Anharmonic phonons and structural phase transitions

Exact results for the order parameter and the meansquare displacement as functions of temperature are given for a quantum interacting phonon Hamiltonian with quartic anharmonicities. Upper bounds for the transition temperature are also derived. Approximate theories including the mean field approximation, the random phase approximation (or quasiharmonic approximation) and the self consistent approach (using Blume-Hubbard scheme) are compared with our exact results. The mean field approximation for the meansquare displacement is found to violate our bounds.The classical value is shown to form a lower bound for the kinetic energy. Upper bounds for the kinetic energy are obtained showing the region of temperature in which the use of the high temperature expansion of the fluctuation-dissipation theorem is justified. Comparison of the Hamiltonian and our results with electron-paramagnetic-resonance measurements are discussed.     

有温度反馈阶跃引入负反应性瞬变的解

考虑有温度反馈反应堆阶跃引入负反应性过程的变化规律,对点堆中子动力学方程的解进行研究,给出不同的分析模型,分析发现,（1）用于瞬发超临界的分析模型及其结果不能用于引入大的负反应性过程的分析.（2）在相同的初始功率时,先驱核瞬跳近似模型的结果要优于目前比较普遍的中子瞬跳近似模型的结果.（3）无论初始功率与引入负阶跃反应性的大小,温度瞬跳近似模型的结果总是优于先驱核瞬跳近似与中子瞬跳近似模型的结果.故而温度瞬跳近似模型是目前最为准确的解析模型. 关键词： 中子动力学 温度反馈 反应性 点堆     

有温度反馈阶跃引入负反应性瞬变的解

考虑有温度反馈反应堆阶跃引入负反应性过程的变化规律,对点堆中子动力学方程的解进行研究,给出不同的分析模型,分析发现,（1）用于瞬发超临界的分析模型及其结果不能用于引入大的负反应性过程的分析.（2）在相同的初始功率时,先驱核瞬跳近似模型的结果要优于目前比较普遍的中子瞬跳近似模型的结果.（3）无论初始功率与引入负阶跃反应性的大小,温度瞬跳近似模型的结果总是优于先驱核瞬跳近似与中子瞬跳近似模型的结果.故而温度瞬跳近似模型是目前最为准确的解析模型.     

The law of corresponding states for the saturation vapor pressure of a liquid

Graphical examination of Maxwell's rule is employed with Van der Waals' equations to give a graphical relation of saturation vapor pressure to temperature from the law of corresponding states. An analytic approximation is compared with experiment and with an approximation for the experimental mean curve. Phenomenological arguments are employed to derive the latent heat of evaporation of the liquid and the critical temperature of the vapor in terms that are correct to a first approximation for all substances.     

二维伊辛模型相变临界点温度的模拟计算

用计算模拟方法计算了二维伊辛模型的相变临界点温度,其结果接近严格解,明显布喇格－威廉斯近似和贝特近似的结果。     

CHIRAL PHASE TRANSITION IN A MODEL WITH DYNAMICAL SPONTANEOUS-SYMMETRY-BREAKING AT FINITE TEMPERATURE AND DENSITY

The chiral-symmetry-restoring phase transition in a model with dynamical spontaneous-symmetry-breaking is discussed qualitatively,making use of an approximation method.The selfconsistency equation of the model is established.The condensation and mass of fermions as well as the temperature or density dependence of energy density and specific heat are obtained.It turns out that,in this approximation,the chiral-phase-transition is second order at zero chemical potential and finite temperature; and the transition is first order for both cases at finite temperature and density and at zero temperature and finite density,this moment.the transition temperature or density from broken phase to normal phase differs from that from normal phase to broken phase.     

Research on the ionospheric ion velocity distribution and the incoherent scattering spectra of the radar with the 16-moments approximation for the relaxation collision model

The distribution function which given by Grad cannot be used to describe the ionospheric ion velocity distribution due to the larger anisotropic temperature appears in the high-latitude ionosphere. In this article, based on the Boltzmann equation, the relaxation collision model (RCM) was used to substitute the Boltzmann collision integration, and a non-Maxwell ion velocity distribution function with the 16-moments approximation for the bi-Maxwell distribution was given, and the ion transport equation with the 16-moments approximation was also derived and solved. Moreover, the ion velocity distribution, the solution of transport equation and the incoherent scattering spectra with the 13-moments and 16-moments approximation for the relaxation collision model were simulated, analyzed and compared. The research shows that compared with the 13-moments approximation, the 16-moments approximation with the bi-Maxwell distribution is more suitable to describe the characteristics of the anisotropic temperature ion distribution in the high-latitude ionosphere.     

Finite-temperature Hartree-Fock approximation to λΦ4 theory

The finite-temperature Hartee-Fock approximation to the effective potential for massless λΦ⁴ theory is calculated. The reflection symmetry which, in the same approximation, turns out to be spontaneously broken at zero temperature, is restored at a critical temperature. The nature of the phase transition is analyzed. A comparison with previous calculations is presented.     

Test for the cumulant approximation in the critical region

A cumulant approximation in wide use is tested, in the critical region, against a straightforward product-average decomposition approximation previously used in conjunction with a new integral representation for the Ising model. It is found that for the calculation of the transition temperature, the cumulant approximation is significantly inferior to the product-average approximation.     

Research on Temperature Field Reconstruction Based on RBF Approximation with Polynomial Reproduction Considering the Refraction Effect of Sound Wave Paths

The temperature field distribution directly reflects the combustion condition in a furnace．In this paper, acoustic thermometry to reconstruct temperature distribution is investigated. A method based on radial basis function approximation with polynomial reproduction (RBF-PR) is proposed in order to improve the accuracy and stability of the method based on RBF approximation. In addition, the refraction effect of sound wave paths is considered in the process of reconstruction. The curved lines with refraction effect are numerically calculated by solving differential equations, which show that sonic waves curve towards the zones of higher temperature. The reconstructed performance is validated via numerical simulation using four temperature distribution models. Results and analysis show that the proposed method has much greater accuracy than the method based on RBF approximation, and when considering the effect of refraction, our method can reconstruct more excellent reconstruction performance than others, which do not take into account the refraction effect of sound wave paths.     

Field-induced spin-orientational phase transitions in Néel ferrimagnets. I

The breakdown of the aligned states of Néel ferrimagnets in an applied magnetic field is considered. The behaviour of isotropic two-and three-sublattice ferrimagnets is treated in the framework of the mean-field approximation. A phenomenological method also limited by the mean-field approximation is used to analyse the behaviour of the anisotropic ferrimagnet. Particular emphasis is placed on the vicinity of the compensation temperature. Approximate analytical expressions which are valid near the compensation temperature are given for the phase-boundary positions, typical magnetic fields, and temperature ranges of the phase diagrams.     

Development of diode laser absorption spectroscopy method for determining temperature and concentration of molecules in remote object

We develop a method of diode laser absorption spectroscopy for noncontact measurements of the temperature and pressure of a gas mixture under unsteady-state conditions at low signal-to-noise ratios. The method is based on the measurement of the absorption spectra of water molecules and approximation of experimental spectra by spectra simulated based on spectroscopic databases. Different approximation algorithms of experimental spectra are tested, such as fitting by individual contours and fitting by a part of the simulated spectrum. We reveal that, at small signal-to-noise ratios, the approximation of experimental data by a simulated spectrum yields more correct data on the temperature of the mixture compared to the fitting by individual contours. For the examined temperature range of 300–1300 K, the determination error of the gas temperature in the test cell proved to be approximately three times lower than upon fitting by individual contours. The developed method of recording and processing spectra is used to measure the temperature, water vapor concentration, and total pressure under the unsteady-state combustion conditions of an air-hydrogen mixture in a supersonic flow.     

Effect of thermal ground state correlations on the statistical properties of the Lipkin model

The renormalized random phase approximation for hot finite Fermi systems is evaluated with the use of the thermo field dynamics formalism. This approximation treats vibrations of a hot finite Fermi system as harmonic ones but takes into account the Pauli principle in a more proper way than the usual thermal RPA, thus incorporating a new type of correlations in a thermal ground state. To demonstrate advantages of the approximation and to analyze a range of its validity, it is applied to the exactly solvable Lipkin model. A comparison is made with the exact grand canonical ensemble calculations, results of the thermal Hartree – Fock approximation and the thermal random phase approximation. The intrinsic energy of the system, the heat capacity, the average value of the quasispin operator z-projection and the particle number variance are calculated as functions of temperature. On the whole, the thermal renormalized RPA appears to be a better approximation than the other two. Its advantage is especially evident in the vicinity of the phase transition point. It is found that within TRRPA the phase transition occurs at lower temperature than in THFA and TRPA. Received: 4 January 1999 / Revised version: 10 March 1999     

N-Midpoint Rule for Calculating the Effective Mesonic Potential at Finite Temperature

The temperature dependence of meson properties is studied by using the effective potential formalism. The effective mesonic potential is numerically calculated using the n-midpoint rule at finite temperature. The meson masses, the phase transition, and the energy density are investigated as functions of temperature. The obtained results are compared with those from other works. The present technique is compared with the Hartree approximation and the imaginary time formalism. We conclude that the calculated effective potential successfully predicts the meson properties, the phase transition, and the critical temperature in comparison with other models and avoid the difficulty that found in the Hartree approximation which depends on cutoff technique.     

Extended random phase approximation for layered copper oxides antiferromagnets

The role of interlayer coupling constant on the Néel temperature of layered copper oxides and other magnetic properties have been studied. The theoretical framework is based on anisotropic Heisenberg model and the two sublattice approach. The higher-order Green functions are decoupled using the second random phase approximation. The Green’s function related to the localized spin correlation functions has been exploited. A self consistent expression for the sublattice magnetization and a corrected form for the Néel temperature are obtained. The free-spin-wave results are obtained under a specific approximation. The theoretical results are compared with that of the random phase approximation and existing experimental results.     

Monte Carlo simulation of in-plane spin-polarized transport in GaAs/GaAlAs quantum well in the three-subband approximation

We develop a Monte Carlo (MC) tool incorporated with the three-subband approximation model to investigate the in-plane spin-polarized transport in GaAs/GaAlAs quantum well. Using the tool, the effects of the electron occupation of higher subbands and the intersubband scattering on the spin dephasing have been studied. Compared with the corresponding results of the simple one-subband approximation model, the spin dephasing length is reduced four times under 0.125\,kV/cm of driving electric field at 300K by the MC tool incorporated with the three-subband approximation model, indicating that the three-subband approximation model predicts significantly shorter spin dephasing length with temperature increasing. Our simulation results suggest that the effects of the electron occupation of higher subbands and the intersubband scattering on the spin-dependent transport of GaAs 2-dimensional electron gas need to be considered when the driving electric field exceeds the moderate value and the lattice temperature is above 100K. The simulation by using the MC tool incorporated with the three-subband approximation model also indicates that, under a certain driving electric field and lattice temperature, larger channel widths cause spins to be depolarized faster. Ranges of the three components of the spins are different for three different injected spin polarizations due to the anisotropy of spin--orbit interaction.     

On the curie temperature of an anisotropic Heisenberg-Ising ferromagnet with crystal-field anisotropy

The effect of crystal-field anisotropy on the Curie temperature is studied in an S = 1 anisotropic Heisenberg-Ising ferromagnet. The Green function technique with a Callen-type approximation is used. The results show that, when the correlations between spins of nearest neighbouring sites are taken into account, the change in the Curie temperature with crystal-field anisotropy is not so great as that calculated in the random phase approximation.     

Lineshape theory of the plasmon-phonon sidebands of a semiconductor plasma gain spectrum

The gain spectrum of an electron-hole plasma in direct-gap semiconductors due to plasmon-phonon-assited radiative transitions is calculated for various plasma densities at zero temperature. The screened Coulomb interaction is treated within a damped plasmon-phonon-pole approximation. The validity of this approximation is checked in the simpler case without phonon participation by comparing it with the dynamical random-phase approximation (RPA). For CdS the calculated spectra are in good qualitative agreement with the spectra experimentally observed by Saito.     

Two-dimensional radiative equilibrium of a gray medium between concentric cylinders

A method for calculating radiative equilibrium temperature and surface heat-flux distributions is developed for an absorbing-emitting medium between concentric cylinders. The cylinder walls are assumed to be gray diffuse absorbers and emitters and have arbitrary temperature distributions along their peripheries. Heat generation may take place within the medium. As a first approximation, the problem is solved for optically-thick systems by using the differential approximation. To obtain accurate results also for the optically-thin and intermediate regimes, the differential approximation is subsequently improved by a number of geometric parameters, as has been discussed in a previous paper. As examples, two cares are presented in detail: (1) a hollow cylinder with uniform internal heat generation and uniform surface temperature and (2) a hollow cylinder with a cosine temperature distribution imposed on the wall, with no internal heat generation. Comparison with some numerical results generated by Hottel's zonal method shows excellent agreement.     

Lattice-gas model of multiple layer adsorption

The phase diagram for a lattice-gas model of physical adsorption on a homogeneous substrate has been calculated in a mean-field approximation. The first-order phase transitions corresponding to the addition of successive layers terminate in individual critical points as the temperature increases. The critical temperatures of successive layers increase, monotonically with layer number, from the critical temperature of the two-dimensional lattice gas to that of the bulk three-dimensional lattice gas. This last feature is probably an artifact of the mean-field approximation.