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Abstract: The many-body iterative T-matrix (MBIT) method is based on the T-matrix method and focuses on scatterers with large aspect ratios. In this study, the MBIT method is extended so that it can be applied to an infinite scatterer with a 1-D periodic finite structure. A semi-analytical solution of infinite scatterers is obtained. In addition, the MBIT method is theoretically extended to include scatterers without axial rotational symmetry. The direct validation of the present method is performed by comparing the analytic solution for an infinite cylinder and the numerically accurate discrete dipole approximation method whereas indirect validation is conducted by using asymptotic solutions. Furthermore, the study also demonstrates that scattering properties of infinite scatterers can be used as a substitute for finite scatterers with large aspect ratios. [Copyright &y& Elsevier]

The T-matrix method is modified with the use of a priori information on the analytic properties of a solution. It is shown that taking into account such information makes it possible to develop correct, effective, and universal algorithms for simulating scattering characteristics of bodies of a wide class of geometries including essentially non-Rayleigh bodies. [ABSTRACT FROM AUTHOR]

Abstract: This paper summarizes the scientific legacy of Peter C. Waterman (1928–2012) who introduced concepts and theoretical techniques that have had a major impact on the fields of scattering by particles and particle groups, optical particle characterization, radiative transfer, and remote sensing. A biographical sketch is also included. [Copyright &y& Elsevier]

Abstract: A surface integral formulation is developed for the T matrix of a homogenous and isotropic particle of arbitrary shape, which employs scalar basis functions represented by the translation matrix elements of the vector spherical wave functions. The formulation begins with the volume integral equation for scattering by the particle, which is transformed so that the vector and dyadic components in the equation are replaced with associated dipole and multipole level scalar harmonic wave functions. The approach leads to a volume integral formulation for the T matrix, which can be extended, by the use of Green's identities, to the surface integral formulation. The result is shown to be equivalent to the traditional surface integral formulas based on the VSWF basis. [Copyright &y& Elsevier]

In this paper a theoretical study of a possible phase transition in dilute 3He-He(II) mixtures is presented using the Galitskii-Migdal-Feynman formalism. The effective scattering length is calculated from the Galitskii-Migdal-Feynman T-matrix, which is essentially the effective scattering amplitude dependent on the medium. It is found that at very low 3He concentrations the s-wave effective scattering length for 3He-He(II) varies discontinuously from positive to negative values at some critical concentration. This indicates a crossover from a regime with dimers to another with the Cooper pairs. The binding energy of the weakly-bound dimers 3He2 is computed. The effective p-wave scattering lengths are calculated and compared to the effective s-wave scattering lengths at low and high concentrations. It is found that p-scattering has an important effect on the instability of these mixtures at concentrations x > 1%. Finally, the transport coefficients are computed and compared to the theoretical predictions of Fu and Pethick and the experimental results of König and Pobell. [ABSTRACT FROM AUTHOR]

Abstract: Elastic wave scattering in a flat thin plate hosting a through obstacle of arbitrary closed form is examined using a numerical technique based on the T-matrix approach, which is applied to describe of flexural waves in plates. The limiting cases of a hole and a rigid obstacle are considered. The vibrations of the plate are described by the Kirchhoff model. The far field backscattered amplitude as a function of wave frequency for inclusions of elliptic, triangular and square form with rounded corners is analysed numerically. Comparison of present results for circular obstacles with the analytical solutions obtained by other authors show excellent agreement. [Copyright &y& Elsevier]

Multiple scattering of acoustic waves in a planar horizontal waveguide by finite-length cylinders is considered. Cylinder height equals the waveguide depth, and both are vertically constrained by the pressure-release boundaries. An analytically exact solution is obtained via normal mode expansion method in conjunction with the concept of the T matrix. The problem is decomposed into an infinite number of two-dimensional multiple scattering problems, modulated by waveguide mode shapes. Examples are presented for an isovelocity waveguide in which the medium is uniform and the waveguide depth is constant. It is found that, in numerical computations, including one or two evanescent modes captures the essence of the evanescent modes. Multiple scattering in the waveguide is compared with the corresponding two-dimensional case. It is concluded that, in low frequencies, the wave patterns in the two cases are very similar, with a shift in the frequency. The similarity diminishes when there are multiple propagating modes. Despite the mode mixing, some key features in the scattering as observed in the two-dimensional problem remain observable in the waveguide case. [ABSTRACT FROM AUTHOR]

Abstract: Acoustic scattering by bounded obstacles is considered, in both two and three dimensions. Relations between the T-matrix and the far-field pattern are derived, and then used to obtain new approximations for the T-matrix for small obstacles. The problem of scattering by a pair of small sound-soft circular cylinders is also solved, in the Rayleigh approximation, using bipolar coordinates. [Copyright &y& Elsevier]

Abstract: We develop a modification of the T-matrix method that allows efficient studies of scattering properties of ensembles of independent irregular particles of different size. The advantage of the modification is quick calculations using the so-called shape-matrices (Sh-matrices), which allow more rapid calculations of scattering by particles of different size and can be used for averaging scattering properties over particle size. To illustrate the advantage we calculate the scattering-angle dependence of the intensity and degree of linear polarization of ensembles of cubes and Chebyshev particles of different size using both the new and traditional methods. Our time savings in calculating scattering properties for the particles with the new methodology is approximately a factor of ten when calculating scattering properties of one hundred of the same type of particles with different size parameter. As can be anticipated, increasing the size interval results in a smoothing of the structure of the photometric curves and a decrease in the linear polarization. [Copyright &y& Elsevier]

A T-matrix based method of solution of the multiple scattering problem was presented by the authors [J. Acoust Soc. Am. 112, 2688–2701 (2002)]. This method can be applied to the computation of relatively small problems, since the number of operations required grows with the number of spheres N as O(N3), and with the sixth power of the wave number. The use of iterative techniques accelerated using the fast multipole method (FMM) can accelerate this solution, as presented by Koc and Chew [J. Acoust. Soc. Am. 103, 721–734 (1998)] originally. In this study we present a method that combines preconditioned Krylov subspace iterative techniques, FMM accelerated matrix vector products, a novel FMM-based preconditioner, and fast translation techniques that enable us to achieve an overall algorithm in which the cost of the matrix-vector multiplication grows with N as O(N log N) and with the third power of the wave number. We discuss the convergence of the iterative techniques, selection of the truncation number, errors in the solution, and other issues. The results of the solution of test problems obtained with the method for N∼102–104 for different wave numbers are presented. © 2005 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates the single-scattering properties of elongated hexagonal ice columns in random orientation. The calculation of these properties becomes more challenging with electromagnetic methods as the aspect ratio and/or the size parameter of the particles increases. The results presented in this paper have been obtained with a new version of a T-matrix implementation which uses only variables of data type real. This re-formulation makes it possible to run the code on a DEC Alpha workstation in quadruple precision. With the increased numerical precision aspect ratios of 10 are obtained at moderate size parameters. The single-scattering properties of elongated hexagonal columns are compared against those of various other particles. Circular cylinders of the same aspect ratio and surface area have quite similar single-scattering properties. They agree well in all phase matrix elements and the extinction efficiency and asymmetry parameter are within 25% and 5%, respectively. The single-scattering properties of elongated hexagonal columns are very different to those with equal surface-area and aspect ratios around unity. The extinction efficiencies of the more compact particles are several times larger than those of the elongated columns and the phase matrix elements are very different. The spheres of equal volume and equal surface area do not mimic the single-scattering properties of elongated hexagonal columns either. The agreement with the smaller sphere of equal volume-to-surface-area ratio is reasonable. It is found that for hexagonal columns with increasing aspect ratios, all phase matrix elements except the phase function converge to the Rayleigh solution. The results of this paper imply that such scattering behaviour, previously demonstrated for elongated spheroids, is more general and does also apply to faceted objects like hexagonal columns. [Copyright &y& Elsevier]