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Surface enhanced Raman scattering (SERS) enhancement factors G for nanoparticles consisting of a single Ag sphere or a dimer of Ag nanospheres are calculated using a T-matrix method that rigorously incorporates dipole reradiation (DR) effects. A comparison with the commonly used plane wave (PW) approximation, |Eloc(ω)|2|Eloc(ω′)|2, which for zero Stokes shift is |Eloc(ω)|4, is made so as to determine the error associated with using the PW enhancement factor instead of DR in modeling SERS intensities. Calculations for the single sphere are performed for various molecule locations, detector locations, and sphere sizes, while the dimer calculations consider the effects of molecule and detector locations for 50 nm diameter spheres with a 2 nm gap. In both the single sphere and dimer calculations, excellent agreement (<0.3%) is found between the PW approximation and DR calculations when the molecule is located along the incident field polarization direction and with the detector along an axis that is orthogonal both to the polarization and wave vector directions. The errors for other molecule locations, different detector locations, and larger sphere sizes can be considerably larger. A qualitative description of the nature of the errors is developed based on interferences between radiation emitted by the sphere and by the molecule and on quadrupole excitation in the metal spheres. An average over molecule and detector locations for both the single sphere and dimer results leads to DR enhancement factors that differ by factors of 2–3 (sometimes higher, sometimes lower) from the PW results. This indicates that for quantitative field enhancement factor calculations, the more rigorous DR result is important. [ABSTRACT FROM AUTHOR]

Highlights • Speckle size from two-dimensional angular optical scattering (TAOS) is strongly negatively correlated with cluster size of aerosol. • Simulations show that analysis of two-dimensional angular optical scattering (TAOS) is able to distinguish between non-absorbing, weakly-absorbing, and strongly-absorbing single aerosol particles. Abstract Measuring the absorption of a single aerosol particle is a challenging endeavor. Of the few techniques available, none are suitable for measuring the single-particle absorption of coarse-mode nonspherical aerosols. Analysis of two-dimensional angular optical scattering (TAOS) patterns provide a possible pathway to perform this measurement. Using a Multiple-Sphere T-Matrix (MSTM) code, we simulate the captured TAOS patterns with geometries similar to a previously designed instrument. By analyzing the size of the speckle and the integrated irradiance of these simulated TAOS patterns, we are able to distinguish between high-absorbing, weak-absorbing, and non-absorbing particles over the size range of 2 µm to 10 µm. In particular, the speckle present in the scattering patterns provides a means to estimate the size of the particle. Once the size of the particle is known, the integrated irradiance provides insight into the absorption of the particle. [ABSTRACT FROM AUTHOR]

Highlights • The spheroidal beam shape coefficients are investigated by using an intrinsic method, for the case of general oblique illumination. • The analytic solution is constructed within the framework of the GLMT. • Numerical results concerning beam shape coefficients in spheroidal coordinates are presented. Abstract When dealing with T-matrix scattering, e.g. in the framework of Generalized Lorenz-Mie Theory (GLMT) or of Extended Boundary Condition Method (EBCM), the incident electromagnetic fields are expanded over a set of vectorial wave functions, with expansion coefficients expressed in terms of beam shape coefficients (BSCs). In the case of structured beams, the evaluation of these BSCs may constitute a challenging issue, particularly in the case of spheroidal coordinates. BSCs in spheroidal coordinates have been originally evaluated using an extrinsic method, i.e. they have been expressed in terms of more conventional BSCs in spherical coordinates. Later on, it has been possible to provide expressions to evaluate spheroidal BSCs using an intrinsic approach, i.e. by working only inside the spheroidal coordinate system used to deal with the scattering problem. Fairly recently, the intrinsic method for the evaluation of BSCs in spheroidal coordinates for on-axis standard configuration has been released in the archival literature. The present paper extends the intrinsic method to the case of oblique illumination. It also serves as a review devoted to GLMTs in spheroidal coordinates. [ABSTRACT FROM AUTHOR]

Highlights • We review the recurrence relations for T-matrix calculation. • It is proved that the recurrence relations of the invariant embedding T-matrix method and the superposition T-matrix method are analytically equivalent. • It is shown that the recurrence schemes of the superposition T-matrix method are morestable than that of the invariant embedding T-matrix method. Abstract In this paper, we present a consistent analysis of the methods dealing with the derivation of recurrence relations for calculation of the T -matrix. Central and forward recurrence relations are obtained in the framework of the invariant embedding T -matrix method, the matrix Riccati equation method, and the superposition T -matrix method. The accuracies and efficiencies of the central and forward recurrence schemes are analyzed, and some implementation issues related to the improvement of the numerical accuracy and to the problem of overcoming of overflow errors are discussed. [ABSTRACT FROM AUTHOR]

The simulation of light scattering by particles on a substrate with the T -matrix method relies on the expansion of the scattered field in spherical waves, followed by a plane wave expansion to allow the evaluation of the reflection from the substrate. In practice, the plane wave expansion (i.e., the Sommerfeld integrals) needs to be truncated at a maximal in-plane wavenumber κ max . An appropriate selection of κ max is essential: counter-intuitively, the overall accuracy can degrade significantly if the integrals are truncated with a too large value. In this paper, we propose an empirical formula for the selection of κ max and discuss its application using a number of example simulations with dielectric and metallic oblate spheroids on dielectric and metallic substrates. The computed differential scattering cross sections are compared to results obtained from the discrete-sources method. [ABSTRACT FROM AUTHOR]

The T -matrix method pioneered by Peter C. Waterman is one of the most versatile and efficient numerically exact computer solvers of the time-harmonic macroscopic Maxwell equations. It is widely used for the computation of electromagnetic scattering by single and composite particles, discrete random media, periodic structures (including metamaterials), and particles in the vicinity of plane or rough interfaces separating media with different refractive indices. This paper is the eighth update to the comprehensive thematic database of peer-reviewed T -matrix publications initiated in 2004 and lists relevant publications that have appeared since 2015. It also references a small number of earlier publications overlooked previously. [ABSTRACT FROM AUTHOR]

Subradiant modes can exhibit sharper spectral response, and lower radiative loss compared to the super-radiant modes of plasmonic nanostructures. Selective excitation of these modes is challenging, and has practical importance. In this paper, a systematic procedure for determining, and individually exciting the subradiant modes of a plasmonic nanostructure is presented by utilizing our previously reported T-matrix formulation. As an example, we calculate various modes of a gold nanodimer, and determine the incident field required for exciting a subradiant mode of this nanostructure. This field is then generated by a modified zone plate lens. The expansion of scattered field, as well as the scattering power spectrum confirms the excitation of the subradiant mode. The total field is compared with those obtained using the finite-difference time domain method and method of moments. [ABSTRACT FROM AUTHOR]

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]

Abstract: This paper is the sixth update to the comprehensive thematic database of peer-reviewed T-matrix publications initiated by us in 2004 and includes relevant publications that have appeared since 2013. It also lists several earlier publications not incorporated in the original database and previous updates. [Copyright &y& Elsevier]

We consider matrix structures in the quantum N-body problem that generalize the Faddeev components for resolvents, T-matrices, and eigenfunctions of the continuous spectrum. We write matrix equations for the introduced components of T-matrices and resolvents and use these equations to obtain matrix operators generalizing the matrix three-particle Faddeev operators to the case of arbitrarily many particles. We determine the eigenfunctions of the continuous spectrum of these matrix operators. [ABSTRACT FROM AUTHOR]

By selecting any one limb of 3-RSR parallel robot as a research object, the paper establishes a position and orientation relationship matrix between the moving platform and the base by means of Denavit-Hartenberg (D-H) transformation matrix. The error mapping model is derived from original error to the error of the platform by using matrix differential method. This model contains all geometric original errors of the robot. The nonlinear implicit function relation between position and orientation error of the platform and the original geometric errors is simplified as a linear explicit function relation. The results provide a basis for further studying error analysis and error compensation. [ABSTRACT FROM AUTHOR]

In this paper, we study the in-medium nucleon-nucleon (NN) cross-section by using the Dirac-Breuckner-Hartree-Fock approximation (DBHF) with T-matrix project technique for determining the nucleon self-energy. By solving Thompson equation for different partial-wave states separately, we find that the discrepancies of nucleon self-energies in various T-matrix project representations are dominated by the channels with smaller angular momentum. Although the cross-section is independent on the project of T-matrix, the medium suppression of the cross-section in various T-matrix representations are apparently different due to the self-consistency of DBHF calculation involving effect mass of nucleon as an iterative parameter. Our results also show that the crosssections in the complete pseudovector (CPV) choices are larger than those obtained with both DBHF in the pseudosealar (PS) choice and nonrelativistic Brueckner-Hartre-Fock with three-body force (BHF+3BF), respectively. Further comparison shows that the neutron-proton (NP) cross-section within DBHF + PV approach, σNPPV, is approximately equal to and slightly larger than that evaluated with BHF+3BF, σNP3BF, while the neutron-neutron (NN) (or proton-proton (PP)) cross-section given by DBHF+PV method, σNNPV, being the closest to the cross-section calculated by using BHF without 3BF in the lower energy region. Additionally, the discrepancies of the in-medium nucleonnucleon differential cross-section induced by different representations of T-matrix in DBHF are discussed for nuclear matter with different densities. [ABSTRACT FROM AUTHOR]

The 2D problem of diffraction of a plane wave by a periodically irregular perfectly conducting surface is solved with the help of the null-field method. Comparative analysis of the computation accuracy is performed for various techniques of choosing an auxiliary contour on which the null-field condition is imposed. It is shown that the choice of an auxiliary contour based on the analytical deformation of the surface contour is an optimal technique. [ABSTRACT FROM AUTHOR]

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: We simulated light-scattering by small and wavelength-sized cubes with three largely different values of the refractive index using the discrete dipole approximation (DDA) and the T-matrix method. Our main goal was to push the accuracy of both methods to the limit. For the DDA we used an earlier developed extrapolation technique based on simulation results for different levels of discretization. For the T-matrix method we developed a procedure to estimate a confidence range for the simulated value, using results for different values of the truncation index (number of multipoles). In most cases this confidence range was reliable, enclosing the corresponding DDA result. We present benchmark results by both methods, including estimated uncertainties, for selected integral and angle-resolved scattering quantities. Estimated relative uncertainties of the DDA result are unprecedentedly small (from 10−7 to 10−3), while relative differences between the T-matrix and DDA results are larger (from 10−4 to 0.2) in accordance with estimated T-matrix uncertainties. [Copyright &y& Elsevier]

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: The T-matrix method is one of the most versatile, efficient, and accurate theoretical techniques widely used for numerically exact computer calculations of electromagnetic scattering by single and composite particles, discrete random media, and particles imbedded in complex environments. This paper presents the fifth update to the comprehensive database of peer-reviewed T-matrix publications initiated by us in 2004 and includes relevant publications that have appeared since 2012. It also lists several earlier publications not incorporated in the original database, including Peter Waterman's reports from the 1960s illustrating the history of the T-matrix approach and demonstrating that John Fikioris and Peter Waterman were the true pioneers of the multi-sphere method otherwise known as the generalized Lorenz–Mie theory. [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]

A simplified calibration procedure using T-matrix concept is presented for two-port vector network analyzer (VNA) with three measurement channels. Compared with Short-Open-Load-Thru (SOLT) calibration method based on 10-term error model where 10 error terms must be solved and saved at each frequency, the proposed method need define fewer characteristic variables. Moreover, a length- unknown 50Ω line can be used instead of a random single-port standard, for example, substituting Load standard with 50Ω line in SOLT calibration procedure. Via the simplified calibration procedure, the scattering parameters of a two-port device under test (DUT) can be finally obtained. Experimental verification is carried out, and good agreement is observed. [ABSTRACT FROM AUTHOR]

A new method is proposed for realizing radar illusion of an electromagnetic target by using active devices. The devices are installed around the target but may closely cover the target or not, leading to closed or open configurations. The amplitudes and phases of the active devices are determined by using T-matrix method. The numerical computation is calculated using MATLAB, and the results show that this method is convenient, flexible, and efficient, which has important significances for implementation of novel electromagnetic devices. [ABSTRACT FROM AUTHOR]

We combine group theory with a perturbation approach to perform T-matrix computations for particles with small-scale surface roughness up to size parameters of 70. The optical properties of high-order 3D-Chebyshev particles differ substantially from those of spheres. CPU times are reduced by more than 4-5 orders of magnitude by the use of group theory, while the perturbation approach circumvents the notorious ill-conditioning problems of the null-field method, thus allowing the treatment of large size parameters. [ABSTRACT FROM AUTHOR]

Abstract: We propose an orientation averaging scheme which we call optimal cubature on the sphere to be used in light scattering computations. The cubature points are optimally arranged on the sphere to produce non-biased and fast convergence in scattering problems requiring numerical orientation averaging. We will compare performance against other possible schemes. [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]

The composition and structure of the NiPd(111) alloy surface are measured using low energy electron diffraction (LEED). The diffracted intensities are analyzed using tensor-LEED methods with the average t-matrix approximation. The major composition results of the study are that the surface is enriched in palladium (≈80% Pd) while the second layer is enriched in nickel (≈28% Pd). No significant structural changes were found, with all measured interlayer displacements being smaller than the corresponding measurement uncertainties. Comparisons of these results are made with literature for other NiPd low-index surfaces, for the well-studied NiPt(111) surface, and with the growing body of theoretical literature for NiPd alloy surfaces. [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]

The screening limit of the three-dimensional half-shell t-matrix for a sharply cut-off Coulomb potential is analytically derived without reference to partial wave expansion. The numerical solutions of the three-dimensional Lippmann–Schwinger equation for increasing cut-off radii provide half-shell t-matrices which are in quite a good agreement with the asymptotic values. [ABSTRACT FROM AUTHOR]

Abstract: The introduction of the Sh-matrices in the T-matrix method allows the shape-dependent parameters to be separated from size- and refractive-index-dependent parameters. This separation also allows for the surface integrals to be solved and for analytic solutions to the light-scattering from particles of some shapes to be found. In this manuscript we derive and analyze the analytical solution for small concave lenses bounded with different spherical surfaces. [Copyright &y& Elsevier]

This paper presents novel modeling methods for accurate and efficient analysis of coupling of multiple vias in finite-sized multilayered parallel-plate structures. The new modeling methods address two open problems related to the modal expansion with the T-matrix method for the analysis of via coupling. First, a novel boundary modeling method, called the frequency-dependent cylinder layer (FDCL), is proposed to resolve the open problem of boundary modeling. In the FDCL, virtual cylinders with dynamic radii are postulated to approximate the original finite-sized boundary of parallel-plate structures. Second, a generalized T-matrix model, which is derived by the mode-matching technique, is created to characterize the coupling effect for vias penetrating more than one layer in a multilayered structure. With the two open problems successfully solved, the modal expansion with the T-matrix method incorporating the FDCL boundary modeling method and the generalized T-matrix model can now be fully utilized for efficient and accurate analysis of finite-sized multilayered parallel-plate structures with a large number of vias. Both numerical and experimental verifications are presented to validate the new modeling methods. [ABSTRACT FROM AUTHOR]

Within the 1D Hubbard model, linear closed chains with various numbers of sites are considered in particle–particle self-consistent random phase approximation (SCRPA) for the T-matrix. Encouraging results with a minimal numerical effort are obtained, confirming earlier results with this theory for other models. SCRPA solves the two-site problem exactly. It therefore contains the two electrons and high density Fermi gas limits correctly. [ABSTRACT FROM AUTHOR]

We propose a generalized T-matrix definition that facilitates the conversion between the S-parameter and T-parameter for multiport networks based on the well understood and mathematically simple two-port relations. This approach generalizes all multiport networks into two cases: balanced and unbalanced. Balanced networks have the same number of en- trance and exit ports and are symmetric to the two-port network. Unbalanced networks generate a nonsquare T-matrix and do not have the same number of entrance and exit ports. Through careful selection of the T-matrix, this method extends two-port symmetry to multiport networks and provides an engineering implementable relationship between the S-parameter and T-parameter for multiport networks. This symmetry extension allows a practical means to cascade and deembed such networks. [ABSTRACT FROM AUTHOR]

Abstract: In a recent paper we proposed a decompositioning method to compute scattering by aggregated cylindrical fibres using a multiple scattering T-matrix approach. In this paper we extend this approach to scatterers lacking rotational symmetry. To investigate the capability of this method a square prism and a cube are decomposed into a number of subscatterers and scattering of the original particle shape is computed using multiple scattering. The results are validated using discrete dipole approximation (DDA). [Copyright &y& Elsevier]

Abstract: We studied numerical orientation averaging with three methods for selection of orientations: lattice-grid division, crude Monte-Carlo (CMC) method, and quasi-Monte-Carlo (QMC) method. Numerical orientation averaging with these methods are carried out with a fixed orientation version of the T-matrix method for clusters of spheres. The errors of numerical orientation averaging as a function of number of orientations are investigated by comparison with results from analytical orientation averaging of the T-matrix method. We studied four types of aggregates: a bisphere, ballistic cluster–cluster aggregates of 4 and 128 monomers (BCCA4 and BCCA128), and a ballistic particle–cluster aggregate of 128 monomers (BPCA128). We studied convergence of the scattering efficiency , absorption efficiency , asymmetry parameter g, intensity , and degree of linear polarization . For the polarization, scattering angles of maximum () and minimum () polarization in results of analytical orientation averaging are considered. For the intensity, in addition to and , forward scattering angle () is also considered. , and g of bisphere, BCCA4, and BPCA128 can be obtained accurately with smallest number of orientations by using QMC among three methods. Errors in , and g of BCCA128 were already small for smaller number of orientations (e.g., 100) with all the three methods. generally shows slow convergence requiring several thousands of orientations to have errors less than 1%. There are also cases where convergence of within 1% error is not attained even for largest number of orientations studied in this paper (i.e., BCCA4 with lattice-grid, BCCA128 with lattice-grid, BCCA128 with CMC). Intensity of , and , and polarization of generally show convergence within 1% error for several hundreds to 1000 orientations with three methods for selection of orientation angles. Among three methods, QMC requires smallest number of orientations for intensity and polarization. We also investigated convergence of and . Convergence of and is generally attained for 100–1000 orientations. We also described the application of the method to the discrete dipole approximation. In these calculations, we considered three shape models with different number of dipoles and different dipole representations to describe BCCA4. The results show that scattering and absorption efficiencies, and asymmetry parameter can generally be obtained within 1% errors for all the three shape models. On the other hand, errors are larger for intensity (up to 10%) and polarization (up to 50–70%). [Copyright &y& Elsevier]

The resonance and radiation characteristics of a spherical microstrip with its circular metallic patch located inside a coating, possessing an arbitrary number of layers, are investigated. The developed methodology combines the Legendre transform with a T-matrix method. The appropriate basis functions for the surface current on the patch are chosen according to the cavity model. The complex resonant frequencies are the singular points of a homogeneous linear system, resulting by following a Galerkin's technique. The numerical results of this article propose novel multi-layered spherical microstrip configurations. More precisely, a new type of excitation that concerns an amplifying layer located between core and patch is proposed. The control mechanism of the amplifying capability via the layer's thickness and dielectric constant is reported. Moreover, the behavior of a microstrip with two airgaps that are surrounded by a zero-index material is analyzed. Finally, a coating's continuous distribution, following a “shifted” Luneburg law, is treated by a step approximation of the radial function of its dielectric constant, and the achieved high quality factor of such a microstrip is discussed. [ABSTRACT FROM AUTHOR]

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: Light scattering is an useful tool for the detection and characterization of different types of particles and simulation of the scattering process can help to understand the scattering characteristics. To simplify the computational simulation often axis-symmetric particles are used, while in reality particles usually do not show such simple structures. To cope with this, advanced methods and algorithms are needed. In this paper we investigate the scattering characteristics by spherical particles with a rough surface, which therefore are non-symmetrical. The light scattering diagrams by these complex structured particles are computed using the nullfield method with discrete sources. The particle shape data is generated by computational methods; here we use the concept of Gardner Series to create spherical particles with a rough surface. [Copyright &y& Elsevier]

Abstract: The T-matrix method is particularly useful for modeling light scattering by mesoscale particles under non-plane wave illumination. Its main advantage lies where repeated calculations with different incident conditions are required, e.g. as particles move through a focused beam, or are optically trapped by a beam. The extended boundary condition method (EBCM) is the most commonly used method for calculating a T-matrix. However, the conventional EBCM is limited to modeling particles that are isotropic and homogeneous. Because scattering by anisotropic and inhomogeneous particles is of practical interest, we have implemented an FDFD T-matrix hybrid method. [Copyright &y& Elsevier]

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 solution to scattering from a cylinder buried arbitrarily in layered media with rough interfaces based on extended boundary condition method (EBCM) and scattering matrix technique is developed. The reflection and transmission matrices of arbitrary rough interfaces as well as an isolated single cylinder are constructed using EBCM and recursive T-matrix algorithm, respectively. The cylinder/rough surface interactions are taken into account by applying the generalized scattering matrix technique. The scattering matrix technique is used to cascade reflection and transmission matrices from individual systems (i.e., rough surfaces or cylinders) in order to obtain the scattering pattern from the overall system. Bistatic scattering coefficients are then obtained by incoherently averaging the power computed from the resulting Floquet modes of the overall system. In numerical simulations, the bistatic scattering coefficients are first validated by comparing the simulation results with the existing solutions which are the limiting cases including scattering from two-interface rough surfaces without any buried object and from a buried cylinder beneath a single rough surface. Subsequently, the numerical simulations of scattering from a buried cylinder in layered rough surfaces are performed to investigate the relative importance and sensitivity of various physical parameters of layered rough surfaces to incoherent scattering coefficients. Results show layered rough interfaces can significantly alter the scattering behaviors of a buried cylinder. [ABSTRACT FROM AUTHOR]

The article elaborates solution to the Parquet Equations for a Two-Matrix Model. The vacuum energy and correlation functions were calculated for the Hermitian zero-dimensional single matrix model. The planar-parquet approximation was also suggested. Considering the symmetric form of the potential, a truncated system of planar-parquet equations for the propagators is analyzed to present a numerical solution. It is concluded that these two approaches are in good agreement.

Abstract: We present calculations of scattering of solar UV radiation from polar mesospheric clouds (PMC) for the wavelengths and scattering angles appropriate to the SBUV/2 series of satellite experiments. Our model includes for the first time the effects of non-sphericity of ice particles whose evidence has been recently gained from lidar depolarization experiments. Our results apply to the scattering cross section averaged over a particle size ensemble which spans the mean size and size ranges expected for PMC. We demonstrate that for the size range 20–100nm (effective spherical particle radius), the wavelength range 252–292nm, and the scattering angle range 100–, non-spherical particles cause only moderate () deviations from conventional Mie theory, which assumes spherical shapes. The total UV scattering efficiency of PMC particles per unit mass of water vapor is not significantly affected by shape effects, in the range of parameters studied. On the other hand, our study suggests that shape effects need to be considered in the analysis of UV spectra of PMC, such as those of Carbary et al. [2004. Evidence for bimodal particle distribution from the spectra of polar mesospheric clouds. Geophysical Research Letters 31 (13), 3108] and DeLand et al. [2005. Spectral measurements of PMCs from SBUV/2 instruments. Journal of Atmospheric and Solar-Terrestrial Physics, to appear, doi: 10.1016/j.astp.2005.08.006]. In particular, attention must also be paid to the scattering angle dependence of the measurements, and the range of scattering angles involved in compiling average spectra of PMC. [Copyright &y& Elsevier]

Abstract: A computer code is described for the calculation of light-scattering properties of randomly oriented, axially symmetric coated particles, in the framework of the T-matrix theory. The underlying mathematical background is outlined briefly and convergence procedures are discussed. After outlining the input–output interaction between user and code, benchmark results are presented for two distinct shapes: coated, centered spheroids and offset coated spheres. [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]

A procedure for analytical averaging of the attenuation and scattering cross sections for systems of chaotically oriented axially symmetric particles was developed for the first time within the framework of the modified T-matrix method and the method of separation of variables for spheroids. These approaches essentially complement each other: one is applicable to axially symmetric scatterers of different shape but is inefficient if the ratio of the maximum to the minimum size of the particles exceeds 3–5; the other is applicable only to spheroids, but the ratio of the major semiaxis to the minor one can be considerable, for example, 100 and larger. © 2004 MAIK “Nauka / Interperiodica”. [ABSTRACT FROM AUTHOR]

Two different types of orthogonality condition models (OCM) are equivalently formulated in the Faddeev formalism. One is the OCM which uses pairwise orthogonality conditions for the relative motion of clusters, and the other is the one which uses the orthogonalizing pseudo-potential method. By constructing a redundancy-free T-matrix, one can exactly eliminate the redundant components of the total wave function for the harmonic-oscillator Pauli-forbidden states, without introducing any limiting procedure. As an example, a three-α-particle model interacting via the deep αα potential by Buck, Friedrich, and Wheatley is investigated. [ABSTRACT FROM AUTHOR]

In this article, we perform a self-consistent calculation for the self-energy, based on the pairing mechanism for the two-dimensional phenomenological model below half filling. The non-Fermi versus Fermi liquid behavior is analyzed and the self-energies are compared. We also investigate the doping dependence of the pseudogap in the underdoped regime of the phase diagram of cuprates superconductors. Comparing the obtained results with experimental data, it is found that Δ[sub pg] scales with characteristic temperature T*. [ABSTRACT FROM AUTHOR]

We discuss the pseudogap phenomena in High-T[sub c] superconductors. The superconducting fluctuation is taken into account as an origin of the pseudogap. Then, the T-matrix approach has been widely used. We report a development along this line. The higher order correction, which is important to capture the effects of the SC fluctuation more precisely, is investigated. It is shown that the vertex correction, which is not included in the self-consistent T-matrix approximation, enhances the pseudogap. [ABSTRACT FROM AUTHOR]

We formulate quantum scattering theory in terms of a discrete L2-basis of eigen differentials. Using projection operators in the Hilbert space, we develop a universal method for constructing finite-dimensional analogues of the basic operators of the scattering theory: S- and T-matrices, resolvent operators, and Möller wave operators as well as the analogues of resolvent identities and the Lippmann-Schwinger equations for the T-matrix. The developed general formalism of the discrete scattering theory results in a very simple calculation scheme for a broad class of interaction operators. [ABSTRACT FROM AUTHOR]