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Journal articles on the topic 'Scattering matrix method'

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Author: Grafiati

Published: 14 March 2023

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1

Tayeb, Gérard, and Stefan Enoch. "Combined fictitious-sources–scattering-matrix method." Journal of the Optical Society of America A 21, no. 8 (August 1, 2004): 1417. http://dx.doi.org/10.1364/josaa.21.001417.

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2

Sheng, Wei-Dong. "The scattering matrix method for quantum waveguides." Journal of Physics: Condensed Matter 9, no. 40 (October 6, 1997): 8369–80. http://dx.doi.org/10.1088/0953-8984/9/40/005.

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3

Rivlin, Tom, Laura K. McKemmish, K. Eryn Spinlove, and Jonathan Tennyson. "Low temperature scattering with the R-matrix method: argon-argon scattering." Molecular Physics 117, no. 21 (May 10, 2019): 3158–70. http://dx.doi.org/10.1080/00268976.2019.1615143.

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4

Alhaidari, A. D. "Deformation of the J-Matrix Method of Scattering." Foundations of Physics Letters 16, no. 6 (December 2003): 579–91. http://dx.doi.org/10.1023/b:fopl.0000012784.06039.6f.

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5

HAMID, A. K. "Generalized scattering matrix method for cascaded waveguide junctions." International Journal of Electronics 80, no. 3 (March 1996): 471–77. http://dx.doi.org/10.1080/002072196137318.

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6

Simons, N. R. S., A. A. Sebak, E. Bridges, and Y. M. M. Antar. "Transmission-line matrix (TLM) method for scattering problems." Computer Physics Communications 68, no. 1-3 (November 1991): 197–212. http://dx.doi.org/10.1016/0010-4655(91)90200-5.

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7

Hu, Shuai, Lei Liu, Taichang Gao, and Qingwei Zeng. "Design and Validation of the Invariant Imbedded T-Matrix Scattering Model for Atmospheric Particles with Arbitrary Shapes." Applied Sciences 9, no. 20 (October 18, 2019): 4423. http://dx.doi.org/10.3390/app9204423.

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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.

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8

Pecheritsin, A. A., A. M. Pupasov, and Boris F. Samsonov. "Singular matrix Darboux transformations in the inverse-scattering method." Journal of Physics A: Mathematical and Theoretical 44, no. 20 (April 21, 2011): 205305. http://dx.doi.org/10.1088/1751-8113/44/20/205305.

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9

Syty, P., Ł. Redynk, and J. E. Sienkiewicz. "Application of the J-matrix method to multichannel scattering." European Physical Journal Special Topics 222, no. 9 (October 2013): 2323–28. http://dx.doi.org/10.1140/epjst/e2013-02012-1.

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10

Yan, Shaohui, and Baoli Yao. "Fast calculation technique for scattering in T-matrix method." Physics Letters A 372, no. 31 (July 2008): 5243–45. http://dx.doi.org/10.1016/j.physleta.2008.06.005.

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11

Alhaidari, A. D., H. Bahlouli, M. S. Abdelmonem, F. Al-Ameen, and T. Al-Abdulaal. "Regularization in the J-matrix method of scattering revisited." Physics Letters A 364, no. 5 (May 2007): 372–77. http://dx.doi.org/10.1016/j.physleta.2006.12.027.

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12

Schlup, W. A. "Matrix inversion for the GR method in surface scattering." Surface Science Letters 152-153 (April 1985): A110. http://dx.doi.org/10.1016/0167-2584(85)90074-x.

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13

Schlup, W. A. "Matrix inversion for the GR method in surface scattering." Surface Science 152-153 (April 1985): 88–92. http://dx.doi.org/10.1016/0039-6028(85)90129-3.

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14

A. Torres, J., and J. J. Sáenz. "Improved Generalized Scattering Matrix Method: Conduction through Ballistic Nanowires." Journal of the Physical Society of Japan 73, no. 8 (August 15, 2004): 2182–93. http://dx.doi.org/10.1143/jpsj.73.2182.

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15

Khachatrian, A. Kh, A. A. Hakopian, and E. A. Melkonian. "A matrix solution method for non-coherent scattering problems." Journal of Quantitative Spectroscopy and Radiative Transfer 45, no. 6 (June 1991): 367–76. http://dx.doi.org/10.1016/0022-4073(91)90073-y.

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16

Baluja, K. L., and J. Singh. "Electron scattering with open-shell molecules: R-matrix method." Indian Journal of Physics 85, no. 12 (December 2011): 1695–704. http://dx.doi.org/10.1007/s12648-011-0182-8.

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17

Custers, C., J. Jansen, and E. Lomonova. "Memory Efficient Method for Electromagnetic Multi-Region Models Using Scattering Matrices." Mathematical and Computational Applications 23, no. 4 (November 9, 2018): 71. http://dx.doi.org/10.3390/mca23040071.

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This paper describes the scattering matrix approach to obtain the solution to electromagnetic field quantities in harmonic multi-layer models. Using this approach, the boundary conditions are solved in such way that the maximum size of any matrix used during the computations is independent of the number of regions defined in the problem. As a result, the method is more memory efficient than classical methods used to solve the boundary conditions. Because electromagnetic sources can be located inside the regions of a configuration, the scattering matrix formulation is developed to incorporate these sources into the solving process. The method is applied to a 3D electromagnetic configuration for verification.

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18

Tennyson, Jonathan, Laura K. McKemmish, and Tom Rivlin. "Low-temperature chemistry using the R-matrix method." Faraday Discussions 195 (2016): 31–48. http://dx.doi.org/10.1039/c6fd00110f.

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Techniques for producing cold and ultracold molecules are enabling the study of chemical reactions and scattering at the quantum scattering limit, with only a few partial waves contributing to the incident channel, leading to the observation and even full control of state-to-state collisions in this regime. A new R-matrix formalism is presented for tackling problems involving low- and ultra-low energy collisions. This general formalism is particularly appropriate for slow collisions occurring on potential energy surfaces with deep wells. The many resonance states make such systems hard to treat theoretically but offer the best prospects for novel physics: resonances are already being widely used to control diatomic systems and should provide the route to steering ultracold reactions. Our R-matrix-based formalism builds on the progress made in variational calculations of molecular spectra by using these methods to provide wavefunctions for the whole system at short internuclear distances, (a regime known as the inner region). These wavefunctions are used to construct collision energy-dependent R-matrices which can then be propagated to give cross sections at each collision energy. The method is formulated for ultracold collision systems with differing numbers of atoms.

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19

Wang, Jun, Yao Lu, and Shaoming Wei. "2D scattering centre intensity pre-estimated method based on matrix pencil method." Journal of Engineering 2019, no. 19 (October 1, 2019): 6160–64. http://dx.doi.org/10.1049/joe.2019.0215.

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20

Liu, Xiaopeng, Cong Liu, and Xiaochen Liu. "Underwater Image Enhancement with the Low-Rank Nonnegative Matrix Factorization Method." International Journal of Pattern Recognition and Artificial Intelligence 35, no. 08 (March 8, 2021): 2154022. http://dx.doi.org/10.1142/s0218001421540227.

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Due to the scattering and absorption effects in the undersea environment, underwater image enhancement is a challenging problem. To obtain the ground-truth data for training is also an open problem. So, the learning process is unavailable. In this paper, we propose a Low-Rank Nonnegative Matrix Factorization (LR-NMF) method, which only uses the degraded underwater image as input to generate the more clear and realistic image. According to the underwater image formation model, the degraded underwater image could be separated into three parts, the directed component, the back and forward scattering components. The latter two parts can be considered as scattering. The directed component is constrained to have a low rank. After that, the restored underwater image is obtained. The quantitative and qualitative analyses illustrate that the proposed method performed equivalent or better than the state-of-the-art methods. Yet, it’s simple to implement without the training process.

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21

DRUET, T., D. BAYE, P. DESCOUVEMONT, and J. M. SPARENBERG. "APPLICATION OF THE R-MATRIX METHOD TO CDCC CALCULATIONS." Modern Physics Letters A 25, no. 21n23 (July 30, 2010): 1745–49. http://dx.doi.org/10.1142/s021773231000023x.

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The R-matrix method is applied to the Continuum Discretized Coupled Channel (CDCC) approximation. The variational basis is chosen as Lagrange functions, which are shown to be efficient and accurate. We apply the general formalism to the d + 58 Ni elastic scattering at Ed = 80 MeV . Future developments are briefly discussed.

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22

Malik, Rashmi, Gulab Singh, Onkar Dikshit, and Yoshio Yamaguchi. "General Five-Component Scattering Power Decomposition with Unitary Transformation (G5U) of Coherency Matrix." Remote Sensing 15, no. 5 (February 27, 2023): 1332. http://dx.doi.org/10.3390/rs15051332.

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The polarimetric synthetic aperture radar (PolSAR) provides us with a two-by-two scattering matrix data set. The ensemble averaged coherency matrix in an imaging window derived using a scattering matrix has all non-zero elements in its three-by-three matrix. It is a full 3 × 3 matrix that bears nine real-valued and independent polarimetric parameters inside. In the proposed decomposition method, G5U, we preprocess observed coherency matrix [T] by using two consecutive unitary transformations to become an ideal form for five-component decomposition. The transformation reduces nine parameters to seven, which is the best fit for five-component scattering model expansion. We can retrieve five powers corresponding to surface scattering, double bounce scattering, volume scattering, oriented dipole scattering, and compound dipole scattering, directly. These powers can be calculated easily and used to display superb polarimetric RBG images as never before, and are further applicable for polarimetric calibration, classification, validation, etc.

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23

Watanabe, Kai, and Noriyoshi Ishii. "The current matrix elements from HAL QCD method." EPJ Web of Conferences 175 (2018): 06008. http://dx.doi.org/10.1051/epjconf/201817506008.

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HAL QCD method is a method to construct a potential (HAL QCD potential) that reproduces the NN scattering phase shift faithful to the QCD. The HAL QCD potential is obtained from QCD by eliminating the degrees of freedom of quarks and gluons and leaving only two particular hadrons. Therefor, in the effective quantum mechanics of two nucleons defined by HAL QCD potential, the conserved current consists not only of the nucleon current but also an extra current originating from the potential (two-body current). Though the form of the two-body current is closely related to the potential, it is not straight forward to extract the former from the latter. In this work, we derive the the current matrix element formula in the quantum mechanics defined by the HAL QCD potential. As a first step, we focus on the non-relativistic case. To give an explicit example, we consider a second quantized non-relativistic two-channel coupling model which we refer to as the original model. From the original model, the HAL QCD potential for the open channel is constructed by eliminating the closed channel in the elastic two-particle scattering region. The current matrix element formula is derived by demanding the effective quantum mechanics defined by the HAL QCD potential to respond to the external field in the same way as the original two-channel coupling model.

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24

ZHANG, JOHN Z. H. "QUANTUM REACTIVE SCATTERING USING THE S-MATRIX KOHN VARIATIONAL METHOD." International Journal of Modern Physics C 03, no. 06 (December 1992): 1351–64. http://dx.doi.org/10.1142/s0129183192000920.

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This paper intends to give a short review on the recent progress and application of the S-matrix Kohn variational method to quantum reactive scattering in gas phase. The basic formalisms of the S-matrix Kohn method are reviewed and several numerical techniques that improve the efficiency of the Kohn method are described in the review. These include the body-fixed representation, quasi-adiabatic basis contraction method, and the use of distorted waves in numerical application. The efficacy of these numerical techniques are illustrated by numerical results obtained by using the latest version of the S-matrix Kohn variational method for three-dimensional F+H2 and F+D2 reactions.

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25

Kröger, Helmut, Anais Smailagic, and Ralph Girard. "Finite-dimensional approximation of the scattering matrix." Canadian Journal of Physics 64, no. 5 (May 1, 1986): 611–16. http://dx.doi.org/10.1139/p86-113.

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A finite-dimensional nonperturbative approximation scheme of the time-evolution operator and the S matrix for relativistic field theories is discussed. It is amenable to computer calculations. Parallels with lattice-field theory are drawn. The method is outlined for the ϕ4 theory. Equivalence to standard perturbation theory in the weak-coupling regime is obtained in the limit of the approximation parameters. The method is tested numerically for nonrelativistic proton–proton s-wave scattering and the the ϕ4 model in the weak-coupling regime in 1 + 1 dimensions. In both examples, convergence to the reference solution is found.

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26

PENG, LINHUI, NING WANG, and ER CHANG SHANG. "NUMERICAL SIMULATION OF EXTRACTING MODAL BACK-SCATTERING MATRIX FROM REVERBERATION IN SHALLOW-WATER WAVEGUIDE." Journal of Computational Acoustics 13, no. 02 (June 2005): 279–85. http://dx.doi.org/10.1142/s0218396x05002700.

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Modal back-scattering matrix is the key component for reverberation predicting and also important for understanding the mechanism of bottom back-scattering. To extract the modal back-scattering matrix from reverberation data is a challening topic. So far, inversion of modal back-scattering matrix from reverberation data is based on some a priori assumptions. A new method for extracting modal back-scattering matrix from reverberation data in shallow-water waveguide is proposed recently [Shang et al., 2002]. In this paper numerical simulation of extracting the modal back-scattering matrix has been performed, it is shown that the inversion by changing the source depth works very well for lower frequency. Alternatively, the inversion by using the reverberation data at different ranges is proposed and it is shown that this approach is suitable on certain conditions.

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27

Sarpal, Baljit K., Kurt Pfingst, Bernd M. Nestmann, and Sigrid D. Peyerimhoff. "Study of electron scattering by using the polyatomicR-matrix method." Journal of Physics B: Atomic, Molecular and Optical Physics 29, no. 4 (February 28, 1996): 857–73. http://dx.doi.org/10.1088/0953-4075/29/4/023.

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28

Zhu Bing and Feng Hao. "Electron scattering studies of NO2 radical using R-matrix method." Acta Physica Sinica 66, no. 24 (2017): 243401. http://dx.doi.org/10.7498/aps.66.243401.

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29

Perino, A., R. Orta, and G. Barla. "Wave Propagation in Discontinuous Media by the Scattering Matrix Method." Rock Mechanics and Rock Engineering 45, no. 5 (July 26, 2012): 901–18. http://dx.doi.org/10.1007/s00603-012-0286-2.

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30

Scheid, Werner. "A method for solving the quantum inverse scattering problem for coupled channels at fixed energy." International Journal of Modern Physics E 25, no. 11 (November 2016): 1650094. http://dx.doi.org/10.1142/s0218301316500944.

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This paper describes the inversion of a scattering problem with coupled channels at fixed energy. The coupling potential matrix is obtained from the [Formula: see text]-matrix with the modified Newton–Sabatier method with a special expansion of the integral kernel and a determination of the potential matrix by using the coupled radial equations. The method is applied to problems restricted to two channels and with a monopole, dipole and quadrupole coupling ([Formula: see text]) between the channels. The inversion is shown to work quite satisfactorily and is useful for heavy ion scattering in nuclear physics.

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31

Wang, J. B., and A. T. Stelbovics. "Invariant Graphical Method for Electron-Atom Scattering Coupled-Channel Equations." Advances in Physical Chemistry 2011 (April 10, 2011): 1–14. http://dx.doi.org/10.1155/2011/541375.

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We present application examples of a graphical method for the efficient construction of potential matrix elements in quantum physics or quantum chemistry. The simplicity and power of this method are illustrated through several examples. In particular, a complete set of potential matrix elements for electron-lithium scattering are derived for the first time using this method, which removes the frozen core approximation adopted by previous studies. This method can be readily adapted to study other many-body quantum systems.

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32

Zheng, Mingxuan, Huiling Zhao, and Zhonghui Zhao. "A Modified Adaptive Integral Method for Analysis of Large-scale Finite Periodic Array." Applied Computational Electromagnetics Society 35, no. 8 (October 7, 2020): 864–71. http://dx.doi.org/10.47037/2020.aces.j.350803.

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A fast algorithm based on AIM is proposed to analyze the scattering problem of the large-scale finite array. In this method, by filling zeros into the local transformation matrix, the near and far fields are isolated thoroughly to eliminate the near correction process. In the far part, a 5-level block-toeplitz matrix is employed to avoid saving the idle grids without adding artificial interfaces. In the near part, only one local cube is required to compute the local translation matrix and near impedance matrix, which can be shared by all elements. Furthermore, the block Jacobi preconditioning technique is applied to improve the convergence, and the principle of pattern multiplication is used to accelerate the calculation of the scattering pattern. Numerical results show that the proposed method can reduce not only the CPU time in filling and solving matrix but also the whole memory requirement dramatically for the large-scale finite array with large spacings.

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33

Zheng, Yang, Jin Jie Zhou, and Hui Zheng. "Subwavelength Defect Characterization Using Guided Wave Scattering Matrix." Applied Mechanics and Materials 330 (June 2013): 504–9. http://dx.doi.org/10.4028/www.scientific.net/amm.330.504.

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Although many imaging algorithms such as ellipse and hyperbola algorithm can roughly locate defects in large plate-like structures with sparse guided wave arrays, quantitative characterization of them is still a challenging problem, especially for those small defects known as subwavelength defects. Scattering signals of defects contain abundant information so that can be used to evaluate defects. A defects recognition method using the S-matrix (scattering matrix) was presented. S-matrices of hole and crack with S0 mode incident were experimentally measured. The results show that defects can be recognized from the morphology of 2D S-matrix chart. This method has great potential to achieve more specific parameters of small defects with sparse guided wave arrays.

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34

Steshenko, S. "Generalization of the mode-matching technique to the problems of scattering by semi-infinite slow-wave structures." RADIOFIZIKA I ELEKTRONIKA 25, no. 4 (2020): 10–17. http://dx.doi.org/10.15407/rej2020.04.010.

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Subject and purpose. The scattering matrix of a semi-infinite slow-wave structure formed by grooves in a rectangular waveguide is investigated. The purpose was to develop a method for calculating a semi-infinite periodic structure. Methods and methodology. A generalization of the mode-matching technique to semi-infinite periodic structures is built. The fields of the periodic part of the structure are expanded in series of the eigenmodes of the periodic structure, taking into account the condition at infinity, which makes it possible to obtain a linear matrix equation for finding the scattering matrix. Only the propagating modes of the periodic structure were considered. To make these expansions reliable the fields were matched at a period somewhat distant from the junction of the regular waveguide with the periodic one. Results. Matrix equations for determining the blocks of the scattering matrix of a semi-infinite structure are obtained. A number of investigations are carried out to check the reliability of the equations obtained. These include test of convergence, reciprocity, energy balance, and conservation of the scattering matrix while adding one period to a semi-infinite structure. The main confirmation was obtained by comparing the scattering matrix of a finite fragment of the slow-wave structure, obtained in two ways: through the scattering matrices of semi-infinite slow-wave structure and through a cascade assembly of the scattering matrices of the waveguide elements that make up the structure. Conclusions. An algorithm for calculating the scattering matrix of a semi-infinite structure is obtained. It can be used to build a rigorous hot model of vacuum electronics devices using slow-wave structures.

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35

Stammes, P. "The Scattering Matrix of Randomly Oriented Infinite Cylinders." International Astronomical Union Colloquium 126 (1991): 207–10. http://dx.doi.org/10.1017/s0252921100066793.

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AbstractA method is outlined to compute the scattering matrix of an ensemble of infinite cylinders in random orientation, as an approximation to the scattering matrix of an ensemble of very long but finite cylinders. Numerical checks are presented, which show that the results for infinite cylinders agree with theoretical results for very thick and very thin cylinders, as well as with numerical data for prolate spheroids and short finite cylinders.

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36

Swoboda, Walter, Burkhard Beckhoff, Birgit Kanngieβer, and J. Scheer. "Matrix Correction With Barkla Excitation Using the Coherent/Incoherent Method." Advances in X-ray Analysis 37 (1993): 667–75. http://dx.doi.org/10.1154/s0376030800016220.

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The scattering of the primary X-ray tube spectrum on a low Z material in 90°-geometry produces polarised excitation radiation, which clearly decreases the background of fluorescence spectra in Cartesian geometry (Barkla excitation). Several publications have shown the advantages of this excitation mode in comparison with both direct excitation and secondary target excitation.

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37

Karge, Lukas, David Lang, Jürgen Schatte, Ralph Gilles, Sebastian Busch, Peter Leibenguth, Helmut Clemens, and Winfried Petry. "Characterization of anisotropic pores and spatially oriented precipitates in sintered Mo-base alloys using small-angle neutron scattering." Journal of Applied Crystallography 51, no. 6 (November 28, 2018): 1706–14. http://dx.doi.org/10.1107/s1600576718014474.

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Small-angle neutron scattering (SANS) is a powerful method for the characterization of materials in the mesoscopic size range. For example, the method can be used to investigate the precipitation mechanisms in powder metallurgically processed materials. As a result of the processing route, the alloy matrix is usually heavily textured. If precipitates have an orientation relationship to the alloy matrix, they can produce an anisotropic scattering pattern showing streaks. The scattering is superimposed by a background with ellipsoidal shape, originating from deformed large-scale structures. The evaluation of such data quickly becomes elaborate and a quantitative analysis of precipitation is difficult. The present work reports a method for treating the anisotropic scattering from such samples. A systematic study of the ellipsoidal background reveals that it originates from uniaxially deformed sinter pores. Irrespective of the degree of deformation during the processing route, SANS shows that sinter pores remain present in the matrix, and their morphology and relative volume fractions are determined. Consequently, their scattering signal can be subtracted to reveal the scattering from aligned precipitates. The method is demonstrated on powder metallurgically produced pure Mo and an Mo–Hf–C alloy.

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38

Rui, Wei, Zhipeng Liu, Chao Tao, and Xiaojun Liu. "Reconstruction of Photoacoustic Tomography Inside a Scattering Layer Using a Matrix Filtering Method." Applied Sciences 9, no. 10 (May 20, 2019): 2071. http://dx.doi.org/10.3390/app9102071.

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Photoacoustic (PA) tomography (PAT) has potential for use in brain imaging due to its rich optical contrast, high acoustic resolution in deep tissue, and good biosafety. However, the skull often poses challenges for transcranial brain imaging. The skull can cause severe distortion and attenuation of the phase and amplitude of PA waves, which leads to poor resolution, low contrast, and strong noise in the images. In this study, we propose an image reconstruction method to recover the PA image insider a skull-like scattering layer. This method reduces the scattering artifacts by combining a correlation matrix filter and a time reversal operator. Both numerical simulations and PA imaging experiments demonstrate that the proposed approach effectively improves the image quality with less speckle noise and better signal-to-noise ratio. The proposed method may improve the quality of PAT in a complex acoustic scattering environment, such as transcranial brain imaging.

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39

McKemmish, Laura K., and Jonathan Tennyson. "General mathematical formulation of scattering processes in atom–diatomic collisions in the RmatReact methodology." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 377, no. 2154 (August 5, 2019): 20180409. http://dx.doi.org/10.1098/rsta.2018.0409.

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Accurately modelling cold and ultracold reactive collisions occurring over deep potential wells, such as D + + H 2 → H + + HD , requires the development of new theoretical and computational methodologies. One potentially useful framework is the R -matrix method adopted widely for electron–molecule collisions which has more recently been applied to non-reactive heavy-particle collisions such as Ar–Ar. The existing treatment of non-reactive elastic and inelastic scattering needs to be substantially extended to enable modelling of reactive collisions: this is the subject of this paper. Herein, we develop the general mathematical formulation for non-reactive elastic and inelastic scattering, photoassociation, photodissociation, charge exchange and reactive scattering using the R -matrix method. Of particular note is that the inner region, of central importance to calculable R -matrix methodologies, must be finite in all scattering coordinates rather than a single scattering coordinate as for non-reactive scattering. This article is part of a discussion meeting issue ‘Advances in hydrogen molecular ions: H 3 + , H 5 + and beyond’.

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40

Zhang, Yaojiang Jiang, and Er Ping Li. "FAST MULTIPOLE ACCELERATED SCATTERING MATRIX METHOD FOR MULTIPLE SCATTERING OF A LARGE NUMBER OF CYLINDERS." Progress In Electromagnetics Research 72 (2007): 105–26. http://dx.doi.org/10.2528/pier07030503.

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41

Feng, Fei Long, Jian Zhong Shen, Jing Jun Deng, and Qiu Ping Wang. "Analytical Solution of Lamb Wave Scattering at Plate End." Advanced Materials Research 199-200 (February 2011): 949–52. http://dx.doi.org/10.4028/www.scientific.net/amr.199-200.949.

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An analytical solution based on modal decomposition is presented to investigate Lamb wave scattering at plate end. Take boundary condition into biorthogonality relation, a matrix equation is established with all matrix elements have analytical expressions. The scattering feature is then expressed in matrix form, named as reflection matrix, which has explicit expression composed of those matrixes. Calculation examples have be implemented when antisymmetric modes are reflected. Scattering coefficients are figured out in a range when frequency-thickness product vary from 0 to 8kHzm, to prove the calculation efficiency. The calculation precision is very close to the least square method based on model discretization.

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42

Wan, Chao, and Hongning Li. "Analytical Method and Semianalytical Method for Analysis of Scattering by Anisotropic Sphere: A Review." International Journal of Antennas and Propagation 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/782320.

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The history of methods for the electromagnetic scattering by an anisotropic sphere has been reviewed. Two main methods, angular expansion method and T-matrix method, which are widely used for the anisotropic sphere, are expressed in Cartesian coordinate firstly. The comparison of those and the further exploration on the scattering field are illustrated afterwards. Based on the most general form concluded by variable separation method, the coupled electric field and magnetic field of radial anisotropic sphere can be derived. By simplifying the condition, simpler case of uniaxial anisotropic media is expressed with confirmed coefficients for the internal and external field. Details of significant phenomenon are presented.

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Lakshmi, L. Vijaya, A. Jaya Lakshmi, M. N. V. S. S. Kumar, and P. Sirish Kumar. "Radar Target Characteristics Extraction using Polarization Scattering Matrix." TELKOMNIKA Indonesian Journal of Electrical Engineering 16, no. 2 (November 1, 2015): 308. http://dx.doi.org/10.11591/tijee.v16i2.1618.

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<p>Now a day’s characterization of targets using radar is very important in Air Traffic Control, Defense, and Stealth etc. In order to know the characteristics of the target it is very essential to know the polarization properties of that particular target which depends upon scattering nature of the target. The polarization properties are important for radar target besides amplitude, phase and frequency. The polarization may be potentially used to improve target detection, anti-interference, and radar target recognition. Polarization properties of a target can be obtained using polarization scattering matrix (PSM). In this paper the polarization matrix of various geometrical shapes are derived. For radar target recognition (RTR), a method using properties of the polarization scattering matrix (PPSM) is presented in this paper. A dipole has been considered to calculate the polarization matrix and polarization properties. The properties of the polarization scattering matrix: the determinant, Trace of Power Scattering Matrix, Depolation, Eigen polarization angle and Module of Polarization Ellipticity are analyzed. These properties are analyzed for different orientation angles of the targets.</p>

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Zhou, Huilin, Youwen Liu, Yuhao Wang, Liangbing Chen, and Rongxing Duan. "Nonlinear Electromagnetic Inverse Scattering Imaging Based on IN-LSQR." International Journal of Antennas and Propagation 2018 (August 2, 2018): 1–9. http://dx.doi.org/10.1155/2018/2794646.

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A nonlinear inversion scheme is proposed for electromagnetic inverse scattering imaging. It exploits inexact Newton (IN) and least square QR factorization (LSQR) methods to tackle the nonlinearity and ill-posedness of the electromagnetic inverse scattering problem. A nonlinear model of the inverse scattering in functional form is developed. At every IN iteration, the sparse storage method is adopted to solve the storage and computational bottleneck of Fréchet derivative matrix, a large-scale sparse Jacobian matrix. Moreover, to address the slow convergence problem encountered in the inexact Newton solution via Landweber iterations, an LSQR algorithm is proposed for obtaining a better solution of the internal large-scale sparse linear equations in the IN step. Numerical results demonstrate the applicability of the proposed IN-LSQR method to quantitative inversion of scatterer electric performance parameters. Moreover, compared with the inexact Newton method based on Landweber iterations, the proposed method significantly improves the convergence rate with less computational and storage cost.

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Miller, William H. "A new variational expression for the scattering matrix." Collection of Czechoslovak Chemical Communications 53, no. 9 (1988): 1873–80. http://dx.doi.org/10.1135/cccc19881873.

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The S-matrix version of the Kohn variational method is used to obtain a new, more concise expression for the scattering matrix, one that has both esthetic and practical advantages over earlier ones that have been used.

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Niwa, Satomi, and Kazuki Takeda. "Usefulness of oils for cleaning the host matrix and for cryoprotection of lipidic cubic phase crystals." Journal of Applied Crystallography 52, no. 4 (July 8, 2019): 864–68. http://dx.doi.org/10.1107/s1600576719007738.

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The lipidic cubic phase method is an effective approach for membrane protein crystallography. The in meso grown crystals are usually cryocooled directly without removing the host matrix from the harvested crystal surface. However, the host matrix often causes the appearance of scattering rings and an increase in background scattering during the data collection. Moreover, the frozen host matrix sometimes becomes opaque and it can hinder conventional crystal centering. In this study, several oils were examined for their ability to clean the host matrix and to provide cryoprotection for crystals grown in the lipidic cubic phase. Several of the tested oils appeared to be useful in terms of their effect on crystal stability and background scattering. This method should be of value for the collection of highly accurate data sets.

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Wu, Peng, Jun Wang, and Wenguang Wang. "A Novel Method of Small Target Detection in Sea Clutter." ISRN Signal Processing 2011 (June 28, 2011): 1–10. http://dx.doi.org/10.5402/2011/651790.

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Detecting low observable targets within sea clutter at low grazing angle is one of the research hotspots in radar signal processing community. In this paper, we have proposed a novel method based on polarimetric decomposition theorem. The polar characteristics of sea clutter has been analyzed, with the parameters after the decomposition of target scattering matrix. The scattering entropy and the scattering angle are the key parameters to discriminate the target from the sea clutter. The technique is designed to suppress unwanted sea clutter at polarimetric domain. Datasets from real marine radar are used to illustrate the performance of the new approach.

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Wan, Ting, Tianhao Chen, Yang Bao, and Shiyi Wang. "Fast and Accurate Prediction of Light Scattering from Plasmonic Nanoarrays in Multiple Directions." Micromachines 13, no. 4 (April 14, 2022): 613. http://dx.doi.org/10.3390/mi13040613.

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The method of moments (MoM) is an efficient electromagnetic numerical method for the accurate prediction of light scattering from plasmonic nanostructures. In practice, the light-scattering properties in different incident directions are often concerning. However, traditional MoM generally resorts to the iterative method, which suffers from the problems of convergence rate and redundant computations for multiple incident excitations. Nanoarray structures will further aggravate these problems due to a large number of unknowns. In this article, an efficient numerical method based on MoM and a hierarchical matrix (H-matrix) algorithm is proposed to solve these problems. Numerical experiments demonstrate the efficiency and accuracy of the proposed method for the prediction of light scattering from plasmonic nanoarrays in multiple directions.

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Gao, Chenxu, and Bingqiang Sun. "Improvement and application of linearized invariant imbedding T-matrix scattering method." Journal of Quantitative Spectroscopy and Radiative Transfer 290 (November 2022): 108322. http://dx.doi.org/10.1016/j.jqsrt.2022.108322.

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Harvey, A. G., and J. Tennyson. "Electron re-scattering from aligned linear molecules using theR-matrix method." Journal of Physics B: Atomic, Molecular and Optical Physics 42, no. 9 (April 21, 2009): 095101. http://dx.doi.org/10.1088/0953-4075/42/9/095101.

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