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.     

Analytical approximations for the hierarchically constrained kinetic Ising chain

The hierarchically constrained kinetic Ising model in one dimension is reviewed, and the results of several analytical approaches to the model are presented. Two standard approximation schemes, an effective-medium approximation and a mode-coupling approximation, are shown to fail. A new class of approximations, termed cluster approximations, is better suited for the model. It yields good results for the spin autocorrelation function, and also elucidates important general properties of the model—its connection with defect-diffusion models and the asymptotic long-time behavior of the autocorrelation function.     

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.     

Thin element approximation for the analysis of blazed gratings: simplified model and validity limits

The thin element approximation is widely used to predict the diffraction efficiency of thin periodic diffractive optical elements (DOEs). However, as the period-to-wavelength ratio is reduced, the approximation becomes inaccurate. A model based on a “shadow concept” can be used to predict the diffraction efficiency with high accuracy. Hereby we extend the model to include the effect of multi-level staircase structures and non-perpendicular incident angles. We also present an error map and define regions of validity for the thin element approximation (TEA) and the shadow model.     

Analytic Approximations for the Velocity of Field-Driven Ising Interfaces

We present analytic approximations for the field, temperature, and orientation dependences of the interface velocity in a two-dimensional kinetic Ising model in a nonzero field. The model, which has nonconserved order parameter, is useful for ferromagnets, ferroelectrics, and other systems undergoing order–disorder phase transformations driven by a bulk free-energy difference. The solid-on-solid (SOS) approximation for the microscopic surface structure is used to estimate mean spin-class populations, from which the mean interface velocity can be obtained for any specific single-spin-flip dynamic. This linear-response approximation remains accurate for higher temperatures than the single-step and polynuclear growth models, while it reduces to these in the appropriate low-temperature limits. The equilibrium SOS approximation is generalized by mean-field arguments to obtain field-dependent spin-class populations for moving interfaces, and thereby a nonlinear-response approximation for the velocity. The analytic results for the interface velocity and the spin-class populations are compared with Monte Carlo simulations. Excellent agreement is found in a wide range of field, temperature, and interface orientation.     

On the convergence of Marumori's boson expansion for pairing vibrations

It is demonstrated analytically for a two-level model with pairing force that Marumori's method converges rapidly if one uses the idea of pairing vibrations. The approximation of Sørensen and the broken-pair approximation are compared with Marumori's boson expansion.     

The truncation of the Mori continued fraction for the spectral function in Heisenberg and XY models

We study the truncation of the Mori continued fraction for the two-spin spectral function of the XY model in various schemes suggested by the 3-pole approximation. These schemes are (i) a fully consistent version of the 3-pole approximation; (ii) 5-pole approximation (not fully consistent); and (iii) 5-pole approximate (fully consistent). We establish the equilivalence between the fully consistent 3-pole approximation and the Bennett-Martin approximation. Finally, we calculate the time-dependent spin-spin correlation function for the classical Heisenberg model in both versions of the 3-pole approximation and compare it with the exact spin-spin correlation function obtained by direct numerical calculation in one dimension.     

A Binomial Approximation Method for the Ising Model

A large portion of the computation required for the partition function of the Ising model can be captured with a simple formula. In this work, we support this claim by defining an approximation to the partition function and other thermodynamic quantities of the Ising model that requires no algorithm at all. This approximation, which uses the high temperature expansion, is solely based on the binomial distribution, and performs very well at low temperatures. At high temperatures, we provide an alternative approximation, which also serves as a lower bound on the partition function and is trivial to compute. We provide theoretical evidence and the results of numerical experiments to support the strength of these approximations.     

A finite element dynamical nonlinear subscale approximation for the low Mach number flow equations

In this work we propose a variational multiscale finite element approximation of thermally coupled low speed flows. The physical model is described by the low Mach number equations, which are obtained as a limit of the compressible Navier–Stokes equations in the small Mach number regime. In contrast to the commonly used Boussinesq approximation, this model permits to take volumetric deformation into account. Although the former is more general than the latter, both systems have similar mathematical structure and their numerical approximation can suffer from the same type of instabilities.     

A nonlinear circuit model for studying the frequency response in buried heterostructure lasers

An equivalent-circuit model of a semiconductor laser is developed. The model includes diffusion and uses the parabolic gain approximation. It can be applied to various buried heterostructure (BH) devices to simulate optical response characteristics. The values of the circuit elements versus injection current clearly indicate that the parabolic gain approximation and carrier diffusion play an important role in obtaining a more accurate frequency response, especially for (BH) lasers with stripe widths greater than the diffusion length.     

云的红外辐射模型综述

介绍了云的分类和组成,以及云的红外辐射模型(包括二流近似、灰体近似和黑体近似模型),测量了云的红外光谱辐射。分析表明:二流近似模型可用于云层对太阳和大气中红外波段的反射、透射和云自身的辐射。黑体近似模型和灰体近似模型主要用于对云层较粗略的估算,灰体模型可近似描述8～12μm波段的辐射,且形式上比较简单,是一种常用的简化模型。     

连续光在生物组织中能流率分布的漫射近似和模拟

分析了半无限大介质漫射近似不同边界条件的镜像光源结构,用镜像光源的方法给出了连续光入射时稳态能流率分布的漫射近似表达式,并用Monte Carlo方法对能流率分布进行模拟,分析了两种模型能流率分布的特点及其形成的机理;用Monte Carlo模拟结果检验了能流率分布漫射近似的精度,结果表明:漫射近似采用EBC边界条件的结果有较高的精度和计算较简单等优点,为能流率分布的快速准确计算提供了依据.     

RPA for the linewidth of the van der Pol Oscillator

The linewidth of then component van der Pol Oxcillator is calculated in random phase approximation. Forn=2 this model describes a single mode laser. This approximation is asymptotically correct for weak and strong pumping and also in the largen limit for all pumping. The result is in good agreement with numerical results forn=2 in the whole range including the threshold. The corresponding vertex renormalized approximation on the other hand yields poor agreement and the wrong asymptotic value in the limit of strong pumping. The reason for this failure is discussed.     

Wigner transform and the eikonal approximation for nonlocal potentials

The same approximation scheme which leads to the Thomas-Fermi theory in bound state problems is applied to scattering by a nonlocal potential. Based on the Wigner transform of the evolution operator, it gives in a very simple way the eikonal approximation for the scattering amplitude. As an application a generalized Fermi gas model for inclusive scattering from nuclei is derived.     

Multidomain spectral method for the helically reduced wave equation

We consider the 2+1 and 3+1 scalar wave equations reduced via a helical Killing field, respectively referred to as the 2-dimensional and 3-dimensional helically reduced wave equation (HRWE). The HRWE serves as the fundamental model for the mixed-type PDE arising in the periodic standing wave (PSW) approximation to binary inspiral. We present a method for solving the equation based on domain decomposition and spectral approximation. Beyond describing such a numerical method for solving strictly linear HRWE, we also present results for a nonlinear scalar model of binary inspiral. The PSW approximation has already been theoretically and numerically studied in the context of the post-Minkowskian gravitational field, with numerical simulations carried out via the “eigenspectral method.” Despite its name, the eigenspectral technique does feature a finite-difference component, and is lower-order accurate. We intend to apply the numerical method described here to the theoretically well-developed post-Minkowski PSW formalism with the twin goals of spectral accuracy and the coordinate flexibility afforded by global spectral interpolation.     

Multidomain spectral method for the helically reduced wave equation

We consider the 2+1 and 3+1 scalar wave equations reduced via a helical Killing field, respectively referred to as the 2-dimensional and 3-dimensional helically reduced wave equation (HRWE). The HRWE serves as the fundamental model for the mixed-type PDE arising in the periodic standing wave (PSW) approximation to binary inspiral. We present a method for solving the equation based on domain decomposition and spectral approximation. Beyond describing such a numerical method for solving strictly linear HRWE, we also present results for a nonlinear scalar model of binary inspiral. The PSW approximation has already been theoretically and numerically studied in the context of the post-Minkowskian gravitational field, with numerical simulations carried out via the “eigenspectral method.” Despite its name, the eigenspectral technique does feature a finite-difference component, and is lower-order accurate. We intend to apply the numerical method described here to the theoretically well-developed post-Minkowski PSW formalism with the twin goals of spectral accuracy and the coordinate flexibility afforded by global spectral interpolation.     

Multidimensional dynamical-statistical model for describing the fission of excited nuclei

A multidimensional stochastic model for describing the decay of excited nuclei is presented. The model takes into account the dynamics of thermal fluctuations of collective variables, the dissipation of the kinetic energy of collective motion, and the emission of light particles from excited nuclei. The potential energy of a deformed nucleus is calculated within the liquid-drop model with a sharp surface and within the finiterange-interaction model. The friction parameters are calculated on the basis of the one-body-dissipation model. The inertia parameters are found in the Werner-Wheeler approximation. The drift components of forces are determined in terms of the entropy of an excited nucleus. The latter in turn is computed within the Fermi gas approximation with allowance for the deformation dependence of the density-level parameter. The fission probability, the mean multiplicity of neutrons emitted prior to scission (prescission neutrons), and the variances of the mass distributions of fission fragments at the most probable kinetic-energy value are calculated on the basis of the model developed here and are compared with experimental data. The dependences of these quantities on the model parameters are considered in detail.     

一种研究非旋波近似演化问题的系统近似方法

以一个与玻色场耦合的二能级粒子为例，证实了在静态极化子问题的研究中取得成功的相干态近似方法，同样也能够有效地用于非旋波近似下量子系统的时间演化问题。结果同时表明，在一般情况下，哈密顿算符中的非旋波项不能被忽略；并提供了在频率空间进一步检测非旋波项效应的可能性。     

Modelling Moran Process with Network Dynamics for the Evolution of Cooperation

We introduce a simple model based on the Moran process with network dynamics. Using pair approximation, the cooperation frequencies at equilibrium states are deduced for general interactions. Three usual social dilemmas are discussed in the framework of our model. It is found that they all have a phase transition at the same value of cost-to-benefit ratio. For the prisoner＇s dilemma game, notably it is exactly the simple rule reported in the literature [Nature 441 （2006） 502]. In our model, the simple rule results from the parent-offspring link. Thus the basic mechanism for cooperation enhancement in network reciprocity is in line with the Hamilton rule of kin selection. Our simulations verify the analysis obtained from pair approximation.