Non-Gaussian statistical models for scattering calculations

In calculating the properties of waves scattered by random media it is almost always assumed that variations of the media constitute a joint Gaussian process. In this paper two alternative models are investigated. It is shown that whilst some features of the statistics of the scattered waves are more sensitive to the spectrum of the fluctuations in the medium than to the basic statistical model, in general significantly different properties are predicted using the alternative models.     

Non-Gaussian models for the statistics of scattered waves

This paper addresses problems associated with the development of widely applicable non-Gaussian noise models, particularly with reference to the statistical properties of scattered waves. A combination of phenomenological arguments and exact solutions of specific scattering problems are used to elucidate the significance of one model—K-distributed noise—which has several attractive features and has already found many applications. A full statistical-mechanical formulation is developed for non-Gaussian compound Markov processes, with this model as a special case. The implications for numerical simulation of correlated non-Gaussian noise are explored and comparisons made with experimental data. A brief review of current applications of the K-distribution model is given.     

Non-Gaussian scattering by a random phase screen

A theoretical investigation of non-Gaussian scattering by a smoothly varying deep random phase screen is presented. New analytical results, valid for arbitrary illuminated area, are derived for the contrast of the intensity pattern in the Fraunhofer region and the effect of two scale sizes in the screen is calculated.     

Improved Monte Carlo model for multiple scattering calculations

The coupling between the Monte Carlo (MC) method and geometrical optics to improve accuracy is inves- tigated. The results obtained show improved agreement with previous experimental data, demonstrating that the MC method, when coupled with simple geometrical optics, can simulate multiple scattering with enhanced fidelity.     

Model calculations of atom-surface scattering

The elastic scattering of light mass, thermal-energy atoms from simple surfaces is investigated. The surface is represented by the model of a single planar square array of hard spheres. The effect of the surface potential well is treated semiclassically by simply shifting the energy of the incident atom ; furthermore a constant imaginary term is added to the energy to account for inelastic scattering and adsorption. As in the multiple scattering formalism of LEED the total scattering matrix of the lattice is expanded in terms of the individual gas atom-surface atom t-matrices. Propagation of the incident atom on the surface is described in terms of a one particle Green's function propagator with complex energy. The terms in the multiple scattering series are summed to all orders, by using standard matrix inversion techniques. The size of the matrix to be inverted limits to ten the total number of phase shifts that are included in the calculation. Thermal effects are included through angle dependent Debye-Waller factors.Model calculations have been performed to study the intensity of the specular and the diffracted beams as a function of the angles of incidence. The importance of surface temperature (introduced by the Debye-Waller factors), the incident energy and the depth of the potential well of the gas-surface interaction are discussed. The main feature of the results is the decrease of the intensity of the specular beam in going from glancing incidence to normal incidence and the presence of structure due to the appearance and disappearance of diffracted beams across the surface. The azimuthal behavior of the specular beam is in agreement with experimental observations.     

Non-Gaussian fluctuations of Stokes parameters in scattering by small particles

Calculations are presented for second-order fluctuations of Stokes parameters that result from singly scattered, coherent, polarized radiation by an ensemble of small spheroidal particles which are randomly oriented in space. The form of the second-order non-Gaussian enhancements are obtained and discussed, but attention is also given to terms describing amplitude fluctuations that are present in the Gaussian scattering regime. These terms provide a generalized Siegert relationship for polarized radiation. The possibility of using measurements of fluctuations to characterize the particle shape is considered.     

Momentum-space calculations for three-nucleon scattering including a three-nucleon force

The formalism to include a three-nucleon force into three-nucleon continuum calculations is presented. First numerical results, obtained in momentum space, are shown. The two- and three-nucleon forces have been restricted to act only in the¹ S ₀ and³ S ₁-³ D ₁ partial-wave states. As two-nucleon interaction the Bonn-B potential and as three-nucleon interaction the Tucson-Melbourne two-pion exchange model has been used.     

Stretched backgrounds for acoustic scattering models

For the computational solution of the acoustic scattering problem, new domain integral equations are proposed. These domain integral equations describe the acoustic wave propagation in some chosen inhomogeneous background, whereas the influence of the scattering object is viewed as a superposition of contrast sources. A stretching procedure of the inhomogeneous background to a homogeneous one leads to a domain integral equation in a stretched space, where the Green function has the same simple functionality as the one of the non-stretched homogeneous background. This leads to improved efficiency in the computation of the scattering problem at hand.     

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.     

Elementary particle scattering and statistical quasi-particles in quantum statistical mechanics

Previous work relating the thermodynamic potential to elementary particle S-matrix elements is generalized and rederived directly from the expressions for the diagrams of many body theory. The divergent physical region poles are shown to introduce energy derivatives of mass shell delta functions which tend to shift the energies of the scattering particles away from the elementary particle mass shell. These shifted energies are related to the statistical quasiparticle energies introduced by Balian and De Dominicis. The work of these authors is generalized to show that to all orders in the coupling strengths the many body diagrams for any system described by a relativistic or non-relativistic field theory can be summed to give: (1) the entropy and the statistical average of a non-spontaneously broken, conserved charge in terms of ideal gas-like formulae involving statistical quasi-particle energies; (2) the thermodynamic potential in terms of diagonal matrix elements of products of transition amplitudes wherein the energies of all external particles and the energy arguments of all ideal gas occupation numbers are the statistical quasi-particle energies.     

Relativistic DWBA calculations for polarization transfer in proton inelastic scattering

The matrix element for inelastic scattering of protons leading to the excitation of collective states in even-even nuclei is calculated in the framework of Dirac phenomenology using a DWBA approach. The deformed parts of the Lorentz scalar and four-vector optical potentials serve as the transition operators. The results are compared with the recently measured polarization transfer coefficients on ⁴⁰Ca and ²⁰⁸Pb at 500 MeV. The agreement with experiment is good.     

Cross section calculations for electron scattering from platinum chemotherapeutic compounds

Cross section for electron impact ionization of carboplatin, C₆H₁₂N₂O₄Pt, and oxaliplatin, C₈H₁₄N₂O₄Pt, have been calculated within binary-encounter-Bethe model for energies from the ionization threshold up to 5000 eV. Cross section for elastic electron scattering from carboplatin and oxaliplatin molecules have also been derived using independent atom method (IAM) and additivity rule for collision energies ranging from 50 eV to 3000 eV. Obtained cross sections have been compared with relevant cross sections for cisplatin molecules.     

Approximation of off-shell scattering operators for non-lorentzian line shape calculations

A previously derived approximation for the matrix elements of the Fano relaxation operator m(ω), which gives rise to non-Lorentzian line wings, is examined. This approximation is expressed in terms of an off-the-energy shell scattering operator. Calculation of this operator by a second-order Born expansion is unsuitable because this procedure limits the radiation frequency dependence to the same order. The main part of this paper is devoted to expressing the off-shell scattering operator in the time-ordered formalism. In this form, a scattering operator approximation suggested by Dillonet al.⁽⁶⁾ can be applied which is not restrictive to the frequency dependence.     

Graphical models for statistical inference and data assimilation

In data assimilation for a system which evolves in time, one combines past and current observations with a model of the dynamics of the system, in order to improve the simulation of the system as well as any future predictions about it. From a statistical point of view, this process can be regarded as estimating many random variables which are related both spatially and temporally: given observations of some of these variables, typically corresponding to times past, we require estimates of several others, typically corresponding to future times.

Graphical models have emerged as an effective formalism for assisting in these types of inference tasks, particularly for large numbers of random variables. Graphical models provide a means of representing dependency structure among the variables, and can provide both intuition and efficiency in estimation and other inference computations. We provide an overview and introduction to graphical models, and describe how they can be used to represent statistical dependency and how the resulting structure can be used to organize computation. The relation between statistical inference using graphical models and optimal sequential estimation algorithms such as Kalman filtering is discussed. We then give several additional examples of how graphical models can be applied to climate dynamics, specifically estimation using multi-resolution models of large-scale data sets such as satellite imagery, and learning hidden Markov models to capture rainfall patterns in space and time.     

Quasi-wavelet calculations of sound scattering behind barriers

Quasi-wavelets (QWs) are a representation of turbulence consisting of self-similar, eddy-like structures with random orientations and positions in space. They are used in this paper to calculate the scattering, due to turbulent velocity fluctuations, of sound behind noise barriers as a function of the size and spatial location of the eddies. The sound scattering cross-section for QWs of an individual size class (eddy size) is derived and shown to reproduce results for the von Kármán spectrum when the scattered energies from a continuous distribution of QW sizes are combined. A Bragg resonance condition is derived for the eddy size that scatters most strongly for a given acoustic wavenumber and scattering angle. Results for scattering over barriers show that, for typical barrier conditions, most of the scattered energy originates from eddies in the size range of approximately one-half to twice the size of the eddies responsible for maximum scattering. The results also suggest that scattering over the barrier due to eddies with a line of sight to both the source and receiver is generally significant only for frequencies above several kilohertz, for sources and receivers no more than a few meters below the top of the barrier, and for very turbulent atmospheric conditions.     

Dephasing calculations of de Haas-van Alphen scattering

A review and assessment of existing dephasing calculations is 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.