Application of the Englert-Schwinger model to the equation of state and the fullerene molecule

The Englert-Schwinger model (ESM) is applied to two problems. One is the calculation of zero-temperature equation of state (EOS) of elements within the spherically symmetric Wigner-Sietz cell approximation. The other is to obtain the equilibrium radius of fullerene molecule using March’s approach [N. H. March, Proc. Camb. Philos. Soc. 48, 665 (1952)]. In each case, the results of the ESM are compared with those of Thomas-Fermi-Dirac (TFD) and Thomas-Fermi-Dirac-Weizsacker (TFDW) models. Zero-temperature equation of state calculations are done for Al and Cu. The results of the ESM show an enormous improvement over those of the TFD model. Also, the ESM is in good agreement with the TFDW model for compressions greater than 2. In the regime of validity of TFDW theory, i.e., compressions greater than 20 and 10 for Al and Cu, respectively, the deviations between the results of the two models are negligible. Hence, the ESM may be used in lieu of the TFDW model for EOS calculations. In the fullerene case, we have obtained the cohesive energy using the models assuming the radius obtained from accurate calculations of the fullerene molecule. We have also obtained the equilibrium radius predicted by each model. The results obtained show that the ESM results are not much of an improvement over the TFD results. This shows that the ESM cannot always improve the results of the TFD model and be a replacement for the TFDW model. However, as in the EOS case, it would give results in good agreement with TFDW results for properties that are dependent on the electron density at the outer reaches of the atom.     

Quadratic interaction effect on the dark energy density in the universe

In this study, we deal with the holographic model of interacting dark components of dark energy and dark matter quadratic case of the equation of state parameter(Eo S). The effective equations of states for the interacting holographic energy density are derived and the results are analyzed and compared with the solution of the linear form in the literature.The result of our work shows that the value of interaction term between dark components affects the fixed points at far future in the DE-dominated universe in the case of quadratic Eo S parameter; it is a different result from the linear case in the theoretical results in the literature, and as the Quintom scenario the equations of state had coincidence at the cosmological constant boundary of -1 from above to below.     

Separation of Variables in the Elliptic Gaudin Model

For the elliptic Gaudin model (a degenerate case of the XYZ integrable spin chain) a separation of variables is constructed in the classical case. The corresponding separated coordinates are obtained as the poles of a suitably normalized Baker-Akhiezer function. The classical results are generalized to the quantum case where the kernel of the separating integral operator is constructed. The simplest one-degree-of-freedom case is studied in detail. Received: 21 August 1998 / Accepted: 12 January 1999     

Triple differential cross-sections for the fast electron/positron impact ionization of hydrogen and helium in the Glauber approximation

Triple differential cross-section for electron and positron impact ionization of hydrogen and helium are calculated by using the Glauber approximation along with post-collision interaction effects which are estimated classically. The present results are compared with the recent absolute data of Ehrhardt, Jung and coworkers for the electron impact case. The positron impact case is found to lead to a larger binary to recoil peak maxima ratio (compared to the electron impact case) which further increases when post-collision interaction effects are included.     

The Spectral Density of Nonlinear O-U Noise and the Influence of Nonlinear Fluctuation on the Transition of Bistable System

A stochastic differential equation driven by N-order nonlinear fluctuation is investigated by defining a novel stochastic process Г(t). The spectral densities of Г(t) for N = 1,2,3 and 4 are obtained. We compare the results of the linear fluctuation case with the nonlinear fluctuation case and find that the extremum of the spectral density for linear case is directly proportional to the noise intensity D and independent of the correlation time τ, the extremum of the spectral density for nonlinear case is determined by both D and τ. An approximate Fockker-Planck equation of the N-order nonlinear fluctuation is derived by Hanggi-like ansatz. The infl uences of nonlinear fluct uation on the transition of bistable system are studied. It is found that the area of unimodal region and bimodal region of the stationary probability is independent of D and τ for linear case, however, the area of two regions is related to D and τ for nonlinear case.     

Collapse in the Stoner-Wohlfarth noninteracting-particle model

A theory of Mössbauer spectra of noninteracting Stoner-Wohlfarth (SW) particles interacting with rf magnetic fields is developed. The theory makes it possible to calculate the absorption spectra for arbitrary frequency and amplitude of the rf field. The main features of the Stoner-Wohlfarth model are discussed. The Liouville superoperator formalism is used to generalize the results to the case of arbitrarily time-varying hyperfine fields at a nucleus. To understand the qualitative features of the collapse effect that are observed in the Mössbauer spectra of SW particles the particular case of a circularly polarized hyperfine field is studied, and an analytical expression is obtained describing the Mössbauer spectra for this case. An analysis is also made for weak rf magnetic fields and in this case the resonance behavior of the Mössbauer lines is traced as a function of the frequency of the rf field.     

热带对流活动日变化的模拟研究

利用一个云分辨与海洋的耦合模式,模拟研究了热带对流活动的日变化.通过对模拟结果的分析,揭示了热带地区不同海温日变化条件下,对流活动的云物理特征.利用热带海洋与全球大气响应观测实验（TOGA COARE）的观测资料作为模式的初始与边界场,来驱动耦合模式.对热带海表温度按照其日变化幅度的大小进行了分类,分为强、弱海表温度日变化两种类型,并在此基础上进行了合成分析.结果表明：1）在弱的海表温度日变化下,云中的云冰含量大于云水含量,说明云中以层状云为主;而在强的海温日变化下,云中的云水含量大于云冰含量,说明云中以 关键词： 热带对流日变化 地面降水率 云冰含量 云水含量     

On the validity of the independent hot-spot model

The results of the independent hot-spot (IHS) model are compared to those of the underlying stochastic amplifier in the regime where the coupling of the amplifier is close to its critical value. The considered case is that of a 1D linear amplifier with at most one hot spot per interaction length. It is shown that the validity of the critical coupling given by the IHS model depends on the correlation function of the pump field and should be discussed in each particular case. The discrepancy between the IHS model and the underlying amplifier is shown to be due to the random fluctuations of the hot-spot field around its dominant, deterministic, component.     

Cross correlation between the dipole-dipole interaction and the Curie spin relaxation: the effect of anisotropic magnetic susceptibility

Cross-correlated relaxation caused by the interference of nuclear dipole-dipole interaction and the Curie spin relaxation (DD-CSR cross relaxation) is generalized to treat the case of anisotropic magnetic susceptibility, including the important case where the latter originates from zero-field splitting. It is shown that the phenomenon of DD-CSR cross relaxation is absolutely general and to be expected under any electronic configuration. The results of the generalization are presented for a model system, and the consequences for paramagnetic metalloproteins are illustrated with an example of cerium(III)-substituted calbindin. The effects of the magnetic anisotropy are found to be substantial.     

Bistatic scattering from an anisotropic sea surface: Numerical comparison between the first-order SSA and the TSM models

The first-order small-slope approximation (SSA-1) model is used for numerical predictions of the normalized radar cross section (NRCS) of an anisotropic ocean surface in bistatic configurations for the K_u-band radar frequency. The calculations were made by assuming the Elfouhaily et al. surface-height spectrum for fully developed seas. In the forward-backward case, the SSA-1 presents an agreement with the geometric optics limit of the Kirchhoff approximation results in the near-specular directions where it is well known that the last model works well. In the fully bistatic case, SSA-1 numerical results are compared with those of the two-scale model in several configurations as a function of wind speed, wind direction, incident/scattering angles and for co-and cross-polarization states. Good agreement between the two models is noted in the co-and cross-polarization case with a small difference of about 1-2 dB. But in certain configurations, the SSA-1 model tends to overestimate the radar cross section peak behaviour. This irregularity is discussed and interpreted. The main purpose of this paper is to analyse NRCS predictions based on the SSA-1 model in a fully bistatic configuration.     

Influence of the sign of the refractive index in the reflectivity of a metamaterial surface with localized roughness

To study the scattering properties of metamaterials, we generalize two scattering methods developed for conventional (non-magnetic) isotropic materials to the case of materials with arbitrary values (positive or negative) of magnetic permeability and electric permittivity. The generalized methods are used to study the changes produced in the reflectivity of a metamaterial surface with localized roughness when the relative refractive index changes sign. Our results show that, unlike the case of a plane surface whose reflectivity is unaffected by the change of sign of the relative refractive index, in rough surfaces the change of sign is manifested in the reflectivity, even for very low roughness, particularly in observation directions away from the specular direction.     

On the glueball spectrum in the Klebanov-Strassler model

The spectrum of the linearized equations of IIB supergravity above the Klebanov-Strassler background solution is investigated. It is shown that the spectrum of a scalar particle minimally interacting with the background is degenerate with the spectrum of the graviton (traceless spin-2 mode), and this spectrum is studied in detail. The results are generalized to the more general case of the solution that is known in the literature as a baryonic branch.     

Numerical study of a modified BBGY integral equation for the primitive model of an electrolyte solution

A modified Poisson-Boltzmann equation derived from the BBGY hierarchy of equations is solved numerically for the restricted primitive model of an electrolyte solution. Computations are carried out for 1 : 1 and 2 : 2 electrolytes, and results compared with 1 : 1 Monte Carlo data and results from the Poisson-Boltzmann extensions arising from the Kirkwood hierarchy. Satisfactory agreement with the Monte Carlo results are found in the 1 : 1 case, and the correct qualitative behaviour of thermodynamic properties obtained in the 2 : 2 case. At low concentrations in the 2 : 2 case the modified Poisson-Boltzmann equations from the Kirkwood and BBGY hierarchies predict the anomalous behaviour found in the thermodynamic properties of real electrolytes. The behaviour of the mean electrostatic potential changes from a damped exponential to a damped oscillatory form for 1·2 < κa < 1·3 (where κ is the Debye-Hückel constant and a is an ionic diameter) in the 1 : 1 case and at κa ～ 0·8 in the 2 : 2 case for the parameters considered.     

线性高分子体系中高分子链间排除体积效应的模型化

提出了线性高分子体系中高分子链间排除体积效应的一个它回避模型，并且针对具体的四个模型系统进行了计算机模拟. 计算结果表明：1)线团的均方末端距〈R²〉与行走步数(N)仍然保持着与无规线团模型一样的线性关系；2)但与无规线团相比，线团的空间尺寸被压缩；3)与两侧方向的回避相比，在行走的前进方向的回避而导致的压缩效应更加明显. 关键词： 排除体积效应 回避行走 无规线团 线性高分子     

Interaction of Three Electromagnetic Fields with a Resonance Medium in EPR. The Case of a Small Local Field in Comparison with the Saturating One

A system of Bloch equations modified with allowance for the presence of a dipole–dipole reservoir for the case where the local magnetic field is small in comparison with the saturating one is suggested. The system is used for solving the problem of interaction of three electromagnetic fields: a saturating field, a probe one, and the third - a combination field resulting from the interaction of the first two in a resonance medium. The imaginary and real parts of the system susceptibility at the probe-field frequency have been investigated in detail at both different frequencies of interacting waves and coinciding ones (degenerate case). For the degenerate case, the dependence of the coefficient of the parametric connection of waves on the frequency is considered. The results of the present work are compared with those obtained by us earlier for the case where the local magnetic field is much in excess of the saturating one (Provotorov's case). It is shown that in the problem considered the amplification of weak waves when they pass through the layer of an absorbing resonance medium is inaccessible.     

State-independent hypothesis to model the behavior of magnetic materials

The problem of modeling the magnetic behavior due to a magnetization process is usually dealt with using the classical scalar Preisach model (CSPM). Recently, it has been shown that in the case of soft magnetic materials better results can be obtained by means of the modified scalar Preisach model (MSPM). The problem of model identification is common to both these two approaches. In the past we used a Lorentzian approximation for CSPM identification. In this paper, after reviewing the method, which allows, in particular, the efficient determination of the parameters controlling the reversible magnetization, we propose an extension of the Lorentzian approximation to the case of MSPM identification. It will be shown that an accurate estimation of the model parameters is possible also in this case, as it is confirmed by comparing the model with experimental data.     

The asymmetric single-impurity Anderson model – the modified perturbation theory

We investigate the single-impurity Anderson model by means of the recently introduced modified perturbation theory. This approximation scheme yields reasonable results away from the symmetric case. The agreement with exactly known results for the symmetric case is checked, and results for the non-symmetric case are presented. With decreasing conduction band occupation, the breakdown of the screening of the local moment is observed. In the crossover regime between Kondo limit and mixed-valence regime, an enhanced zero-temperature susceptibility is found.     

A two-scale model from the point of view of the small-slope approximation

Abstract

General results for the scattering cross section following from the small-slope approximation (SSA) are applied to the case of two-scale surface roughness which can be represented as a superposition of small-scale and large-scale components. The purpose of the paper is to obtain analytically tractable results with obvious physical meaning which can be used for estimates prior to undertaking extensive numerical calculations according to exact unambiguous expressions of the SSA. The general case of vector (electromagnetic) or scalar (sound) waves is considered. The statistics of small-scale roughness is not assumed to be Gaussian (in any sense) or space-homogeneous, and the possible dependence of the statistics of small-scale roughness on a large-scale undulating surface is taken into account. As a result, a modified local spectrum of small-scale components of roughness enters into corresponding expressions for the scattering cross section. It is demonstrated that under appropriate conditions, the resulting formulae for the scattering cross section reduce to the conventional two-scale model.