Radiative transfer in an LTE atmosphere: An integral kernel formulation of the Compton scatter source term

The purpose of this paper is the computation of the spectrum of the radiation scattered by an LTE atmosphere irradiated by a given spectrum. The expression given for the integral kernel of Compton scatter takes into account both the Doppler shift and the Compton frequency shift. Collective (plasma) phenomena are neglected, and we use throughout the binary encounter approximation. Our result is accurate to terms of 2nd order in v/c (v being the electron velocity, c the light velocity). A comparison is made with some previous results ( ,^{(1) (2)}).     

轴对称介质内辐射源项反演算法

结合Abel变换和离散坐标法,提出了一种基于CCD相机采集的单幅辐射图像重建轴对称发射-吸收介质内辐射源项分布的反演算法。通过在求解辐射正问题得到的准确值的基础上,添加随机噪声模拟试验测量数据,分析了网格数目、辐射源项分布形式、吸收系数和测量误差对算法反演精度的影响。测试结果表明:该算法对测量误差不敏感,在有测量误差的情况下也能够准确的重建介质内的辐射源项分布。     

Generalized reference fields and source interpolation for the difference formulation of radiation transport

In the difference formulation for the transport of thermally emitted photons the photon intensity is defined relative to a reference field, the black body at the local material temperature. This choice of reference field combines the separate emission and absorption terms that nearly cancel, thereby removing the dominant cause of noise in the Monte Carlo solution of thick systems, but introduces time and space derivative source terms that cannot be determined until the end of the time step. The space derivative source term can also lead to noise induced crashes under certain conditions where the real physical photon intensity differs strongly from a black body at the local material temperature.In this paper, we consider a difference formulation relative to the material temperature at the beginning of the time step, or in cases where an alternative temperature better describes the radiation field, that temperature. The result is a method where iterative solution of the material energy equation is efficient and noise induced crashes are avoided. We couple our generalized reference field scheme with an ad hoc interpolation of the space derivative source, resulting in an algorithm that produces the correct flux between zones as the physical system approaches the thick limit.     

Fluctuating characteristics of radiative source term in hydrogen turbulent jet diffusion flame

The laminar flamelet model in combination with joint probability density function transport equation of mixture fraction and turbulence frequency is used to simulate turbulent jet diffusion flames of hydrogen. The frequency distributions of radiative source terms are calculated for four important infrared bands of water vapor. The results show that, for the given ensemble, about 95% samples of radiative source term for each band locate within the region of ±3.0 standard deviation of the mean radiative source term. Due to the different relation between band intensity parameters and temperature for every band, the symmetrization of frequency distributions for each band is different.     

Frequency-domain acoustic pressure formulation for rotating source in uniform subsonic inflow with arbitrary direction

This paper presents a frequency-domain formulation for predicting noise radiated from the rotating thickness and loading sources in uniform subsonic inflow with arbitrary direction. The proposed frequency-domain formulation is an extension of the recently published frequency-domain formulation for the stationary medium. It avoids the singular integral and numerical interpolation problems encountered in the time-domain numerical method. Three test cases, i.e., noise radiation from the rotating monopole and dipole point sources and the Isom thickness noise of a transonic rotor in the subsonic uniform flow, have been carried out to validate the proposed formulation. Both the acoustic pressure spectrum and directivity pattern computed with the present frequency-domain method are in good agreement with those obtained from the time-domain method, thus validating the correctness of the present formulation. Furthermore, the numerical results indicate that the frequency-domain formulation is suitable for tonal noise prediction, while it is inefficient for broadband noise prediction.     

带源项的变系数非线性反应扩散方程的精确解

本文利用广义条件对称方法对带源项的变系数非线性反应扩散方程 f(x)u_t=(g(x)D(u)u_x)_x+h(x)P(u)u_x+q(x)Q(u)进行研究. 当扩散项D(u)取u^m (m≠-1,0,1)和e^u两种重要情形时, 对该方程进行对称约化,得到了具有广义泛函分离变量形式的精确解. 这些精确解包含了该方程对应常系数情况下的解. 关键词： 广义条件对称 精确解 非线性反应扩散方程     

基于自发参量下转换源二阶激发过程产生四光子超纠缠态

目前,多光子纠缠态的制备大多通过线性光学器件演化自发参量下转换一阶激发过程产生的纠缠光子对得到.本文考虑由自发参量下转换源二阶激发产生四个不可区分的纠缠光子制备四光子超纠缠态的情况.通过几组分束器、半波片和偏振分束器等线性光学器件设计量子线路演化四光子系统,结合四模符合探测,可得到同时具有偏振纠缠和空间纠缠的四光子超纠缠态.     

Lattice Boltzmann method for n-dimensional nonlinear hyperbolic conservation laws with the source term

It is important for nonlinear hyperbolic conservation laws (NHCL) to own a simulation scheme with high order accuracy, simple computation, and non-oscillatory character. In this paper, a unified and novel lattice Boltzmann model is presented for solving n-dimensional NHCL with the source term. By introducing the high order source term of explicit lattice Boltzmann method (LBM) and the optimum dimensionless relaxation time varied with the specific issues, the effects of space and time resolutions on the accuracy and stability of the model are investigated for the different problems in one to three dimensions. Both the theoretical analysis and numerical simulation validate that the results by the proposed LBM have second-order accuracy in both space and time, which agree well with the analytical solutions.     

Divergence structure in chiral hyperbag

In a previous paper by Park and Rho, an SU(3)_f chiral bag or chiral hyperbag was constructed and studied in detail, with a focus on the Cheshire Cat structure of the hyperons. This paper supplies some of the details left out in that paper, i.e., calculational procedure of vacuum contributions, their divegence structure and subtraction procedure to the inertia parameters that figure in the hyperons. We calculate them numerically by means of eigenmode sums including all the quark eigenstates up to ¦ ER ¦=250. We are able to isolate the leading divergences, in particular, their chiral-angle dependences, and consequently make subtractions to make the inertia parameters finite and consistent, in a manner quite analogous to the SU(2)_f case.     

圈图函数中的红外发散

介绍一种判断和计算圈图函数红外发散的有效方法.利用该方法研究了C函数(即三点圈图函数)和D函数(即四点圈图函数)的红外发散性质,并且给出常见的C函数的红外发散形式.     

Divergence of perturbation theory for bosons

Perturbation theory is studied in two dimensional space-time. There all non-derivative boson self-interactions are renormalizable and in each order of perturbation theory there are no divergences, that is all renormalizations are finite in perturbation theory. Thus the unrenormalized perturbation series may be studied and it is shown that any interaction of the general form leads to Green's functions which are not analytic in at =0. This result holds in momentum space at a large set of points, enough to show that the Green's functions are not distributions in the momenta which are analytic in at =0. Furthermore the proper self energy and the two-particle scattering amplitude are shown not to be analytic in at =0 for certain momenta on or below the bare mass shell. In the course of this analysis we use the integral representations for Feynman graphs to derive a minorization of the form |I)p ₁,...,p _e )|>A B ⁿ for the contribution from alln ^th order connected graphs in a theory with an interaction of the form . Then the constantsA andB depend only on the momentap _i , and not on the structure of a particular graph.     

Dynamical behaviors of the shock compacton in the nonlinearly Schrödinger equation with a source term

In this paper, the dynamics from the shock compacton to chaos in the nonlinearly Schrödinger equation with a source term is investigated in detail. The existence of unclosed homoclinic orbits which are not connected with the saddle point indicates that the system has a discontinuous fiber solution which is a shock compacton. We prove that the shock compacton is a weak solution. The Melnikov technique is used to detect the conditions for the occurrence from the shock compacton to chaos and further analysis of the conditions for chaos suppression. The results show that the system turns to chaos easily under external disturbances. The critical parameter values for chaos appearing are obtained analytically and numerically using the Lyapunov exponents and the bifurcation diagrams.     

Update of Prior Probabilities by Minimal Divergence

The present paper investigates the update of an empirical probability distribution with the results of a new set of observations. The update reproduces the new observations and interpolates using prior information. The optimal update is obtained by minimizing either the Hellinger distance or the quadratic Bregman divergence. The results obtained by the two methods differ. Updates with information about conditional probabilities are considered as well.     

Divergence and Shannon information in genomes

Shannon information (SI) and its special case, divergence, are defined for a DNA sequence in terms of probabilities of chemical words in the sequence and are computed for a set of complete genomes highly diverse in length and composition. We find the following: SI (but not divergence) is inversely proportional to sequence length for a random sequence but is length independent for genomes; the genomic SI is always greater and, for shorter words and longer sequences, hundreds to thousands times greater than the SI in a random sequence whose length and composition match those of the genome; genomic SIs appear to have word-length dependent universal values. The universality is inferred to be an evolution footprint of a universal mode for genome growth.     

Divergence cancellations in the renormalization of electroweak couplings

Cancellations of nonuniversal ultraviolet divergent contributions to the renormalization of couplingsvlW,vvZ,llZ (in the lowest nontrivial order) in theunitary (U) gauge of the Weinberg-Salam model are reconsidered. The expansion ofU-gauge Feynman diagrams into a set of simpler “secondary” graphs devised some time ago by Kummer and Lane is employed. It is shown that this approach reveals details of the cancellation mechanism which have not been discussed in previous treatments. The connection of cancellations in question with underlying gauge symmetry and the corresponding Higgs mechanism thus becomes more transparent.     

Divergence and aperture angle of conical light guides

Relations derived for the angle of divergence and the aperture of hollow metallic or dielectric cones may not directly be assigned to dielectric core/cladding light guides. The accurate results for the angle of aperture and divergence are stated here under consideration of the total internal reflection at the junction of the core to the surroundings. Furthermore the full angle of the conical element, the geometrical length and the varying diameters, the refractive indices and non-axial ray entrance are considered. All derivations are made by means of geometrical optics for meridional rays.