Effect of multiple scattering on the critical electric field for runaway electrons in the atmosphere

A simple method for taking into account the multiple Coulomb scattering in construction of a separatrix (the line separating the regions of runaway and decelerating electrons in an electric field) is described. The desired line is obtained by solving a simple transcendental equation.     

A reduced basis method for electromagnetic scattering by multiple particles in three dimensions

We consider the development of efficient and fast computational methods for parametrized electromagnetic scattering problems involving many scattering three dimensional bodies. The parametrization may describe the location, orientation, size, shape and number of scattering bodies as well as properties of the source field such as frequency, polarization and incident direction. The emphasis is on problems that need to be solved rapidly to accurately simulate the interaction of scattered fields under parametric variation, e.g., for design, detection, or uncertainty quantification. For such problems, the use of a brute force approach is often ruled out due to the computational cost associated with solving the problem for each parameter value.In this work, we propose an iterative reduced basis method based on a boundary element discretization of few reference scatterers to resolve the computationally challenging large scale problem. The approach includes (i) a computationally intensive offline procedure to create a selection of a set of snapshot parameters and the construction of an associated reduced basis for each reference scatterer and (ii) an inexpensive online algorithm to generate the surface current and scattered field of the parametrized configuration, for any choice of parameters within the parameter domains used in the offline procedure. Comparison of our numerical results with directly measured results for some benchmark configurations demonstrate the power of our method to rapidly simulate the interacting electromagnetic fields under parametric variation of the overall multiple particle configuration.     

Study of multiple small-angle neutron scattering by the warren method

A procedure for studying multiple small-angle neutron scattering using a double-crystal spectrometer is presented. It is based on measuring the linear coefficient of beam attenuation caused by smallangle scattering. The method has been substantiated theoretically, and the range of its applicability has been determined.     

Coherent multiple scattering effects and Monte Carlo method

Based on the comparison of the iteration procedure of solving the Bethe-Salpeter equation and the Monte Carlo method, we developed a method for simulating coherent multiple-scattering effects within the framework of a unified stochastic approach. The time correlation function and the interference component were calculated for the coherent backscattering from a multiply scattering medium.     

A method for rapid characterization of diffusion

This paper describes a method to determine molecular displacements as a function of time in just two scans: one reference scan using the Carr-Purcell-Meiboom-Gill (CPMG) sequence, a second scan using a modified CPMG sequence (KCPMG). Measurements on free diffusion in bulk fluids, and on restricted diffusion in porous rock samples are reported. This technique can also be used for rapid measurement of flow and chemical exchange.     

“A simple way of eliminating the α exchange parameter in the multiple scattering method”

A straighforward way to treat the exchange potential within the framework of the multiple scattering method is suggested. The procedure, which eliminates the difficulties related with the X_α potential, is applied to the study of the molecular clusters of Ga As.     

Universal amplitudes for critical surface scattering

Scattering of x-rays or neutrons at grazing angles is studied for semi-infinite systems which exhibit a second order phase-transition in the bulk. We present the results of a calculation to order ² (ind=4- dimensions) of the amplitudes of leading and next-to-leading terms in the angular dependence and in the temperatur dependence (forT>T _c) of the scattering cross-section. The results are discussed for the three-dimensional Ising case.This work was supported by Bundesministerium für Forschung und Technologie     

Scaling functions for critical surface scattering

Scattering of x-rays at grazing angles is studied for semi-infinite systems which exhibit a second order phase transition. We calculate the scaling functions for the diffuse scattering intensity aboveT _c and for the Bragg-intensity belowT _c, using -expansion techniques. Corrections to the leading critical surface behaviour and the size of the asymptotic scaling region are discussed. In addition, we obtain the crossover function for the excess susceptibility _s.This work was supported by Bundesministerium für Forschung und Technologie     

A two-way parabolic equation that accounts for multiple scattering

A two-way parabolic equation that accounts for multiple scattering is derived and tested. A range-dependent medium is divided into a sequence of range-independent regions. The field is decomposed into outgoing and incoming fields in each region. The conditions between vertical interfaces are implemented using rational approximations for the square root of an operator. Rational approximations are also used to relate fields between neighboring interfaces. An iteration scheme is used to solve for the outgoing and incoming fields at the vertical interfaces. The approach is useful for solving problems involving scattering from waveguide features and compact objects.     

A novel method for solving the three-body scattering problem

A numerical scheme for solving a three-body scattering problem within the framework of the configuration space Faddeev equations in three-dimension, i.e., without resort to explicit partial wave expansion, is presented. The method is applied to calculate the low-energy n-d observables.     

A coordinate-spectral method for rough surface scattering

In this paper, we deal with the time-harmonic scattering by one-dimensional rough surfaces separating two homogeneous and isotropic media. The method is based on a rigorous integral formalism. The unknown of the integral equation is projected onto a Fourier basis while the equation itself is sampled as in a classical method of moments. The accuracy is tested against both other methods and experimental results. One of the main interests in choosing a Fourier basis lies in the ability to solve rigorously the scattering of a p polarized incident beam by a shallow metallic rough surface. The role of the surface waves is accurately taken into account and phenomena such as enhanced backscattering are well described. With this method, one can consider that the gap between the domain of validity of perturbation theories and the domain of practical use of rigorous methods is filled.     

A three-parameter analytic phase function for multiple scattering calculations

A very simple procedure has been developed to fit the first three moments of an actual phase function with a three parameter analytic phase function. The exact Legendre Polynomial decomposition of this function is known which makes it quite suitable for multiple scattering calculations. The use of this function can be expected to yield excellent flux values at all depths within a medium. Since it is capable of reproducing the glory, it can be used in synthetic spectra computations from planetary atmospheres. Accurate asymptotic radiance values can also be achieved as long as the single scattering albedo ω₀ ?0.9.     

An alternative method for scattering angle evaluation in monte carlo simulation

The analytic expression of scattering angle determination using Lindhard's differencial cross section:     

A rapid boundary perturbation algorithm for scattering by families of rough surfaces

In this paper we describe a novel algorithm for the computation of scattering returns by families of rough surfaces. This algorithm makes explicit use of the fact that some scattering profiles of engineering interest (e.g., traveling ocean waves) come in branches parameterized analytically by a bifurcation quantity. Our approach delivers recursions which not only can be implemented to yield a rapid, robust and high-order numerical scheme, but also give a new proof of analyticity of scattering quantities with respect to the bifurcation parameter of the surface family. The real advantage of this new approach is that it computes, in one step, the scattered field for all possible members of the family of surfaces. By contrast, other state-of-the-art schemes must restart when the returns from a new surface are desired, so that the cost of our new approach is greatly advantaged when the number of samples of the family reaches even modest values. Numerical results which verify the accuracy of our approach and demonstrate their utility in computing grating efficiencies scattered by traveling surface ocean waves are presented.     

Inverse scattering method and soliton solutionfamily for the Einstein--Maxwell theory with multiple Abelian gauge fields

A Hauser-Ernst-type extended hyperbolic complex linear system given in our previous paper [Gao Y J 2004 Chin. Phys. 13 602] is slightly modified and used to develop a new inverse scattering method for the stationary axisymmetric Einstein-Maxwell theory with multiple Abelian gauge fields. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the inverse scattering method be fine and effective in practical application. As an example, a concrete family of soliton solutions for the considered theory is obtained.     

A critical evaluation of isotropic potential functions for chlorine

A survey of many crystal structures shows that short intermolecular chlorine-chlorine contacts are anisotropic. This observation challenges the currently used potential function models which allow only for isotropic exp-6 and coulomb interactions. In this study the polymorphic p-dichlorobenzene DCB system is used to illustrate the difficulties encountered by relying on the isotropic atom-atom approximation. It is found that exp-6 potential functions cannot be extrapolated beyond the range of contacts used in their derivation. Addition of coulomb terms provides needed additional flexibility to the potential function but the derived C-Cl bond polarization is not found to be a constant of the molecule, i.e. the optimum value is not the same for each phase of DCB. Furthermore, no single exp-6 potential function could satisfy the structural constraints provided by the three phases of crystalline DCB and by hexachlorobenzene. These findings are typical of curve-fitting methods which employ an incorrect mathematical form for the curve and indicate the necessity of including anisotropic terms in the interaction potential.     

A robust noniterative method for obtaining scattering strengths of multiply scattering point targets

A noniterative method based on the least squares technique is presented in this letter to obtain the scattering strengths of multiply scattering point targets. Benefiting from the least squares' optimization property, this new method achieves a good estimation of the scattering strengths. Compared with the noniterative method proposed in a recent paper [E. A. Marengo and F. K. Gruber "Noniterative analytical formula for inverse scattering of multiply scattering point targets," J. Acoust. Soc. Am. 120, 3782-3788 (2006)], the new method produces more accurate results in the presence of noise.     

A new method for measuring the threshold of stimulated Brillouin scattering

A new method for measuring the threshold of stimulated Brillouin scattering (SBS) based on the generation location of a Stokes beam is proposed for the first time to our knowledge. The length of the medium cell is selected to be longer than the free gain length of pump pulses in the Brillouin medium. The reflected light from a certain mirror in front of the medium cell is chosen as the reference beam, and the SBS threshold is measured by the "jump" of the delay between the Stokes beam and the reference beam. An 8-ns Q-switched single-longitudinal-mode pulse is used as the pump and the typical SBS medium FC-72 is selected as the nonlinear medium in our experiment. The SBS threshold intensity is measured to be 173-178 mW/cm 2 , which is consistent with existing results measured with the transmitted energy limiting method.     

The iteration method in multiple scattering: The transfer equation

Using the iteration method, the author obtains the transfer equation for the scattering of electromagnetic waves in a system comprising a large number of statistically independent particles spherical in shape under the condition c^–1 1 c is the density of the number of particles, the scattering cross section for a single particle, and the wave number. The method is easily extended to the scattering of scalar waves.In conclusion the author expresses his thanks to V. E. Zuev and S. D. Tvorogov for their guidance and observations on the study.