Raman perturbation and surface core soliton in hollow photonic crystal fiber

Effect of Raman scattering and higher order dispersion are investigated in case of surface core or gap solitons, known to exist in hollow core photonic crystal fibers. The necessary conditions for the existence of the soliton are analyzed in the parameter plane. It is observed that these conditions are compatible with the famous Vakhitov-Kolokolov (VK) criterion. In the later part the system of partial differential equations are solved by ETDRK method from which the shapes of the pulses are investigated as it travels along the z direction. Both the terms, intrapulse Raman scattering and higher order dispersion have important effect on the propagation characteristics     

Microscopic calculation of low-energy deuteron-deuteron scattering on the basis of the cluster-reduction method

The cluster-reduction method is used to solve numerically the differential equations for the s-wave Yakubovsky components characterizing the nnpp system in the S=2 spin state. Elastic deuteron-deuteron scattering is analyzed for the case where nucleon-nucleon interaction is simulated by the MT I–III potentials. Effective equations describing the relative motion of clusters is derived. The scattering length and phase shifts for low-energy deuteron-deuteron scattering are calculated.     

A modified K-matrix approach to many-channel processes

The definition of a K-matrix, that does not have the direct channel singularities of the scattering amplitude, is not unique. Different choices lead to different integral equations for K with different physical content. We discuss the choice where the intermediate states have a simple off-shell behaviour for each partial wave. Crossing leads to an identification of the singularities of the K-matrix elements and to an iterative method of finding the scattering amplitude starting from a “bare” world.     

Solution of the three-dimensional problem of wave diffraction by an ensemble of objects

The pattern equations method is extended to solving three-dimensional problems of wave diffraction by an ensemble of bodies. The method is based on the reduction of the initial problem to a system of N (N is the number of scatterers in the ensemble) integro-operator equations of the second kind for the scattering patterns of scatterers. With the use of the series expansions of the scattering patterns in angular spherical harmonics, the problem is reduced to an algebraic system of equations in the expansion coefficients. An explicit (asymptotic) solution to the problems is obtained in the case when the scattering bodies are separated by sufficiently long distances. It is shown that the method can be used to model the characteristics of wave scattering by complex-shaped bodies.     

On the numerical approximation of high-frequency acoustic multiple scattering problems by circular cylinders

The aim of this paper is to propose a numerical strategy for computing the solution of two-dimensional time-harmonic acoustic multiple scattering problems at high-frequency. The scatterers are assumed to be circular, leading therefore to semi-analytical representation formulae of the scattered field through the solution of a large linear system of equations. Taking advantage of the special block Toeplitz structure of the matrix of the linear system, a fast iterative and preconditioned numerical method yielding large memory savings is proposed. Several numerical experiments for general configurations are presented to show the efficiency of the numerical method.     

High-order quadratures for the solution of scattering problems in two dimensions

We construct an iterative algorithm for the solution of forward scattering problems in two dimensions. The scheme is based on the combination of high-order quadrature formulae, fast application of integral operators in Lippmann–Schwinger equations, and the stabilized bi-conjugate gradient method (BI-CGSTAB). While the FFT-based fast application of integral operators and the BI-CGSTAB for the solution of linear systems are fairly standard, a large part of this paper is devoted to constructing a class of high-order quadrature formulae applicable to a wide range of singular functions in two and three dimensions; these are used to obtain rapidly convergent discretizations of Lippmann–Schwinger equations. The performance of the algorithm is illustrated with several numerical examples.     

Consistency of the wave function equations of channel coupling array theory

In a previous article, Austern has claimed that certain wave function equations of an approximate form of the channel coupling array (CCA) theory of n-particle scattering are probably inconsistent. By imposing the relevant boundary conditions, ignored in Austern's work, the CCA equations are shown in fact to be consistent. Comments comparing CCA and the well-known CRC method are also included.     

An open-boundary integrable model of three coupled XY spin chains

The integrable open-boundary conditions for the model of three coupled one-dimensional XY spin chains are considered in the framework of the quantum inverse scattering method. The diagonal boundary K-matrices are found and a class of integrable boundary terms is determined. The boundary model Hamiltonian is solved by using the coordinate space Bethe ansatz technique and Bethe ansatz equations are derived.     

TN method for the critical thickness of one-speed neutrons in a slab with forward and backward scattering

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 T_N method based on Chebyshev polynomial approximation and Marshak boundary conditions. It is shown that T_N method gives accurate results in one-dimensional geometry and is very efficient both in derivation of equations and rapid convergence. Numerical results obtained by T_N method are compared against the P_N method in tabular form, which agreed quite well.     

Polarization of multiple scattered light in planetary atmospheres from solution of the coupled linear integral equations derived for mixed rayleigh-isotropic scattering

A set of coupled integral equations describing nonconservative multiple scattering for a mixed isotropic and Rayleigh single scattering phase function in inhomogeneous, plane-parallel planetary atmospheres is derived. The equations are applicable for the frequency redistributions MRE (monochromatic radiative equilibrium), CFR (complete frequency redistribution), or PFR (partial frequency redistribution). Solution of the equations permits one to calculate the intensity and degree of polarization in an arbitrary direction outside or inside the plane-parallel scattering medium. The equations are readily adaptable to more complicated geometries. Solutions for several cases are presented to demonstrate the versatility and validity of the method. These include a calculation of MRE pure Rayleigh scattering of sunlight in an optically-thick planetary atmosphere to demonstrate agreement with the results of Coulson⁽¹⁾et al. (1960), calculations of the altitude profile of the degree of polarization of the earth's Ly-α 1216A and helium 584A dayglow, and the center to limb variation of the degree of polarization of the sunlight diffusely reflected from a distant planet such that the scattering is pure Rayleigh and conservative at the top of the planet's atmosphere, varying smoothly to conditions of nonconservative and pure isotropic scattering deep in the planet's atmosphere. Tables of functions that one might utilize (without resort to a digital computer) to obtain solutions in the escape function approximation are also given.     

Variational calculations on the three-body scattering problem

An extended resonating-group method is used to calculate the elastic scattering amplitudes (up to L = 2 for a system of three identical bosons interacting through local Yukawa potentials. The results are compared to approximate solutions of the Faddeev equations.     

On the Regge-pole description of nucleus-nucleus scattering

The properties of the Regge poles of theS-matrix for scattering of strongly-absorbed nuclear particles are considered. Simple formulae are obtained for describing the Regge trajectories in terms of the nuclear radius, the quasi stationary levels in the combined nuclear-Coulomb-potential and the widths of these levels. The predictions of these formulae are compared with the Regge trajectories obtained previously, for a Woods-Saxon potential, and with those required to fit¹⁶O-¹²C backward scattering.     

Scattering length and effective range in closed form for the Coulomb plus Yamaguchi potential

From the known expression for the off-shell T-matrix corresponding to the potential consisting of the sum of the Coulomb potential and the Yamaguchi potential, the physical scattering amplitude can be derived in a satisfactory way. We derive simple exact closed formulae for the scattering length a_cs and the effective range r_cs from this amplitude. These are compared with approximate formulae derived by Harrington. Also a few numerical calculations are reported and compared with results obtained by Harrington and by Ali et al.     

Integrable open boundary conditions for the Bariev model of three coupled XY spin chains

The integrable open-boundary conditions for the Bariev model of three coupled one-dimensional XY spin chains are studied in the framework of the boundary quantum inverse scattering method. Three kinds of diagonal boundary K-matrices leading to nine classes of possible choices of boundary fields are found and the corresponding integrable boundary terms are presented explicitly. The boundary Hamiltonian is solved by using the coordinate Bethe ansatz technique and the Bethe ansatz equations are derived.     

Benchmark solutions of radiative transfer equation for three-dimensional rectangular homogeneous media

Three-dimensional steady-state radiative integral transfer equations (RITEs) for a cubic absorbing and isotropically scattering homogeneous medium are solved using the method of “subtraction of singularity”. Surface integrals and volume integrals are carried out analytically to eliminate singularities, to assure highly accurate solutions, and to reduce the computational time. The resulting system of linear equations for the incident energy is solved iteratively. Six benchmark problems for cold participating media subjected to various combinations of externally uniform/non-uniform diffuse radiation loads are considered. The solutions for the incident energy and the net heat flux components are given in tabular form for scattering albedos of ω=0, 0.5 and 1.     

Efficient method for solving the problems of wave diffraction by scatterers with broken boundaries

The pattern equations method is extended to solving the problems of wave scattering by bodies with piecewise smooth boundaries. The method is based on the reduction of the initial boundary-value problem to an integro-operator equation of the second kind in the scattering pattern of a body. With the use of the series expansion of the scattering pattern in angular spherical harmonics, the problem is ultimately reduced to solving an infinite algebraic system of equations in the expansion coefficients of the scattering pattern. The conditions at which this system can be solved by the method of reduction are formulated. Examples of solving the problems of wave scattering by bodies with impedance boundaries are considered. Essential advantages of the proposed method over other known methods are demonstrated.     

粒子模拟中激励源的一种等效设置方法

 基于计算电磁学中对强迫激励源消除虚假反射的算法分析，提出了用等效电流和等效磁流在FDTD公式中引入电场激励源和磁场激励源的方法。从粒子模拟方法的基本方程和迭代公式出发，分析了激励源的引入过程，推导出激励源所等效的电流项和磁流项表达式，实现了新的激励源设置方法，并进行了数值验证和结果讨论。研究表明：这类等效模型与标准FDTD公式能紧密结合，引入非常方便；不必专门设置一个附加的散射场区来处理散射场的计算，大大节省了计算时间和计算内存，比常规总场/散射场体系方法的效率高20%以上，对粒子模拟这类耗时的计算较为适用。通过对2维柱坐标系下相对论速调管放大器(RKA)的模拟，证明了此类激励源设置方法的实用性。     

Eine Integralgleichungsmethode zur Behandlung der Streuung an gebundenen Teilchen

First it is pointed out that various methods known for the treatment of multi-particle scattering problems such as the methods ofLax, Watson, andFaddeev are based on the same type ofT-operator equations with eliminated interactions. They only differ by the identification of the interactions. — Then an integral equation treatment for the scattering of a particle by a system ofn bound particles is developed. If the scattering occurs via local two-body forces, the interaction matrix element splits into that of the two-particle case and a momentum-dependent factor. This fact is used to simplify the scattering equations which then get a mathematical structure similar to that of theT-operator equations discussed at the beginning (however, involving sums of bound states rather than sums of interactions) and which, therefore, can be handled in a similar way. When the interactions are eliminated by means of the two-particle scattering amplitudes, the off-shell energy parameter of these amplitudes may be chosen to be dependent on quantum numbers of the bound system. Such a choice shows indeed to be favorable if one likes to keep only the lowest order approximation of the integral equations. The resulting approximate formula leads, after some further approximations, for resonant scattering to a formula ofLamb, and for weakly energy-dependent amplitudes to a formula ofFermi (being related to the impulse approximation). — The resonant scattering formula is applied to a quantum-mechanical derivation of a method for the determination of nuclear lifetimes which had been proposed on semiclassical arguments byCiocchetti et al. — Finally the method developed for the scattering of a particle by a system of bound particles is extended to collisions between composite particles.     

Theory of closed interacting strings

Using the equations of motion obtained from the Nambu Lagrangian, we study closed strings. Interactions are introduced in the system via certain topological transformations. using the method of functional integration. The Born term turns out to be equal to the Virasoro-Shapiro amplitude. Not all the variables used in the calculation are independent and the physical states therefore satisfy certain conditions. However the interactions are such that those states not satisfying the extra conditions decouple from the rest. The amplitude for the scattering of excited states, the vertex functions and the volume elements for tree aand one-loop amplitudes are calculated. The amplitude for tree or one-loop graphs can be simply obtained from the corresponding amplitude in open string theory.     

Integrable open-boundary conditions for the q-deformed supersymmetric U model of strongly correlated electrons

A general graded reflection equation algebra is proposed and the corresponding boundary quantum inverse scattering method is formulated. The formalism is applicable to all boundary lattice systems where an invertible R-matrix exists. As an application, the integrable open-boundary conditions for the q-deformed supersymmetric U model of strongly correlated electrons are investigated. The diagonal boundary K-matrices are found and a class of integrable boundary terms are determined. The boundary system is solved by means of the coordinate space Bethe ansatz technique and the Bethe ansatz equations are derived. As a sideline, it is shown that all R-matrices associated with a quantum affine superalgebra enjoy the crossing-unitarity property.