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Flexural-gravity wave scattering by an array of vertical porous barriers of various configurations is investigated in finite water depth from the viewpoint of blocking dynamics. A scattering matrix is introduced for the velocity potentials using the canonical eigenfunction expansion method developed for a single propagating wave mode to account for the multiple propagating wave modes. Subsequently, appropriate matching conditions are applied at the interface boundaries and edges to solve the physical problem. Apart from multiple barriers of equal length, the efficiency of four different barrier configurations of unequal lengths is investigated. This study shows that out of these four barrier configurations, the convex and increasing order of the barrier arrangements are more effective as wave-dissipating systems than the concave and decreasing order of the barriers. Bragg reflection occurs in the case of two or more barriers for a specific value of porosity and suitable barrier configuration, whose amplitude decreases with an increase in the number of barriers due to the dissipation of wave energy. The presence of three propagating wave modes in the blocking paradigm leads to mode conversion within a certain range of the frequency space. Both the scattering and dissipation coefficients are influenced by the wave energy transfer rates and the amplitudes of incident, reflected, and transmitted wave modes. This investigation exhibits the presence of discontinuities in the scattering coefficients at frequencies where blocking and mode conversion occur. The frequency domain results are used to simulate the plate displacement in the time domain by applying the Fourier transform. [ABSTRACT FROM AUTHOR]

The scattering matrix (S-matrix) encodes the elastodynamic scattering behaviour of a defect. For the case of guided waves in the low-frequency regime, we explore how to minimise the number of incident/scattered directions used to accurately simulate the S-matrix of an arbitrary defect. The general approach is to use three-dimensional finite element (FE) analysis, implemented in a commercial FE package, to simulate the wave-defect interactions. The scattered wave field is measured at monitoring nodes on a circle that surrounds the defect. These scattered waves are decomposed into the multi-modal far-field scattering amplitudes. The angular order of the scattering is found and used to minimise the number of incident and scattered directions that must be computed. The method is then used to simulate the S-matrices of surface-breaking semi-elliptical cracks and circular through-holes with arbitrary sizes. It is found that the required number of incident/scattered directions varies with the scattered mode, and this is due to the differing scattering orders of these scattered fields. These results demonstrate how to achieve more efficient modelling of guided wave scattering, and also contribute to an understanding of experimental defect characterisation. [ABSTRACT FROM AUTHOR]

We study the interactions of systems of two and three nondegenerate mesons composed of pions and kaons at maximal isospin using lattice QCD, specifically π+K+, π+π+K+ and K+K+π+. Utilizing the stochastic LapH method, we determine the spectrum of these systems on two CLS Nf = 2 + 1 ensembles with pion masses of 200 MeV and 340 MeV, and include many levels in different momentum frames. We constrain the K matrices describing two- and three-particle interactions by fitting the spectrum to the results predicted by the finite-volume formalism, including up to p waves. This requires also results for the π+π+ and K+K+ spectrum, which have been obtained previously on the same configurations. We explore different fitting strategies, comparing fits to energy shifts with fits to energies boosted to the rest frame, and also comparing simultaneous global fits to all relevant two- and three-particle channels to those where we first fit two-particle channels and then add in the three-particle information. We provide the first determination of the three-particle K matrix in π+π+K+ and K+K+π+ systems, finding statistically significant nonzero results in most cases. We include s and p waves in the K matrix for π+K+ scattering, finding evidence for an attractive p-wave scattering length. We compare our results to Chiral Perturbation Theory, including an investigation of the impact of discretization errors, for which we provide the leading order predictions obtained using Wilson Chiral Perturbation Theory. [ABSTRACT FROM AUTHOR]

A thorough understanding of the scattering mechanism of Lamb waves at discontinuities is of interest for quantitative evaluation of structural properties and mode control. This study extends the generalized scattering matrix method to investigate the interaction of straight crested Lamb waves with multiple cascaded rectangular notches. Based on the orthogonality and completeness of Lamb modes, the mode matching method is utilized to determine the scattering matrices of downward and upward step discontinuities. After that, the generalized scattering matrix method is employed to determine the scattering matrices of a single rectangular notch and the recurrence relations between the scattering matrices of n + 1 cascaded notches and those of n cascaded notches. Finally, the scattering matrices of multiple cascaded notches can be easily obtained taking advantage of the recurrence relations. As the number of cascaded notches increases, more and sharper peaks appear in the scattering coefficient curves. The finite element simulations conducted in the time domain validate the theoretical results for cascaded notches with identical or different depths, which demonstrate that this method can be applied to find the scattering coefficients at piece-wise periodic or nonperiodic waveguides. The generalized scattering matrix method may have potential applications in quantitative nondestructive evaluation and mode control. [ABSTRACT FROM AUTHOR]

A new approach for the quantum-state resolved analysis of polyatomic reactions is introduced. Based on the singular value decomposition of the S-matrix, energy-dependent natural reaction channels and natural reaction probabilities are defined. It is shown that the natural reaction probabilities are equal to the eigenvalues of the reaction probability operator [U. Manthe and W. H. Miller, J. Chem. Phys. 99, 3411 (1993)]. Consequently, the natural reaction channels can be interpreted as uniquely defined pathways through the transition state of the reaction. The analysis can efficiently be combined with reactive scattering calculations based on the propagation of thermal flux eigenstates. In contrast to a decomposition based straightforwardly on thermal flux eigenstates, it does not depend on the choice of the dividing surface separating reactants from products. The new approach is illustrated studying a prototypical example, the H + CH4 → H2 + CH3 reaction. The natural reaction probabilities and the contributions of the different vibrational states of the methyl product to the natural reaction channels are calculated and discussed. The relation between the thermal flux eigenstates and the natural reaction channels is studied in detail. [ABSTRACT FROM AUTHOR]

When wave scattering systems are subject to certain symmetries, resonant states may decouple from the far-field continuum; they remain localized to the structure and cannot be excited by incident waves from the far field. In this work, we use layer-potential techniques to prove the existence of such states, known as bound states in the continuum, in systems of subwavelength resonators. When the symmetry is slightly broken, this resonant state can be excited from the far field. Remarkably, this may create asymmetric (Fano-type) scattering behavior where the transmission is fundamentally different for frequencies on either side of the resonant frequency. Using asymptotic analysis, we compute the scattering matrix of the system explicitly, thereby characterizing this Fano-type transmission anomaly. [ABSTRACT FROM AUTHOR]

The scattering of flexural-gravity waves in a thin floating plate is investigated in the presence of compression. In this case, wave blocking occurs, which is associated with both a zero in the group velocity and coalition of two or more roots of the related dispersion relation. There exists a region in the frequency space in which there are three real roots of the dispersion equation and hence three propagating modes. This multiplicity leads to mode conversion when scattering occurs. In one of these modes, the energy propagation direction is opposite to the wavenumber, making enforcement of the Sommerfeld radiation condition challenging. The focus here is on a canonical problem in flexural-gravity wave scattering, the scattering of waves by a crack. Formulae are developed that apply uniformly at all frequencies, including through the blocking frequencies. This solution is developed by tracking the movement of the dispersion relation roots carefully in the complex plane. The mode conversion is verified by the scattering matrix of the process and through an energy identity. This energy identity for the case of more than one progressive modes is established using Green’s theorem and later applied in the scattering matrix to identify the incident and transmitted waves in the scattering process and derive the radiation condition. Appropriate scaling of the reflection and transmission coefficients are provided with the energy identity. The solution method is illustrated with numerical examples. [ABSTRACT FROM AUTHOR]

The scattering phenomena of the fundamental antisymmetric Lamb wave mode with a horizontal notch enabling the partial energy transfer (PET) option is addressed in this paper. The PET functionality for a given waveguide is realized using the material interface. The energy scattering coefficients are identified using two methods, namely, a hybrid approach, which utilizes the finite element method (FEM) and the general orthogonality relation, and the semi-analytical approach, which combines the modal expansion technique with the orthogonal property of Lamb waves. Using the stress and displacement continuity conditions on the present (sub)waveguide interfaces, one can explicitly derive the global scattering matrix, which allows detailed analysis of the scattering process across the considered interfaces. Both methods are then adopted on a simple representation of a surface breaking crack in the form of a vertical notch, of which a certain section enables not only the reflection of the incident energy, but also its nonzero transfer. The presented results show very good conformity between both utilized approaches, thus leading to further development of an alternative technique. [ABSTRACT FROM AUTHOR]

We present a theoretical study of the indirect dissociative recombination of linear polyatomic ions at low collisional energies. The approach is based on the computation of the scattering matrix just above the ionization threshold and enables the explicit determination of all diabatic electronic couplings responsible for dissociative recombination. In addition, we use the multi-channel quantumdefect theory to demonstrate the precision of the scattering matrix by reproducing accurately ab initio Rydberg state energies of the neutral molecule. We consider the molecular ions N2H+ and HCO+ as benchmark systems of astrophysical interest and improve former theoretical studies, which had repeatedly produced smaller cross sections than experimentally measured. Specifically, we demonstrate the crucial role of the previously overlooked stretching modes for linear polyatomic ions with large permanent dipole moment. The theoretical cross sections for both ions agree well with experimental data over a wide energy range. Finally, we consider the potential role of the HOC+ isomer in the experimental cross sections of HCO+ at energies below 10 meV. [ABSTRACT FROM AUTHOR]

Scattering on an ultralow potential in an armchair graphene nanoribbon is studied. Using the continuous Dirac model and including a couple of artificial waves in the scattering process, described by an augmented scattering matrix, a condition is derived for the existence of a trapped mode. Threshold energies, where the multiplicity of the continuous spectrum changes, are considered, and it is shown that a trapped mode may appear for energies slightly less than a threshold and its multiplicity does not exceed one. For energies that are higher than a threshold, there are no trapped modes, provided that the potential is sufficiently small. [ABSTRACT FROM AUTHOR]

We construct asymptotic representations for large values of the hyperradius for the scattering wave function of an -particles system regarded as a generalized function of angular coordinates. We express the coefficients of the asymptotic representations in terms of the -particle scattering matrix. We discover the phenomenon of asymptotic filtration: only scattering processes in which all particles are free both before and after interaction contribute to the leading terms of such an asymptotic representation. We use the obtained representations to construct the correct asymptotic forms of the partial components of the -particle wave function in the hyperspherical representation. [ABSTRACT FROM AUTHOR]

• Semi-analytical approach presenting derivation of the scattering matrix related to the region with adhesively bonded joint. • Effect of the energy balance convergence of local sub-waveguide sections on the global scattering matrix. • Effect of the number of considered complex wavenumbers entering the computational process on the predicted results accuracy. Problems related to scattering phenomena of the antisymmetric fundamental Lamb wave mode with an adhesively bonded lap joint containing a disbond in the adhesive layer is being solved within the framework of this paper. Overall, two methods are used in order to identify energy scattering coefficients of reflected as well as transmitted Lamb waves. These methods include a hybrid approach, which incorporates the finite element method (FEM) with general orthogonality relation, and semi-analytical approach, combining the modal expansion technique and orthogonal property of Lamb waves. With the use of the stress and displacement continuity condition on selected interfaces, it is possible to explicitly derive the global scattering matrix, containing the information related to the scattering process of present Lamb wave modes in a given geometry. Both approaches are then adopted on three configurations of the adhesively bonded lap joint in terms of the length of the disbond, which is then positioned within the overlapped region. The obtained results, among others, clarify the relationship between geometric parameters of the region containing the overlapping with the horizontal disbond and the role of non-propagating modes in the computational process of energy scattering coefficients of propagating modes. [ABSTRACT FROM AUTHOR]

Two forms of carbon‐rich microfossils were discovered in the breccias of the Onaping Formation, Sudbury impact structure. The first form is represented by single particles scattered in the matrix of the breccias and included in the vesicles in altered glass. These particles are leaf‐shaped, stem‐shaped, tubular, and spherical objects ranging from 5–10 μm to 200–300 µm in size. It is suggested that algal flora inhabiting the ocean basin before the Sudbury impact was the source of plant material in the Onaping Formation. The second form of carbon‐rich microparticles in the Onaping Formation is represented by plant detritus in carbon‐bearing fragments of mudstones included in the breccia matrix. The microparticles in the mudstones are mainly ribbon‐like shreds from 3–5 µm to 200–300 µm long, while rare particles have more complex shapes. The matrix of the mudstones is a fine‐grained clay‐like substance with a network of micron‐wide open‐joint fissures. Contents of carbon in the mudstone matrix are 12–15 wt%. Muddy bottom sediments of the pre‐impact sea are supposed as a source of mudstone fragments in the breccias. Fragments of mudstones and carbon‐rich microparticles are an important source of organic carbon in the breccias of the Onaping Formation. Discovery of microfossils in the breccias of the Onaping Formation suggests the presence of a previously unknown complex algal flora that inhabited the pre‐impact sea before the impact event 1.85 billion years ago at the very end of the Paleoproterozoic. [ABSTRACT FROM AUTHOR]

Three new contributions to the complex angular momentum (CAM) theory of differential cross sections (DCSs) for chemical reactions are reported. They exploit recent advances in the Padé reconstruction of a scattering (S) matrix in a region surrounding the ReJ axis, where J is the total angular momentum quantum variable, starting from the discrete values, J = 0, 1, 2, .... In particular, use is made of Padé continuations obtained by Sokolovski, Castillo, and Tully [Chem. Phys. Lett. 313, 225 (1999)] for the S matrix of the benchmark F + H2(vi = 0, ji = 0, mi = 0) → FH(vf = 3, jf = 3, mf = 0) + H reaction. Here vi, ji, mi and vf, jf, mf are the initial and final vibrational, rotational, and helicity quantum numbers, respectively. The three contributions are: (1) A new exact decomposition of the partial wave (PW) S matrix is introduced, which is called the QP decomposition. The P part contains information on the Regge poles. The Q part is then constructed exactly by subtracting a rapidly oscillating phase and the PW P matrix from the input PW S matrix. After a simple modification, it is found that the corresponding scattering subamplitudes provide insight into the angular-scattering dynamics using simple partial wave series (PWS) computations. It is shown that the leading n = 0 Regge pole contributes to the small-angle scattering in the centre-of-mass frame. (2) The Q matrix part of the QP decomposition has simpler properties than the input S matrix. This fact is exploited to deduce a parametrized (analytic) formula for the PW S matrix in which all terms have a direct physical interpretation. This is a long sort-after goal in reaction dynamics, and in particular for the state-to-state F + H2 reaction. (3) The first definitive test is reported for the accuracy of a uniform semiclassical (asymptotic) CAM theory for a DCS based on the Watson transformation. The parametrized S matrix obtained in contribution (2) is used in both the PW and semiclassical parts of the calculation. Powerful uniform asymptotic approximations are employed for the background integral; they allow for the proximity of a Regge pole and a saddle point. The CAM DCS agrees well with the PWS DCS, across the whole angular range, except close to the forward and backward directions, where, as expected, the CAM theory becomes non-uniform. At small angles, θR <= 40°, the PWS DCS can be reproduced using a nearside semiclassical subamplitude, which allows for a pole being close to a saddle point, plus the farside surface wave of the n = 0 pole sub-subamplitude, with the oscillations in the DCS arising from nearside-farside interference. This proves that the n = 0 Regge resonance pole contributes to the small-angle scattering. [ABSTRACT FROM AUTHOR]

We present a time-dependent, hyperspherical wave packet method for calculating three-atom state-to-state S-matrix elements. The wave packet is propagated in time using adiabatically adjusting, principal axes hyperspherical coordinates that treat all arrangement channels equivalently, allowing the simultaneous analysis of the products in all three arrangement channels. We take advantage of the symmetry of the potential energy surface and decompose the initial wave packet into its component irreducible representations, propagating each component separately. Each irreducible representation component of the wave packet is analyzed by projecting it onto the hyperspherical basis at a fixed, asymptotic hyperradius, and irreducible representation dependent S-matrix elements are obtained by matching the hyperspherical projections to symmetry-adapted Jacobi coordinate boundary conditions. We obtain arrangement channel-dependent S-matrix elements as linear combinations of the irreducible representation dependent elements. State-to-state H + H2 and F + H2 results for zero total angular momentum are presented. [ABSTRACT FROM AUTHOR]

This article is meant as an encomium of the life-span endeavor of Jacques Raynal to relate nuclear scattering density matrices with numerical methods. The mathematical investigations he made involved intricate hypergeometric coupling algebras and transformations. He was among the first to appreciate the general importance of these studies. His efforts over 60 years are most praiseworthy and, for them, Jacques has gained much respect. [ABSTRACT FROM AUTHOR]

Today polarization-processing devices are widely used in satellite information systems. Waveguide polarizers are the key element of antenna systems used to convert signal polarization from linear to circular type and vice versa. The circularly polarized signals have many significant advantages over the signals with other types of polarization. Consequently, simultaneous application of polarizers with other radio signal processing devices highly increases the efficiency of new satellite information and telecommunication systems for various purposes, wireless data transmission systems, mobile communication systems, radar systems and medical diagnostic systems. In this article, we have developed a new matrix technique for the calculation of parameters and characteristics of a polarizer based on a square waveguide with three irises, which are inductive or capacitive loads depending on the wave’s polarization. Based on the theory of microwave circuits, the analytical expressions of the general wave scattering matrix were derived using the transmission and scattering wave matrices of elements of a polarizer structure. As a result, the main characteristics of the polarizer were obtained: differential phase shift, voltage standing wave ratio for vertical and horizontal polarizations, axial ratio and cross-polar discrimination. The presented method makes it possible to study the influence of the polarizer dimensions, such as the heights of the irises and the distances between them, on its main characteristics. Obtained analytical model makes it possible to find theoretically optimal sizes, which provide the required polarization characteristics of the device with the best matching in the operating frequency band. In addition, the developed wave matrix technique can be applied for further optimization using the specialized programs for microwave device simulation. [ABSTRACT FROM AUTHOR]

It is established that low frequency waves in a symmetric orthotropic elastic waveguide pass almost without distortion through a local perturbation of the straight cylinder, i.e., the reflection coefficient is small and the transmission coefficient slightly differs from 1. The results are obtained by the asymptotic analysis of low frequency waves and the corresponding scattering matrix. The formal asymptotic analysis is also performed for an anisotropic elastic waveguide with asymmetric cross-section, but since the canonical system of Jordan chains for the corresponding operator pencil is too complicated, the known results of the theory of perturbations of nonselfadjoint operators provide asymptotic formulas only under additional elastic and geometric symmetry conditions. We define the polarization matrix and prove its main properties. [ABSTRACT FROM AUTHOR]

Motivated by recent interest in the zeroes of S-matrix entries in the complex energy plane, the Heidelberg model of resonance scattering is used to introduce the notion of reflection time difference. As is shown, it plays the same role for the zeroes as the Wigner time delay plays for the S-matrix poles. [ABSTRACT FROM AUTHOR]

Light scattering by non-spherical particles is an important factor influencing atmospheric radiative transfer. To accurately simulate the scattering properties of non-spherical particles, the Invariant Imbedded T-matrix method (IIM T-Matrix) is developed by combining the Lorenz–Mie theory and invariant imbedding technique. In this model, the non-spherical particle is regarded as an inhomogeneous sphere and discretized into multiple spherical layers in the spherical coordinate system. The T-matrix of the inscribed sphere is firstly calculated by the Lorenz–Mie theory, and then taking it as the initial value, the T-matrix is updated layer by layer by using the invariant imbedding technique. To improve the computational efficiency, the model is further parallelized by the OpenMP technique. To verify the simulation accuracy of the IIM T-Matrix method, the results of the model are compared with those of the EBCM (Extended Boundary Condition Method) T-Matrix method, DDA (Discrete Dipole Approximation) and MRTD (Multi-Resolution Time Domain). The results show that the scattering phase matrix simulated by the IIM T-Matrix method closely agrees with that of the well-tested models, indicating that the IIM T-Matrix method is a powerful tool for the light scattering simulation of non-spherical particles. Since the IIM T-Matrix method is derived from the volume integral equation, compared to the T-Matrix method which is based on surface integral principles (i.e., "EBCM" or the "null field method"), it can be applied to the scattering calculations of particle with arbitrary shapes and inhomogeneous compositions, which can greatly expand the application scope of the T-Matrix method. [ABSTRACT FROM AUTHOR]

We investigate the relation between $S$ -matrix unitarity ($SS^\dagger=1$) and renormalizability in theories with negative-norm states. The relation has been confirmed in many field theories, including gauge theories and Einstein gravity, by analyzing the unitarity bound, which follows from the $S$ -matrix unitarity and the norm positivity. On the other hand, renormalizable theories with a higher-derivative kinetic term do not necessarily satisfy the unitarity bound because of the negative-norm states. In these theories it is not known whether the $S$ -matrix unitarity provides a nontrivial constraint related to the renormalizability. In this paper, by relaxing the assumption of norm positivity we derive a bound on scattering amplitudes weaker than the unitarity bound, which may be used as a consistency requirement for $S$ -matrix unitarity. We demonstrate in scalar field models with a higher-derivative kinetic term that the weaker bound and the renormalizability imply identical constraints. [ABSTRACT FROM AUTHOR]

• The Generalized Source Method is used to develop T-matrix calculation methods: scattering matrix and scattering vector algorithms. • Scattering matrix algorithm provide a new recurrence for T-matrix calculation. • Scattering vector algorithm is highly parallelizable and yields accurate power balance. • A method for consideration of arbitrary polyhedral particles is suggested. The paper presents a scattering matrix and scattering vector methods for calculation of non-spherical particle T-matrices, which are based on the volume integral equation and the spherical vector wave function basis, and rely on the Generalized Source Method rationale. The derivation of the scattering matrix method is based on ideas previously used within the matrix operator method of the radiative transfer theory and the S-matrix method of the grating diffraction theory, and provides a new T-matrix recurrence relation being alternative to the recurrences used within the Invariant Imbedding and the Superposition T-matrix methods. The developed scattering vector algorithm for calculation of T-matrix single columns is shown to have a potential for parallelization and to yield an almost zero power balance for purely dielectric particles. Demonstrated results of electromagnetic scattering simulations include examples for spheroids and a complex non-symmetric polyhedron particle. [ABSTRACT FROM AUTHOR]

This paper is concerned with diffusive approximations of some numerical schemes for several linear (or weakly nonlinear) kinetic models which are motivated by wide-range applications, including radiative transfer or neutron transport, run-and-tumble models of chemotaxis dynamics, and Vlasov-Fokker-Planck plasma modeling. The well-balanced method applied to such kinetic equations leads to time-marching schemes involving a "scattering S-matrix", itself derived from a normal modes decomposition of the stationary solution. One common feature these models share is the type of diffusive approximation: their macroscopic densities solve drift-diffusion systems, for which a distinguished numerical scheme is Il'in/Scharfetter-Gummel's "exponential fitting" discretization. We prove that these well-balanced schemes relax, within a parabolic rescaling, towards such type of discretization by means of an appropriate decomposition of the S-matrix, hence are asymptotic preserving. [ABSTRACT FROM AUTHOR]

This study assesses and compares two alternative approaches to determine the acoustic scattering matrix of a premixed turbulent swirl combustor: (1) The acoustic scattering matrix coefficients are obtained directly from a compressible large eddy simulation (LES). Specifically, the incoming and outgoing characteristic waves f and g extracted from the LES are used to determine the respective transmission and reflection coefficients via System Identification (SI) techniques. (2) The flame transfer function (FTF) is identified from LES time series data of upstream velocity and heat release rate. The transfer matrix of the reactive combustor is then derived by combining the FTF with the Rankine-Hugoniot (RH) relations across a compact heat source and a transfer matrix of the cold combustor, which is deduced from a linear network model. Linear algebraic transformation of the transfer matrix consequently yields the combustor scattering matrix. In a cross-comparison study that includes comprehensive experimental data, it is shown that both approaches successfully predict the scattering matrix of the reactive turbulent swirl combustor. [ABSTRACT FROM AUTHOR]

The extension of classical S-matrix theory to chaotic scattering systems is considered. It is shown that if the fractal structure of the chattering region is understood then the contribution to the S-matrix elements and the transition probabilities can be expressed as a sum over the infinite number of contributing trajectories and that by using the scaling laws of the fractal that this sum can be evaluated. It is shown that if the transition is classically forbidden then the contribution from the chattering region is significant. © 1994 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A novel time-dependent quantum mechanical formulation of scattering theory is developed which is well suited for the calculation of individual S-matrix elements. Wave packets corresponding to well-defined reactant and product channel quantum numbers are propagated in to the interaction region using Mo\ller operators, the former forward in time and the latter backwards in time. The S-matrix element Sβα(E) is then simply related to the Fourier transform at energy E of the time-dependent correlation function between the two wave packets in the interaction region. The symmetric treatment of reactants and products allows the entrance and exit channel dynamics to be performed highly efficiently using different coordinate systems and different interaction representations. As a result, the formulation is expected to provide an improved route to the calculation of S-matrix elements using quantum mechanical, as well as semiclassical propagation methods. The new formulation combines elements of classical S-matrix theory, the wave packet correlation formulation of spectroscopy, and quantum transition state theory, and should be a good starting point for a variety of new approximations to and interpretations of individual S-matrix elements. [ABSTRACT FROM AUTHOR]

A collocation approach to quantum scattering is presented. The method is based on the S-matrix version of the Kohn variational principle with a different linear expansion used for the two wave functions—one is a linear combination of basis functions and the other is a pointwise representation with proper asymptotic conditions imposed. The resulting equations are similar in structure to the usual version of the Kohn variational principle, however, in the present approach there are no integrals between the square integrable (L2) basis functions. In addition, the method does not require the knowledge of quadrature weights associated with the collocation points as was the case in a previous pointwise method for quantum scattering. This property means that the method is readily applicable to reactive scattering problems which use different sets of coordinates for reactants and products. Appliction to a simple inelastic test problem (collinear He–H2 vibrationally inelastic scattering) shows the accuracy of the approach to be comparable to that of the usual variatinal form of the S-matrix Kohn method. [ABSTRACT FROM AUTHOR]

The Mueller scattering matrix for sickle cell hemoglobin polymers is calculated using the coupled-dipole approximation method. The complex polarizability of the fiber is calculated using the absorption spectrum of hemoglobin to obtain the imaginary part and a Kramer-Kronig transform to obtain the real part. An anisotropy in the polarizability is calculated based on previous work using linear dichroism. The results of the polarized light scattering calculations are compared to previous measurements of total intensity light scattering and circular intensity differential scattering (CIDS) made on sickle red blood cells. Calculations of CIDS are found to be very sensitive to structural and optical parameters but reasonable agreement between experimental measurements and calculations are obtained. Further measurements and calculations should provide new structural information concerning the sickle fiber. [ABSTRACT FROM AUTHOR]

Reports on the calculation of the time-varying charge buildup in the quantum well region of a resonant tunneling diode (RTD) and related capacitive effects using the scattering matrix method. Band structure of a resonant tunneling diode under bias; Scattering matrix between regions with different modulation phases; Discussion on the capacitive effect in a RTD.

Presents a spectral method for solving the Boltzmann equation by the scattering matrix approach. Information on the rationale behind the choice of the basis function; Discussion of the orthogonal transformation; Application in the simulation of both the bulk and device properties with arbitrary field profiles.

Abstract: A technique for quantization of the electromagnetic field in photonic nanostructures with three-dimensional modulation of the dielectric constant is developed on the basis of the scattering matrix formalism (S quantization in the three-dimensional case). Quantization is based on equating the eigenvalues of the scattering matrix to unity, which is equivalent to equating each other the sets of Fourier expansions for the fields of the waves incident on the structure and propagating away from the structure. The spatial distribution of electromagnetic fields of the modes in a photonic nanostructure is calculated on the basis of the R and T matrices describing the reflection and transmission of the Fourier components by the structure. To calculate the reflection and transmission coefficients of individual real-space and Fourier-space components, the structure is divided into parallel layers within which the dielectric constant varies as a function of two-dimensional coordinates. Using the Fourier transform, Maxwell’s equations are written in the form of a matrix connecting the Fourier components of the electric field at the boundaries of neighboring layers. Based on the calculated reflection and transmission vectors for all polarizations and Fourier components, the scattering matrix for the entire structure is formed and quantization is carried out by equating the eigenvalues of the scattering matrix to unity. The developed method makes it possible to obtain the spatial profiles of eigenmodes without solving a system of nonlinear integro-differential equations and significantly reduces the computational resources required for calculating the probability of spontaneous emission in three-dimensional systems. [ABSTRACT FROM AUTHOR]

We discuss the scattering of a quantum particle by two independent successive point interactions in one dimension. The parameter space for two point interactions is given by U ( 2 ) × U ( 2 ) , which is described by eight real parameters. We perform an analysis of perfect resonant transmission on the whole parameter space. By investigating the effects of the two point interactions on the scattering matrix of plane wave, we find the condition under which perfect resonant transmission occurs. We also provide the physical interpretation of the resonance condition. [ABSTRACT FROM AUTHOR]

A comparative analysis of three different time-independent approaches to studying open quantum structures in a uniform electric field [ABSTRACT FROM AUTHOR]

A novel efficient method to calculate the scattering matrix (SM) of arbitrary tight-binding Hamiltonians is proposed, including cases with multiterminal structures. In particular, the SM of two kinds of fundamental structures is given, which can be used to obtain the SM of bigger systems iteratively. Also, a procedure to obtain the SM of layer-composed periodic leads is described. This method allows renormalization approaches, which permits computations over macroscopic length systems without introducing additional approximations. Finally, the transmission coefficient of a ring-shaped multiterminal system and the transmission function of a square-lattice nanoribbon with a reduced width region are calculated. [ABSTRACT FROM AUTHOR]

The M-dimensional unitary matrix S(E), which describes scattering of waves, is a strongly fluctuating function of the energy for complex systems such as ballistic cavities, whose geometry induces chaotic ray dynamics. Its statistical behaviour can be expressed by means of correlation functions of the kind 〈Sij(E + ε)Spq†(E - ε)〉, which have been much studied within the random matrix approach. In this work, we consider correlations involving an arbitrary number of matrix elements and express them as infinite series in 1/M, whose coefficients are rational functions of ε. From a mathematical point of view, this may be seen as a generalization of the Weingarten functions of circular ensembles. [ABSTRACT FROM AUTHOR]

Elastodynamic scattering matrices are known to contain geometrical information about a given scatterer, such as its size and shape. Here, the extent to which this scattered information can be retrieved using an ultrasonic array and used to characterise defects for Non-Destructive Evaluation is explored. Experimentally measured defect scattering matrices are compared to a database of possible scatterers and the nearest neighbour used to characterise the defect's geometry in terms of crack length and orientation. As an example, a database of scattering matrices for small (lengths 0.2–2.0 mm) cracks at a range of frequencies (2–20 MHz) is formed. The short range similarity (i.e. that between close neighbours) and the long range similarity (i.e. uniqueness) are used to understand the uncertainties inherent in this approach. In addition, the effect of spatially coherent noise, such as grain scattering in a polycrystalline metal, on the scattered information content is quantified. It is shown that as the noise level or frequency increases, so the information retrievable from a given crack is reduced, setting bounds on the accuracy of characterisation possible from a given ultrasonic dataset. [ABSTRACT FROM AUTHOR]

A simple, causal and analytic model of final state rescattering is used to describe all available data on the exotic resonances and . The model provides a compelling and accurate representation of experiment with no need for poles in the scattering matrix. [ABSTRACT FROM AUTHOR]

Scattering experiments are indispensable for the study of classical and quantum systems. In the Heidelberg approach, universal features are addressed by assuming that the reaction zone is fully quantum chaotic. Although it stems from nuclear physics, it later on turned out to be applicable to a large variety of systems on different scales, including classical wave systems. For a long time, the distribution of the off-diagonal scattering-matrix elements resisted analytical treatment. I review two recent studies in which my collaborators and I fully solved this problem. We also carried out a comparison with data from microwave experiments. [ABSTRACT FROM AUTHOR]

The Full Matrix Capture (FMC) technique and its related post-processing algorithms can provide improved array image quality and accurate defect characterisation. Therefore, there is an increasing demand for efficient simulation tools to generate FMC array data sets to optimise array configurations for defect's detection and characterisation. A hybrid ray-tracing technique combined with the far-field scattering response of the defect (defect's far-field scattering matrix) represents a fast and efficient modelling tool, but relies on the far-field assumption. When the scatterer is large, or located close to the array, the far-field assumption becomes inaccurate, and the model breaks down. In this paper the near-field model of ultrasonic array data for immersion and direct contact measurement configurations is developed. It is shown that the near-field scattering behaviour can be extracted from the far-field scattering matrix. The model is validated using experimental measurements and its performance is illustrated on modelling and experimental examples. [ABSTRACT FROM AUTHOR]

Using the closed time path formalism in thermal field theory, we give a derivation of the fluctuation-dissipation (FD) theorem which is based on the unitarity of the S-matrix. [ABSTRACT FROM AUTHOR]

In this letter, we propose an alternative proof for the uniqueness of Maronna's M-estimator of scatter for N vector observations y1, ..., yN ∈ Rm under a mild constraint of linear independence of any subset of m of these vectors. This entails in particular almost sure uniqueness for random vectors yi with a density as long as N > m. This approach allows to establish further relations that demonstrate that a properly normalized Tyler's M-estimator of scatter can be considered as a limit of Maronna's M-estimator. More precisely, the contribution is to show that each M-estimator, verifying some mild conditions, converges towards a particular Tyler's M-estimator. These results find important implications in recent works on the large dimensional (random matrix) regime of robust M-estimation. [ABSTRACT FROM AUTHOR]

A general method to obtain a matrix which allows the compensation of mutual coupling effects in transmitting arrays for the total field in all directions is introduced. This method is independent of the numerical method used in the analysis and it can include the effect of the antenna platform. The starting point can be the active element patterns or the spherical mode expansion from spherical near-field antenna measurements. Additionally, the spherical mode expansion is also used to find a matrix which allows the compensation of mutual coupling effects in receiving arrays. Through this theory, a simple relation between the compensation matrices of the transmitting and the receiving arrays is found. As a consequence, the scattering matrix of a circuit that allows the simultaneous compensation of mutual coupling effects for the transmission and the reception problem can be easily defined. Finally, it will be shown how the capabilities of the compensation in all directions depend strongly on the array element. [ABSTRACT FROM PUBLISHER]

Using the evolutionary model-independent S-matrix approach, we show that a simultaneous correct description of the pictures of nuclear rainbow, prerainbow, and anomalous large-angle scattering (ALAS) in the 4He-40Ca elastic scattering can be achieved with help of the S-matrix moduli and the real nuclear phases exhibiting smooth monotonic dependencies on angular momentum, while the quantum deflection functions have a form characteristic of the nuclear rainbow case. The special role of the surface partial waves in the formation of ALAS is revealed. [ABSTRACT FROM AUTHOR]

Dimension reduction (DR) is a necessary and helpful preprocessing for hyperspectral image (HSI) classification. In this paper, we propose a spatial and spectral regularized local discriminant embedding (SSRLDE) method for DR of hyperspectral data. In SSRLDE, hyperspectral pixels are first smoothed by the multiscale spatial weighted mean filtering. Then, the local similarity information is described by integrating a spectral-domain regularized local preserving scatter matrix and a spatial-domain local pixel neighborhood preserving scatter matrix. Finally, the optimal discriminative projection is learned by minimizing a local spatial-spectral scatter and maximizing a modified total data scatter. Experimental results on benchmark hyperspectral data sets show that the proposed SSRLDE significantly outperforms the state-of-the-art DR methods for HSI classification. [ABSTRACT FROM PUBLISHER]