共查询到20条相似文献,搜索用时 78 毫秒
1.
J.V.P. de OliveiraA.V. Cardona M.T. VilhenaR.C. Barros 《Journal of Quantitative Spectroscopy & Radiative Transfer》2002,73(1):55-62
We describe a semi-analytical numerical method for coherent isotropic scattering time-dependent radiative transfer problems in slab geometry. This numerical method is based on a combination of two classes of numerical methods: the spectral methods and the Laplace transform (LTSN) methods applied to the radiative transfer equation in the discrete ordinates (SN) formulation. The basic idea is to use the essence of the spectral methods and expand the intensity of radiation in a truncated series of Laguerre polynomials in the time variable and then solve recursively the resulting set of “time-independent” SN problems by using the LTSN method. We show some numerical experiments for a typical model problem. 相似文献
2.
C. Yildiz 《Journal of Quantitative Spectroscopy & Radiative Transfer》2002,74(4):521-529
The one-speed time-dependent and stationary neutron transport equation in spherical geometry with forward scattering is considered. A formal equivalence between the transport equations for a critical and for a decaying system is established. By considering the pseudo-slab problem the scaled transport equation is solved using the FN method. Numerical values of radii for a critical and time-dependent systems are tabulated as a function of the scattering parameters and the fundamental decay constant. Some of the results are discussed and compared with others obtained using various methods. The results agree for four or five significant figures with the published results. It is shown that the FN method yields good numerical results for the problem considered. Finally, a few remarks about the effect of the forward anisotropy on the radius is also given. 相似文献
3.
M.T. Jaekel 《Nuclear Physics B》1977,118(5):506-532
The quantum treatment of soliton scattering in the sine-Gordon model, using the path integral collective coordinate method is generalized to N solitons. The solitions. The first quantum correction to the phase shift of N-soliton scattering is equal to the zero-point energy of an effective multi-soliton Hamiltonian. The energies of the oscillators of this Hamiltonian are shown to be equal to the stability angles of a complete set of solutions of the Schrödinger equation for small fluctuations around a classical N-soliton. Consequently, calculating the fluctuations and their stability angles by the inverse scattering method, we obtain the energies of the oscillators. The first quantum correction to the phase shift (the O(1) part in a development in powers of γ) is evaluated by summing the stability angles. This result is in agreement with the “exact” scattering amplitude conjectured by Faddeev, Kulish and Korepin. 相似文献
4.
Michael F. Modest Jun Yang 《Journal of Quantitative Spectroscopy & Radiative Transfer》2008,109(9):1641-1666
The inherent complexity of the radiative transfer equation makes the exact treatment of radiative heat transfer impossible even for idealized situations and simple boundary conditions. Therefore, a wide variety of efficient solution methods have been developed for the RTE. Among these solution methods the spherical harmonics method, the moment method, and the discrete ordinates method provide means to obtain higher-order approximate solutions to the equation of radiative transfer. Although the assembly of the governing equations for the spherical harmonics method requires tedious algebra, their final form promises great accuracy for any given order, since it is a spectral method (rather than finite difference/finite volume in the case of discrete ordinates). In this study, a new methodology outlined in a previous paper on the spherical harmonics method (PN) is further developed. The new methodology employs successive elimination of spherical harmonic tensors, thus reducing the number of first-order partial differential equations needed to be solved simultaneously by previous PN approximations (=(N+1)2). The result is a relatively small set (=N(N+1)/2) of second-order, elliptic partial differential equations, which can be solved with standard PDE solution packages. General boundary conditions and supplementary conditions using rotation of spherical harmonics in terms of local coordinates are formulated for the general PN approximation for arbitrary three-dimensional geometries. Accuracy of the PN approximation can be further improved by applying the “modified differential approximation” approach first developed for the P1-approximation. Numerical computations are carried out with the P3 approximation for several new two-dimensional problems with emitting, absorbing, and scattering media. Results are compared to Monte Carlo solutions and discrete ordinates simulations and a discussion of ray effects and false scattering is provided. 相似文献
5.
Fikret Anli Faruk Ya?a Hakan Öztürk 《Journal of Quantitative Spectroscopy & Radiative Transfer》2006,101(1):129-134
The critical slab problem has been studied in one-speed neutron transport equation with isotropic scattering by using the TN method. TN moment criticality solutions are obtained for the uniform finite slab using Mark and Marshak type vacuum boundary conditions. Results obtained by TN method, using the two type boundary conditions mentioned above, were presented in the Tables and also the Tables included the results obtained by PN method for the comparisons. 相似文献
6.
Zekeriya Altaç Mesut Tekkalmaz 《Journal of Quantitative Spectroscopy & Radiative Transfer》2004,83(1):115-117
The effects of variable medium properties on radiation transfer in participating and anisotropically scattering one-dimensional spherical medium were investigated by Tsai et al. (JQSRT 42(3) (1989) 187). The discrete ordinates method solutions they provided for hollow spherical medium cases are incorrect. The correct DOM S8 and the integral transfer equation solutions are provided. 相似文献
7.
This paper is concerned with the fast solution of high-frequency electromagnetic scattering problems using the boundary integral formulation. We extend the O(N log N) directional multilevel algorithm previously proposed for the acoustic scattering case to the vector electromagnetic case. We also detail how to incorporate the curl operator of the magnetic field integral equation into the algorithm. When combined with a standard iterative method, this results in an almost linear complexity solver for the combined field integral equations. In addition, the butterfly algorithm is utilized to compute the far field pattern and radar cross section with O(N log N) complexity. 相似文献
8.
C.E. Siewert J.R. Maiorino M.N. Özişik 《Journal of Quantitative Spectroscopy & Radiative Transfer》1980,23(6):565-573
The FN method is used to compute the net radiative heat flux relevant to radiative transfer in an anisotropically scattering, plane-parallel medium with specularly and diffusely reflecting boundaries. 相似文献
9.
I.A. Eganova 《Reports on Mathematical Physics》1984,20(2):217-233
The scattering of a low-energy particle by a potential of a small range is known to be described satisfactorily by the s-wave alone. In the present paper we give a method of describing low-energy scattering by N potentials with the aid of N waves. For this purpose, a special system of Laplacian eigenfunctions is suggested. The scattering amplitude depends on only N parameters, irrespective of overlapping of potentials. The physical significance of these parameters δλ, λ=1,2,…N, is shown by exp (2iδλ)=Sλ where Sλ is the eigenvalue of the S matrix. The parameters δλ may be obtained by direct methods and perturbation theory.The low-energy scattering by an arbitrary configuration of N centres is discussed. The differential cross-section is averaged over all orientations of the configuration and radially about the direct beam, giving it as a function of the scattering angle. This formula may be used for the phase shift analysis. 相似文献
10.
Hakan Öztürk Fikret Anli 《Journal of Quantitative Spectroscopy & Radiative Transfer》2007,105(2):211-216
The critical slab problem in the case of combination of forward and backward scattering with usual isotropic scattering is studied for one-speed neutrons in a uniform finite slab by using TN method based on Chebyshev polynomial approximation and Marshak boundary conditions. It is shown that TN method gives accurate results in one-dimensional geometry and is very efficient both in derivation of equations and rapid convergence. Numerical results obtained by TN method are compared against the PN method in tabular form, which agreed quite well. 相似文献
11.
A. V. Gurevich N. G. Mazur K. P. Zybin 《Journal of Experimental and Theoretical Physics》2000,90(4):695-713
The asymptotic behavior of the solutions of the KdV equation in the classical limit with an oscillating nonperiodic initial function u 0(x) prescribed on the entire x axis is investigated. For such an initial condition, nonlinear oscillations, which become stochastic in the asymptotic limit t→∞, develop in the system. The complete system of conservation laws is formulated in the integral form, and it is demonstrated that this system is equivalent to the spectral density of the discrete levels of the initial problem. The scattering problem is studied for the Schrödinger equation with the initial potential ?u 0(x), and it is shown that the scattering phase is a uniformly distributed random quantity. A modified method is developed for solving the inverse scattering problem by constructing the maximizer for an N-soliton solution with random initial phases. A one-to-one relation is established between the spectrum of the discrete levels of the initial state of the system and the spectrum established in phase space. It is shown that when the system passes into the stochastic state, all KdV integral conservation laws are satisfied. The first three laws are satisfied exactly, while the remaining laws are satisfied in the WKB approximation, i.e., to within the square of a small dispersion parameter. The concept of a quasisoliton, playing in the stochastic state of the system the role of a standard soliton in the dynamical limit, is introduced. A method is developed for determining the probability density f(u), which is calculated for a specific initial problem. Physically, the problem studied describes a developed one-dimensional turbulent state in dispersion hydrodynamics. 相似文献
12.
Alexey A. Shcherbakov Alexandre V. Tishchenko 《Journal of Quantitative Spectroscopy & Radiative Transfer》2012,113(2):158-171
A method is presented that performs the exact electromagnetic analysis of 2D periodic dielectric structures of arbitrary profile or index distribution and possibly large period. The generalized source method is used to formulate the problem of light diffraction in the form of a volume integral equation reduced to a linear equation system, which is solvable by known fast algorithms. The calculation time and required memory are linearly proportional to the total number No of considered diffraction orders instead of No3 typical for conventional methods. Numerical examples are provided to demonstrate the potential of the method for the analysis of complex periodic structures. 相似文献
13.
D.W. Mueller Jr 《Journal of Quantitative Spectroscopy & Radiative Transfer》2005,92(4):457-477
The topic of this work is the generalized X- and Y-functions of multidimensional radiative transfer. The physical problem considered is spatially varying, collimated radiation incident on the upper boundary of an isotropically scattering, plane-parallel medium. An integral transform is used to reduce the three-dimensional transport equation to a one-dimensional form, and a modified Ambarzumian's method is used to derive coupled, integro-differential equations for the source functions at the boundaries of the medium. The resulting equations are said to be in double-integral form because the integration is over both angular variables. Numerical results are presented to illustrate the computational characteristics of the formulation. 相似文献
14.
B.R. Karlsson 《Physics letters. [Part B]》1977,69(1):13-16
A generalized form of the two-body Kowalski-Noyes method is shown to provide a both simple and powerful unitary reduction of the three- and N-body scattering equations. Employing generalized half-off-shell functions that satisfy of-sshell but real and non-singular integral equations, the reduction directly leads to on-shell integral equations for the scattering amplitudes. Physically, it is simple example of how the scattering problem can be split into an internal and an external part. 相似文献
15.
Edward F. Redish 《Nuclear Physics A》1974,235(1):82-122
The recently derived connected kernel equation (CKE) for N-body scattering operators is applied to direct nuclear reactions. A spectral representation is derived for the kernel of the CKE in order to obtain manageable approximations. This allows the kernel to be split into orders corresponding to the propagation of different numbers of bound clusters. By formally solving one part of the kernel at a time, the CKE is written as a hierarchy of nested equations in increasingly many variables. The first equation of this hierarchy is a set of coupled channel Lippmann-Schwinger equations coupling together all two-cluster channels. These equations reduce to the usual coupled channel equations for inelastic scattering and to the coupled channel Born approximation for rearrangement reactions when weak coupling assumptions are made. The second equation of the hierarchy is a two-variable integral equation for the effective interactions appearing in the coupled channel equations. The driving terms and kernel of this integral equation are obtained from the third equation of the hierarchy which is a three-variable integral equation and so forth. The use of the spectral expansion results in a renormalized theory in the sense that the bound state and reaction problems are separated. This permits the inclusion of nuclear models in the theory in a straightforward manner. The hierarchy is applied to a particular example, that of nucleon-nucleus scattering. For this case the hierarchy is truncated at the level allowing no more than three clusters in the continuum. By suppressing exchange and keeping only one-particle transfer and single-nucléon knockout channels, a set of equations for the optical potentials and transfer operators is obtained. These equations provide a three-body treatment of the single scattering approximation to the optical potential. Iteration of the equations yields the usual single scattering approximation in first order including three-body off-shell effects. After suppression of Fermi motion and off-shell effects, the standard impulse approximation is recovered. Modifications of the method for other cases are discussed and other possible applications suggested. 相似文献
16.
The problem of radiative heat transfer in an absorbing, emitting, isotropically scattering two-layer slab with diffusely and specularly reflecting boundaries is solved by the FN method and results are presented for the transmissivity and reflectivity of the slab. 相似文献
17.
Hélène Frisch Claude Bardos 《Journal of Quantitative Spectroscopy & Radiative Transfer》1981,26(2):119-134
Resonance-line scattering in static low density media with large optical thickness has a diffusive behavior in both space and frequency because photons belonging to the Lorentzian wings of the line may be scattered almost monochromatically a very large number of times. This diffusive behavior holds on frequency scales and spatial scales, χc and τc, much larger than the scales associated with one elementary scattering of a wing-photon.A method developed for diffusion approximations in neutron transport theory, suitably generalized to handle diffusion in frequency space, is applied to the case of conservative scattering in a bounded medium with interior sources and zero incoming radiation. The method is to separate the line radiation field into an interior part and a boundary layer part which goes to zero in the interior. Each part is expanded in terms of a small parameter ?, which is the ratio of the mean free-path at frequency χc to the characteristic spatial scale τc.It is shown that the leading term in the interior asymptotic expansion is isotropic, zero on the boundary, and obeys a space and frequency diffusion equation. In the boundary-layer expansion, the leading term is of order ? and is a solution to a monochromatic transfer equation in a semi-infinite, plane-parallel medium. The emergent radiation field is shown to be of order ? and proportional to the gradient of the interior solution at the boundary. Its angular dependence, in the case of isotropic scattering in the atom frame, is given by the Ambartsoumian H-function. A comparison is presented between numerical solutions of the full transfer equation and asymptotic solutions. Non-conservative scattering and time-dependent problems are briefly discussed. 相似文献
18.
The shape of the x-ray K absorption spectrum of sulfur in the normal spinel CdIn2S4 is calculated using the FEFF7 program. Local densities of free electron states of S, Cd, and In are calculated in the theory of multiple scattering in the local coherent potential approximation. A comparison of the obtained results with the experimental x-ray SK spectrum demonstrates good agreement between them. 相似文献
19.
The coupled, two-variable integral equations that determine the 4ΛHe and 4ΛH bound states, when the NN and ΛN interactions are represented by separable potentials, are derived from the Schrödinger equation. The integral equations are solved numerically for simple s-wave potentials and for tensor potentials in the truncated t-matrix approximation without resort to separable expansion of the kernels. The Λ-separation energy difference ΔBΛ resulting from the genuine four-body model is shown to be approximately twice as large as that coming from an “effective two-body” model calculation, when identical central potentials are used. The four-body model estimate of ΔBΛ made with tensor forces is consistent with the experimental value, indicating that charge symmetry breaking implied by the low energy Λ N scattering parameters is compatible with that suggested by the known binding energy difference in the A = 4 hypernuclear isodoublet. 相似文献
20.
N. G. Mazur V. V. Geogdzhaev A. V. Gurevich K. P. Zybin 《Journal of Experimental and Theoretical Physics》2002,94(4):834-851
We investigate the semiclassical limit for the nonlinear Schrödinger equation in the case of a defocusing medium under oscillating nonperiodic initial conditions specified on the entire x axis. We formulate a system of integral conservation laws in terms of an infinite number of spatially averaged densities explicitly calculated from the initial conditions. We study the direct scattering problem and show that the scattering phase is a uniformly distributed random variable. The evolution of this system leads to the development of nonlinear oscillations, which become statistical in nature on long time scales. A modified inverse scattering method based on constructing a maximizer of the N-soliton solution in the continuum limit for N → is used to obtain an asymptotic solution. Using the maximizer, we found an infinite set of conserved averaged densities in the statistical state. This allowed us to couple the initial state with the limiting statistical steady (for t → ∞) state and, thus, to unambiguously determine the level spectrum in the statistical limit. 相似文献