some new results are presented for the solid-on-solid models of wetting in two dimensions (i.e., line interfaces) with an emphasis on the difference equations arising in the transfer matrix calculations for these models. Methods for solving the appropriate difference equations exactly or approximately are surveyed, including specific results for short-range, long-range power-law, and applied field-like (binding) external potentials.     

真空热流法测定不良导体的导热系数

以恒定导热原理为基础,选用由温度表和温差电偶组成的温度测量装置,在真空环境下测量试样上下压杆对称位置的温度、有效传热面积和试样的厚度,通过计算机计算试样的导热系数.与传统的稳态法比较,采用真空热流法测定导热系数,材料内部的温度分布很快达到稳定,可以减小测量过程中试样及上加热盘和下散热盘侧面散热产生的影响.     

Observation of a two level thermal conductivity in the low-dimensional materials

The recent theoretical one-dimensional models display invariably anomalous thermal conductivity. Thermal conductivity of several low-dimensional crystalline systems has been investigated using our new techniques. The results show that for most of the measured materials in the high temperature range the thermal conductivity is composed of two extremes: a low- and a high-conductive state. The effective thermal conductivity jumps abruptly between these two states giving rise to apparent discontinuities or “spikes”.     

Lattice thermal conductivity of II–VI compounds

The lattice thermal conductivity of three II–VI compounds, ZnS, ZnSe, and ZnTe has been analysed on the basis of full Callaway's formalism by considering the scattering of phonons by boundary, point defects, normal, and Umklapp processes. An acceptable agreement with the experimental results is found up to 250 K. From the analysis of the adjustable parameters useful information about the lattice anharmonicity and defects have been obtained.     

Estimation of thermal conductivity coefficient for solid-state crystal dielectrics at high temperatures

A generalized expression for approximate estimation of lattice component of thermal conductivity coefficient for solid-state crystal dielectrics at temperatures higher than the Debye temperature, is obtained, which is convenient for preliminary estimation of thermal conductivity coefficient and enables one to conduct a goal-directed search for low-conductivity materials. On the example of rare-earth magnesium hexaaluminates, it is shown that estimations according to the obtained expression are in good compliance with experimental data.     

Determination of thermal conductivity coefficient of crystals with the garnet structure at high temperatures

At high temperatures, the simple expression for thermal conductivity of crystals with the garnet structure is obtained, which allows one to determine this quantity if the lattice constant or density of these crystals is known. The thermal conductivity coefficients for the garnet crystals of different compositions calculated from the obtained formula are in a good agreement with the experimentally measured values.     

Molecular dynamics calculation of the thermal conductivity coefficient of single-layer and multilayer graphene sheets

The thermal conductivity coefficients of single-layer and multilayer graphene sheets have been calculated using the molecular dynamics simulation. Calculations have been performed for graphene sheets with lengths in the range 20–130 nm and at average temperatures in the range 230–630 K. The results obtained have been compared with the experimental data and results of calculations carried out in other works.     

超稳定TO-8型压力传感器在气体导热系数测定实验中的应用

介绍了TO-8型压力传感器的性能及电源电路.以气体导热系数测定实验为例,用TO-8型压力传感器制成的测压装置代替旋转式麦氏真空计,利用可调针孔式放气阀对真空气压进行连续调节,实现了对测试系统真空度的实时监测.