Comparison of matrix methods for elastic wave scattering problems
International Nuclear Information System (INIS)
Tsao, S.J.; Varadan, V.K.; Varadan, V.V.
1983-01-01
This article briefly describes the T-matrix method and the MOOT (method of optimal truncation) of elastic wave scattering as they apply to A-D, SH- wave problems as well as 3-D elastic wave problems. Two methods are compared for scattering by elliptical cylinders as well as oblate spheroids of various eccentricity as a function of frequency. Convergence, and symmetry of the scattering cross section are also compared for ellipses and spheroidal cavities of different aspect ratios. Both the T-matrix approach and the MOOT were programmed on an AMDHL 470 computer using double precision arithmetic. Although the T-matrix method and MOOT are not always in agreement, it is in no way implied that any of the published results using MOOT are in error
Description of elastic scattering in U-matrix method
International Nuclear Information System (INIS)
Edneral, V.F.; Troshin, S.M.; Tyurin, N.E.; Khrustalev, O.A.
1975-01-01
The elastic pp-scattering has been analyzed using a generalized reaction matrix (the U-matrix). A good agreement has been reached with the experimental total cross sections for the (pp) reaction beginning with an energy of 30 GeV and for the dsub(t)(dt)(pp) for four ISR energies [ru
Direct determination of scattering time delays using the R-matrix propagation method
International Nuclear Information System (INIS)
Walker, R.B.; Hayes, E.F.
1989-01-01
A direct method for determining time delays for scattering processes is developed using the R-matrix propagation method. The procedure involves the simultaneous generation of the global R matrix and its energy derivative. The necessary expressions to obtain the energy derivative of the S matrix are relatively simple and involve many of the same matrix elements required for the R-matrix propagation method. This method is applied to a simple model for a chemical reaction that displays sharp resonance features. The test results of the direct method are shown to be in excellent agreement with the traditional numerical differentiation method for scattering energies near the resonance energy. However, for sharp resonances the numerical differentiation method requires calculation of the S-matrix elements at many closely spaced energies. Since the direct method presented here involves calculations at only a single energy, one is able to generate accurate energy derivatives and time delays much more efficiently and reliably
J-matrix method of scattering in one dimension: The nonrelativistic theory
International Nuclear Information System (INIS)
Alhaidari, A.D.; Bahlouli, H.; Abdelmonem, M.S.
2009-01-01
We formulate a theory of nonrelativistic scattering in one dimension based on the J-matrix method. The scattering potential is assumed to have a finite range such that it is well represented by its matrix elements in a finite subset of a basis that supports a tridiagonal matrix representation for the reference wave operator. Contrary to our expectation, the 1D formulation reveals a rich and highly nontrivial structure compared to the 3D formulation. Examples are given to demonstrate the utility and accuracy of the method. It is hoped that this formulation constitutes a viable alternative to the classical treatment of 1D scattering problem and that it will help unveil new and interesting applications.
A method for accurate computation of elastic and discrete inelastic scattering transfer matrix
International Nuclear Information System (INIS)
Garcia, R.D.M.; Santina, M.D.
1986-05-01
A method for accurate computation of elastic and discrete inelastic scattering transfer matrices is discussed. In particular, a partition scheme for the source energy range that avoids integration over intervals containing points where the integrand has discontinuous derivative is developed. Five-figure accurate numerical results are obtained for several test problems with the TRAMA program which incorporates the porposed method. A comparison with numerical results from existing processing codes is also presented. (author) [pt
Somerville, W. R. C.; Auguié, B.; Le Ru, E. C.
2013-07-01
We propose, describe, and demonstrate a new numerically stable implementation of the extended boundary-condition method (EBCM) to compute the T-matrix for electromagnetic scattering by spheroidal particles. Our approach relies on the fact that for many of the EBCM integrals in the special case of spheroids, a leading part of the integrand integrates exactly to zero, which causes catastrophic loss of precision in numerical computations. This feature was in fact first pointed out by Waterman in the context of acoustic scattering and electromagnetic scattering by infinite cylinders. We have recently studied it in detail in the case of electromagnetic scattering by particles. Based on this study, the principle of our new implementation is therefore to compute all the integrands without the problematic part to avoid the primary cause of loss of precision. Particular attention is also given to choosing the algorithms that minimise loss of precision in every step of the method, without compromising on speed. We show that the resulting implementation can efficiently compute in double precision arithmetic the T-matrix and therefore optical properties of spheroidal particles to a high precision, often down to a remarkable accuracy (10-10 relative error), over a wide range of parameters that are typically considered problematic. We discuss examples such as high-aspect ratio metallic nanorods and large size parameter (≈35) dielectric particles, which had been previously modelled only using quadruple-precision arithmetic codes.
Sun, B.; Yang, P.; Kattawar, G. W.; Zhang, X.
2017-12-01
The ice cloud single-scattering properties can be accurately simulated using the invariant-imbedding T-matrix method (IITM) and the physical-geometric optics method (PGOM). The IITM has been parallelized using the Message Passing Interface (MPI) method to remove the memory limitation so that the IITM can be used to obtain the single-scattering properties of ice clouds for sizes in the geometric optics regime. Furthermore, the results associated with random orientations can be analytically achieved once the T-matrix is given. The PGOM is also parallelized in conjunction with random orientations. The single-scattering properties of a hexagonal prism with height 400 (in units of lambda/2*pi, where lambda is the incident wavelength) and an aspect ratio of 1 (defined as the height over two times of bottom side length) are given by using the parallelized IITM and compared to the counterparts using the parallelized PGOM. The two results are in close agreement. Furthermore, the integrated single-scattering properties, including the asymmetry factor, the extinction cross-section, and the scattering cross-section, are given in a completed size range. The present results show a smooth transition from the exact IITM solution to the approximate PGOM result. Because the calculation of the IITM method has reached the geometric regime, the IITM and the PGOM can be efficiently employed to accurately compute the single-scattering properties of ice cloud in a wide spectral range.
Electron re-scattering from aligned linear molecules using the R-matrix method
International Nuclear Information System (INIS)
Harvey, A G; Tennyson, J
2009-01-01
Electron re-scattering in a strong laser field provides an important probe of molecular structure and processes. The laser field drives the ionization of the molecule, followed by acceleration and subsequent recollision of the electron with the parent molecular ion, the scattered electrons carry information about the nuclear geometry and electronic states of the molecular ion. It is advantageous in strong field experiments to work with aligned molecules, which introduces extra physics compared to the standard gas-phase, electron-molecule scattering problem. The formalism for scattering from oriented linear molecules is presented and applied to H 2 and CO 2 . Differential cross sections are presented for (re-)scattering by these systems concentrating on the most common, linear alignment. In H 2 these cross sections show significant angular structure which, particularly for a scattering angle of 90 deg., are predicted to vary significantly between re-collisions stimulated by an even or an odd number of photons. In CO 2 these cross sections are zero indicating the necessity of using non-parallel alignment with this molecule.
Reflection Matrix Method for Controlling Light After Reflection From a Diffuse Scattering Surface
2016-12-22
of Philosophy Kenneth W. Burgi, BS, MS Major, USAF 22 December 2016 DISTRIBUTION STATEMENT A APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED. AFIT...refocusing light through thin films of a turbid medium. When coherent light is trans- mitted through a stationary diffuser (i.e. a turbid medium), a fine...resultant light scatter [14, 15, 21, 23]. Transmission matrices were measured with microscopic objectives and thin films of turbid media, resulting in
Energy Technology Data Exchange (ETDEWEB)
Zhuo, Ye [Iowa State Univ., Ames, IA (United States)
2011-01-01
In this thesis, we theoretically study the electromagnetic wave propagation in several passive and active optical components and devices including 2-D photonic crystals, straight and curved waveguides, organic light emitting diodes (OLEDs), and etc. Several optical designs are also presented like organic photovoltaic (OPV) cells and solar concentrators. The first part of the thesis focuses on theoretical investigation. First, the plane-wave-based transfer (scattering) matrix method (TMM) is briefly described with a short review of photonic crystals and other numerical methods to study them (Chapter 1 and 2). Next TMM, the numerical method itself is investigated in details and developed in advance to deal with more complex optical systems. In chapter 3, TMM is extended in curvilinear coordinates to study curved nanoribbon waveguides. The problem of a curved structure is transformed into an equivalent one of a straight structure with spatially dependent tensors of dielectric constant and magnetic permeability. In chapter 4, a new set of localized basis orbitals are introduced to locally represent electromagnetic field in photonic crystals as alternative to planewave basis. The second part of the thesis focuses on the design of optical devices. First, two examples of TMM applications are given. The first example is the design of metal grating structures as replacements of ITO to enhance the optical absorption in OPV cells (chapter 6). The second one is the design of the same structure as above to enhance the light extraction of OLEDs (chapter 7). Next, two design examples by ray tracing method are given, including applying a microlens array to enhance the light extraction of OLEDs (chapter 5) and an all-angle wide-wavelength design of solar concentrator (chapter 8). In summary, this dissertation has extended TMM which makes it capable of treating complex optical systems. Several optical designs by TMM and ray tracing method are also given as a full complement of this
Time delay correlations in chaotic scattering and random matrix approach
International Nuclear Information System (INIS)
Lehmann, N.; Savin, D.V.; Sokolov, V.V.; Sommers, H.J.
1994-01-01
We study the correlations in the time delay a model of chaotic resonance scattering based on the random matrix approach. Analytical formulae which are valid for arbitrary number of open channels and arbitrary coupling strength between resonances and channels are obtained by the supersymmetry method. The time delay correlation function, through being not a Lorentzian, is characterized, similar to that of the scattering matrix, by the gap between the cloud of complex poles of the S-matrix and the real energy axis. 28 refs.; 4 figs
An estimate on the purely imaginary poles of scattering matrix
International Nuclear Information System (INIS)
Bozhkov, Y.D.
1988-12-01
In this work we obtain two estimates (upper and lower) on the number of purely imaginary poles of the scattering matrix for the wave equation in the exterior of a compact smooth obstacle in R n , n ≥ 3 odd. The method of Lax and Phillips is used. (author). 5 refs
Significance of matrix diagonalization in modelling inelastic electron scattering
Energy Technology Data Exchange (ETDEWEB)
Lee, Z. [University of Ulm, Ulm 89081 (Germany); Hambach, R. [University of Ulm, Ulm 89081 (Germany); University of Jena, Jena 07743 (Germany); Kaiser, U.; Rose, H. [University of Ulm, Ulm 89081 (Germany)
2017-04-15
Electron scattering is always applied as one of the routines to investigate nanostructures. Nowadays the development of hardware offers more and more prospect for this technique. For example imaging nanostructures with inelastic scattered electrons may allow to produce component-sensitive images with atomic resolution. Modelling inelastic electron scattering is therefore essential for interpreting these images. The main obstacle to study inelastic scattering problem is its complexity. During inelastic scattering, incident electrons entangle with objects, and the description of this process involves a multidimensional array. Since the simulation usually involves fourdimensional Fourier transforms, the computation is highly inefficient. In this work we have offered one solution to handle the multidimensional problem. By transforming a high dimensional array into twodimensional array, we are able to perform matrix diagonalization and approximate the original multidimensional array with its twodimensional eigenvectors. Our procedure reduces the complicated multidimensional problem to a twodimensional problem. In addition, it minimizes the number of twodimensional problems. This method is very useful for studying multiple inelastic scattering. - Highlights: • 4D problems are involved in modelling inelastic electron scattering. • By means of matrix diagonalization, the 4D problems can be simplified as 2D problems. • The number of 2D problems is minimized by using this approach.
New method for solving multidimensional scattering problem
International Nuclear Information System (INIS)
Melezhik, V.S.
1991-01-01
A new method is developed for solving the quantum mechanical problem of scattering of a particle with internal structure. The multichannel scattering problem is formulated as a system of nonlinear functional equations for the wave function and reaction matrix. The method is successfully tested for the scattering from a nonspherical potential well and a long-range nonspherical scatterer. The method is also applicable to solving the multidimensional Schroedinger equation with a discrete spectrum. As an example the known problem of a hydrogen atom in a homogeneous magnetic field is analyzed
International Nuclear Information System (INIS)
Tyynelae, Jani; Nousiainen, Timo; Goeke, Sabine; Muinonen, Karri
2009-01-01
We study the applicability of the discrete-dipole approximation by modeling centimeter (C-band) radar echoes for hydrometeors, and compare the results to exact theories. We use ice and water particles of various shapes with varying water-content to investigate how the backscattering, extinction, and absorption cross sections change as a function of particle radius. We also compute radar parameters, such as the differential reflectivity, the linear depolarization ratio, and the copolarized correlation coefficient. We find that using discrete-dipole approximation (DDA) to model pure ice and pure water particles at the C-band, is a lot more accurate than particles containing both ice and water. For coated particles, a large grid-size is recommended so that the coating is modeled adequately. We also find that the absorption cross section is significantly less accurate than the scattering and backscattering cross sections. The accuracy of DDA can be increased by increasing the number of dipoles, but also by using the filtered coupled dipole-option for the polarizability. This halved the relative errors in cross sections.
Li, Ming
In this dissertation, a set of numerical simulation tools are developed under previous work to efficiently and accurately study one-dimensional (1D), two-dimensional (2D), 2D slab and three-dimensional (3D) photonic crystal structures and their defects effects by means of spectrum (transmission, reflection, absorption), band structure (dispersion relation), and electric and/or magnetic fields distribution (mode profiles). Further more, the lasing property and spontaneous emission behaviors are studied when active gain materials are presented in the photonic crystal structures. First, the planewave based transfer (scattering) matrix method (TMM) is described in every detail along with a brief review of photonic crystal history (Chapter 1 and 2). As a frequency domain method, TMM has the following major advantages over other numerical methods: (1) the planewave basis makes Maxwell's Equations a linear algebra problem and there are mature numerical package to solve linear algebra problem such as Lapack and Scalapack (for parallel computation). (2) Transfer (scattering) matrix method make 3D problem into 2D slices and link all slices together via the scattering matrix (S matrix) which reduces computation time and memory usage dramatically and makes 3D real photonic crystal devices design possible; and this also makes the simulated domain no length limitation along the propagation direction (ideal for waveguide simulation). (3) It is a frequency domain method and calculation results are all for steady state, without the influences of finite time span convolution effects and/or transient effects. (4) TMM can treat dispersive material (such as metal at visible light) naturally without introducing any additional computation; and meanwhile TMM can also deal with anisotropic material and magnetic material (such as perfectly matched layer) naturally from its algorithms. (5) Extension of TMM to deal with active gain material can be done through an iteration procedure with gain
Connection between Dirac and matrix Schroedinger inverse-scattering transforms
International Nuclear Information System (INIS)
Jaulent, M.; Leon, J.J.P.
1978-01-01
The connection between two applications of the inverse scattering method for solving nonlinear equations is established. The inverse method associated with the massive Dirac system (D) : (iσ 3 d/dx - i q 3 σ 1 - q 1 σ 2 + mσ 2 )Y = epsilonY is rediscovered from the inverse method associated with the 2 x 2 matrix Schroedinger equation (S) : Ysub(xx) + (k 2 -Q)Y = 0. Here Q obeys a nonlinear constraint equivalent to a linear constraint on the reflection coefficient for (S). (author)
The scattering matrix element of the three body reactive collision
International Nuclear Information System (INIS)
Morsy, M.W.; Hilal, A.A.; El-Sabagh, M.A.
1980-08-01
The optical model approximation has been applied to a previously derived set of coupled equations representing the dynamics of the three-body reactive scattering. The Schroedinger equation obtained describing the scattering problem has then been solved by inserting the effective mass approximation. The asymptotic requirements for both the entrance and exit channels, respectively, have been supplied to give the scattering matrix element of the reactive collision. (author)
Hierarchy of Poisson brackets for elements of a scattering matrix
International Nuclear Information System (INIS)
Konopelchenko, B.G.; Dubrovsky, V.G.
1984-01-01
The infinite family of Poisson brackets [Ssub(i1k1) (lambda 1 ), Ssub(i2k2) (lambda 2 )]sub(n) (n=0, 1, 2, ...) between the elements of a scattering matrix is calculated for the linear matrix spectral problem. (orig.)
Quasinormal-Mode Expansion of the Scattering Matrix
Directory of Open Access Journals (Sweden)
Filippo Alpeggiani
2017-06-01
Full Text Available It is well known that the quasinormal modes (or resonant states of photonic structures can be associated with the poles of the scattering matrix of the system in the complex-frequency plane. In this work, the inverse problem, i.e., the reconstruction of the scattering matrix from the knowledge of the quasinormal modes, is addressed. We develop a general and scalable quasinormal-mode expansion of the scattering matrix, requiring only the complex eigenfrequencies and the far-field properties of the eigenmodes. The theory is validated by applying it to illustrative nanophotonic systems with multiple overlapping electromagnetic modes. The examples demonstrate that our theory provides an accurate first-principles prediction of the scattering properties, without the need for postulating ad hoc nonresonant channels.
Hanle-Zeeman Scattering Matrix for Magnetic Dipole Transitions
Energy Technology Data Exchange (ETDEWEB)
Megha, A.; Sampoorna, M.; Nagendra, K. N.; Sankarasubramanian, K., E-mail: megha@iiap.res.in, E-mail: sampoorna@iiap.res.in, E-mail: knn@iiap.res.in, E-mail: sankar@iiap.res.in [Indian Institute of Astrophysics, Koramangala, Bengaluru 560 034 (India)
2017-06-01
The polarization of the light that is scattered by the coronal ions is influenced by the anisotropic illumination from the photosphere and the magnetic field structuring in the solar corona. The properties of the coronal magnetic fields can be well studied by understanding the polarization properties of coronal forbidden emission lines that arise from magnetic dipole ( M 1) transitions in the highly ionized atoms that are present in the corona. We present the classical scattering theory of the forbidden lines for a more general case of arbitrary-strength magnetic fields. We derive the scattering matrix for M 1 transitions using the classical magnetic dipole model of Casini and Lin and applying the scattering matrix approach of Stenflo. We consider a two-level atom model and neglect collisional effects. The scattering matrix so derived is used to study the Stokes profiles formed in coronal conditions in those regions where the radiative excitations dominate collisional excitations. To this end, we take into account the integration over a cone of an unpolarized radiation from the solar disk incident on the scattering atoms. Furthermore, we also integrate along the line of sight to calculate the emerging polarized line profiles. We consider radial and dipole magnetic field configurations and spherically symmetric density distributions. For our studies we adopt the atomic parameters corresponding to the [Fe xiii] 10747 Å coronal forbidden line. We also discuss the nature of the scattering matrix for M 1 transitions and compare it with that for the electric dipole ( E 1) transitions.
The scattering matrix is non-trivial for weakly coupled P(phi)2 models
International Nuclear Information System (INIS)
Osterwalder, K.; Seneor, R.
1976-01-01
It is shown that for sufficiently small coupling constant lambda the lambdaP(phi) 2 quantum field theory models have a scattering matrix which is different from 1. The other method is to write the scattering matrix elements as polynomials in lambda, whose coefficients, though themselves functions of lamda, are uniformly bounded for lambda sufficiently small. The first order term in that expansion is the one given by perturbation theory. (Auth.)
A wave propagation matrix method in semiclassical theory
International Nuclear Information System (INIS)
Lee, S.Y.; Takigawa, N.
1977-05-01
A wave propagation matrix method is used to derive the semiclassical formulae of the multiturning point problem. A phase shift matrix and a barrier transformation matrix are introduced to describe the processes of a particle travelling through a potential well and crossing a potential barrier respectively. The wave propagation matrix is given by the products of phase shift matrices and barrier transformation matrices. The method to study scattering by surface transparent potentials and the Bloch wave in solids is then applied
Convergent J-matrix calculation of the Poet-Temkin model of electron-hydrogen scattering
International Nuclear Information System (INIS)
Konovalov, D.A.; McCarthy, I.E.
1994-01-01
It is shown that the Poet-Temkin model of electron-hydrogen scattering could be solved to any required accuracy using the J-matrix method. The convergence in the basis size is achieved to an accuracy of better than 2% with the inclusion of 37 basis L 2 functions. Previously observed pseudoresonances in the J-matrix calculation naturally disappear with an increase in basis size. No averaging technique is necessary to smooth the convergent J-matrix results. (Author)
Liu, Jia; Zhang, Yongming; Zhang, Qixing; Wang, Jinjun
2018-03-01
The complete scattering matrix for cement dust was measured as a function of scattering angle from 5° to 160° at a wavelength of 532 nm, as a representative of mineral dust of anthropogenic origin in urban areas. Other related characteristics of cement dust, such as particle size distribution, chemical composition, refractive index, and micromorphology, were also analyzed. For this objective, a newly improved apparatus was built and calibrated using water droplets. Measurements of water droplets were in good agreement with Lorenz-Mie calculations. To facilitate the direct applicability of measurements for cement dust in radiative transfer calculation, the synthetic scattering matrix was computed and defined over the full scattering angle range from 0° to 180°. The scattering matrices for cement dust and typical natural mineral dusts were found to be similar in trends and angular behaviors. Angular distributions of all matrix elements were confined to rather limited domains. To promote the application of light-scattering matrix in atmospheric observation and remote sensing, discrimination methods for various atmospheric particulates (cement dust, soot, smolder smoke, and water droplets) based on the angular distributions of their scattering matrix elements are discussed. The ratio -F12/F11 proved to be the most effective discrimination method when a single matrix element is employed; aerosol identification can be achieved based on -F12/F11 values at 90° and 160°. Meanwhile, the combinations of -F12/F11 with F22/F11 (or (F11 - F22)/(F11 + F22)) or -F12/F11 with F44/F11 at 160° can be used when multiple matrix elements at the same scattering angle are selected.
The S-matrix for abstract scattering systems
International Nuclear Information System (INIS)
Amrein, W.O.; Pearson, D.B.
1979-01-01
Let S(lambda) be the S-matrix at energy lambda for an abstract scattering system. A bound is derived in terms of the interaction, on integrals of the form ∫ h(lambda)/S(lambda) - I/ 2 sub(HS) dlambda, where /./sub(HS) denotes the Hilbert-Schmidt norm. (Auth.)
Modal Ring Method for the Scattering of Electromagnetic Waves
Baumeister, Kenneth J.; Kreider, Kevin L.
1993-01-01
The modal ring method for electromagnetic scattering from perfectly electric conducting (PEC) symmetrical bodies is presented. The scattering body is represented by a line of finite elements (triangular) on its outer surface. The infinite computational region surrounding the body is represented analytically by an eigenfunction expansion. The modal ring method effectively reduces the two dimensional scattering problem to a one-dimensional problem similar to the method of moments. The modal element method is capable of handling very high frequency scattering because it has a highly banded solution matrix.
Numerical methods in matrix computations
Björck, Åke
2015-01-01
Matrix algorithms are at the core of scientific computing and are indispensable tools in most applications in engineering. This book offers a comprehensive and up-to-date treatment of modern methods in matrix computation. It uses a unified approach to direct and iterative methods for linear systems, least squares and eigenvalue problems. A thorough analysis of the stability, accuracy, and complexity of the treated methods is given. Numerical Methods in Matrix Computations is suitable for use in courses on scientific computing and applied technical areas at advanced undergraduate and graduate level. A large bibliography is provided, which includes both historical and review papers as well as recent research papers. This makes the book useful also as a reference and guide to further study and research work. Åke Björck is a professor emeritus at the Department of Mathematics, Linköping University. He is a Fellow of the Society of Industrial and Applied Mathematics.
Scattering-matrix elements of coated infinite-length cylinders
International Nuclear Information System (INIS)
Manickavasagam, S.; Menguec, M.P.
1998-01-01
The angular variations of scattering-matrix elements of coated cylindrical particles are presented. The sensitivity of different elements for a number of physical parameters are discussed, including size parameter, real and imaginary parts of the refractive index of the outer coat, and the inner core. The numerical predictions are presented for typical index-of-refraction values of cotton fibers. These results show that the physical structure of coated cylinders can be determined from carefully conducted light-scattering experiments. copyright 1998 Optical Society of America
Analytical techniques for instrument design - Matrix methods
International Nuclear Information System (INIS)
Robinson, R.A.
1997-01-01
The authors take the traditional Cooper-Nathans approach, as has been applied for many years for steady-state triple-axis spectrometers, and consider its generalization to other inelastic scattering spectrometers. This involves a number of simple manipulations of exponentials of quadratic forms. In particular, they discuss a toolbox of matrix manipulations that can be performed on the 6-dimensional Cooper-Nathans matrix. They show how these tools can be combined to solve a number of important problems, within the narrow-band limit and the gaussian approximation. They will argue that a generalized program that can handle multiple different spectrometers could (and should) be written in parallel to the Monte-Carlo packages that are becoming available. They also discuss the complementarity between detailed Monte-Carlo calculations and the approach presented here. In particular, Monte-Carlo methods traditionally simulate the real experiment as performed in practice, given a model scattering law, while the Cooper-Nathans method asks the inverse question: given that a neutron turns up in a particular spectrometer configuration (e.g. angle and time of flight), what is the probability distribution of possible scattering events at the sample? The Monte-Carlo approach could be applied in the same spirit to this question
Analytical techniques for instrument design - matrix methods
International Nuclear Information System (INIS)
Robinson, R.A.
1997-01-01
We take the traditional Cooper-Nathans approach, as has been applied for many years for steady-state triple-axis spectrometers, and consider its generalisation to other inelastic scattering spectrometers. This involves a number of simple manipulations of exponentials of quadratic forms. In particular, we discuss a toolbox of matrix manipulations that can be performed on the 6- dimensional Cooper-Nathans matrix: diagonalisation (Moller-Nielsen method), coordinate changes e.g. from (Δk I ,Δk F to ΔE, ΔQ ampersand 2 dummy variables), integration of one or more variables (e.g. over such dummy variables), integration subject to linear constraints (e.g. Bragg's Law for analysers), inversion to give the variance-covariance matrix, and so on. We show how these tools can be combined to solve a number of important problems, within the narrow-band limit and the gaussian approximation. We will argue that a generalised program that can handle multiple different spectrometers could (and should) be written in parallel to the Monte-Carlo packages that are becoming available. We will also discuss the complementarity between detailed Monte-Carlo calculations and the approach presented here. In particular, Monte-Carlo methods traditionally simulate the real experiment as performed in practice, given a model scattering law, while the Cooper-Nathans method asks the inverse question: given that a neutron turns up in a particular spectrometer configuration (e.g. angle and time of flight), what is the probability distribution of possible scattering events at the sample? The Monte-Carlo approach could be applied in the same spirit to this question
International Nuclear Information System (INIS)
Allen, L.J.; Spargo, A.E.C.; Leeb, H.
1998-01-01
The retrieval of a unique crystal potential from the scattering matrix S in high energy transmission electron diffraction is discussed. It is shown that, in general, data taken at a single orientation are not sufficient to determine all the elements of S. Additional measurements with tilted incident beam are required for the determination of the whole S-matrix. An algorithm for the extraction of the crystal potential from the S-matrix measured at a single energy and thickness is presented. The limiting case of thin crystals is discussed. Several examples with simulated data are considered
A new path-integral representation of the T-matrix in potential scattering
International Nuclear Information System (INIS)
Carron, J.; Rosenfelder, R.
2011-01-01
We employ the method used by Barbashov and collaborators in Quantum Field Theory to derive a path-integral representation of the T-matrix in nonrelativistic potential scattering which is free of functional integration over fictitious variables as was necessary before. The resulting expression serves as a starting point for a variational approximation applied to high-energy scattering from a Gaussian potential. Good agreement with exact partial-wave calculations is found even at large scattering angles. A novel path-integral representation of the scattering length is obtained in the low-energy limit. -- Highlights: → We derive a new path-integral representation for the T-matrix in quantum scattering from a potential. → The method is based on a technique used by Barbashov and collaborators in Quantum Field Theory. → Unlike previous approaches no unphysical degrees of freedom in the path integral are needed. → The new representation is used for a variational approximation of the T-matrix at high energies. → A new expression for the scattering length at low energy is derived.
Coherent scattering and matrix correction in bone-lead measurements
International Nuclear Information System (INIS)
Todd, A.C.
2000-01-01
The technique of K-shell x-ray fluorescence of lead in bone has been used in many studies of the health effects of lead. This paper addresses one aspect of the technique, namely the coherent conversion factor (CCF) which converts between the matrix of the calibration standards and those of human bone. The CCF is conventionally considered a constant but is a function of scattering angle, energy and the elemental composition of the matrices. The aims of this study were to quantify the effect on the CCF of several assumptions which may not have been tested adequately and to compare the CCFs for plaster of Paris (the present matrix of calibration standards) and a synthetic apatite matrix. The CCF was calculated, using relativistic form factors, for published compositions of bone, both assumed and assessed compositions of plaster, and the synthetic apatite. The main findings of the study were, first, that impurities in plaster, lead in the plaster or bone matrices, coherent scatter from non-bone tissues and the individual subject's measurement geometry are all minor or negligible effects; and, second, that the synthetic apatite matrix is more representative of bone mineral than is plaster of Paris. (author)
Formal scattering theory approach to S-matrix relations in supersymmetric quantum mechanics
International Nuclear Information System (INIS)
Amado, R.D.; Cannata, F.; Dedonder, J.P.
1988-01-01
Combining the methods of scattering theory and supersymmetric quantum mechanics we obtain relations between the S matrix and its supersymmetric partner. These relations involve only asymptotic quantities and do not require knowledge of the dynamical details. For example, for coupled channels with no threshold differences the relations involve the asymptotic normalization constant of the bound state removed by supersymmetry
Off-shell two-particle scattering amplitude in the P-matrix approach
International Nuclear Information System (INIS)
Babenko, V.A.; Petrov, N.M.
1988-01-01
A generalization of the P-matrix approach which makes it possible to describe the interaction of two particles off the energy shell is proposed. Explicit separation in the wave function of a part corresponding to free motion yields a compact expression for the off-shell scattering amplitude and gives directly a method for separable expansion of the amplitude
Radiation scatter apparatus and method
International Nuclear Information System (INIS)
Molbert, J. L.; Riddle, E. R.
1985-01-01
A radiation scatter gauge includes multiple detector locations for developing separate and independent sets of data from which multiple physical characteristics of a thin material and underlying substrate may be determined. In an illustrated embodiment, the apparatus and method of the invention are directed to determining characteristics of resurfaced pavement by nondestructive testing. More particularly, the density and thickness of a thin asphalt overlay and the density of the underlying pavement may be determined
Hybrid transfer-matrix FDTD method for layered periodic structures.
Deinega, Alexei; Belousov, Sergei; Valuev, Ilya
2009-03-15
A hybrid transfer-matrix finite-difference time-domain (FDTD) method is proposed for modeling the optical properties of finite-width planar periodic structures. This method can also be applied for calculation of the photonic bands in infinite photonic crystals. We describe the procedure of evaluating the transfer-matrix elements by a special numerical FDTD simulation. The accuracy of the new method is tested by comparing computed transmission spectra of a 32-layered photonic crystal composed of spherical or ellipsoidal scatterers with the results of direct FDTD and layer-multiple-scattering calculations.
A mathematical formulation of the Mahaux-Weidenmueller formula for the scattering matrix
International Nuclear Information System (INIS)
Christiansen, T J; Zworski, M
2009-01-01
This paper gives a mathematical exposition of a formula for the scattering matrix for a manifold with infinite cylindrical ends or a waveguide. This formula is well known in the physics literature and we show that a variant of this formula gives the scattering matrix of the mathematics literature. Moreover, we bound the difference between the scattering matrix and an approximation of it computed using a finite rank approximation of the interaction matrix.
Directory of Open Access Journals (Sweden)
E DU
2014-01-01
Full Text Available We developed a model to describe polarized photon scattering in biological tissues. In this model, tissues are simplified to a mixture of scatterers and surrounding medium. There are two types of scatterers in the model: solid spheres and infinitely long solid cylinders. Variables related to the scatterers include: the densities and sizes of the spheres and cylinders, the orientation and angular distribution of cylinders. Variables related to the surrounding medium include: the refractive index, absorption coefficient and birefringence. In this paper, as a development we introduce an optical activity effect to the model. By comparing experiments and Monte Carlo simulations, we analyze the backscattering Mueller matrix patterns of several tissue-like media, and summarize the different effects coming from anisotropic scattering and optical properties. In addition, we propose a possible method to extract the optical activity values for tissues. Both the experimental and simulated results show that, by analyzing the Mueller matrix patterns, the microstructure and optical properties of the medium can be obtained. The characteristic features of Mueller matrix patterns are potentially powerful tools for studying the contrast mechanisms of polarization imaging for medical diagnosis.
Solution of the inverse scattering problem at fixed energy with non-physical S matrix elements
International Nuclear Information System (INIS)
Eberspaecher, M.; Amos, K.; Apagyi, B.
1999-12-01
The quantum mechanical inverse elastic scattering problem is solved with the modified Newton-Sabatier method. A set of S matrix elements calculated from a realistic analytic optical model potential serves as input data. It is demonstrated that the quality of the inversion potential can be improved by including non-physical S matrix elements to half, quarter and eighth valued partial waves if the original set does not contain enough information to determine the interaction potential. We demonstrate that results can be very sensitive to the choice of those non-physical S matrix values both with the analytic potential model and in a real application in which the experimental cross section for the symmetrical scattering system of 12 C+ 12 C at E=7.998 MeV is analyzed
On the isobaric spin and the scattering matrix
International Nuclear Information System (INIS)
Hategan, Cornel
2002-01-01
The isobaric spin and the scattering matrix are fundamental nuclear physics concepts invented by Werner Heisenberg. The cardinal impact of the Heisenberg concepts on historical developpement of nuclear physics and other quantum and classical physics branches is discussed in this communication. Heisenberg in physics is synonymous to monumental scientific creations, namely: -'Creation of quantum mechanics' (Nobel Prize, 1932), -'Heisenberg relations', or 'Heisenberg inequalities' or 'Uncertainty principle' or 'Indeterminacy principle', - Basis for Copenhagen interpretation of Quantum Mechanics, -'world formula', - Project for a unitary theory representing all existing particles. Heisenberg does signify also important/cardinal contributions to many fields of physics as follows: - hydrodynamical theory of turbulence, (Dissertation, Sommerfeld); - theory of ferromagnetism; - study of cosmic rays; - nuclear physics. Heisenberg has invented two nuclear physics concepts, isobaric spin and scattering matrix which became cornerstones of the two main fields of the nuclear theory, namely, the nuclear structure (nuclear spectroscopy) and the nuclear reactions. This communication intends to illustrate the impact of the Heisenberg concepts on developpement of nuclear physics. (author)
Correlation expansion: a powerful alternative multiple scattering calculation method
International Nuclear Information System (INIS)
Zhao Haifeng; Wu Ziyu; Sebilleau, Didier
2008-01-01
We introduce a powerful alternative expansion method to perform multiple scattering calculations. In contrast to standard MS series expansion, where the scattering contributions are grouped in terms of scattering order and may diverge in the low energy region, this expansion, called correlation expansion, partitions the scattering process into contributions from different small atom groups and converges at all energies. It converges faster than MS series expansion when the latter is convergent. Furthermore, it takes less memory than the full MS method so it can be used in the near edge region without any divergence problem, even for large clusters. The correlation expansion framework we derive here is very general and can serve to calculate all the elements of the scattering path operator matrix. Photoelectron diffraction calculations in a cluster containing 23 atoms are presented to test the method and compare it to full MS and standard MS series expansion
Modeling cometary photopolarimetric characteristics with Sh-matrix method
Kolokolova, L.; Petrov, D.
2017-12-01
Cometary dust is dominated by particles of complex shape and structure, which are often considered as fractal aggregates. Rigorous modeling of light scattering by such particles, even using parallelized codes and NASA supercomputer resources, is very computer time and memory consuming. We are presenting a new approach to modeling cometary dust that is based on the Sh-matrix technique (e.g., Petrov et al., JQSRT, 112, 2012). This method is based on the T-matrix technique (e.g., Mishchenko et al., JQSRT, 55, 1996) and was developed after it had been found that the shape-dependent factors could be separated from the size- and refractive-index-dependent factors and presented as a shape matrix, or Sh-matrix. Size and refractive index dependences are incorporated through analytical operations on the Sh-matrix to produce the elements of T-matrix. Sh-matrix method keeps all advantages of the T-matrix method, including analytical averaging over particle orientation. Moreover, the surface integrals describing the Sh-matrix elements themselves can be solvable analytically for particles of any shape. This makes Sh-matrix approach an effective technique to simulate light scattering by particles of complex shape and surface structure. In this paper, we present cometary dust as an ensemble of Gaussian random particles. The shape of these particles is described by a log-normal distribution of their radius length and direction (Muinonen, EMP, 72, 1996). Changing one of the parameters of this distribution, the correlation angle, from 0 to 90 deg., we can model a variety of particles from spheres to particles of a random complex shape. We survey the angular and spectral dependencies of intensity and polarization resulted from light scattering by such particles, studying how they depend on the particle shape, size, and composition (including porous particles to simulate aggregates) to find the best fit to the cometary observations.
Simplified expressions of the T-matrix integrals for electromagnetic scattering.
Somerville, Walter R C; Auguié, Baptiste; Le Ru, Eric C
2011-09-01
The extended boundary condition method, also called the null-field method, provides a semianalytic solution to the problem of electromagnetic scattering by a particle by constructing a transition matrix (T-matrix) that links the scattered field to the incident field. This approach requires the computation of specific integrals over the particle surface, which are typically evaluated numerically. We introduce here a new set of simplified expressions for these integrals in the commonly studied case of axisymmetric particles. Simplifications are obtained using the differentiation properties of the radial functions (spherical Bessel) and angular functions (associated Legendre functions) and integrations by parts. The resulting simplified expressions not only lead to faster computations, but also reduce the risks of loss of precision and provide a simpler framework for further analytical work.
Scattering matrix approach to non-stationary quantum transport
Moskalets, Michael V
2012-01-01
The aim of this book is to introduce the basic elements of the scattering matrix approach to transport phenomena in dynamical quantum systems of non-interacting electrons. This approach admits a physically clear and transparent description of transport processes in dynamical mesoscopic systems promising basic elements of solid-state devices for quantum information processing. One of the key effects, the quantum pump effect, is considered in detail. In addition, the theory for a recently implemented new dynamical source - injecting electrons with time delay much larger than the electron coherence time - is offered. This theory provides a simple description of quantum circuits with such a single-particle source and shows in an unambiguous way that the tunability inherent to the dynamical systems leads to a number of unexpected but fundamental effects.
Elastic scattering of positronium: Application of the confined variational method
Zhang, Junyi
2012-08-01
We demonstrate for the first time that the phase shift in elastic positronium-atom scattering can be precisely determined by the confined variational method, in spite of the fact that the Hamiltonian includes an unphysical confining potential acting on the center of mass of the positron and one of the atomic electrons. As an example, we study the S-wave elastic scattering for the positronium-hydrogen scattering system, where the existing 4% discrepancy between the Kohn variational calculation and the R-matrix calculation is resolved. © Copyright EPLA, 2012.
Elastic scattering of positronium: Application of the confined variational method
Zhang, Junyi; Yan, Zong-Chao; Schwingenschlö gl, Udo
2012-01-01
We demonstrate for the first time that the phase shift in elastic positronium-atom scattering can be precisely determined by the confined variational method, in spite of the fact that the Hamiltonian includes an unphysical confining potential acting on the center of mass of the positron and one of the atomic electrons. As an example, we study the S-wave elastic scattering for the positronium-hydrogen scattering system, where the existing 4% discrepancy between the Kohn variational calculation and the R-matrix calculation is resolved. © Copyright EPLA, 2012.
Scattering matrix for magnetic potentials with Coulomb decay at infinity
Yafaev, D
2003-01-01
We consider the Schr\\"odinger operator $H$ in the space $L_2({\\R}^d)$ with a magnetic potential $A(x)$ decaying as $|x|^{-1}$ at infinity and satisfying the transversal gauge condition $ =0$. Such potentials correspond, for example, to magnetic fields $B(x)$ with compact support and hence are quite general. Our goal is to study properties of the scattering matrix $S(\\lambda)$ associated to the operator $H$. In particular, we find the essential spectrum $\\sigma_{ess}$ of $S(\\lambda)$ in terms of the behaviour of $A(x)$ at infinity. It turns out that $\\sigma_{ess}(S(\\lambda))$ is normally a rich subset of the unit circle ${\\Bbb T}$ or even coincides with ${\\Bbb T}$. We find also the diagonal singularity of the scattering amplitude (of the kernel of $S(\\lambda)$ regarded as an integral operator). In general, $S(\\lambda)$ is a sum of a multiplication operator and of a singular integral operator. However, if the magnetic field decreases faster than $ |x|^{-2}$ for $d\\geq 3$ (and the total magnetic flux is an integ...
Classical-limit S-matrix for heavy ion scattering
International Nuclear Information System (INIS)
Donangelo, R.J.
1977-01-01
An integral representation for the classical limit of the quantum mechanical S-matrix is developed and applied to heavy-ion Coulomb excitation and Coulomb-nuclear interference. The method combines the quantum principle of superposition with exact classical dynamics to describe the projectile-target system. A detailed consideration of the classical trajectories and of the dimensionless parameters that characterize the system is carried out. The results are compared, where possible, to exact quantum mechanical calculations and to conventional semiclassical calculations. It is found that in the case of backscattering the classical limit S-matrix method is able to almost exactly reproduce the quantum-mechanical S-matrix elements, and therefore the transition probabilities, even for projectiles as light as protons. The results also suggest that this approach should be a better approximation for heavy-ion multiple Coulomb excitation than earlier semiclassical methods, due to a more accurate description of the classical orbits in the electromagnetic field of the target nucleus. Calculations using this method indicate that the rotational excitation probabilities in the Coulomb-nuclear interference region should be very sensitive to the details of the potential at the surface of the nucleus, suggesting that heavy-ion rotational excitation could constitute a sensitive probe of the nuclear potential in this region. The application to other problems as well as the present limits of applicability of the formalism are also discussed
A multi-dimensional sampling method for locating small scatterers
International Nuclear Information System (INIS)
Song, Rencheng; Zhong, Yu; Chen, Xudong
2012-01-01
A multiple signal classification (MUSIC)-like multi-dimensional sampling method (MDSM) is introduced to locate small three-dimensional scatterers using electromagnetic waves. The indicator is built with the most stable part of signal subspace of the multi-static response matrix on a set of combinatorial sampling nodes inside the domain of interest. It has two main advantages compared to the conventional MUSIC methods. First, the MDSM is more robust against noise. Second, it can work with a single incidence even for multi-scatterers. Numerical simulations are presented to show the good performance of the proposed method. (paper)
Measuring methods of matrix diffusion
International Nuclear Information System (INIS)
Muurinen, A.; Valkiainen, M.
1988-03-01
In Finland the spent nuclear fuel is planned to be disposed of at large depths in crystalline bedrock. The radionuclides which are dissolved in the groundwater may be able to diffuse into the micropores of the porous rock matrix and thus be withdrawn from the flowing water in the fractures. This phenomenon is called matrix diffusion. A review over matrix diffusion is presented in the study. The main interest is directed to the diffusion of non-sorbing species. The review covers diffusion experiments and measurements of porosity, pore size, specific surface area and water permeability
Lectures on the inverse scattering method
International Nuclear Information System (INIS)
Zakharov, V.E.
1983-06-01
In a series of six lectures an elementary introduction to the theory of inverse scattering is given. The first four lectures contain a detailed theory of solitons in the framework of the KdV equation, together with the inverse scattering theory of the one-dimensional Schroedinger equation. In the fifth lecture the dressing method is described, while the sixth lecture gives a brief review of the equations soluble by the inverse scattering method. (author)
Response matrix method for large LMFBR analysis
International Nuclear Information System (INIS)
King, M.J.
1977-06-01
The feasibility of using response matrix techniques for computational models of large LMFBRs is examined. Since finite-difference methods based on diffusion theory have generally found a place in fast-reactor codes, a brief review of their general matrix foundation is given first in order to contrast it to the general strategy of response matrix methods. Then, in order to present the general method of response matrix technique, two illustrative examples are given. Matrix algorithms arising in the application to large LMFBRs are discussed, and the potential of the response matrix method is explored for a variety of computational problems. Principal properties of the matrices involved are derived with a view to application of numerical methods of solution. The Jacobi iterative method as applied to the current-balance eigenvalue problem is discussed
Higher order spin-dependent terms in D0-brane scattering from the matrix model
International Nuclear Information System (INIS)
McArthur, I.N.
1998-01-01
The potential describing long-range interactions between D0-branes contains spin-dependent terms. In the matrix model, these should be reproduced by the one-loop effective action computed in the presence of a non-trivial fermionic background ψ. The v 3 ψ 2 /r 8 term in the effective action has been computed by Kraus and shown to correspond to a spin-orbit interaction between D0-branes, and the ψ 8 /r 11 term in the static potential has been obtained by Barrio et al. In this paper, the v 2 ψ 4 /r 9 term is computing in the matrix model and compared with the corresponding results of Morales et al. obtained using string theoretic methods. The technique employed is adapted to the underlying supersymmetry of the matrix model, and should be useful in the calculation of spin-dependent effects in more general Dp-brane scatterings. (orig.)
The Fourier-grid formalism: philosophy and application to scattering problems using R-matrix theory
International Nuclear Information System (INIS)
Layton, E.G.
1993-01-01
The Fourier-grid (FG) method is a recent L 2 variational treatment of the quantum mechanical eigenvalue problem that does not require the use of a set of basis functions; it is rather a discrete variable representation approach. In this article we restate the FG philosophy in more general terms, examine and compare this method with other approaches to the eigenvalue problem, and begin the development of an FG R-matrix method for scattering. The philosophy of the FG method is to use the simplest representation for each of the kinetic and potential energy operators of the Hamiltonian, and use a generalized Fourier transform to put the matrix elements of one of the above operators in the same representation as the other, so the Hamiltonian has a single representation. (author)
The J-Matrix Method Developments and Applications
Alhaidari, Abdulaziz D; Heller, Eric J; Abdelmonem, Mohamed S
2008-01-01
This volume aims to provide the fundamental knowledge to appreciate the advantages of the J-matrix method and to encourage its use and further development. The J-matrix method is an algebraic method of quantum scattering with substantial success in atomic and nuclear physics. The accuracy and convergence property of the method compares favourably with other successful scattering calculation methods. Despite its thirty-year long history new applications are being found for the J-matrix method. This book gives a brief account of the recent developments and some selected applications of the method in atomic and nuclear physics. New findings are reported in which experimental results are compared to theoretical calculations. Modifications, improvements and extensions of the method are discussed using the language of the J-matrix. The volume starts with a Foreword by the two co-founders of the method, E.J. Heller and H.A. Yamani and it contains contributions from 24 prominent international researchers.
Matrix Krylov subspace methods for image restoration
Directory of Open Access Journals (Sweden)
khalide jbilou
2015-09-01
Full Text Available In the present paper, we consider some matrix Krylov subspace methods for solving ill-posed linear matrix equations and in those problems coming from the restoration of blurred and noisy images. Applying the well known Tikhonov regularization procedure leads to a Sylvester matrix equation depending the Tikhonov regularized parameter. We apply the matrix versions of the well known Krylov subspace methods, namely the Least Squared (LSQR and the conjugate gradient (CG methods to get approximate solutions representing the restored images. Some numerical tests are presented to show the effectiveness of the proposed methods.
International Nuclear Information System (INIS)
Smith, A.E.; Josefsson, T.W.
1994-01-01
An extension to include general inelastic scattering effects is developed for the case of reflection electron diffraction scattering from surfaces. In this extension of work by Lynch and Moodie, it is shown how the resultant non-Hermitian matrix problem can be recast in a form that is suitable for computation. In particular, a computational method is outlined based on techniques developed by Eberlein for matrix diagonalisation using complex rotations and shears. The resultant methods are applied to the problem of Convergent Beam RHEED. 23 refs., 3 figs
Reducing the orientation influence of Mueller matrix measurements for anisotropic scattering media
Sun, Minghao; He, Honghui; Zeng, Nan; Du, E.; He, Yonghong; Ma, Hui
2014-09-01
Mueller matrix polarimetry techniques contain rich micro-structural information of samples, such as the sizes and refractive indices of scatterers. Recently, Mueller matrix imaging methods have shown great potentials as powerful tools for biomedical diagnosis. However, the orientations of anisotropic fibrous structures in tissues have prominent influence on Mueller matrix measurements, resulting in difficulties for extracting micro-structural information effectively. In this paper, we apply the backscattering Mueller matrix imaging technique to biological samples with different microstructures, such as chicken heart muscle, bovine skeletal muscle, porcine liver and fat tissues. Experimental results show that the directions of the muscle fibers have prominent influence on the Mueller matrix elements. In order to reduce the orientation influence, we adopt the rotation-independent MMT and RLPI parameters, which were proposed in our previous studies, to the tissue samples. Preliminary results in this paper show that the orientation-independent parameters and their statistic features are helpful for analyzing the tissues to obtain their micro-structural properties. Since the micro-structure variations are often related to the pathological changes, the method can be applied to microscope imaging techniques and used to detect abnormal tissues such as cancer and other lesions for diagnosis purposes.
Rui, Wei; Tao, Chao; Liu, Xiaojun
2017-09-18
Acoustic scattering medium is a fundamental challenge for photoacoustic imaging. In this study, we reveal the different coherent properties of the scattering photoacoustic waves and the direct photoacoustic waves in a matrix form. Direct waves show a particular coherence on the antidiagonals of the matrix, whereas scattering waves do not. Based on this property, a correlation matrix filter combining with a time reversal operator is proposed to preserve the direct waves and recover the image behind a scattering layer. Both numerical simulations and photoacoustic imaging experiments demonstrate that the proposed approach effectively increases the image contrast and decreases the background speckles in a scattering medium. This study might improve the quality of photoacoustic imaging in an acoustic scattering environment and extend its applications.
Transfer matrix method for four-flux radiative transfer.
Slovick, Brian; Flom, Zachary; Zipp, Lucas; Krishnamurthy, Srini
2017-07-20
We develop a transfer matrix method for four-flux radiative transfer, which is ideally suited for studying transport through multiple scattering layers. The model predicts the specular and diffuse reflection and transmission of multilayer composite films, including interface reflections, for diffuse or collimated incidence. For spherical particles in the diffusion approximation, we derive closed-form expressions for the matrix coefficients and show remarkable agreement with numerical Monte Carlo simulations for a range of absorption values and film thicknesses, and for an example multilayer slab.
Theory of the particle matrix elements for Helium atom scattering in surfaces
International Nuclear Information System (INIS)
Khater, A.; Toennies, J.P.
2000-01-01
Full text.A brief review is presented for the recent development of the theory of the particle transition matrix elements, basic to the cross section for Helium and inert particle scattering at thermal energies in solid surfaces. the Jackson and Mott matrix elements are presented and discussed for surface scattering processes, habitually classified as elastic and inelastic. Modified transition matrix elements, introduced originally to account for the cut-off effects, are presented in a direct and simple manner. the Debye-Waller factor is introduced and discussed. A recent calculation for the particle transition matrix elements is presented for the specular and inelastic transition matrix elements and the corresponding inelastic scattering cross section is compared in detail to experimental data. the specular and inelastic transition matrix elements are found to be intrinsically similar owing to the intermediate role of a proposed virtual particle squeezed state near the surface
A method to measure the antikaon-nucleon scattering length in lattice QCD
International Nuclear Information System (INIS)
Lage, Michael; Meissner, Ulf-G.; Rusetsky, Akaki
2009-01-01
We propose a method to determine the isoscalar K-bar N scattering length on the lattice. Our method represents the generalization of Luescher's approach in the presence of inelastic channels (complex scattering length). In addition, the proposed approach allows one to find the position of the S-matrix pole corresponding the Λ(1405) resonance.
Matrix method for acoustic levitation simulation.
Andrade, Marco A B; Perez, Nicolas; Buiochi, Flavio; Adamowski, Julio C
2011-08-01
A matrix method is presented for simulating acoustic levitators. A typical acoustic levitator consists of an ultrasonic transducer and a reflector. The matrix method is used to determine the potential for acoustic radiation force that acts on a small sphere in the standing wave field produced by the levitator. The method is based on the Rayleigh integral and it takes into account the multiple reflections that occur between the transducer and the reflector. The potential for acoustic radiation force obtained by the matrix method is validated by comparing the matrix method results with those obtained by the finite element method when using an axisymmetric model of a single-axis acoustic levitator. After validation, the method is applied in the simulation of a noncontact manipulation system consisting of two 37.9-kHz Langevin-type transducers and a plane reflector. The manipulation system allows control of the horizontal position of a small levitated sphere from -6 mm to 6 mm, which is done by changing the phase difference between the two transducers. The horizontal position of the sphere predicted by the matrix method agrees with the horizontal positions measured experimentally with a charge-coupled device camera. The main advantage of the matrix method is that it allows simulation of non-symmetric acoustic levitators without requiring much computational effort.
International Nuclear Information System (INIS)
Josefsson, T.W.; Smith, A.E.
1994-01-01
Inelastic scattering of electrons in a crystalline environment may be represented by a complex non-hermitian potential. Completed generalised expressions for this inelastic electron scattering potential matrix, including virtual inelastic scattering, are derived for outer-shell electron and plasmon excitations. The relationship between these expressions and the general anisotropic dielectric response matrix of the solid is discussed. These generalised expressions necessarily include the off-diagonal terms representing effects due to departure from translational invariance in the interaction. Results are presented for the diagonal back structure dependent inelastic and virtual inelastic scattering potentials for Si, from a calculation of the inverse dielectric matrix in the random phase approximation. Good agreement is found with experiment as a function of incident energies from 10 eV to 100 keV. Anisotropy effects and hence the interaction de localisation represented by the off-diagonal scattering potential terms, are found to be significant below 1 keV. 38 refs., 2 figs
WWW scattering matrix database for small mineral particles at 441.6 and 632.8 nm
International Nuclear Information System (INIS)
Volten, H.; Munoz, O.; Hovenier, J.W.; Haan, J.F. de; Vassen, W.; Zande, W.J. van der; Waters, L.B.F.M.
2005-01-01
We present a new extensive database containing experimental scattering matrix elements as functions of the scattering angle measured at 441.6 and 632.8 nm for a large collection of micron-sized mineral particles in random orientation. This unique database is accessible through the World-Wide Web. Size distribution tables of the particles are also provided, as well as other characteristics relevant to light scattering. The database provides the light scattering community with easily accessible information that is useful, for a variety of applications such as testing theoretical methods, and the interpretation of measurements of scattered radiation. To illustrate the use of the database, we consider cometary observations and compare them with (1) cometary analog data from the database, and (2) with results of Mie calculations for homogeneous spheres, having the same refractive index and size distribution as those of the analog data
Das, Nandan Kumar; Dey, Rajib; Chakraborty, Semanti; Panigrahi, Prasanta K.; Meglinski, Igor; Ghosh, Nirmalya
2018-04-01
A number of tissue-like disordered media exhibit local anisotropy of scattering in the scaling behavior. Scaling behavior contains wealth of fractal or multifractal properties. We demonstrate that the spatial dielectric fluctuations in a sample of biological tissue exhibit multifractal anisotropy. Multifractal anisotropy encoded in the wavelength variation of the light scattering Mueller matrix and manifesting as an intriguing spectral diattenuation effect. We developed an inverse method for the quantitative assessment of the multifractal anisotropy. The method is based on the processing of relevant Mueller matrix elements in Fourier domain by using Born approximation, followed by the multifractal analysis. The approach promises for probing subtle micro-structural changes in biological tissues associated with the cancer and precancer, as well as for non-destructive characterization of a wide range of scattering materials.
Directory of Open Access Journals (Sweden)
Chao Wan
2012-01-01
Full Text Available 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.
Interface matrix method in AFEN framework
Energy Technology Data Exchange (ETDEWEB)
Pogosbekyan, Leonid; Cho, Jin Young; Kim, Young Jin [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
1997-12-31
In this study, we extend the application of the interface-matrix(IM) method for reflector modeling to Analytic Flux Expansion Nodal (AFEN) method. This include the modifications of the surface-averaged net current continuity and the net leakage balance conditions for IM method in accordance with AFEN formula. AFEN-interface matrix (AFEN-IM) method has been tested against ZION-1 benchmark problem. The numerical result of AFEN-IM method shows 1.24% of maximum error and 0.42% of root-mean square error in assembly power distribution, and 0.006% {Delta} k of neutron multiplication factor. This result proves that the interface-matrix method for reflector modeling can be useful in AFEN method. 3 refs., 4 figs. (Author)
Interface matrix method in AFEN framework
Energy Technology Data Exchange (ETDEWEB)
Pogosbekyan, Leonid; Cho, Jin Young; Kim, Young Jin [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
1998-12-31
In this study, we extend the application of the interface-matrix(IM) method for reflector modeling to Analytic Flux Expansion Nodal (AFEN) method. This include the modifications of the surface-averaged net current continuity and the net leakage balance conditions for IM method in accordance with AFEN formula. AFEN-interface matrix (AFEN-IM) method has been tested against ZION-1 benchmark problem. The numerical result of AFEN-IM method shows 1.24% of maximum error and 0.42% of root-mean square error in assembly power distribution, and 0.006% {Delta} k of neutron multiplication factor. This result proves that the interface-matrix method for reflector modeling can be useful in AFEN method. 3 refs., 4 figs. (Author)
Solution of the nonlinear inverse scattering problem by T-matrix completion. I. Theory.
Levinson, Howard W; Markel, Vadim A
2016-10-01
We propose a conceptually different method for solving nonlinear inverse scattering problems (ISPs) such as are commonly encountered in tomographic ultrasound imaging, seismology, and other applications. The method is inspired by the theory of nonlocality of physical interactions and utilizes the relevant formalism. We formulate the ISP as a problem whose goal is to determine an unknown interaction potential V from external scattering data. Although we seek a local (diagonally dominated) V as the solution to the posed problem, we allow V to be nonlocal at the intermediate stages of iterations. This allows us to utilize the one-to-one correspondence between V and the T matrix of the problem. Here it is important to realize that not every T corresponds to a diagonal V and we, therefore, relax the usual condition of strict diagonality (locality) of V. An iterative algorithm is proposed in which we seek T that is (i) compatible with the measured scattering data and (ii) corresponds to an interaction potential V that is as diagonally dominated as possible. We refer to this algorithm as to the data-compatible T-matrix completion. This paper is Part I in a two-part series and contains theory only. Numerical examples of image reconstruction in a strongly nonlinear regime are given in Part II [H. W. Levinson and V. A. Markel, Phys. Rev. E 94, 043318 (2016)10.1103/PhysRevE.94.043318]. The method described in this paper is particularly well suited for very large data sets that become increasingly available with the use of modern measurement techniques and instrumentation.
The finite element response matrix method
International Nuclear Information System (INIS)
Nakata, H.; Martin, W.R.
1983-02-01
A new technique is developed with an alternative formulation of the response matrix method implemented with the finite element scheme. Two types of response matrices are generated from the Galerkin solution to the weak form of the diffusion equation subject to an arbitrary current and source. The piecewise polynomials are defined in two levels, the first for the local (assembly) calculations and the second for the global (core) response matrix calculations. This finite element response matrix technique was tested in two 2-dimensional test problems, 2D-IAEA benchmark problem and Biblis benchmark problem, with satisfatory results. The computational time, whereas the current code is not extensively optimized, is of the same order of the well estabilished coarse mesh codes. Furthermore, the application of the finite element technique in an alternative formulation of response matrix method permits the method to easily incorporate additional capabilities such as treatment of spatially dependent cross-sections, arbitrary geometrical configurations, and high heterogeneous assemblies. (Author) [pt
Ivanov, K. A.; Nikolaev, V. V.; Gubaydullin, A. R.; Kaliteevski, M. A.
2017-10-01
Based on the scattering matrix formalism, we have developed a method of quantization of an electromagnetic field in two-dimensional photonic nanostructures ( S-quantization in the two-dimensional case). In this method, the fields at the boundaries of the quantization box are expanded into a Fourier series and are related with each other by the scattering matrix of the system, which is the product of matrices describing the propagation of plane waves in empty regions of the quantization box and the scattering matrix of the photonic structure (or an arbitrary inhomogeneity). The quantization condition (similarly to the onedimensional case) is formulated as follows: the eigenvalues of the scattering matrix are equal to unity, which corresponds to the fact that the set of waves that are incident on the structure (components of the expansion into the Fourier series) is equal to the set of waves that travel away from the structure (outgoing waves). The coefficients of the matrix of scattering through the inhomogeneous structure have been calculated using the following procedure: the structure is divided into parallel layers such that the permittivity in each layer varies only along the axis that is perpendicular to the layers. Using the Fourier transform, the Maxwell equations have been written in the form of a matrix that relates the Fourier components of the electric field at the boundaries of neighboring layers. The product of these matrices is the transfer matrix in the basis of the Fourier components of the electric field. Represented in a block form, it is composed by matrices that contain the reflection and transmission coefficients for the Fourier components of the field, which, in turn, constitute the scattering matrix. The developed method considerably simplifies the calculation scheme for the analysis of the behavior of the electromagnetic field in structures with a two-dimensional inhomogeneity. In addition, this method makes it possible to obviate
Energy-dependent applications of the transfer matrix method
International Nuclear Information System (INIS)
Oeztunali, O.I.; Aronson, R.
1975-01-01
The transfer matrix method is applied to energy-dependent neutron transport problems for multiplying and nonmultiplying media in one-dimensional plane geometry. Experimental cross sections are used for total, elastic, and inelastic scattering and fission. Numerical solutions are presented for the problem of a unit point isotropic source in an infinite medium of water and for the problem of the critical 235 U slab with finite water reflectors. No iterations were necessary in this method. Numerical results obtained are consistent with physical considerations and compare favorably with the moments method results for the problem of the unit point isotropic source in an infinite water medium. (U.S.)
Chaotic scattering: the supersymmetry method for large number of channels
International Nuclear Information System (INIS)
Lehmann, N.; Saher, D.; Sokolov, V.V.; Sommers, H.J.
1995-01-01
We investigate a model of chaotic resonance scattering based on the random matrix approach. The hermitian part of the effective hamiltonian of resonance states is taken from the GOE whereas the amplitudes of coupling to decay channels are considered both random or fixed. A new version of the supersymmetry method is worked out to determine analytically the distribution of poles of the S-matrix in the complex energy plane as well as the mean value and two-point correlation function of its elements when the number of channels scales with the number of resonance states. Analytical formulae are compared with numerical simulations. All results obtained coincide in both models provided that the ratio m of the numbers of channels and resonances is small enough and remain qualitatively similar for larger values of m. The relation between the pole distribution and the fluctuations in scattering is discussed. It is shown in particular that the clouds of poles of the S-matrix in the complex energy plane are separated from the real axis by a finite gap Γ g which determines the correlation length in the scattering fluctuations and leads to the exponential asymptotics of the decay law of a complicated intermediate state. ((orig.))
Chaotic scattering: the supersymmetry method for large number of channels
Energy Technology Data Exchange (ETDEWEB)
Lehmann, N. (Essen Univ. (Gesamthochschule) (Germany). Fachbereich 7 - Physik); Saher, D. (Essen Univ. (Gesamthochschule) (Germany). Fachbereich 7 - Physik); Sokolov, V.V. (Essen Univ. (Gesamthochschule) (Germany). Fachbereich 7 - Physik); Sommers, H.J. (Essen Univ. (Gesamthochschule) (Germany). Fachbereich 7 - Physik)
1995-01-23
We investigate a model of chaotic resonance scattering based on the random matrix approach. The hermitian part of the effective hamiltonian of resonance states is taken from the GOE whereas the amplitudes of coupling to decay channels are considered both random or fixed. A new version of the supersymmetry method is worked out to determine analytically the distribution of poles of the S-matrix in the complex energy plane as well as the mean value and two-point correlation function of its elements when the number of channels scales with the number of resonance states. Analytical formulae are compared with numerical simulations. All results obtained coincide in both models provided that the ratio m of the numbers of channels and resonances is small enough and remain qualitatively similar for larger values of m. The relation between the pole distribution and the fluctuations in scattering is discussed. It is shown in particular that the clouds of poles of the S-matrix in the complex energy plane are separated from the real axis by a finite gap [Gamma][sub g] which determines the correlation length in the scattering fluctuations and leads to the exponential asymptotics of the decay law of a complicated intermediate state. ((orig.))
S-matrix formulation of thermodynamics with N-body scatterings
Energy Technology Data Exchange (ETDEWEB)
Lo, Pok Man [University of Wroclaw, Institute of Theoretical Physics, Wroclaw (Poland); Extreme Matter Institute EMMI, GSI, Darmstadt (Germany)
2017-08-15
We apply a phase space expansion scheme to incorporate the N-body scattering processes in the S-matrix formulation of statistical mechanics. A generalized phase shift function suitable for studying the thermal contribution of N → N processes is motivated and examined in various models. Using the expansion scheme, we revisit how the hadron resonance gas model emerges from the S-matrix framework, and consider an example of structureless scattering in which the phase shift function can be exactly worked out. Finally we analyze the influence of dynamics on the phase shift function in a simple example of 3- and 4-body scattering. (orig.)
Meromorphic extension of the scattering matrix for long range two-body problems
International Nuclear Information System (INIS)
Gerard, C.; Martinez, A.
1989-01-01
We prove the existence of a meromorphic extension of the scattering matrix for long range potentials analytic at infinity. This extension exists as a bounded operator on some Gevrey spaces on S n-1 , with critical depending on the rate of decay of the potential at infinity. We use a semi-stationary definition of the scattering operator due to Isozaki-Kitada, using time independent modifiers. We show that the poles of the scattering matrix coincide with the resonances of the Hamiltonian [fr
The Bateman method for multichannel scattering theory
International Nuclear Information System (INIS)
Kim, Y. E.; Kim, Y. J.; Zubarev, A. L.
1997-01-01
Accuracy and convergence of the Bateman method are investigated for calculating the transition amplitude in multichannel scattering theory. This approximation method is applied to the calculation of elastic amplitude. The calculated results are remarkably accurate compared with those of exactly solvable multichannel model
On using of R-matrix approach for description of nucleon scattering by potential with diffuse edge
International Nuclear Information System (INIS)
Tertychnyj, G.Ya.; Yadrovskij, E.L.
1982-01-01
Problems of convergence of R-matrix method for calculation of scattering phases and bound states of neutrons in the Woods-Saxon potential are investigated. It is revealed that this convergence in respect to the number of R-matrix poles turns to be faster if the value of the parameter of boundary conditions bsub(ej)sup(0) is close to the value of logarithmic derivative of the function of continuous spectrum at given energy E and radius of joining a. Bound states are satisfactorily described in unipolar approximation in a wide range of energy and bsub(ej)sup(0) parameter variations. The conducted comparison of the R-matrix method with the method of numerical integration testifies to their equivalence irrespective of the choice of a and bsub(ej)sup(0) parameters, but under the condition that the R-matrix series comprises a large number of members
A discrete ordinate response matrix method for massively parallel computers
International Nuclear Information System (INIS)
Hanebutte, U.R.; Lewis, E.E.
1991-01-01
A discrete ordinate response matrix method is formulated for the solution of neutron transport problems on massively parallel computers. The response matrix formulation eliminates iteration on the scattering source. The nodal matrices which result from the diamond-differenced equations are utilized in a factored form which minimizes memory requirements and significantly reduces the required number of algorithm utilizes massive parallelism by assigning each spatial node to a processor. The algorithm is accelerated effectively by a synthetic method in which the low-order diffusion equations are also solved by massively parallel red/black iterations. The method has been implemented on a 16k Connection Machine-2, and S 8 and S 16 solutions have been obtained for fixed-source benchmark problems in X--Y geometry
Scattering theory on the lattice and with a Monte Carlo method
International Nuclear Information System (INIS)
Kroeger, H.; Moriarty, K.J.M.; Potvin, J.
1990-01-01
We present an alternative time-dependent method of calculating the S matrix in quantum systems governed by a Hamiltonian. In the first step one constructs a new Hamiltonian that describes the physics of scattering at energy E with a reduced number of degrees of freedom. Its matrix elements are computed with a Monte Carlo projector method. In the second step the scattering matrix is computed algebraically via diagonalization and exponentiation of the new Hamiltonian. Although we have in mind applications in many-body systems and quantum field theory, the method should be applicable and useful in such diverse areas as atomic and molecular physics, nuclear physics, high-energy physics and solid-state physics. As an illustration of the method, we compute s-wave scattering of two nucleons in a nonrelativistic potential model (Yamaguchi potential), for which the S matrix is known exactly
A two-stage method for inverse medium scattering
Ito, Kazufumi; Jin, Bangti; Zou, Jun
2013-01-01
We present a novel numerical method to the time-harmonic inverse medium scattering problem of recovering the refractive index from noisy near-field scattered data. The approach consists of two stages, one pruning step of detecting the scatterer
A direct sampling method for inverse electromagnetic medium scattering
Ito, Kazufumi; Jin, Bangti; Zou, Jun
2013-01-01
In this paper, we study the inverse electromagnetic medium scattering problem of estimating the support and shape of medium scatterers from scattered electric/magnetic near-field data. We shall develop a novel direct sampling method based
A nodal method based on matrix-response method
International Nuclear Information System (INIS)
Rocamora Junior, F.D.; Menezes, A.
1982-01-01
A nodal method based in the matrix-response method, is presented, and its application to spatial gradient problems, such as those that exist in fast reactors, near the core - blanket interface, is investigated. (E.G.) [pt
Delayed coherent quantum feedback from a scattering theory and a matrix product state perspective
Guimond, P.-O.; Pletyukhov, M.; Pichler, H.; Zoller, P.
2017-12-01
We study the scattering of photons propagating in a semi-infinite waveguide terminated by a mirror and interacting with a quantum emitter. This paradigm constitutes an example of coherent quantum feedback, where light emitted towards the mirror gets redirected back to the emitter. We derive an analytical solution for the scattering of two-photon states, which is based on an exact resummation of the perturbative expansion of the scattering matrix, in a regime where the time delay of the coherent feedback is comparable to the timescale of the quantum emitter’s dynamics. We compare the results with numerical simulations based on matrix product state techniques simulating the full dynamics of the system, and extend the study to the scattering of coherent states beyond the low-power limit.
The finite element response Matrix method
International Nuclear Information System (INIS)
Nakata, H.; Martin, W.R.
1983-01-01
A new method for global reactor core calculations is described. This method is based on a unique formulation of the response matrix method, implemented with a higher order finite element method. The unique aspects of this approach are twofold. First, there are two levels to the overall calculational scheme: the local or assembly level and the global or core level. Second, the response matrix scheme, which is formulated at both levels, consists of two separate response matrices rather than one response matrix as is generally the case. These separate response matrices are seen to be quite beneficial for the criticality eigenvalue calculation, because they are independent of k /SUB eff/. The response matrices are generated from a Galerkin finite element solution to the weak form of the diffusion equation, subject to an arbitrary incoming current and an arbitrary distributed source. Calculational results are reported for two test problems, the two-dimensional International Atomic Energy Agency benchmark problem and a two-dimensional pressurized water reactor test problem (Biblis reactor), and they compare well with standard coarse mesh methods with respect to accuracy and efficiency. Moreover, the accuracy (and capability) is comparable to fine mesh for a fraction of the computational cost. Extension of the method to treat heterogeneous assemblies and spatial depletion effects is discussed
Lee, KyeoReh; Park, YongKeun
2016-10-31
The word 'holography' means a drawing that contains all of the information for light-both amplitude and wavefront. However, because of the insufficient bandwidth of current electronics, the direct measurement of the wavefront of light has not yet been achieved. Though reference-field-assisted interferometric methods have been utilized in numerous applications, introducing a reference field raises several fundamental and practical issues. Here we demonstrate a reference-free holographic image sensor. To achieve this, we propose a speckle-correlation scattering matrix approach; light-field information passing through a thin disordered layer is recorded and retrieved from a single-shot recording of speckle intensity patterns. Self-interference via diffusive scattering enables access to impinging light-field information, when light transport in the diffusive layer is precisely calibrated. As a proof-of-concept, we demonstrate direct holographic measurements of three-dimensional optical fields using a compact device consisting of a regular image sensor and a diffusor.
The current matrix elements from HAL QCD method
Watanabe, Kai; Ishii, Noriyoshi
2018-03-01
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.
Solution of the scattering T matrix equation in discrete complex momentum space
International Nuclear Information System (INIS)
Rawitscher, G.H.; Delic, G.
1984-01-01
The scattering solution to the Lippmann-Schwinger equation is expanded into a set of spherical Bessel functions of complex wave numbers, K/sub j/, with j = 1,2 , . . . , M. The value of each K/sub j/ is determined from the condition that the spherical Bessel function smoothly matches onto an asymptotically outgoing spherical Hankel (or Coulomb) function of the correct physical wave number at a matching point R. The spherical Bessel functions thus determined are Sturmian functions, and they form a complete set in the interval 0 to R. The coefficients of the expansion of the scattering function are determined by matrix inversion of a linear set of algebraic equations, which are equivalent to the solution of the T-matrix equation in complex momentum space. In view of the presence of a matching radius, no singularities are encountered for the Green's functions, and the inclusion of Coulomb potentials offers no computational difficulties. Three numerical examples are performed in order to illustrate the convergence of the elastic scattering matrix S with M. One of these consists of a set of coupled equations which describe the breakup of a deuteron as it scatters from the nucleus on 58 Ni. A value of M of 15 or less is found sufficient to reproduce the exact S matrix element to an accuracy of four figures after the decimal point
Classical versus quantum structure of the scattering probability matrix: Chaotic waveguides
Czech Academy of Sciences Publication Activity Database
Luna-Acosta, G. A.; Méndez-Bermúdez, J. A.; Šeba, Petr; Pichugin, K. N.
2002-01-01
Roč. 65, č. 4 (2002), 046605/1-046605/8 ISSN 1063-651X Grant - others:CONACYT(MX) 26163-E Institutional research plan: CEZ:AV0Z1010914 Keywords : scattering matrix * waveguids Subject RIV: BE - Theoretical Physics Impact factor: 2.397, year: 2002
Nonlinear response matrix methods for radiative transfer
International Nuclear Information System (INIS)
Miller, W.F. Jr.; Lewis, E.E.
1987-01-01
A nonlinear response matrix formalism is presented for the solution of time-dependent radiative transfer problems. The essential feature of the method is that within each computational cell the temperature is calculated in response to the incoming photons from all frequency groups. Thus the updating of the temperature distribution is placed within the iterative solution of the spaceangle transport problem, instead of being placed outside of it. The method is formulated for both grey and multifrequency problems and applied in slab geometry. The method is compared to the more conventional source iteration technique. 7 refs., 1 fig., 4 tabs
Wapenaar, C.P.A.; Slob, E.C.; Snieder, R.
2010-01-01
We have analyzed the far-field approximation of the Green's function representation for seismic interferometry. By writing each of the Green's functions involved in the correlation process as a superposition of a direct wave and a scattered wave, the Green's function representation is rewritten as a
ABCD Matrix Method a Case Study
Seidov, Zakir F; Yahalom, Asher
2004-01-01
In the Israeli Electrostatic Accelerator FEL, the distance between the accelerator's end and the wiggler's entrance is about 2.1 m, and 1.4 MeV electron beam is transported through this space using four similar quadrupoles (FODO-channel). The transfer matrix method (ABCD matrix method) was used for simulating the beam transport, a set of programs is written in the several programming languages (MATHEMATICA, MATLAB, MATCAD, MAPLE) and reasonable agreement is demonstrated between experimental results and simulations. Comparison of ABCD matrix method with the direct "numerical experiments" using EGUN, ELOP, and GPT programs with and without taking into account the space-charge effects showed the agreement to be good enough as well. Also the inverse problem of finding emittance of the electron beam at the S1 screen position (before FODO-channel), by using the spot image at S2 screen position (after FODO-channel) as function of quad currents, is considered. Spot and beam at both screens are described as tilted eel...
Efficient computation method of Jacobian matrix
International Nuclear Information System (INIS)
Sasaki, Shinobu
1995-05-01
As well known, the elements of the Jacobian matrix are complex trigonometric functions of the joint angles, resulting in a matrix of staggering complexity when we write it all out in one place. This article addresses that difficulties to this subject are overcome by using velocity representation. The main point is that its recursive algorithm and computer algebra technologies allow us to derive analytical formulation with no human intervention. Particularly, it is to be noted that as compared to previous results the elements are extremely simplified throughout the effective use of frame transformations. Furthermore, in case of a spherical wrist, it is shown that the present approach is computationally most efficient. Due to such advantages, the proposed method is useful in studying kinematically peculiar properties such as singularity problems. (author)
Directory of Open Access Journals (Sweden)
A. Gogoi
2011-09-01
Full Text Available Scattering properties of bentonite clay particles were investigated at 543.5 nm incident laser wavelength by using a designed and fabricated light scattering setup. The scattering samples were held in front of a laser beam by using a transparent cylindrical thermosetting epoxy matrix.
Roundtrip matrix method for calculating the leaky resonant modes of open nanophotonic structures
DEFF Research Database (Denmark)
de Lasson, Jakob Rosenkrantz; Kristensen, Philip Trøst; Mørk, Jesper
2014-01-01
We present a numerical method for calculating quasi-normal modes of open nanophotonic structures. The method is based on scattering matrices and a unity eigenvalue of the roundtrip matrix of an internal cavity, and we develop it in detail with electromagnetic fields expanded on Bloch modes...
Neutron-deuteron scattering calculations with W-matrix representation of the two-body input
International Nuclear Information System (INIS)
Bartnik, E.A.; Haberzettl, H.; Januschke, T.; Kerwath, U.; Sandhas, W.
1987-05-01
Employing the W-matrix representation of the partial-wave T matrix introduced by Bartnik, Haberzettl, and Sandhas, we show for the example of the Malfliet-Tjon potentials I and III that the single-term separable part of the W-matrix representation, when used as input in three-nucleon neutron-deuteron scattering calculations, is fully capable of reproducing the exact results obtained by Kloet and Tjon. This approximate two-body input not only satisfies the two-body off-shell unitarity relation but, moreover, it also contains a parameter which may be used in optimizing the three-body data. We present numerical evidence that there exists a variational (minimum) principle for the determination of the three-body binding energy which allows one to choose this parameter also in the absence of an exact reference calculation. Our results for neutron-deuteron scattering show that it is precisely this choice of the parameter which provides optimal scattering data. We conclude that the W-matrix approach, despite its simplicity, is a remarkably efficient tool for high-quality three-nucleon calculations. (orig.)
Resonant Raman scattering in ion-beam-synthesized Mg2Si in a silicon matrix
International Nuclear Information System (INIS)
Baleva, M.; Zlateva, G.; Atanassov, A.; Abrashev, M.; Goranova, E.
2005-01-01
Resonant Raman scattering by ion beam synthesized in silicon matrix Mg 2 Si phase is studied. The samples are prepared with the implantation of 24 Mg + ions with dose 4x10 17 cm -2 and with two different energies 40 and 60 keV into (100)Si substrates. The far infrared spectra are used as criteria for the formation of the Mg 2 Si phase. The Raman spectra are excited with different lines of Ar + laser, with energies of the lines lying in the interval from 2.40 to 2.75 eV. The resonant scattering can be investigated using these laser lines, as far as according to the Mg 2 Si band structure, there are direct gaps with energies in the same region. The energy dependences of the scattered intensities in the case of the scattering by the allowed F 2g and the forbidden LO-type modes are experimentally obtained and theoretically interpreted. On the base of the investigation energies of the interband transitions in the Mg 2 Si are determined. It is found also that the resonant Raman scattering appears to be a powerful tool for characterization of a material with inclusions in it. In the particular case it is concluded that the Mg 2 Si phase is present in the form of a surface layer in the sample, prepared with implantation energy 40 keV and as low-dimensional precipitates, embedded in the silicon matrix, in the sample, prepared with the higher implantation energy
The matrix element for radiative Bhabha scattering in the forward direction
International Nuclear Information System (INIS)
Kleiss, R.
1993-09-01
We present an approximation to the matrix element for the process e + e - →e + e - γ, appropriate to the situation where one or both of the fermions are scattered over very small angles. The leading terms in the situation where all scattering angles are small contains not only terms quadratic in the electron mass, but also quartic and even sextic terms must be included. Special attention is devoted to the numerical stability of the resultant expression. Its relation to several existing formulae is discussed. (orig.)
A direct sampling method to an inverse medium scattering problem
Ito, Kazufumi; Jin, Bangti; Zou, Jun
2012-01-01
In this work we present a novel sampling method for time harmonic inverse medium scattering problems. It provides a simple tool to directly estimate the shape of the unknown scatterers (inhomogeneous media), and it is applicable even when
International Nuclear Information System (INIS)
Wong, C.F.; Light, J.C.
1984-01-01
Based on the R-matrix approach of Schneider et al. [J. Phys. B 12, L 365 (1979)] to reactive electron-molecule scattering, a new propagative R-matrix method (PRMM) is presented which is more appropriate for polyatomic systems. The new method should be useful in other calculations where complicated integrals need to be propagated. We also introduce an effective R-matrix model (ERMM) in which the usual resonance parameters (potential and width) can be used as input in model R-matrix calculations. The PRMM and ERMM have been applied to the electron-N 2 system and the electron-F 2 system. The results agree very well with previous calculations for both vibrationally inelastic scattering and dissociative attachment when identical potentials and parameters are used
A S-matrix-like approximation in the charged particle scattering by the hydrogen atom
International Nuclear Information System (INIS)
Mignaco, J.A.; Tort, A.C.
1979-01-01
The Born approximation for charged particle scattering by the hydrogen atom is unfit at low energies. From a S-matrix-like consideration on the dominance of the neighbour singularities, the calculation of other contributions is suggested. The inclusion of bound states is made, following Eden's and his colaborators' ideas, which are described by their interest and likeness with procedures in the intermediate energy physics. (Author) [pt
Elastic wave scattering methods: assessments and suggestions
International Nuclear Information System (INIS)
Gubernatis, J.E.
1985-01-01
The author was asked by the meeting organizers to review and assess the developments over the past ten or so years in elastic wave scattering methods and to suggest areas of future research opportunities. He highlights the developments, focusing on what he feels were distinct steps forward in our theoretical understanding of how elastic waves interact with flaws. For references and illustrative figures, he decided to use as his principal source the proceedings of the various annual Reviews of Progress in Quantitative Nondestructive Evaluation (NDE). These meetings have been the main forum not only for presenting results of theoretical research but also for demonstrating the relevance of the theoretical research for the design and interpretation of experiment. In his opinion a quantitative NDE is possible only if this relevance exists, and his major objective is to discuss and illustrate the degree to which relevance has developed
A nodal method based on the response-matrix method
International Nuclear Information System (INIS)
Cunha Menezes Filho, A. da; Rocamora Junior, F.D.
1983-02-01
A nodal approach based on the Response-Matrix method is presented with the purpose of investigating the possibility of mixing two different allocations in the same problem. It is found that the use of allocation of albedo combined with allocation of direct reflection produces good results for homogeneous fast reactor configurations. (Author) [pt
On quasiclassical approximation in the inverse scattering method
International Nuclear Information System (INIS)
Geogdzhaev, V.V.
1985-01-01
Using as an example quasiclassical limits of the Korteweg-de Vries equation and nonlinear Schroedinger equation, the quasiclassical limiting variant of the inverse scattering problem method is presented. In quasiclassical approximation the inverse scattering problem for the Schroedinger equation is reduced to the classical inverse scattering problem
The impact of ice particle roughness on the scattering phase matrix
International Nuclear Information System (INIS)
Baum, Bryan A.; Yang Ping; Hu Yongxiang; Feng Qian
2010-01-01
The goal of this study is to explore the influence of ice particle habit (or shape) and surface roughness on the scattering phase matrix. As an example, reported here are the results for two wavelengths: 0.67 and 1.61 μm. For this effort, a database of single-scattering properties has been computed for a set of habits including hexagonal plates, hollow and solid columns, hollow and solid 3D bullet rosettes, droxtals, aggregates of solid columns, and aggregates of plates. The database provides properties for each of the habits at 101 wavelengths between 0.45 and 2.24 μm for smooth, moderately roughened, and severely roughened particles. At each wavelength, the scattering properties are provided at 233 discrete particle diameters ranging from 2 to 10,000 μm. A single particle size distribution from a very cold ice cloud sampled during the CRYSTAL-FACE field campaign (T cld =-76 o C) is used to illustrate the influence of habit and roughness on the phase matrix. In all, four different habit mixtures are evaluated. The nonzero elements of the phase matrix are shown to be quite sensitive to the assumed habit, particularly in the case of -P 12 /P 11 that is associated with the degree of linear polarization of scattered radiation. Surface roughness is shown to smooth out maxima in the scattering phase function and in the other elements of the phase matrix, consistent with other studies. To compare with the theoretical simulations of the phase matrix for smooth and roughened particles, a full year of cloud-aerosol lidar with orthogonal polarization (CALIOP) data from 2008 is analyzed to provide global statistics on the values of P 11 and P 22 /P 11 in the backscattering direction. In a comparison of two of the habit mixtures (one used for MODIS Collection 5 and another that incorporates new habits including hollow bullet rosettes and aggregates of plates) with the CALIOP data, the values for P 11 are higher regardless of the degree of particle surface roughness, and the
Scattering of the (p - 3H) system with the Lorentz integral transform method
International Nuclear Information System (INIS)
Marchisio, M.A.; Leidemann, W.; Orlandini, G.; Barnea, N.
2003-01-01
It was shown how the Lorentz integral transform method (LIT), which in recent years has revealed to be a powerful tool in few-body calculations, can be applied to calculate the T matrix in (p- 3 H) scattering also for energies above the three-body breakup threshold. Refs. 7 (nevyjel)
Acoustic scattering by multiple elliptical cylinders using collocation multipole method
International Nuclear Information System (INIS)
Lee, Wei-Ming
2012-01-01
This paper presents the collocation multipole method for the acoustic scattering induced by multiple elliptical cylinders subjected to an incident plane sound wave. To satisfy the Helmholtz equation in the elliptical coordinate system, the scattered acoustic field is formulated in terms of angular and radial Mathieu functions which also satisfy the radiation condition at infinity. The sound-soft or sound-hard boundary condition is satisfied by uniformly collocating points on the boundaries. For the sound-hard or Neumann conditions, the normal derivative of the acoustic pressure is determined by using the appropriate directional derivative without requiring the addition theorem of Mathieu functions. By truncating the multipole expansion, a finite linear algebraic system is derived and the scattered field can then be determined according to the given incident acoustic wave. Once the total field is calculated as the sum of the incident field and the scattered field, the near field acoustic pressure along the scatterers and the far field scattering pattern can be determined. For the acoustic scattering of one elliptical cylinder, the proposed results match well with the analytical solutions. The proposed scattered fields induced by two and three elliptical–cylindrical scatterers are critically compared with those provided by the boundary element method to validate the present method. Finally, the effects of the convexity of an elliptical scatterer, the separation between scatterers and the incident wave number and angle on the acoustic scattering are investigated.
Scattering Amplitudes via Algebraic Geometry Methods
DEFF Research Database (Denmark)
Søgaard, Mads
Feynman diagrams. The study of multiloop scattering amplitudes is crucial for the new era of precision phenomenology at the Large Hadron Collider (LHC) at CERN. Loop-level scattering amplitudes can be reduced to a basis of linearly independent integrals whose coefficients are extracted from generalized...
Liu, Xiaodong
2017-08-01
A sampling method by using scattering amplitude is proposed for shape and location reconstruction in inverse acoustic scattering problems. Only matrix multiplication is involved in the computation, thus the novel sampling method is very easy and simple to implement. With the help of the factorization of the far field operator, we establish an inf-criterion for characterization of underlying scatterers. This result is then used to give a lower bound of the proposed indicator functional for sampling points inside the scatterers. While for the sampling points outside the scatterers, we show that the indicator functional decays like the bessel functions as the sampling point goes away from the boundary of the scatterers. We also show that the proposed indicator functional continuously depends on the scattering amplitude, this further implies that the novel sampling method is extremely stable with respect to errors in the data. Different to the classical sampling method such as the linear sampling method or the factorization method, from the numerical point of view, the novel indicator takes its maximum near the boundary of the underlying target and decays like the bessel functions as the sampling points go away from the boundary. The numerical simulations also show that the proposed sampling method can deal with multiple multiscale case, even the different components are close to each other.
Covariance Matrix of a Double-Differential Doppler-Broadened Elastic Scattering Cross Section
Arbanas, G.; Becker, B.; Dagan, R.; Dunn, M. E.; Larson, N. M.; Leal, L. C.; Williams, M. L.
2012-05-01
Legendre moments of a double-differential Doppler-broadened elastic neutron scattering cross section on 238U are computed near the 6.67 eV resonance at temperature T = 103 K up to angular order 14. A covariance matrix of these Legendre moments is computed as a functional of the covariance matrix of the elastic scattering cross section. A variance of double-differential Doppler-broadened elastic scattering cross section is computed from the covariance of Legendre moments. Notice: This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes.
Mapping local anisotropy axis for scattering media using backscattering Mueller matrix imaging
He, Honghui; Sun, Minghao; Zeng, Nan; Du, E.; Guo, Yihong; He, Yonghong; Ma, Hui
2014-03-01
Mueller matrix imaging techniques can be used to detect the micro-structure variations of superficial biological tissues, including the sizes and shapes of cells, the structures in cells, and the densities of the organelles. Many tissues contain anisotropic fibrous micro-structures, such as collagen fibers, elastin fibers, and muscle fibers. Changes of these fibrous structures are potentially good indicators for some pathological variations. In this paper, we propose a quantitative analysis technique based on Mueller matrix for mapping local anisotropy axis of scattering media. By conducting both experiments on silk sample and Monte Carlo simulation based on the sphere-cylinder scattering model (SCSM), we extract anisotropy axis parameters from different backscattering Mueller matrix elements. Moreover, we testify the possible applications of these parameters for biological tissues. The preliminary experimental results of human cancerous samples show that, these parameters are capable to map the local axis of fibers. Since many pathological changes including early stage cancers affect the well aligned structures for tissues, the experimental results indicate that these parameters can be used as potential tools in clinical applications for biomedical diagnosis purposes.
On iteration-separable method on the multichannel scattering theory
International Nuclear Information System (INIS)
Zubarev, A.L.; Ivlieva, I.N.; Podkopaev, A.P.
1975-01-01
The iteration-separable method for solving the equations of the Lippman-Schwinger type is suggested. Exponential convergency of the method of proven. Numerical convergency is clarified on the e + H scattering. Application of the method to the theory of multichannel scattering is formulated
Excess noise in Lidar Thomson scattering methods
International Nuclear Information System (INIS)
Smith, R J; Drake, L A P; Lestz, J B
2012-01-01
Fundamental detection limits for the Lidar Thomson scattering technique and in particular pulsed polarimetry are presented for the first time for the long wavelength limit of incoherent Thomson scattering. Pulsed polarimetry generalizes Lidar Thomson scattering to include local magnetic field sensing. The implication for these techniques is explored for two experimental regimes where shot limited detection no longer applies: tokamaks of ITER size and cm-size wire Z pinch plasmas of High Energy Density (HED) science. The utility and importance of developing Lidar Thomson scattering at longer wavelengths for the magnetic fusion program is illustrated by a study of sightline (local) polarimetry measurements on a 15MA ITER scenario. Polarimetric measurements in the far infrared regime are shown to reach sensitivities that are instructive and useful but with a complex behaviour that make spatially resolved measurements all but mandatory.
Scattering Amplitudes via Algebraic Geometry Methods
Søgaard, Mads; Damgaard, Poul Henrik
This thesis describes recent progress in the understanding of the mathematical structure of scattering amplitudes in quantum field theory. The primary purpose is to develop an enhanced analytic framework for computing multiloop scattering amplitudes in generic gauge theories including QCD without Feynman diagrams. The study of multiloop scattering amplitudes is crucial for the new era of precision phenomenology at the Large Hadron Collider (LHC) at CERN. Loop-level scattering amplitudes can be reduced to a basis of linearly independent integrals whose coefficients are extracted from generalized unitarity cuts. We take advantage of principles from algebraic geometry in order to extend the notion of maximal cuts to a large class of two- and three-loop integrals. This allows us to derive unique and surprisingly compact formulae for the coefficients of the basis integrals. Our results are expressed in terms of certain linear combinations of multivariate residues and elliptic integrals computed from products of ...
Energy Technology Data Exchange (ETDEWEB)
Zhang, Le; Yu, Yu; Zhang, Pengjie, E-mail: lezhang@sjtu.edu.cn [Department of Astronomy, Shanghai Jiao Tong University, Shanghai, 200240 (China)
2017-10-10
Photo- z error is one of the major sources of systematics degrading the accuracy of weak-lensing cosmological inferences. Zhang et al. proposed a self-calibration method combining galaxy–galaxy correlations and galaxy–shear correlations between different photo- z bins. Fisher matrix analysis shows that it can determine the rate of photo- z outliers at a level of 0.01%–1% merely using photometric data and do not rely on any prior knowledge. In this paper, we develop a new algorithm to implement this method by solving a constrained nonlinear optimization problem arising in the self-calibration process. Based on the techniques of fixed-point iteration and non-negative matrix factorization, the proposed algorithm can efficiently and robustly reconstruct the scattering probabilities between the true- z and photo- z bins. The algorithm has been tested extensively by applying it to mock data from simulated stage IV weak-lensing projects. We find that the algorithm provides a successful recovery of the scatter rates at the level of 0.01%–1%, and the true mean redshifts of photo- z bins at the level of 0.001, which may satisfy the requirements in future lensing surveys.
NLTE steady-state response matrix method.
Faussurier, G.; More, R. M.
2000-05-01
A connection between atomic kinetics and non-equilibrium thermodynamics has been recently established by using a collisional-radiative model modified to include line absorption. The calculated net emission can be expressed as a non-local thermodynamic equilibrium (NLTE) symmetric response matrix. In the paper, this connection is extended to both cases of the average-atom model and the Busquet's model (RAdiative-Dependent IOnization Model, RADIOM). The main properties of the response matrix still remain valid. The RADIOM source function found in the literature leads to a diagonal response matrix, stressing the absence of any frequency redistribution among the frequency groups at this order of calculation.
Regularization method for solving the inverse scattering problem
International Nuclear Information System (INIS)
Denisov, A.M.; Krylov, A.S.
1985-01-01
The inverse scattering problem for the Schroedinger radial equation consisting in determining the potential according to the scattering phase is considered. The problem of potential restoration according to the phase specified with fixed error in a finite range is solved by the regularization method based on minimization of the Tikhonov's smoothing functional. The regularization method is used for solving the problem of neutron-proton potential restoration according to the scattering phases. The determined potentials are given in the table
Method of forming a ceramic matrix composite and a ceramic matrix component
de Diego, Peter; Zhang, James
2017-05-30
A method of forming a ceramic matrix composite component includes providing a formed ceramic member having a cavity, filling at least a portion of the cavity with a ceramic foam. The ceramic foam is deposited on a barrier layer covering at least one internal passage of the cavity. The method includes processing the formed ceramic member and ceramic foam to obtain a ceramic matrix composite component. Also provided is a method of forming a ceramic matrix composite blade and a ceramic matrix composite component.
Study of the nuclear-coulomb low-energy scattering parameters on the basis of the p-matrix approach
International Nuclear Information System (INIS)
Babenko, V.A.; Petrov, N.M.
1993-01-01
The P-matrix approach application to the description of two charged strongly interacting particles nuclear-Coulomb scattering parameters is considered. The nuclear-Coulomb scattering length and effective range explicit expressions in terms of the P-matrix parameters are found. The nuclear-Coulomb low-energy parameters expansions in powers of small parameter β ≡ R/a b , involving terms with big logarithms, are obtained. The nuclear-Coulomb scattering length and effective range for the square-well and the delta-shell short range potentials are found in an explicit form. (author). 21 refs
Peter Waterman and T-Matrix Methods
Mishchenko, M. I.; Martin, P.A.
2013-01-01
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 particletcharacterization, radiative transfer, and remote sensing. A biographical sketch is also included.
Determining the water content in concrete by gamma scattering method
International Nuclear Information System (INIS)
Priyada, P.; Ramar, R.; Shivaramu
2014-01-01
Highlights: • Gamma scattering technique for estimation of water content in concrete is given. • The scattered intensity increases with the volumetric water content. • Attenuation correction is provided to the scattered intensities. • Volumetric water content of 137 Cs radioactive source and a high resolution HPGe detector based energy dispersive gamma ray spectrometer. Concrete samples of uniform density ≈2.4 g/cm 3 are chosen for the study and the scattered intensities found to vary with the amount of water present in the specimen. The scattered intensities are corrected for attenuation effects and the results obtained with reference to a dry sample are compared with those obtained by gravimetrical and gamma transmission methods. A good agreement is seen between gamma scattering results and those obtained by gravimetric and transmission methods within accuracy of 6% and <2% change in water content can be detected
The isomonodromy method for black hole scattering
Energy Technology Data Exchange (ETDEWEB)
Carneiro da Cunha, Bruno, E-mail: bcunha@df.ufpe.br [Departamento de Física, Universidade Federal de Pernambuco, 50670-901, Recife, Pernambuco (Brazil); Novaes, Fábio, E-mail: fabio.nsantos@gmail.com [International Institute of Physics, Federal University of Rio Grande do Norte, Av. Odilon Gomes de Lima 1722, Capim Macio, Natal-RN 59078-400 (Brazil)
2015-12-17
We summarize recent results by the authors [7, 8, 35] on the extraction of scattering amplitudes for scalar fields in Kerr/Kerr-de Sitter backgrounds. Analytical, closed forms are found in terms of the Painlevé V and VI transcendents for generic values of the physical parameters.
A Golub-Kahan-type reduction method for matrix pairs
Hochstenbach, M.E.; Reichel, L.; Yu, X.
2015-01-01
We describe a novel method for reducing a pair of large matrices {A;B} to a pair of small matrices {H;K}. The method is an extension of Golub-Kahan bidiagonalization to matrix pairs, and simplifies to the latter method when B is the identity matrix. Applications to Tikhonov regularization of large
A Golub-Kahan-type reduction method for matrix pairs
Hochstenbach, M.E.; Reichel, L.; Yu, X.
2015-01-01
We describe a novel method for reducing a pair of large matrices {A,B} to a pair of small matrices {H,K}. The method is an extension of Golub–Kahan bidiagonalization to matrix pairs, and simplifies to the latter method when B is the identity matrix. Applications to Tikhonov regularization of large
International Nuclear Information System (INIS)
Kamphuis, C.; Beekman, F.J.; Van Rijk, P.P.; Viergever, M.A.
1998-01-01
Three-dimensional (3D) iterative maximum likelihood expectation maximization (ML-EM) algorithms for single-photon emission tomography (SPET) are capable of correcting image-degrading effects of non-uniform attenuation, distance-dependent camera response and patient shape-dependent scatter. However, the resulting improvements in quantitation, resolution and signal-to-noise ratio (SNR) are obtained at the cost of a huge computational burden. This paper presents a new acceleration method for ML-EM: dual matrix ordered subsets (DM-OS). DM-OS combines two acceleration methods: (a) different matrices for projection and back-projection and (b) ordered subsets of projections. DM-OS was compared with ML-EM on simulated data and on physical thorax phantom data, for both 180 and 360 orbits. Contrast, normalized standard deviation and mean squared error were calculated for the digital phantom experiment. DM-OS resulted in similar image quality to ML-EM, even for speed-up factors of 200 compared to ML-EM in the case of 120 projections. The thorax phantom data could be reconstructed 50 times faster (60 projections) using DM-OS with preservation of image quality. ML-EM and DM-OS with scatter compensation showed significant improvement of SNR compared to ML-EM without scatter compensation. Furthermore, inclusion of complex image formation models in the computer code is simplified in the case of DM-OS. It is thus shown that DM-OS is a fast and relatively simple algorithm for 3D iterative scatter compensation, with similar results to conventional ML-EM, for both 180 and 360 acquired data. (orig.)
Characterization of Diesel Soot Aggregates by Scattering and Extinction Methods
Kamimoto, Takeyuki
2006-07-01
Characteristics of diesel soot particles sampled from diesel exhaust of a common-rail turbo-charged diesel engine are quantified by scattering and extinction diagnostics using newly build two laser-based instruments. The radius of gyration representing the aggregates size is measured by the angular distribution of scattering intensity, while the soot mass concentration is measured by a two-wavelength extinction method. An approach to estimate the refractive index of diesel soot by an analysis of the extinction and scattering data using an aggregates scattering theory is proposed.
Characterization of Diesel Soot Aggregates by Scattering and Extinction Methods
International Nuclear Information System (INIS)
Kamimoto, Takeyuki
2006-01-01
Characteristics of diesel soot particles sampled from diesel exhaust of a common-rail turbo-charged diesel engine are quantified by scattering and extinction diagnostics using newly build two laser-based instruments. The radius of gyration representing the aggregates size is measured by the angular distribution of scattering intensity, while the soot mass concentration is measured by a two-wavelength extinction method. An approach to estimate the refractive index of diesel soot by an analysis of the extinction and scattering data using an aggregates scattering theory is proposed
A massively parallel discrete ordinates response matrix method for neutron transport
International Nuclear Information System (INIS)
Hanebutte, U.R.; Lewis, E.E.
1992-01-01
In this paper a discrete ordinates response matrix method is formulated with anisotropic scattering for the solution of neutron transport problems on massively parallel computers. The response matrix formulation eliminates iteration on the scattering source. The nodal matrices that result from the diamond-differenced equations are utilized in a factored form that minimizes memory requirements and significantly reduces the number of arithmetic operations required per node. The red-black solution algorithm utilizes massive parallelism by assigning each spatial node to one or more processors. The algorithm is accelerated by a synthetic method in which the low-order diffusion equations are also solved by massively parallel red-black iterations. The method is implemented on a 16K Connection Machine-2, and S 8 and S 16 solutions are obtained for fixed-source benchmark problems in x-y geometry
A direct sampling method for inverse electromagnetic medium scattering
Ito, Kazufumi
2013-09-01
In this paper, we study the inverse electromagnetic medium scattering problem of estimating the support and shape of medium scatterers from scattered electric/magnetic near-field data. We shall develop a novel direct sampling method based on an analysis of electromagnetic scattering and the behavior of the fundamental solution. It is applicable to a few incident fields and needs only to compute inner products of the measured scattered field with the fundamental solutions located at sampling points. Hence, it is strictly direct, computationally very efficient and highly robust to the presence of data noise. Two- and three-dimensional numerical experiments indicate that it can provide reliable support estimates for multiple scatterers in the case of both exact and highly noisy data. © 2013 IOP Publishing Ltd.
Uniqueness and numerical methods in inverse obstacle scattering
International Nuclear Information System (INIS)
Kress, Rainer
2007-01-01
The inverse problem we consider in this tutorial is to determine the shape of an obstacle from the knowledge of the far field pattern for scattering of time-harmonic plane waves. In the first part we will concentrate on the issue of uniqueness, i.e., we will investigate under what conditions an obstacle and its boundary condition can be identified from a knowledge of its far field pattern for incident plane waves. We will review some classical and some recent results and draw attention to open problems. In the second part we will survey on numerical methods for solving inverse obstacle scattering problems. Roughly speaking, these methods can be classified into three groups. Iterative methods interpret the inverse obstacle scattering problem as a nonlinear ill-posed operator equation and apply iterative schemes such as regularized Newton methods, Landweber iterations or conjugate gradient methods for its solution. Decomposition methods, in principle, separate the inverse scattering problem into an ill-posed linear problem to reconstruct the scattered wave from its far field and the subsequent determination of the boundary of the scatterer from the boundary condition. Finally, the third group consists of the more recently developed sampling methods. These are based on the numerical evaluation of criteria in terms of indicator functions that decide whether a point lies inside or outside the scatterer. The tutorial will give a survey by describing one or two representatives of each group including a discussion on the various advantages and disadvantages
A two-stage method for inverse medium scattering
Ito, Kazufumi
2013-03-01
We present a novel numerical method to the time-harmonic inverse medium scattering problem of recovering the refractive index from noisy near-field scattered data. The approach consists of two stages, one pruning step of detecting the scatterer support, and one resolution enhancing step with nonsmooth mixed regularization. The first step is strictly direct and of sampling type, and it faithfully detects the scatterer support. The second step is an innovative application of nonsmooth mixed regularization, and it accurately resolves the scatterer size as well as intensities. The nonsmooth model can be efficiently solved by a semi-smooth Newton-type method. Numerical results for two- and three-dimensional examples indicate that the new approach is accurate, computationally efficient, and robust with respect to data noise. © 2012 Elsevier Inc.
A transfer matrix method for the analysis of fractal quantum potentials
International Nuclear Information System (INIS)
Monsoriu, Juan A; Villatoro, Francisco R; Marin, Maria J; UrchueguIa, Javier F; Cordoba, Pedro Fernandez de
2005-01-01
The scattering properties of quantum particles on a sequence of potentials converging towards a fractal one are obtained by means of the transfer matrix method. The reflection coefficients for both the fractal potential and finite periodic potential are calculated and compared. It is shown that the reflection coefficient for the fractal potential has a self-similar structure associated with the fractal distribution of the potential whose degree of self-similarity has been quantified by means of the correlation function
A transfer matrix method for the analysis of fractal quantum potentials
Energy Technology Data Exchange (ETDEWEB)
Monsoriu, Juan A [Departamento de Fisica Aplicada, Universidad Politecnica de Valencia, E-46022 Valencia (Spain); Villatoro, Francisco R [Departamento de Lenguajes y Ciencias de la Computacion, Universidad de Malaga, E-29071 Malaga (Spain); Marin, Maria J [Departamento de Termodinamica, Universitat de Valencia, E-46100 Burjassot (Spain); UrchueguIa, Javier F [Departamento de Fisica Aplicada, Universidad Politecnica de Valencia, E-46022 Valencia (Spain); Cordoba, Pedro Fernandez de [Departamento de Matematica Aplicada, Universidad Politecnica de Valencia, E-46022 Valencia (Spain)
2005-07-01
The scattering properties of quantum particles on a sequence of potentials converging towards a fractal one are obtained by means of the transfer matrix method. The reflection coefficients for both the fractal potential and finite periodic potential are calculated and compared. It is shown that the reflection coefficient for the fractal potential has a self-similar structure associated with the fractal distribution of the potential whose degree of self-similarity has been quantified by means of the correlation function.
An improved 4-step commutation method application for matrix converter
DEFF Research Database (Denmark)
Guo, Yu; Guo, Yougui; Deng, Wenlang
2014-01-01
A novel four-step commutation method is proposed for matrix converter cell, 3 phase inputs to 1 phase output in this paper, which is obtained on the analysis of published commutation methods for matrix converter. The first and fourth step can be shorter than the second or third one. The discussed...... method here is implemented by programming in VHDL language. Finally, the novel method in this paper is verified by experiments....
S-matrix description of anomalous large-angle heavy-ion scattering
Energy Technology Data Exchange (ETDEWEB)
Frahn, W E; Hussein, M S [Sao Paulo Univ. (Brazil). Inst. de Fisica; Canto, L F; Donangelo, R [Rio de Janeiro Univ. (Brazil). Inst. de Fisica
1981-10-12
We present a quantitative description of the well-known anomalous features observed in the large-angle scattering of n..cap alpha.. type heavy ions, in particular of the pronounced structures in the backangle excitation function for /sup 16/O + /sup 28/Si. Our treatment is based on the close connection between these anomalies and particular structural deviations of the partial-wave S-matrix from normal strong-absorption behaviour. The properties of these deviations are found to be rather well specified by the data: they are localized within a narrow 'l-window' centered at a critical angular momentum significantly smaller than the grazing value, and have a parity-dependent as well as a parity-independent part. These properties provide important clues as to the physical processes causing the large-angle enhancement.
A T-matrix calculation for in-medium heavy-quark gluon scattering
International Nuclear Information System (INIS)
Huggins, K.; Rapp, R.
2012-01-01
The interactions of charm and bottom quarks in a quark-gluon plasma (QGP) are evaluated using a thermodynamic 2-body T-matrix. We specifically focus on heavy-quark (HQ) interactions with thermal gluons with an input potential motivated by lattice-QCD computations of the HQ free energy. The latter is implemented into a field-theoretic ansatz for color-Coulomb and (remnants of) confining interactions. This, in particular, enables to discuss corrections to the potential approach, specifically hard-thermal-loop corrections to the vertices, relativistic corrections deduced from pertinent Feynman diagrams, and a suitable projection on transverse thermal gluons. The resulting potentials are applied to compute scattering amplitudes in different color channels and utilized for a calculation of the corresponding HQ drag coefficient in the QGP. A factor of ∼2-3 enhancement over perturbative results is obtained, mainly driven by the resummation in the attractive color-channels.
S-matrix description of anomalus large-angle heavy-ion scattering
International Nuclear Information System (INIS)
Frahn, W.E.; Hussein, M.S.; Canto, L.F.; Donangelo, R.J.
1981-01-01
A quantitative description of the well-known anomalous features observed in the large-angle scattering of n.α type heavy ions, in particular of the pronounced structures in the backangle excitation function or 16 O + 28 Si is presented. This treatment is based on the close connection between these anomalies and particular structural deviations of the partial-wave S-matrix from normal strong-absorption behaviour. The properties of these deviations are found to be rather well specified by the data: they are localized within a narrow 'l-window' centered at a critical angular momentum significantly smaller than the grazing value, and have a parity-dependent as well as a parity-independent part. These properties provide important clues as to the physical processes causing the large-angle enhancement. (Author) [pt
Variational, projection methods and Pade approximants in scattering theory
International Nuclear Information System (INIS)
Turchetti, G.
1980-12-01
Several aspects on the scattering theory are discussed in a perturbative scheme. The Pade approximant method plays an important role in such a scheme. Solitons solutions are also discussed in this same scheme. (L.C.) [pt
A direct sampling method to an inverse medium scattering problem
Ito, Kazufumi
2012-01-10
In this work we present a novel sampling method for time harmonic inverse medium scattering problems. It provides a simple tool to directly estimate the shape of the unknown scatterers (inhomogeneous media), and it is applicable even when the measured data are only available for one or two incident directions. A mathematical derivation is provided for its validation. Two- and three-dimensional numerical simulations are presented, which show that the method is accurate even with a few sets of scattered field data, computationally efficient, and very robust with respect to noises in the data. © 2012 IOP Publishing Ltd.
Method for measuring multiple scattering corrections between liquid scintillators
Energy Technology Data Exchange (ETDEWEB)
Verbeke, J.M., E-mail: verbeke2@llnl.gov; Glenn, A.M., E-mail: glenn22@llnl.gov; Keefer, G.J., E-mail: keefer1@llnl.gov; Wurtz, R.E., E-mail: wurtz1@llnl.gov
2016-07-21
A time-of-flight method is proposed to experimentally quantify the fractions of neutrons scattering between scintillators. An array of scintillators is characterized in terms of crosstalk with this method by measuring a californium source, for different neutron energy thresholds. The spectral information recorded by the scintillators can be used to estimate the fractions of neutrons multiple scattering. With the help of a correction to Feynman's point model theory to account for multiple scattering, these fractions can in turn improve the mass reconstruction of fissile materials under investigation.
Algebraic collapsing acceleration of the characteristics method with anisotropic scattering
International Nuclear Information System (INIS)
Le Tellier, R.; Hebert, A.; Roy, R.
2004-01-01
In this paper, the characteristics solvers implemented in the lattice code Dragon are extended to allow a complete anisotropic treatment of the collision operator. An efficient synthetic acceleration method, called Algebraic Collapsing Acceleration (ACA), is presented. Tests show that this method can substantially speed up the convergence of scattering source iterations. The effect of boundary conditions, either specular or white reflections, on anisotropic scattering lattice-cell problems is also considered. (author)
Scattering theory in quantum mechanics. Physical principles and mathematical methods
International Nuclear Information System (INIS)
Amrein, W.O.; Jauch, J.M.; Sinha, K.B.
1977-01-01
A contemporary approach is given to the classical topics of physics. The purpose is to explain the basic physical concepts of quantum scattering theory, to develop the necessary mathematical tools for their description, to display the interrelation between the three methods (the Schroedinger equation solutions, stationary scattering theory, and time dependence) to derive the properties of various quantities of physical interest with mathematically rigorous methods
Two-loop massive operator matrix elements for polarized and unpolarized deep-inelastic scattering
Energy Technology Data Exchange (ETDEWEB)
Bierenbaum, I.; Bluemlein, J.; Klein, S.
2007-06-15
The O({alpha}{sup 2}{sub s}) massive operator matrix elements for unpolarized and polarized heavy flavor production at asymptotic values Q{sup 2} >> m{sup 2} are calculated in Mellin space without applying the integration-by-parts method. (orig.)
A Matrix Splitting Method for Composite Function Minimization
Yuan, Ganzhao
2016-12-07
Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization and cardinality regularized optimization as special cases. This paper proposes and analyzes a new Matrix Splitting Method (MSM) for minimizing composite functions. It can be viewed as a generalization of the classical Gauss-Seidel method and the Successive Over-Relaxation method for solving linear systems in the literature. Incorporating a new Gaussian elimination procedure, the matrix splitting method achieves state-of-the-art performance. For convex problems, we establish the global convergence, convergence rate, and iteration complexity of MSM, while for non-convex problems, we prove its global convergence. Finally, we validate the performance of our matrix splitting method on two particular applications: nonnegative matrix factorization and cardinality regularized sparse coding. Extensive experiments show that our method outperforms existing composite function minimization techniques in term of both efficiency and efficacy.
A Matrix Splitting Method for Composite Function Minimization
Yuan, Ganzhao; Zheng, Wei-Shi; Ghanem, Bernard
2016-01-01
Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization and cardinality regularized optimization as special cases. This paper proposes and analyzes a new Matrix Splitting Method (MSM) for minimizing composite functions. It can be viewed as a generalization of the classical Gauss-Seidel method and the Successive Over-Relaxation method for solving linear systems in the literature. Incorporating a new Gaussian elimination procedure, the matrix splitting method achieves state-of-the-art performance. For convex problems, we establish the global convergence, convergence rate, and iteration complexity of MSM, while for non-convex problems, we prove its global convergence. Finally, we validate the performance of our matrix splitting method on two particular applications: nonnegative matrix factorization and cardinality regularized sparse coding. Extensive experiments show that our method outperforms existing composite function minimization techniques in term of both efficiency and efficacy.
International Nuclear Information System (INIS)
Uberall, H.; Gaunaurd, G.C.; Tanglis, E.
1983-01-01
The T-matrix approach, which describes the scattering of acoustic waves (or of other waves) from objects of arbitrary shape and geometry, is here 'married' to the resonance scattering theory in order to obtain the (complex) resonance frequencies of an arbitrary shaped target. For the case of nearly impenetrable targets the partial-wave scattering amplitudes are splitted into terms corresponding to 'internal' resonances, plus an apparently nonresonant background amplitude which, however, contains the broad resonances caused by 'external' diffracted (or Franz-type, creeping) waves, in addition to geometrically reflected and refracted (ray) contributions
Simulating elastic light scattering using high performance computing methods
Hoekstra, A.G.; Sloot, P.M.A.; Verbraeck, A.; Kerckhoffs, E.J.H.
1993-01-01
The Coupled Dipole method, as originally formulated byPurcell and Pennypacker, is a very powerful method tosimulate the Elastic Light Scattering from arbitraryparticles. This method, which is a particle simulationmodel for Computational Electromagnetics, has one majordrawback: if the size of the
An iterative method to invert the LTSn matrix
Energy Technology Data Exchange (ETDEWEB)
Cardona, A.V.; Vilhena, M.T. de [UFRGS, Porto Alegre (Brazil)
1996-12-31
Recently Vilhena and Barichello proposed the LTSn method to solve, analytically, the Discrete Ordinates Problem (Sn problem) in transport theory. The main feature of this method consist in the application of the Laplace transform to the set of Sn equations and solve the resulting algebraic system for the transport flux. Barichello solve the linear system containing the parameter s applying the definition of matrix invertion exploiting the structure of the LTSn matrix. In this work, it is proposed a new scheme to invert the LTSn matrix, decomposing it in blocks and recursively inverting this blocks.
Evaluation of a scattering correction method for high energy tomography
Tisseur, David; Bhatia, Navnina; Estre, Nicolas; Berge, Léonie; Eck, Daniel; Payan, Emmanuel
2018-01-01
One of the main drawbacks of Cone Beam Computed Tomography (CBCT) is the contribution of the scattered photons due to the object and the detector. Scattered photons are deflected from their original path after their interaction with the object. This additional contribution of the scattered photons results in increased measured intensities, since the scattered intensity simply adds to the transmitted intensity. This effect is seen as an overestimation in the measured intensity thus corresponding to an underestimation of absorption. This results in artifacts like cupping, shading, streaks etc. on the reconstructed images. Moreover, the scattered radiation provides a bias for the quantitative tomography reconstruction (for example atomic number and volumic mass measurement with dual-energy technique). The effect can be significant and difficult in the range of MeV energy using large objects due to higher Scatter to Primary Ratio (SPR). Additionally, the incident high energy photons which are scattered by the Compton effect are more forward directed and hence more likely to reach the detector. Moreover, for MeV energy range, the contribution of the photons produced by pair production and Bremsstrahlung process also becomes important. We propose an evaluation of a scattering correction technique based on the method named Scatter Kernel Superposition (SKS). The algorithm uses a continuously thickness-adapted kernels method. The analytical parameterizations of the scatter kernels are derived in terms of material thickness, to form continuously thickness-adapted kernel maps in order to correct the projections. This approach has proved to be efficient in producing better sampling of the kernels with respect to the object thickness. This technique offers applicability over a wide range of imaging conditions and gives users an additional advantage. Moreover, since no extra hardware is required by this approach, it forms a major advantage especially in those cases where
The Hilbert-Schmidt method for nucleon-deuteron scattering
International Nuclear Information System (INIS)
Moeller, K.; Narodetskii, I.M.
1984-01-01
The Hilbert-Schmidt technique is used for computing the divergent multiple-scattering series for scattering of nucleons by deuterons at energies above the deuteron breakup. We have found that for each partial amplitude a series of s-channel resonances diverges because of the logarithmic singularities which reflect the t-channel singularities of the total amplitude. However, the convergence of the Hilbert-Schmidt series may be improved by iterating the Faddeev equations thereby extracting the most strong logarithmic singularities. We show that the series for the amplitudes with the first two iteration subtracted converges rapidly. Our final results are in excellent agreement with exact results obtained by a direct matrix technique. (orig.)
Hilbert-Schmidt method for nucleon-deuteron scattering
International Nuclear Information System (INIS)
Moeller, K.; Narodetskij, I.M.
1983-01-01
The Hilbert-Schmidt technique is used for computing the divergent multiple-scattering series for scattering of nucleons by deuterons at energies above the deuteron breakup. It is found that for each partial amplitude a series of s-channel resonances diverges because of the logarithmic singularities which reflect the t-channel singularities of the total amplitude. However, the convergence of the Hilbert-Schmidt series may be improved by iterating the Faddeev equations thereby extracting the most strong logarithmic singularities. It is shown that the series for the amplitudes with first two iterations subtracted converges rapidly. Final results are in excellent agreement with exact results obtained by a direct matrix technique
Refractive index inversion based on Mueller matrix method
Fan, Huaxi; Wu, Wenyuan; Huang, Yanhua; Li, Zhaozhao
2016-03-01
Based on Stokes vector and Jones vector, the correlation between Mueller matrix elements and refractive index was studied with the result simplified, and through Mueller matrix way, the expression of refractive index inversion was deduced. The Mueller matrix elements, under different incident angle, are simulated through the expression of specular reflection so as to analyze the influence of the angle of incidence and refractive index on it, which is verified through the measure of the Mueller matrix elements of polished metal surface. Research shows that, under the condition of specular reflection, the result of Mueller matrix inversion is consistent with the experiment and can be used as an index of refraction of inversion method, and it provides a new way for target detection and recognition technology.
Improvement of the Convergence of the Invariant Imbedding T-Matrix Method
Zhai, S.; Panetta, R. L.; Yang, P.
2017-12-01
The invariant imbedding T-matrix method (IITM) is based on an electromagnetic volume integral equation to compute the T-matrix of an arbitrary scattering particle. A free-space Green's function is chosen as the integral kernel and thus each source point is placed in an imaginary vacuum spherical shell extending from the center to that source point. The final T-matrix (of the largest circumscribing sphere) is obtained through an iterative relation that, layer by layer, computes the T-matrix from the particle center to the outermost shell. On each spherical shell surface, an integration of the product of the refractive index 𝜀(𝜃, 𝜑) and vector spherical harmonics must be performed, resulting in the so-called U-matrix, which directly leads to the T-matrix on the spherical surface. Our observations indicate that the matrix size and sparseness are determined by the particular refractive index function 𝜀(𝜃, 𝜑). If 𝜀(𝜃, 𝜑) is an analytic function on the surface, then the matrix elements resulting from the integration decay rapidly, leading to sparse matrix; if 𝜀(𝜃, 𝜑) is not (for example, contains jump discontinuities), then the matrix elements decay slowly, leading to a large dense matrix. The intersection between an irregular scatterer and each spherical shell can leave jump discontinuities in 𝜀(𝜃, 𝜑) distributed over the shell surface. The aforementioned feature is analogous to the Gibbs phenomenon appearing in the orthogonal expansion of non-smooth functions with Hermitian eigenfunctions (complex exponential, Legendre, Bessel,...) where poor convergence speed is a direct consequence of the slow decay rate of the expansion coefficients. Various methods have been developed to deal with this slow convergence in the presence of discontinuities. Among the different approaches the most practical one may be a spectral filter: a filter is applied on the
Invariant Imbedding T-Matrix Method for Axial Symmetric Hydrometeors with Extreme Aspect Ratios
Pelissier, C.; Clune, T.; Kuo, K. S.; Munchak, S. J.; Adams, I. S.
2017-12-01
The single-scattering properties (SSPs) of hydrometeors are the fundamental quantities for physics-based precipitation retrievals. Thus, efficient computation of their electromagnetic scattering is of great value. Whereas the semi-analytical T-Matrix methods are likely the most efficient for nonspherical hydrometeors with axial symmetry, they are not suitable for arbitrarily shaped hydrometeors absent of any significant symmetry, for which volume integral methods such as those based on Discrete Dipole Approximation (DDA) are required. Currently the two leading T-matrix methods are the Extended Boundary Condition Method (EBCM) and the Invariant Imbedding T-matrix Method incorporating Lorentz-Mie Separation of Variables (IITM+SOV). EBCM is known to outperform IITM+SOV for hydrometeors with modest aspect ratios. However, in cases when aspect ratios become extreme, such as needle-like particles with large height to diameter values, EBCM fails to converge. Such hydrometeors with extreme aspect ratios are known to be present in solid precipitation and their SSPs are required to model the radiative responses accurately. In these cases, IITM+SOV is shown to converge. An efficient, parallelized C++ implementation for both EBCM and IITM+SOV has been developed to conduct a performance comparison between EBCM, IITM+SOV, and DDSCAT (a popular implementation of DDA). We present the comparison results and discuss details. Our intent is to release the combined ECBM & IITM+SOV software to the community under an open source license.
π π scattering by pole extrapolation methods
International Nuclear Information System (INIS)
Lott, F.W. III.
1978-01-01
A 25-inch hydrogen bubble chamber was used at the Lawrence Berkeley Laboratory Bevatron to produce 300,000 pictures of π + p interactions at an incident momentum of the π + of 2.67 GeV/c. The 2-prong events were processed using the FSD and the FOG-CLOUDY-FAIR data reduction system. Events of the nature π + p→π + pπ 0 and π + p→π + π + n with values of momentum transfer to the proton of -t less than or equal to 0.238 GeV 2 were selected. These events were used to extrapolate to the pion pole (t = m/sub π/ 2 ) in order to investigate the π π interaction with isospins of both T=1 and T=2. Two methods were used to do the extrapolation: the original Chew-Low method developed in 1959 and the Durr-Pilkuhn method developed in 1965, which takes into account centrifugal barrier penetration factors. At first it seemed that, while the Durr-Pilkuhn method gave better values for the total π π cross section, the Chew-Low method gave better values for the angular distribution. Further analysis, however, showed that, if the requirement of total OPE (one-pion-exchange) was dropped, then the Durr-Pilkuhn method gave more reasonable values of the angular distribution as well as for the total π π cross section
π π scattering by pole extrapolation methods
International Nuclear Information System (INIS)
Lott, F.W. III.
1977-01-01
A 25-inch hydrogen bubble chamber was used at the Lawrence Berkeley Laboratory Bevatron to produce 300,000 pictures of π + p interactions at an incident momentum of the π + of 2.67 GeV/c. The 2-prong events were processed using the FSD and the FOG-CLOUDY-FAIR data reduction system. Events of the nature π + p → π + pπ 0 and π + p → π + π + n with values of momentum transfer to the proton of -t less than or equal to 0.238 GeV 2 were selected. These events were used to extrapolate to the pion pole (t = m/sub π/ 2 ) in order to investigate the π π interaction with isospins of both T = 1 and T = 2. Two methods were used to do the extrapolation: the original Chew-Low method developed in 1959 and the Durr-Pilkuhn method developed in 1965 which takes into account centrifugal barrier penetration factors. At first it seemed that, while the Durr-Pilkuhn method gave better values for the total π π cross section, the Chew-Low method gave better values for the angular distribution. Further analysis, however, showed that if the requirement of total OPE (one-pion-exchange) were dropped, then the Durr-Pilkuhn method gave more reasonable values of the angular distribution as well as for the total π π cross section
Scattering theory methods for bound state problems
International Nuclear Information System (INIS)
Raphael, R.B.; Tobocman, W.
1978-01-01
For the analysis of the properties of a bound state system one may use in place of the Schroedinger equation the Lippmann-Schwinger (LS) equation for the wave function or the LS equation for the reactance operator. Use of the LS equation for the reactance operator constrains the solution to have correct asymptotic behaviour, so this approach would appear to be desirable when the bound state wave function is to be used to calculate particle transfer form factors. The Schroedinger equation based N-level analysis of the s-wave bound states of a square well is compared to the ones based on the LS equation. It is found that the LS equation methods work better than the Schroedinger equation method. The method that uses the LS equation for the wave function gives the best results for the wave functions while the method that uses the LS equation for the reactance operator gives the best results for the binding energies. The accuracy of the reactance operator based method is remarkably insensitive to changes in the oscillator constant used for the harmonic oscillator function basis set. It is also remarkably insensitive to the number of nodes in the bound state wave function. (Auth.)
Successive Over Relaxation Method Which Uses Matrix Norms for ...
African Journals Online (AJOL)
An algorithm for S.O.R functional iteration which uses matrix norms for the Jacobi iteration matrices rather than the usual Power method, feasible in Newton Operator for the solution of nonlinear system of equations is proposed. We modified the S.O.R. iterative method known as Multiphase S.O.R. method for Newton ...
An integrating factor matrix method to find first integrals
International Nuclear Information System (INIS)
Saputra, K V I; Quispel, G R W; Van Veen, L
2010-01-01
In this paper we develop an integrating factor matrix method to derive conditions for the existence of first integrals. We use this novel method to obtain first integrals, along with the conditions for their existence, for two- and three-dimensional Lotka-Volterra systems with constant terms. The results are compared to previous results obtained by other methods.
Response Matrix Method Development Program at Savannah River Laboratory
International Nuclear Information System (INIS)
Sicilian, J.M.
1976-01-01
The Response Matrix Method Development Program at Savannah River Laboratory (SRL) has concentrated on the development of an effective system of computer codes for the analysis of Savannah River Plant (SRP) reactors. The most significant contribution of this program to date has been the verification of the accuracy of diffusion theory codes as used for routine analysis of SRP reactor operation. This paper documents the two steps carried out in achieving this verification: confirmation of the accuracy of the response matrix technique through comparison with experiment and Monte Carlo calculations; and establishment of agreement between diffusion theory and response matrix codes in situations which realistically approximate actual operating conditions
The Matrix Element Method at Next-to-Leading Order
Campbell, John M.; Giele, Walter T.; Williams, Ciaran
2012-01-01
This paper presents an extension of the matrix element method to next-to-leading order in perturbation theory. To accomplish this we have developed a method to calculate next-to-leading order weights on an event-by-event basis. This allows for the definition of next-to-leading order likelihoods in exactly the same fashion as at leading order, thus extending the matrix element method to next-to-leading order. A welcome by-product of the method is the straightforward and efficient generation of...
Convergence Improvement of Response Matrix Method with Large Discontinuity Factors
International Nuclear Information System (INIS)
Yamamoto, Akio
2003-01-01
In the response matrix method, a numerical divergence problem has been reported when extremely small or large discontinuity factors are utilized in the calculations. In this paper, an alternative response matrix formulation to solve the divergence problem is discussed, and properties of iteration matrixes are investigated through eigenvalue analyses. In the conventional response matrix formulation, partial currents between adjacent nodes are assumed to be discontinuous, and outgoing partial currents are converted into incoming partial currents by the discontinuity factor matrix. Namely, the partial currents of the homogeneous system (i.e., homogeneous partial currents) are treated in the conventional response matrix formulation. In this approach, the spectral radius of an iteration matrix for the partial currents may exceed unity when an extremely small or large discontinuity factor is used. Contrary to this, an alternative response matrix formulation using heterogeneous partial currents is discussed in this paper. In the latter approach, partial currents are assumed to be continuous between adjacent nodes, and discontinuity factors are directly considered in the coefficients of a response matrix. From the eigenvalue analysis of the iteration matrix for the one-group, one-dimensional problem, the spectral radius for the heterogeneous partial current formulation does not exceed unity even if an extremely small or large discontinuity factor is used in the calculation; numerical stability of the alternative formulation is superior to the conventional one. The numerical stability of the heterogeneous partial current formulation is also confirmed by the two-dimensional light water reactor core analysis. Since the heterogeneous partial current formulation does not require any approximation, the converged solution exactly reproduces the reference solution when the discontinuity factors are directly derived from the reference calculation
Coherent methods in X-ray scattering
International Nuclear Information System (INIS)
Gorobtsov, Oleg
2017-05-01
X-ray radiation has been used to study structural properties of materials for more than a hundred years. Construction of extremely coherent and bright X-ray radiation sources such as free electron lasers (FELs) and latest generationstorage rings led to rapid development of experimental methods relying on high radiation coherence. These methods allow to perform revolutionary studies in a wide range of fields from solid state physics to biology. In this thesis I focus on several important problems connected with the coherent methods. The first part considers applications of dynamical diffraction theory on crystals to studies with coherent X-ray radiation. It presents the design of a high-resolution spectrometer for free electron lasers that should allow to resolve spectral structure of individual FEL pulses. The spectrometer is based on the principle of dynamical diffraction focusing. The knowledge of individual FEL pulse spectra is necessary for understanding FEL longitudinal coherence. In the same part I present quasi-kinematical approximation to dynamical theory which allows to treat analytically phase effects observed in X-ray coherent imaging on nanocrystals. These effects may play a big role when methods such as ptychography are used to study crystalline samples. The second part deals with measurements of FEL coherence properties using intensity - intensity interferometry. Results of several experiments performed at FELs FLASH and LCLS are revealed in this section. I have developed models and theories to explain the behavior observed in experiments on FLASH. These models allowed to extract information about external positional jitter of FEL pulses and secondary beams present in FEL radiation. In the LCLS experiment the Hanbury Brown and Twiss type interferometry was performed on Bragg peaks from colloidal crystal. This did not require additional measurements without the sample and information was extracted directly from diffraction patterns. Therefore intensity
Coherent methods in X-ray scattering
Energy Technology Data Exchange (ETDEWEB)
Gorobtsov, Oleg
2017-05-15
X-ray radiation has been used to study structural properties of materials for more than a hundred years. Construction of extremely coherent and bright X-ray radiation sources such as free electron lasers (FELs) and latest generationstorage rings led to rapid development of experimental methods relying on high radiation coherence. These methods allow to perform revolutionary studies in a wide range of fields from solid state physics to biology. In this thesis I focus on several important problems connected with the coherent methods. The first part considers applications of dynamical diffraction theory on crystals to studies with coherent X-ray radiation. It presents the design of a high-resolution spectrometer for free electron lasers that should allow to resolve spectral structure of individual FEL pulses. The spectrometer is based on the principle of dynamical diffraction focusing. The knowledge of individual FEL pulse spectra is necessary for understanding FEL longitudinal coherence. In the same part I present quasi-kinematical approximation to dynamical theory which allows to treat analytically phase effects observed in X-ray coherent imaging on nanocrystals. These effects may play a big role when methods such as ptychography are used to study crystalline samples. The second part deals with measurements of FEL coherence properties using intensity - intensity interferometry. Results of several experiments performed at FELs FLASH and LCLS are revealed in this section. I have developed models and theories to explain the behavior observed in experiments on FLASH. These models allowed to extract information about external positional jitter of FEL pulses and secondary beams present in FEL radiation. In the LCLS experiment the Hanbury Brown and Twiss type interferometry was performed on Bragg peaks from colloidal crystal. This did not require additional measurements without the sample and information was extracted directly from diffraction patterns. Therefore intensity
A simple method for solving the inverse scattering problem
International Nuclear Information System (INIS)
Melnikov, V.N.; Rudyak, B.V.; Zakhariev, V.N.
1977-01-01
A new method is proposed for approximate reconstruction of a potential as a step function from scattering data using the completeness relation of solutions of the Schroedinger equation. The suggested method allows one to take into account exactly the additional centrifugal barrier for partial waves with angular momentum l>0, and also the Coulomb potential. The method admits different generalizations. Numerical calculations for checking the method have been performed
Nucleon matrix elements using the variational method in lattice QCD
International Nuclear Information System (INIS)
Dragos, J.; Kamleh, W.; Leinweber, D.B.; Zanotti, J.M.; Rakow, P.E.L.; Young, R.D.; Adelaide Univ., SA
2016-06-01
The extraction of hadron matrix elements in lattice QCD using the standard two- and threepoint correlator functions demands careful attention to systematic uncertainties. One of the most commonly studied sources of systematic error is contamination from excited states. We apply the variational method to calculate the axial vector current g_A, the scalar current g_S and the quark momentum fraction left angle x right angle of the nucleon and we compare the results to the more commonly used summation and two-exponential fit methods. The results demonstrate that the variational approach offers a more efficient and robust method for the determination of nucleon matrix elements.
A 19-state R-matrix investigation of resonances in e--He scattering at low energies. Pt. 4
International Nuclear Information System (INIS)
Fon, W.C.; Lim, K.P.
1993-01-01
The authors have previously reported the 11-state and 19-state R-matrix calculations of 1 1 S-2 3,1 S and 1 1 S-2 3 P differential cross sections at low energies. In this paper, the same R-matrix calculations are extended to obtain the differential cross sections and the electron-photon coincidence parameters λ and |Χ| for the excitation of the ground state helium to the 2 1 P state. Convergence studies are carried out between the 11-state and 19-state R-matrix calculations. Only the 19-state R-matrix results are presented in full at scattering angles of 20 o , 30 o , 60 o , 90 o , 120 o and 140 o from the excitation threshold up to 23.8 eV. (author)
Phan, Quoc-Hung; Lo, Yu-Lung
2017-04-01
A surface plasmon resonance (SPR)-enhanced method is proposed for measuring the circular dichroism (CD), circular birefringence (CB), and degree of polarization (DOP) of turbid media using a Stokes–Mueller matrix polarimetry technique. The validity of the analytical model is confirmed by means of numerical simulations. The simulation results show that the proposed detection method enables the CD and CB properties to be measured with a resolution of 10 ? 4 refractive index unit (RIU) and 10 ? 5 ?? RIU , respectively, for refractive indices in the range of 1.3 to 1.4. The practical feasibility of the proposed method is demonstrated by detecting the CB/CD/DOP properties of glucose–chlorophyllin compound samples containing polystyrene microspheres. It is shown that the extracted CB value decreases linearly with the glucose concentration, while the extracted CD value increases linearly with the chlorophyllin concentration. However, the DOP is insensitive to both the glucose concentration and the chlorophyllin concentration. Consequently, the potential of the proposed SPR-enhanced Stokes–Mueller matrix polarimetry method for high-resolution CB/CD/DOP detection is confirmed. Notably, in contrast to conventional SPR techniques designed to detect relative refractive index changes, the SPR technique proposed in the present study allows absolute measurements of the optical properties (CB/CD/DOP) to be obtained.
Variational methods in electron-atom scattering theory
Nesbet, Robert K
1980-01-01
The investigation of scattering phenomena is a major theme of modern physics. A scattered particle provides a dynamical probe of the target system. The practical problem of interest here is the scattering of a low energy electron by an N-electron atom. It has been difficult in this area of study to achieve theoretical results that are even qualitatively correct, yet quantitative accuracy is often needed as an adjunct to experiment. The present book describes a quantitative theoretical method, or class of methods, that has been applied effectively to this problem. Quantum mechanical theory relevant to the scattering of an electron by an N-electron atom, which may gain or lose energy in the process, is summarized in Chapter 1. The variational theory itself is presented in Chapter 2, both as currently used and in forms that may facilitate future applications. The theory of multichannel resonance and threshold effects, which provide a rich structure to observed electron-atom scattering data, is presented in Cha...
Direct sampling methods for inverse elastic scattering problems
Ji, Xia; Liu, Xiaodong; Xi, Yingxia
2018-03-01
We consider the inverse elastic scattering of incident plane compressional and shear waves from the knowledge of the far field patterns. Specifically, three direct sampling methods for location and shape reconstruction are proposed using the different component of the far field patterns. Only inner products are involved in the computation, thus the novel sampling methods are very simple and fast to be implemented. With the help of the factorization of the far field operator, we give a lower bound of the proposed indicator functionals for sampling points inside the scatterers. While for the sampling points outside the scatterers, we show that the indicator functionals decay like the Bessel functions as the sampling point goes away from the boundary of the scatterers. We also show that the proposed indicator functionals continuously dependent on the far field patterns, which further implies that the novel sampling methods are extremely stable with respect to data error. For the case when the observation directions are restricted into the limited aperture, we firstly introduce some data retrieval techniques to obtain those data that can not be measured directly and then use the proposed direct sampling methods for location and shape reconstructions. Finally, some numerical simulations in two dimensions are conducted with noisy data, and the results further verify the effectiveness and robustness of the proposed sampling methods, even for multiple multiscale cases and limited-aperture problems.
Multi-frequency direct sampling method in inverse scattering problem
Kang, Sangwoo; Lambert, Marc; Park, Won-Kwang
2017-10-01
We consider the direct sampling method (DSM) for the two-dimensional inverse scattering problem. Although DSM is fast, stable, and effective, some phenomena remain unexplained by the existing results. We show that the imaging function of the direct sampling method can be expressed by a Bessel function of order zero. We also clarify the previously unexplained imaging phenomena and suggest multi-frequency DSM to overcome traditional DSM. Our method is evaluated in simulation studies using both single and multiple frequencies.
Matrix-based image reconstruction methods for tomography
International Nuclear Information System (INIS)
Llacer, J.; Meng, J.D.
1984-10-01
Matrix methods of image reconstruction have not been used, in general, because of the large size of practical matrices, ill condition upon inversion and the success of Fourier-based techniques. An exception is the work that has been done at the Lawrence Berkeley Laboratory for imaging with accelerated radioactive ions. An extension of that work into more general imaging problems shows that, with a correct formulation of the problem, positron tomography with ring geometries results in well behaved matrices which can be used for image reconstruction with no distortion of the point response in the field of view and flexibility in the design of the instrument. Maximum Likelihood Estimator methods of reconstruction, which use the system matrices tailored to specific instruments and do not need matrix inversion, are shown to result in good preliminary images. A parallel processing computer structure based on multiple inexpensive microprocessors is proposed as a system to implement the matrix-MLE methods. 14 references, 7 figures
Benchmarking the inelastic neutron scattering soil carbon method
The herein described inelastic neutron scattering (INS) method of measuring soil carbon was based on a new procedure for extracting the net carbon signal (NCS) from the measured gamma spectra and determination of the average carbon weight percent (AvgCw%) in the upper soil layer (~8 cm). The NCS ext...
Scattering in an intense radiation field: Time-independent methods
International Nuclear Information System (INIS)
Rosenberg, L.
1977-01-01
The standard time-independent formulation of nonrelativistic scattering theory is here extended to take into account the presence of an intense external radiation field. In the case of scattering by a static potential the extension is accomplished by the introduction of asymptotic states and intermediate-state propagators which account for the absorption and induced emission of photons by the projectile as it propagates through the field. Self-energy contributions to the propagator are included by a systematic summation of forward-scattering terms. The self-energy analysis is summarized in the form of a modified perturbation expansion of the type introduced by Watson some time ago in the context of nuclear-scattering theory. This expansion, which has a simple continued-fraction structure in the case of a single-mode field, provides a generally applicable successive approximation procedure for the propagator and the asymptotic states. The problem of scattering by a composite target is formulated using the effective-potential method. The modified perturbation expansion which accounts for self-energy effects is applicable here as well. A discussion of a coupled two-state model is included to summarize and clarify the calculational procedures
Halo-independent methods for inelastic dark matter scattering
International Nuclear Information System (INIS)
Bozorgnia, Nassim; Schwetz, Thomas; Herrero-Garcia, Juan; Zupan, Jure
2013-01-01
We present halo-independent methods to analyze the results of dark matter direct detection experiments assuming inelastic scattering. We focus on the annual modulation signal reported by DAMA/LIBRA and present three different halo-independent tests. First, we compare it to the upper limit on the unmodulated rate from XENON100 using (a) the trivial requirement that the amplitude of the annual modulation has to be smaller than the bound on the unmodulated rate, and (b) a bound on the annual modulation amplitude based on an expansion in the Earth's velocity. The third test uses the special predictions of the signal shape for inelastic scattering and allows for an internal consistency check of the data without referring to any astrophysics. We conclude that a strong conflict between DAMA/LIBRA and XENON100 in the framework of spin-independent inelastic scattering can be established independently of the local properties of the dark matter halo
Slot technique - an alternative method of scatter reduction in radiography
International Nuclear Information System (INIS)
Panzer, W.; Widenmann, L.
1983-01-01
The most common method of scatter reduction in radiography is the use of an antiscatter grid. Its disadvantage is the absorption of a certain percentage of primary radiation in the lead strips of the grid and the fact that due to the limited thickness of the lead strips their scatter absorption is also limited. A possibility for avoiding this disadvantage is offered by the so-called slot technique, ie, the successive exposure of the subject with a narrow fan beam provided by slots in rather thick lead plates. The results of a comparison between grid and slot technique regarding dose to the patient, scatter reduction, image quality and the effect of automatic exposure control are reported. (author)
In situ surface roughness measurement using a laser scattering method
Tay, C. J.; Wang, S. H.; Quan, C.; Shang, H. M.
2003-03-01
In this paper, the design and development of an optical probe for in situ measurement of surface roughness are discussed. Based on this light scattering principle, the probe which consists of a laser diode, measuring lens and a linear photodiode array, is designed to capture the scattered light from a test surface with a relatively large scattering angle ϕ (=28°). This capability increases the measuring range and enhances repeatability of the results. The coaxial arrangement that incorporates a dual-laser beam and a constant compressed air stream renders the proposed system insensitive to movement or vibration of the test surface as well as surface conditions. Tests were conducted on workpieces which were mounted on a turning machine that operates with different cutting speeds. Test specimens which underwent different machining processes and of different surface finish were also studied. The results obtained demonstrate the feasibility of surface roughness measurement using the proposed method.
Analysis of Nonlinear Dynamics by Square Matrix Method
Energy Technology Data Exchange (ETDEWEB)
Yu, Li Hua [Brookhaven National Lab. (BNL), Upton, NY (United States). Energy and Photon Sciences Directorate. National Synchrotron Light Source II
2016-07-25
The nonlinear dynamics of a system with periodic structure can be analyzed using a square matrix. In this paper, we show that because the special property of the square matrix constructed for nonlinear dynamics, we can reduce the dimension of the matrix from the original large number for high order calculation to low dimension in the first step of the analysis. Then a stable Jordan decomposition is obtained with much lower dimension. The transformation to Jordan form provides an excellent action-angle approximation to the solution of the nonlinear dynamics, in good agreement with trajectories and tune obtained from tracking. And more importantly, the deviation from constancy of the new action-angle variable provides a measure of the stability of the phase space trajectories and their tunes. Thus the square matrix provides a novel method to optimize the nonlinear dynamic system. The method is illustrated by many examples of comparison between theory and numerical simulation. Finally, in particular, we show that the square matrix method can be used for optimization to reduce the nonlinearity of a system.
A nonlinearity compensation method for a matrix converter drive
DEFF Research Database (Denmark)
Lee, Kyo-Beum; Blaabjerg, Frede
2005-01-01
converter model using the direction of current. The proposed method does not need any additional hardware or complicated software and it is easy to realize by applying the algorithm to the conventional vector control. The proposed compensation method is applied for high-performance induction motor drives...... using a 3-kW matrix converter system without a speed sensor. Experimental results show the proposed method provides good compensating characteristics....
A stochastic method for computing hadronic matrix elements
Energy Technology Data Exchange (ETDEWEB)
Alexandrou, Constantia [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; The Cyprus Institute, Nicosia (Cyprus). Computational-based Science and Technology Research Center; Dinter, Simon; Drach, Vincent [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Jansen, Karl [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Hadjiyiannakou, Kyriakos [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; Renner, Dru B. [Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); Collaboration: European Twisted Mass Collaboration
2013-02-15
We present a stochastic method for the calculation of baryon three-point functions that is more versatile compared to the typically used sequential method. We analyze the scaling of the error of the stochastically evaluated three-point function with the lattice volume and find a favorable signal-to-noise ratio suggesting that our stochastic method can be used efficiently at large volumes to compute hadronic matrix elements.
Scattering of long folded strings and mixed correlators in the two-matrix model
International Nuclear Information System (INIS)
Bourgine, J.-E.; Hosomichi, K.; Kostov, I.; Matsuo, Y.
2008-01-01
We study the interactions of Maldacena's long folded strings in two-dimensional string theory. We find the amplitude for a state containing two long folded strings to come and go back to infinity. We calculate this amplitude both in the worldsheet theory and in the dual matrix model, the matrix quantum mechanics. The matrix model description allows to evaluate the amplitudes involving any number of long strings, which are given by the mixed trace correlators in an effective two-matrix model
International Nuclear Information System (INIS)
Palmai, T.; Apagyi, B.; Horvath, M.
2008-01-01
Solution of the Cox-Thompson inverse scattering problem at fixed energy 1-3 is reformulated resulting in semi-analytic equations. The new set of equations for the normalization constants and the nonphysical (shifted) angular momenta are free of matrix inversion operations. This simplification is a result of treating only the input phase shifts of partial waves of a given parity. Therefore, the proposed method can be applied for identical particle scattering of the bosonic type (or for certain cases of identical fermionic scattering). The new formulae are expected to be numerically more efficient than the previous ones. Based on the semi-analytic equations an approximate method is proposed for the generic inverse scattering problem, when partial waves of arbitrary parity are considered. (author)
Monaghan, Philip Harold; Delvaux, John McConnell; Taxacher, Glenn Curtis
2015-06-09
A pre-form CMC cavity and method of forming pre-form CMC cavity for a ceramic matrix component includes providing a mandrel, applying a base ply to the mandrel, laying-up at least one CMC ply on the base ply, removing the mandrel, and densifying the base ply and the at least one CMC ply. The remaining densified base ply and at least one CMC ply form a ceramic matrix component having a desired geometry and a cavity formed therein. Also provided is a method of forming a CMC component.
Decomposition of spectra in EPR dosimetry using the matrix method
International Nuclear Information System (INIS)
Sholom, S.V.; Chumak, V.V.
2003-01-01
The matrix method of EPR spectra decomposition is developed and adapted for routine application in retrospective EPR dosimetry with teeth. According to this method, the initial EPR spectra are decomposed (using methods of matrix algebra) into several reference components (reference matrices) that are specific for each material. Proposed procedure has been tested on the example of tooth enamel. Reference spectra were a spectrum of an empty sample tube and three standard signals of enamel (two at g=2.0045, both for the native signal and one at g perpendicular =2.0018, g parallel =1.9973 for the dosimetric signal). Values of dosimetric signals obtained using the given method have been compared with data obtained by manual manipulation of spectra, and good coincidence was observed. This allows considering the proposed method as potent for application in routine EPR dosimetry
Proper comparison among methods using a confusion matrix
CSIR Research Space (South Africa)
Salmon
2015-07-01
Full Text Available -1 IGARSS 2015, Milan, Italy, 26-31 July 2015 Proper comparison among methods using a confusion matrix 1,2 B.P. Salmon, 2,3 W. Kleynhans, 2,3 C.P. Schwegmann and 1J.C. Olivier 1School of Engineering and ICT, University of Tasmania, Australia 2...
An assessment of the DORT method on simple scatterers using boundary element modelling.
Gélat, P; Ter Haar, G; Saffari, N
2015-05-07
The ability to focus through ribs overcomes an important limitation of a high-intensity focused ultrasound (HIFU) system for the treatment of liver tumours. Whilst it is important to generate high enough acoustic pressures at the treatment location for tissue lesioning, it is also paramount to ensure that the resulting ultrasonic dose on the ribs remains below a specified threshold, since ribs both strongly absorb and reflect ultrasound. The DORT (décomposition de l'opérateur de retournement temporel) method has the ability to focus on and through scatterers immersed in an acoustic medium selectively without requiring prior knowledge of their location or geometry. The method requires a multi-element transducer and is implemented via a singular value decomposition of the measured matrix of inter-element transfer functions. The efficacy of a method of focusing through scatterers is often assessed by comparing the specific absorption rate (SAR) at the surface of the scatterer, and at the focal region. The SAR can be obtained from a knowledge of the acoustic pressure magnitude and the acoustic properties of the medium and scatterer. It is well known that measuring acoustic pressures with a calibrated hydrophone at or near a hard surface presents experimental challenges, potentially resulting in increased measurement uncertainties. Hence, the DORT method is usually assessed experimentally by measuring the SAR at locations on the surface of the scatterer after the latter has been removed from the acoustic medium. This is also likely to generate uncertainties in the acoustic pressure measurement. There is therefore a strong case for assessing the efficacy of the DORT method through a validated theoretical model. The boundary element method (BEM) applied to exterior acoustic scattering problems is well-suited for such an assessment. In this study, BEM was used to implement the DORT method theoretically on locally reacting spherical scatterers, and to assess its focusing
Comparative Study of Inference Methods for Bayesian Nonnegative Matrix Factorisation
DEFF Research Database (Denmark)
Brouwer, Thomas; Frellsen, Jes; Liò, Pietro
2017-01-01
In this paper, we study the trade-offs of different inference approaches for Bayesian matrix factorisation methods, which are commonly used for predicting missing values, and for finding patterns in the data. In particular, we consider Bayesian nonnegative variants of matrix factorisation and tri......-factorisation, and compare non-probabilistic inference, Gibbs sampling, variational Bayesian inference, and a maximum-a-posteriori approach. The variational approach is new for the Bayesian nonnegative models. We compare their convergence, and robustness to noise and sparsity of the data, on both synthetic and real...
Directory of Open Access Journals (Sweden)
Yasuhiro Nakamura
2012-07-01
Full Text Available The present study introduces the four-component scattering power decomposition (4-CSPD algorithm with rotation of covariance matrix, and presents an experimental proof of the equivalence between the 4-CSPD algorithms based on rotation of covariance matrix and coherency matrix. From a theoretical point of view, the 4-CSPD algorithms with rotation of the two matrices are identical. Although it seems obvious, no experimental evidence has yet been presented. In this paper, using polarimetric synthetic aperture radar (POLSAR data acquired by Phased Array L-band SAR (PALSAR on board of Advanced Land Observing Satellite (ALOS, an experimental proof is presented to show that both algorithms indeed produce identical results.
Widening the Scope of R-matrix Methods
Energy Technology Data Exchange (ETDEWEB)
Thompson, Ian J. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Dimitriou, Paraskevi [IAEA, Vienna (Austria); DeBoer, Richard J. [Nieuwland Science Hall, Notre Dame, IN (United States); Kunieda, Satoshi [Nuclear Data Center (JAEA), Tokai (Japan); Paris, Mark [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Thompson, Ian [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Trkov, Andrej [IAEA, Vienna (Austria)
2016-03-01
A Consultant’s Meeting was held at the IAEA Headquarters, from 7 to 9 December 2015, to discuss the status of R-matrix codes currently used in calculations of charged-particle induced reaction cross sections at low energies. The ultimate goal was to initiate an international effort, coordinated by the IAEA, to evaluate charged-particle induced reactions in the resolved-resonance region. Participants reviewed the capabilities of the codes, the different implementations of R-matrix theory and translatability of the R-matrix parameters, the evaluation methods and suitable data formats for broader dissemination. The details of the presentations and technical discussions, as well as the actions that were proposed to achieve the goal of the meeting are summarized in this report.
Generalized Hartree-Fock method for electron-atom scattering
International Nuclear Information System (INIS)
Rosenberg, L.
1997-01-01
In the widely used Hartree-Fock procedure for atomic structure calculations, trial functions in the form of linear combinations of Slater determinants are constructed and the Rayleigh-Ritz minimum principle is applied to determine the best in that class. A generalization of this approach, applicable to low-energy electron-atom scattering, is developed here. The method is based on a unique decomposition of the scattering wave function into open- and closed-channel components, so chosen that an approximation to the closed-channel component may be obtained by adopting it as a trial function in a minimum principle, whose rigor can be maintained even when the target wave functions are imprecisely known. Given a closed-channel trial function, the full scattering function may be determined from the solution of an effective one-body Schroedinger equation. Alternatively, in a generalized Hartree-Fock approach, the minimum principle leads to coupled integrodifferential equations to be satisfied by the basis functions appearing in a Slater-determinant representation of the closed-channel wave function; it also provides a procedure for optimizing the choice of nonlinear parameters in a variational determination of these basis functions. Inclusion of additional Slater determinants in the closed-channel trial function allows for systematic improvement of that function, as well as the calculated scattering parameters, with the possibility of spurious singularities avoided. Electron-electron correlations can be important in accounting for long-range forces and resonances. These correlation effects can be included explicitly by suitable choice of one component of the closed-channel wave function; the remaining component may then be determined by the generalized Hartree-Fock procedure. As a simple test, the method is applied to s-wave scattering of positrons by hydrogen. copyright 1997 The American Physical Society
Bonitati, Joey; Slimmer, Ben; Li, Weichuan; Potel, Gregory; Nunes, Filomena
2017-09-01
The calculable form of the R-matrix method has been previously shown to be a useful tool in approximately solving the Schrodinger equation in nuclear scattering problems. We use this technique combined with the Gauss quadrature for the Lagrange-mesh method to efficiently solve for the wave functions of projectile nuclei in low energy collisions (1-100 MeV) involving an arbitrary number of channels. We include the local Woods-Saxon potential, the non-local potential of Perey and Buck, a Coulomb potential, and a coupling potential to computationally solve for the wave function of two nuclei at short distances. Object oriented programming is used to increase modularity, and parallel programming techniques are introduced to reduce computation time. We conclude that the R-matrix method is an effective method to predict the wave functions of nuclei in scattering problems involving both multiple channels and non-local potentials. Michigan State University iCER ACRES REU.
International Nuclear Information System (INIS)
Ruehrnschopf and, Ernst-Peter; Klingenbeck, Klaus
2011-01-01
The main components of scatter correction procedures are scatter estimation and a scatter compensation algorithm. This paper completes a previous paper where a general framework for scatter compensation was presented under the prerequisite that a scatter estimation method is already available. In the current paper, the authors give a systematic review of the variety of scatter estimation approaches. Scatter estimation methods are based on measurements, mathematical-physical models, or combinations of both. For completeness they present an overview of measurement-based methods, but the main topic is the theoretically more demanding models, as analytical, Monte-Carlo, and hybrid models. Further classifications are 3D image-based and 2D projection-based approaches. The authors present a system-theoretic framework, which allows to proceed top-down from a general 3D formulation, by successive approximations, to efficient 2D approaches. A widely useful method is the beam-scatter-kernel superposition approach. Together with the review of standard methods, the authors discuss their limitations and how to take into account the issues of object dependency, spatial variance, deformation of scatter kernels, external and internal absorbers. Open questions for further investigations are indicated. Finally, the authors refer on some special issues and applications, such as bow-tie filter, offset detector, truncated data, and dual-source CT.
A study of radiative properties of fractal soot aggregates using the superposition T-matrix method
International Nuclear Information System (INIS)
Li Liu; Mishchenko, Michael I.; Patrick Arnott, W.
2008-01-01
We employ the numerically exact superposition T-matrix method to perform extensive computations of scattering and absorption properties of soot aggregates with varying state of compactness and size. The fractal dimension, D f , is used to quantify the geometrical mass dispersion of the clusters. The optical properties of soot aggregates for a given fractal dimension are complex functions of the refractive index of the material m, the number of monomers N S , and the monomer radius a. It is shown that for smaller values of a, the absorption cross section tends to be relatively constant when D f f >2. However, a systematic reduction in light absorption with D f is observed for clusters with sufficiently large N S , m, and a. The scattering cross section and single-scattering albedo increase monotonically as fractals evolve from chain-like to more densely packed morphologies, which is a strong manifestation of the increasing importance of scattering interaction among spherules. Overall, the results for soot fractals differ profoundly from those calculated for the respective volume-equivalent soot spheres as well as for the respective external mixtures of soot monomers under the assumption that there are no electromagnetic interactions between the monomers. The climate-research implications of our results are discussed
Shan, Xiao; Xiahou, Chengkui; Connor, J N L
2018-01-03
In earlier research, we have demonstrated that broad "hidden" rainbows can occur in the product differential cross sections (DCSs) of state-to-state chemical reactions. Here we ask the question: can pronounced and localized rainbows, rather than broad hidden ones, occur in reactive DCSs? Further motivation comes from recent measurements by H. Pan and K. Liu, J. Phys. Chem. A, 2016, 120, 6712, of a "bulge" in a reactive DCS, which they conjecture is a rainbow. Our theoretical approach uses a "weak" version of Heisenberg's scattering matrix program (wHSMP) introduced by X. Shan and J. N. L. Connor, Phys. Chem. Chem. Phys., 2011, 13, 8392. This wHSMP uses four general physical principles for chemical reactions to suggest simple parameterized forms for the S matrix; it does not employ a potential energy surface. We use a parameterization in which the modulus of the S matrix is a smooth-step function of the total angular momentum quantum number, J, and (importantly) its phase is a cubic polynomial in J. We demonstrate for a Legendre partial wave series (PWS) the existence of pronounced rainbows, supernumerary rainbows, and other interference effects, in reactive DCSs. We find that reactive rainbows can be more complicated in their structure than the familiar rainbows of elastic scattering. We also analyse the angular scattering using Nearside-Farside (NF) PWS theory and NF PWS Local Angular Momentum (LAM) theory, including resummations of the PWS. In addition, we apply full and NF asymptotic (semiclassical) rainbow theories to the PWS - in particular, the uniform Airy and transitional Airy approximations for the farside scattering. This lets us prove that structure in the DCSs are indeed rainbows, supernumerary rainbows as well as other interference effects.
Lvovich, I. Ya; Preobrazhenskiy, A. P.; Choporov, O. N.
2018-05-01
The paper deals with the issue of electromagnetic scattering on a perfectly conducting diffractive body of a complex shape. Performance calculation of the body scattering is carried out through the integral equation method. Fredholm equation of the second time was used for calculating electric current density. While solving the integral equation through the moments method, the authors have properly described the core singularity. The authors determined piecewise constant functions as basic functions. The chosen equation was solved through the moments method. Within the Kirchhoff integral approach it is possible to define the scattered electromagnetic field, in some way related to obtained electrical currents. The observation angles sector belongs to the area of the front hemisphere of the diffractive body. To improve characteristics of the diffractive body, the authors used a neural network. All the neurons contained a logsigmoid activation function and weighted sums as discriminant functions. The paper presents the matrix of weighting factors of the connectionist model, as well as the results of the optimized dimensions of the diffractive body. The paper also presents some basic steps in calculation technique of the diffractive bodies, based on the combination of integral equation and neural networks methods.
Advanced methods for scattering amplitudes in gauge theories
Energy Technology Data Exchange (ETDEWEB)
Peraro, Tiziano
2014-09-24
We present new techniques for the evaluation of multi-loop scattering amplitudes and their application to gauge theories, with relevance to the Standard Model phenomenology. We define a mathematical framework for the multi-loop integrand reduction of arbitrary diagrams, and elaborate algebraic approaches, such as the Laurent expansion method, implemented in the software Ninja, and the multivariate polynomial division technique by means of Groebner bases.
Canonical transformations method in the potential scattering problem
International Nuclear Information System (INIS)
Pavlenko, Yu.G.
1984-01-01
Canonical formalism of the first order is used in the present paper to solve the problem of scattering and other problems of quantum mechanics. The theory of canonical transformations (CT) being the basis of hamiltonian approach permits to develop several methods of integration being beyond the scope of the standard theory of perturbations. In this case it is essential for numerical counting that the theory permits to obtain algorithm for plotting highest approximations
Advanced methods for scattering amplitudes in gauge theories
International Nuclear Information System (INIS)
Peraro, Tiziano
2014-01-01
We present new techniques for the evaluation of multi-loop scattering amplitudes and their application to gauge theories, with relevance to the Standard Model phenomenology. We define a mathematical framework for the multi-loop integrand reduction of arbitrary diagrams, and elaborate algebraic approaches, such as the Laurent expansion method, implemented in the software Ninja, and the multivariate polynomial division technique by means of Groebner bases.
Quantum method of the inverse scattering problem. Pt. 1
International Nuclear Information System (INIS)
Sklyamin, E.K.; Takhtadzhyan, L.A.; Faddeev, L.D.
1978-12-01
In this work the authors use a formulation for the method of the inverse scattering problem for quantum-mechanical models of the field theory, that can be found in a quantization of these fully integrable systems. As the most important example serves the system (sinγ) 2 with the movement equation: γtt -γxx + m 2 /β sinβγ = 0 that is known under the specification Sine-Gordon-equation. (orig.) [de
Energy Technology Data Exchange (ETDEWEB)
Costescu, A [Department of Physics, University of Bucharest, MG11, Bucharest-Magurele 76900 (Romania); Spanulescu, S [Department of Physics, University of Bucharest, MG11, Bucharest-Magurele 76900 (Romania); Stoica, C [Department of Physics, University of Bucharest, MG11, Bucharest-Magurele 76900 (Romania)
2007-08-14
The right expressions of the nonrelativistic K-shell Rayleigh scattering amplitudes and cross-sections are obtained by using the Coulomb Green's function method. Our analytical result does not have the spurious poles that occur in the old nonrelativistic result with retardation (Gavrila and Costescu 1970 Phys. Rev. A 2 1752). Starting from the expression of the second-order S-matrix element for the case of the elastic scattering of photons by K-shell bound electrons, we obtain the correct nonrelativistic Rayleigh angular distribution (valid for photon energies {omega} up to {alpha}Zm) by removing the relativistic higher order terms in {alpha}Z and {omega}/m. The imaginary part of the Rayleigh amplitudes is obtained for any scattering angles in a closed form in terms of elementary functions. Thereby a simple formula for the exact nonrelativistic photoeffect total cross-section is obtained via the optical theorem, giving significantly better predictions than Fischer's nonrelativistic photoeffect formula. Comparing the predictions given by our formulae with the full relativistic numerical calculations of Kissel et al (Phys. Rev. 1980 A 22 1970), and with experimental results, a fairly good agreement within 10% is found for the angular distribution of Rayleigh scattering for photon energies up to 200 keV and both below and above the first resonance.
Inelastic neutron scattering method in hard coal quality monitoring
International Nuclear Information System (INIS)
Cywicka-Jakiel, T.; Loskiewicz, J.; Tracz, G.
1994-07-01
Nuclear methods in mining industry and power generation plants are nowadays very important especially because of the need for optimization of combustion processes and reduction of environmental pollution. On-line analysis of coal quality not only economic benefits but contribute to environmental protection too. Neutron methods especially inelastic scattering and PGNAA are very useful for analysis of coal quality where calorific valve, ash and moisture content are the most important. Using Pu-Be or Am-Be isotopic sources and measuring carbon 4.43 MeV γ-rays from neutron inelastic scattering: 12 C(n,n'γ) 12 C we can evaluate calorific valve in hard coals with precision better than in PGNAA method. This is mainly because of large cross-section for inelastic scattering and the strong correlation between carbon content and calorific value shown in the paper for different coal basins. The influence of moisture on 4.43 MeV carbon γ-rays in considered in the paper in theoretical and experimental aspects and appropriate formula is introduced. Also the possibilities of determine ash, moisture, Cl, Na and Si in coal are shown. (author). 11 refs, 15 figs
Inelastic neutron scattering method in hard coal quality monitoring
Energy Technology Data Exchange (ETDEWEB)
Cywicka-Jakiel, T.; Loskiewicz, J.; Tracz, G. [Institute of Nuclear Physics, Cracow (Poland)
1994-07-01
Nuclear methods in mining industry and power generation plants are nowadays very important especially because of the need for optimization of combustion processes and reduction of environmental pollution. On-line analysis of coal quality not only economic benefits but contribute to environmental protection too. Neutron methods especially inelastic scattering and PGNAA are very useful for analysis of coal quality where calorific valve, ash and moisture content are the most important. Using Pu-Be or Am-Be isotopic sources and measuring carbon 4.43 MeV {gamma}-rays from neutron inelastic scattering: {sup 12}C(n,n`{gamma}){sup 12}C we can evaluate calorific valve in hard coals with precision better than in PGNAA method. This is mainly because of large cross-section for inelastic scattering and the strong correlation between carbon content and calorific value shown in the paper for different coal basins. The influence of moisture on 4.43 MeV carbon {gamma}-rays in considered in the paper in theoretical and experimental aspects and appropriate formula is introduced. Also the possibilities of determine ash, moisture, Cl, Na and Si in coal are shown. (author). 11 refs, 15 figs.
Matrix method for two-dimensional waveguide mode solution
Sun, Baoguang; Cai, Congzhong; Venkatesh, Balajee Seshasayee
2018-05-01
In this paper, we show that the transfer matrix theory of multilayer optics can be used to solve the modes of any two-dimensional (2D) waveguide for their effective indices and field distributions. A 2D waveguide, even composed of numerous layers, is essentially a multilayer stack and the transmission through the stack can be analysed using the transfer matrix theory. The result is a transfer matrix with four complex value elements, namely A, B, C and D. The effective index of a guided mode satisfies two conditions: (1) evanescent waves exist simultaneously in the first (cladding) layer and last (substrate) layer, and (2) the complex element D vanishes. For a given mode, the field distribution in the waveguide is the result of a 'folded' plane wave. In each layer, there is only propagation and absorption; at each boundary, only reflection and refraction occur, which can be calculated according to the Fresnel equations. As examples, we show that this method can be used to solve modes supported by the multilayer step-index dielectric waveguide, slot waveguide, gradient-index waveguide and various plasmonic waveguides. The results indicate the transfer matrix method is effective for 2D waveguide mode solution in general.
An interlaboratory comparison of methods for measuring rock matrix porosity
International Nuclear Information System (INIS)
Rasilainen, K.; Hellmuth, K.H.; Kivekaes, L.; Ruskeeniemi, T.; Melamed, A.; Siitari-Kauppi, M.
1996-09-01
An interlaboratory comparison study was conducted for the available Finnish methods of rock matrix porosity measurements. The aim was first to compare different experimental methods for future applications, and second to obtain quality assured data for the needs of matrix diffusion modelling. Three different versions of water immersion techniques, a tracer elution method, a helium gas through-diffusion method, and a C-14-PMMA method were tested. All methods selected for this study were established experimental tools in the respective laboratories, and they had already been individually tested. Rock samples for the study were obtained from a homogeneous granitic drill core section from the natural analogue site at Palmottu. The drill core section was cut into slabs that were expected to be practically identical. The subsamples were then circulated between the different laboratories using a round robin approach. The circulation was possible because all methods were non-destructive, except the C-14-PMMA method, which was always the last method to be applied. The possible effect of drying temperature on the measured porosity was also preliminarily tested. These measurements were done in the order of increasing drying temperature. Based on the study, it can be concluded that all methods are comparable in their accuracy. The selection of methods for future applications can therefore be based on practical considerations. Drying temperature seemed to have very little effect on the measured porosity, but a more detailed study is needed for definite conclusions. (author) (4 refs.)
Development of new methods for studying nanostructures using neutron scattering
International Nuclear Information System (INIS)
Pynn, Roger
2016-01-01
The goal of this project was to develop improved instrumentation for studying the microscopic structures of materials using neutron scattering. Neutron scattering has a number of advantages for studying material structure but suffers from the well-known disadvantage that neutrons' ability to resolve structural details is usually limited by the strength of available neutron sources. We aimed to overcome this disadvantage using a new experimental technique, called Spin Echo Scattering Angle Encoding (SESAME) that makes use of the neutron's magnetism. Our goal was to show that this innovation will allow the country to make better use of the significant investment it has recently made in a new neutron source at Oak Ridge National Laboratory (ORNL) and will lead to increases in scientific knowledge that contribute to the Nation's technological infrastructure and ability to develop advanced materials and technologies. We were successful in demonstrating the technical effectiveness of the new method and established a baseline of knowledge that has allowed ORNL to start a project to implement the method on one of its neutron beam lines.
Development of new methods for studying nanostructures using neutron scattering
Energy Technology Data Exchange (ETDEWEB)
Pynn, Roger [Indiana Univ., Bloomington, IN (United States)
2016-03-18
The goal of this project was to develop improved instrumentation for studying the microscopic structures of materials using neutron scattering. Neutron scattering has a number of advantages for studying material structure but suffers from the well-known disadvantage that neutrons’ ability to resolve structural details is usually limited by the strength of available neutron sources. We aimed to overcome this disadvantage using a new experimental technique, called Spin Echo Scattering Angle Encoding (SESAME) that makes use of the neutron’s magnetism. Our goal was to show that this innovation will allow the country to make better use of the significant investment it has recently made in a new neutron source at Oak Ridge National Laboratory (ORNL) and will lead to increases in scientific knowledge that contribute to the Nation’s technological infrastructure and ability to develop advanced materials and technologies. We were successful in demonstrating the technical effectiveness of the new method and established a baseline of knowledge that has allowed ORNL to start a project to implement the method on one of its neutron beam lines.
Optimization of MIMO Systems Capacity Using Large Random Matrix Methods
Directory of Open Access Journals (Sweden)
Philippe Loubaton
2012-11-01
Full Text Available This paper provides a comprehensive introduction of large random matrix methods for input covariance matrix optimization of mutual information of MIMO systems. It is first recalled informally how large system approximations of mutual information can be derived. Then, the optimization of the approximations is discussed, and important methodological points that are not necessarily covered by the existing literature are addressed, including the strict concavity of the approximation, the structure of the argument of its maximum, the accuracy of the large system approach with regard to the number of antennas, or the justification of iterative water-filling optimization algorithms. While the existing papers have developed methods adapted to a specific model, this contribution tries to provide a unified view of the large system approximation approach.
On a novel matrix method for three-dimensional photoelasticity
International Nuclear Information System (INIS)
Theocaris, P.S.; Gdoutos, E.E.
1978-01-01
A non-destructive method for the photoelastic determination of three-dimensional stress distributions, based on the Mueller and Jones calculi, is developed. The differential equations satisfied by the Stokes and Jones vectors, when a polarized light beam passes through a photoelastic model, presenting rotation of the secondary principal stress directions, are established in matrix form. The Peano-Baker method is used for the solution of these differential equations in a matrix series form, establishing the elements of the Mueller and Jones matrices of the photoelastic model. These matrices are experimentally determined by using different wavelengths in conjunction with Jones' 'equivalence theorem'. The Neumann equations are immediately deduced from the above-mentioned differential equations. (orig.) [de
A collocation finite element method with prior matrix condensation
International Nuclear Information System (INIS)
Sutcliffe, W.J.
1977-01-01
For thin shells with general loading, sixteen degrees of freedom have been used for a previous finite element solution procedure using a Collocation method instead of the usual variational based procedures. Although the number of elements required was relatively small, nevertheless the final matrix for the simultaneous solution of all unknowns could become large for a complex compound structure. The purpose of the present paper is to demonstrate a method of reducing the final matrix size, so allowing solution for large structures with comparatively small computer storage requirements while retaining the accuracy given by high order displacement functions. Collocation points, a number are equilibrium conditions which must be satisfied independently of the overall compatibility of forces and deflections for a complete structure. (Auth.)
Improved determination of hadron matrix elements using the variational method
International Nuclear Information System (INIS)
Dragos, J.; Kamleh, W.; Leinweber, D.B.; Zanotti, J.M.; Rakow, P.E.L.; Young, R.D.; Adelaide Univ.
2015-11-01
The extraction of hadron form factors in lattice QCD using the standard two- and three-point correlator functions has its limitations. One of the most commonly studied sources of systematic error is excited state contamination, which occurs when correlators are contaminated with results from higher energy excitations. We apply the variational method to calculate the axial vector current g A and compare the results to the more commonly used summation and two-exponential fit methods. The results demonstrate that the variational approach offers a more efficient and robust method for the determination of nucleon matrix elements.
Shan, Huihui; Zhang, Hui; Liu, Junjian; Tao, Zongming; Wang, Shenhao; Ma, Xiaomin; Zhou, Pucheng; Yao, Ling; Liu, Dong; Xie, Chenbo; Wang, Yingjian
2018-03-01
Aerosol extinction coefficient profile is an essential parameter for atmospheric radiation model. It is difficult to get higher signal to noise ratio (SNR) of backscattering lidar from the ground to the tropopause especially in near range. Higher SNR problem can be solved by combining side-scattering and backscattering lidar. Using Raman-scattering lidar, aerosol extinction to backscatter ratio (lidar ratio) can be got. Based on side-scattering, backscattering and Raman-scattering lidar system, aerosol extinction coefficient is retrieved precisely from the earth's surface to the tropopause. Case studies show this method is reasonable and feasible.
Agrawal, A. P.; Carnegie, D. W.; Boerner, W.-M.
This paper presents an evaluation of polarimetric rain backscatter measurements collected with coherent dual polarization radar systems in the X (8.9 GHz) and Q (45GHz) bands, the first being operated in a pulsed mode and the second being a FM-CW system. The polarimetric measurement data consisted for each band of fifty files of time-sequential scattering matrix measurements expressed in terms of a linear (H, V) antenna polarization state basis. The rain backscattering takes place in a rain cell defined by the beam widths and down range distances of 275 ft through 325 ft and the scattering matrices were measured far below the hydrometeoric scattering center decorrelation time so that ensemble averaging of time-sequential scattering matrices may be applied. In the data evaluation great care was taken in determining: (1) polarimetric Doppler velocities associated with the motion of descending oscillating raindrops and/or eddies within the moving swaths of coastal rain showers, and (2) also the properties of the associated co/cross-polarization rain clutter nulls and their distributions on the Poincare polarization sphere.
Workshop report on large-scale matrix diagonalization methods in chemistry theory institute
Energy Technology Data Exchange (ETDEWEB)
Bischof, C.H.; Shepard, R.L.; Huss-Lederman, S. [eds.
1996-10-01
The Large-Scale Matrix Diagonalization Methods in Chemistry theory institute brought together 41 computational chemists and numerical analysts. The goal was to understand the needs of the computational chemistry community in problems that utilize matrix diagonalization techniques. This was accomplished by reviewing the current state of the art and looking toward future directions in matrix diagonalization techniques. This institute occurred about 20 years after a related meeting of similar size. During those 20 years the Davidson method continued to dominate the problem of finding a few extremal eigenvalues for many computational chemistry problems. Work on non-diagonally dominant and non-Hermitian problems as well as parallel computing has also brought new methods to bear. The changes and similarities in problems and methods over the past two decades offered an interesting viewpoint for the success in this area. One important area covered by the talks was overviews of the source and nature of the chemistry problems. The numerical analysts were uniformly grateful for the efforts to convey a better understanding of the problems and issues faced in computational chemistry. An important outcome was an understanding of the wide range of eigenproblems encountered in computational chemistry. The workshop covered problems involving self- consistent-field (SCF), configuration interaction (CI), intramolecular vibrational relaxation (IVR), and scattering problems. In atomic structure calculations using the Hartree-Fock method (SCF), the symmetric matrices can range from order hundreds to thousands. These matrices often include large clusters of eigenvalues which can be as much as 25% of the spectrum. However, if Cl methods are also used, the matrix size can be between 10{sup 4} and 10{sup 9} where only one or a few extremal eigenvalues and eigenvectors are needed. Working with very large matrices has lead to the development of
International Nuclear Information System (INIS)
Broome, J.
1965-11-01
The programme SCATTER is a KDF9 programme in the Egtran dialect of Fortran to generate normalized angular distributions for elastically scattered neutrons from data input as the coefficients of a Legendre polynomial series, or from differential cross-section data. Also, differential cross-section data may be analysed to produce Legendre polynomial coefficients. Output on cards punched in the format of the U.K. A. E. A. Nuclear Data Library is optional. (author)
Iterative approach as alternative to S-matrix in modal methods
Semenikhin, Igor; Zanuccoli, Mauro
2014-12-01
The continuously increasing complexity of opto-electronic devices and the rising demands of simulation accuracy lead to the need of solving very large systems of linear equations making iterative methods promising and attractive from the computational point of view with respect to direct methods. In particular, iterative approach potentially enables the reduction of required computational time to solve Maxwell's equations by Eigenmode Expansion algorithms. Regardless of the particular eigenmodes finding method used, the expansion coefficients are computed as a rule by scattering matrix (S-matrix) approach or similar techniques requiring order of M3 operations. In this work we consider alternatives to the S-matrix technique which are based on pure iterative or mixed direct-iterative approaches. The possibility to diminish the impact of M3 -order calculations to overall time and in some cases even to reduce the number of arithmetic operations to M2 by applying iterative techniques are discussed. Numerical results are illustrated to discuss validity and potentiality of the proposed approaches.
Ordered array of ω particles in β-Ti matrix studied by small-angle X-ray scattering
International Nuclear Information System (INIS)
Šmilauerová, J.; Harcuba, P.; Stráský, J.; Stráská, J.; Janeček, M.; Pospíšil, J.; Kužel, R.; Brunátová, T.; Holý, V.; Ilavský, J.
2014-01-01
Nanosized particles of ω phase in a β-Ti alloy were investigated by small-angle X-ray scattering using synchrotron radiation. We demonstrated that the particles are spontaneously weakly ordered in a three-dimensional cubic array along the 〈100〉-directions in the β-Ti matrix. The small-angle scattering data fit well to a three-dimensional short-range-order model; from the fit we determined the evolution of the mean particle size and mean distance between particles during ageing. The self-ordering of the particles is explained by elastic interaction between the particles, since the relative positions of the particles coincide with local minima of the interaction energy. We performed numerical Monte Carlo simulation of the particle ordering and we obtained a good agreement with the experimental data
Regge-pole description of potential scattering by means of the phase-integral method
International Nuclear Information System (INIS)
Amaha, A.
1992-01-01
The application of Regge-pole theory to different atomic and molecular scattering has shown to have promising interpretational power in the differential cross sections. Differential cross sections can be analysed in terms of interference between the 'background' amplitude and a few Regge-pole positions of the scattering matrix (S matrix) representing surface waves around the interaction region. By the analytic continuation of the radial Schroedinger differential equation into the complex plane of angular momentum one can determine the analytic properties of the S matrix which contains the physical information in the scattering processes. For interaction potentials fulfilling certain properties, the study of the S matrix leads to the study of the F matrix introduced by Froeman and Froeman for the treatment of connection problems for phase-integral solutions of the differential equation. In this thesis the quantum mechanical scattering problem is analysed in the framework of Regge-pole theory with the use of the complex-angular-momentum formalism. To determine the S matrix, the relevant F matrix elements which give the stokes constants are derived and their properties are studied. The poles of the S matrix for particular complex values of the angular momentum quantum number are the Regge-poles. Using the Regge-pole positions and residues together with the background integral, the differential cross sections are calculated and compared with corresponding partial-wave representations
Bond, Tiziana C.; Miles, Robin; Davidson, James C.; Liu, Gang Logan
2014-07-22
Methods for fabricating nanoscale array structures suitable for surface enhanced Raman scattering, structures thus obtained, and methods to characterize the nanoscale array structures suitable for surface enhanced Raman scattering. Nanoscale array structures may comprise nanotrees, nanorecesses and tapered nanopillars.
Bond, Tiziana C; Miles, Robin; Davidson, James; Liu, Gang Logan
2015-11-03
Methods for fabricating nanoscale array structures suitable for surface enhanced Raman scattering, structures thus obtained, and methods to characterize the nanoscale array structures suitable for surface enhanced Raman scattering. Nanoscale array structures may comprise nanotrees, nanorecesses and tapered nanopillars.
Bond, Tiziana C.; Miles, Robin; Davidson, James C.; Liu, Gang Logan
2015-07-14
Methods for fabricating nanoscale array structures suitable for surface enhanced Raman scattering, structures thus obtained, and methods to characterize the nanoscale array structures suitable for surface enhanced Raman scattering. Nanoscale array structures may comprise nanotrees, nanorecesses and tapered nanopillars.
International Nuclear Information System (INIS)
Mery, P.
1977-01-01
The operator and matrix Pade approximation are defined. The fact that these approximants can be derived from the Schwinger variational principle is emphasized. In potential theory, using this variational aspect it is shown that the matrix Pade approximation allow to reproduce the exact solution of the Lippman-Schwinger equation with any required accuracy taking only into account the knowledge of the first two coefficients in the Born expansion. The deep analytic structure of this variational matrix Pade approximation (hyper Pade approximation) is discussed
The time-dependent density matrix renormalisation group method
Ma, Haibo; Luo, Zhen; Yao, Yao
2018-04-01
Substantial progress of the time-dependent density matrix renormalisation group (t-DMRG) method in the recent 15 years is reviewed in this paper. By integrating the time evolution with the sweep procedures in density matrix renormalisation group (DMRG), t-DMRG provides an efficient tool for real-time simulations of the quantum dynamics for one-dimensional (1D) or quasi-1D strongly correlated systems with a large number of degrees of freedom. In the illustrative applications, the t-DMRG approach is applied to investigate the nonadiabatic processes in realistic chemical systems, including exciton dissociation and triplet fission in polymers and molecular aggregates as well as internal conversion in pyrazine molecule.
Modelling of packet traffic with matrix analytic methods
DEFF Research Database (Denmark)
Andersen, Allan T.
1995-01-01
BISDN network. The heuristic formula did not seem to yield substantially better results than already available approximations. Finally, some results for the finite capacity BMAP/G/1 queue have been obtained. The steady state probability vector of the embedded chain is found by a direct method where...... process. A heuristic formula for the tail behaviour of a single server queue fed by a superposition of renewal processes has been evaluated. The evaluation was performed by applying Matrix Analytic methods. The heuristic formula has applications in the Call Admission Control (CAC) procedure of the future...
A transfer-matrix method for spatially modulated structures
International Nuclear Information System (INIS)
Surda, A.
1991-03-01
A cluster transfer-matrix method convenient for calculation of spatially modulated structures of a wide class of lattice-gas models is developed. The method formulates the problem of calculation of the partition function in terms of non-linear mapping of effective multi-site fields. It is applied to a lattice-gas model qualitatively describing the system of oxygen atoms in the basal planes of high-temperature superconductors. The properties of an incommensurate structure occurring at intermediate temperatures are discussed in detail. (author). 21 refs, 15 figs
Exact solution of some linear matrix equations using algebraic methods
Djaferis, T. E.; Mitter, S. K.
1977-01-01
A study is done of solution methods for Linear Matrix Equations including Lyapunov's equation, using methods of modern algebra. The emphasis is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The action f sub BA is introduced a Basic Lemma is proven. The equation PA + BP = -C as well as the Lyapunov equation are analyzed. Algorithms are given for the solution of the Lyapunov and comment is given on its arithmetic complexity. The equation P - A'PA = Q is studied and numerical examples are given.
Photonic band structures solved by a plane-wave-based transfer-matrix method.
Li, Zhi-Yuan; Lin, Lan-Lan
2003-04-01
Transfer-matrix methods adopting a plane-wave basis have been routinely used to calculate the scattering of electromagnetic waves by general multilayer gratings and photonic crystal slabs. In this paper we show that this technique, when combined with Bloch's theorem, can be extended to solve the photonic band structure for 2D and 3D photonic crystal structures. Three different eigensolution schemes to solve the traditional band diagrams along high-symmetry lines in the first Brillouin zone of the crystal are discussed. Optimal rules for the Fourier expansion over the dielectric function and electromagnetic fields with discontinuities occurring at the boundary of different material domains have been employed to accelerate the convergence of numerical computation. Application of this method to an important class of 3D layer-by-layer photonic crystals reveals the superior convergency of this different approach over the conventional plane-wave expansion method.
Photonic band structures solved by a plane-wave-based transfer-matrix method
International Nuclear Information System (INIS)
Li Zhiyuan; Lin Lanlan
2003-01-01
Transfer-matrix methods adopting a plane-wave basis have been routinely used to calculate the scattering of electromagnetic waves by general multilayer gratings and photonic crystal slabs. In this paper we show that this technique, when combined with Bloch's theorem, can be extended to solve the photonic band structure for 2D and 3D photonic crystal structures. Three different eigensolution schemes to solve the traditional band diagrams along high-symmetry lines in the first Brillouin zone of the crystal are discussed. Optimal rules for the Fourier expansion over the dielectric function and electromagnetic fields with discontinuities occurring at the boundary of different material domains have been employed to accelerate the convergence of numerical computation. Application of this method to an important class of 3D layer-by-layer photonic crystals reveals the superior convergency of this different approach over the conventional plane-wave expansion method
Radon movement simulation in overburden by the 'Scattered Packet Method'
International Nuclear Information System (INIS)
Marah, H.; Sabir, A.; Hlou, L.; Tayebi, M.
1998-01-01
The analysis of Radon ( 222 Rn) movement in overburden needs the resolution of the General Equation of Transport in porous medium, involving diffusion and convection. Generally this equation was derived and solved analytically. The 'Scattered Packed Method' is a recent mathematical method of resolution, initially developed for the electrons movements in the semiconductors studies. In this paper, we have adapted this method to simulate radon emanation in porous medium. The keys parameters are the radon concentration at the source, the diffusion coefficient, and the geometry. To show the efficiency of this method, several cases of increasing complexity are considered. This model allows to follow the migration, in the time and space, of radon produced as a function of the characteristics of the studied site. Forty soil radon measurements were taken from a North Moroccan fault. Forward modeling of the radon anomalies produces satisfactory fits of the observed data and allows the overburden thickness determination. (author)
The Green Function cellular method and its relation to multiple scattering theory
International Nuclear Information System (INIS)
Butler, W.H.; Zhang, X.G.; Gonis, A.
1992-01-01
This paper investigates techniques for solving the wave equation which are based on the idea of obtaining exact local solutions within each potential cell, which are then joined to form a global solution. The authors derive full potential multiple scattering theory (MST) from the Lippmann-Schwinger equation and show that it as well as a closely related cellular method are techniques of this type. This cellular method appears to have all of the advantages of MST and the added advantage of having a secular matrix with only nearest neighbor interactions. Since this cellular method is easily linearized one can rigorously reduce electronic structure calculation to the problem of solving a nearest neighbor tight-binding problem
Sensitivity of the elastic scattering matrix elements to the range of the inelastic potentials
International Nuclear Information System (INIS)
Rawitscher, G.H.; Rasoanaivo, R.Y.
1983-01-01
The solution to a system of coupled equations is examined with regard to the effect of the long range part of the inelastic potentials upon the elastic phase shifts. It is found that those parts of the inelastic potentials which occur beyond the range of the elastic to inelastic transition potentials affect the elastic phase shifts in only a minor way. The proof is given theoretically by means of a Green's function formulation which includes the long range part of the inelastic potentials perturbatively. When applied to the calculation of the effect of breakup on the deuteron-nucleus elastic scattering, the argument confirms the finding that errors in the long range part of the potentials in the breakup channels do not sensitively affect the elastic deuteron scattering cross section. This result explains why the elastic scattering is not very sensitive to the choice of the discretization procedure of the breakup space
Stoykov, S.; Atanassov, E.; Margenov, S.
2016-10-01
Many of the scientific applications involve sparse or dense matrix operations, such as solving linear systems, matrix-matrix products, eigensolvers, etc. In what concerns structural nonlinear dynamics, the computations of periodic responses and the determination of stability of the solution are of primary interest. Shooting method iswidely used for obtaining periodic responses of nonlinear systems. The method involves simultaneously operations with sparse and dense matrices. One of the computationally expensive operations in the method is multiplication of sparse by dense matrices. In the current work, a new algorithm for sparse matrix by dense matrix products is presented. The algorithm takes into account the structure of the sparse matrix, which is obtained by space discretization of the nonlinear Mindlin's plate equation of motion by the finite element method. The algorithm is developed to use the vector engine of Intel Xeon Phi coprocessors. It is compared with the standard sparse matrix by dense matrix algorithm and the one developed by Intel MKL and it is shown that by considering the properties of the sparse matrix better algorithms can be developed.
Near specular scatter analysis method with a new goniophotometer
Meyen, Stephanie; Sutter, Florian; Heller, Peter
2014-09-01
The challenge of improving component quality and reducing cost has focused the attention of the solar thermal power industry on reliable component characterization methods. Since the reflector plays a key role in the energy conversion chain, the analysis of its reflectance properties has become a lively discussed issue in recent years. State of the art measurement instruments for specular reflectance do not give satisfying results, because they do not resolve sufficiently the near specular scatter of possible low cost mirror material candidates. The measurement of the BRDF offers a better solution than the traditional approach of placing a detector in the specular reflected beam path. However, due to the requirement of high angular resolution in the range of 1 mrad (0.057°) or better and the challenge of measuring high dynamic differences between the specular peak and the scatter signal, typical commercial scanning goniophotometers capable of this are rare. These instruments also face the disadvantages of impractically long acquisition times and, to reach the high angular resolution, occupy a large space (several meters side length). We have taken on the appealing idea of a parallel imaging goniophotometer and designed a prototype based on this principle. A mirrored ellipsoid is used to redirect the reflected light coming from a sample towards a camera with a fisheye lens. This way the complete light distribution is captured simultaneously. A key feature allows the distinction of the high intensity specular peak and the low intensity scatter. In this article we explain the prototype design and demonstrate its functionality based on comparison measurements done with a commercial scanning goniophotometer. We identify limitations related in part to the concept and in part to the specific prototype and suggest improvements. Finally we conclude that the concept is well suitable for the analysis of near specular scatter of mirror materials, although less adequate for
International Nuclear Information System (INIS)
He, Cenlin; Takano, Yoshi; Liou, Kuo-Nan; Yang, Ping; Li, Qinbin; Mackowski, Daniel W.
2016-01-01
We perform a comprehensive intercomparison of the geometric-optics surface-wave (GOS) approach, the superposition T-matrix method, and laboratory measurements for optical properties of fresh and coated/aged black carbon (BC) particles with complex structures. GOS and T-matrix calculations capture the measured optical (i.e., extinction, absorption, and scattering) cross sections of fresh BC aggregates, with 5–20% differences depending on particle size. We find that the T-matrix results tend to be lower than the measurements, due to uncertainty in theoretical approximations of realistic BC structures, particle property measurements, and numerical computations in the method. On the contrary, the GOS results are higher than the measurements (hence the T-matrix results) for BC radii 100 nm. We find good agreement (differences 100 nm. We find small deviations (≤10%) in asymmetry factors computed from the two methods for most BC coating structures and sizes, but several complex structures have 10–30% differences. This study provides the foundation for downstream application of the GOS approach in radiative transfer and climate studies. - Highlights: • The GOS and T-matrix methods capture laboratory measurements of BC optical properties. • The GOS results are consistent with the T-matrix results for BC optical properties. • BC optical properties vary remarkably with coating structures and sizes during aging.
On the use of transition matrix methods with extended ensembles.
Escobedo, Fernando A; Abreu, Charlles R A
2006-03-14
Different extended ensemble schemes for non-Boltzmann sampling (NBS) of a selected reaction coordinate lambda were formulated so that they employ (i) "variable" sampling window schemes (that include the "successive umbrella sampling" method) to comprehensibly explore the lambda domain and (ii) transition matrix methods to iteratively obtain the underlying free-energy eta landscape (or "importance" weights) associated with lambda. The connection between "acceptance ratio" and transition matrix methods was first established to form the basis of the approach for estimating eta(lambda). The validity and performance of the different NBS schemes were then assessed using as lambda coordinate the configurational energy of the Lennard-Jones fluid. For the cases studied, it was found that the convergence rate in the estimation of eta is little affected by the use of data from high-order transitions, while it is noticeably improved by the use of a broader window of sampling in the variable window methods. Finally, it is shown how an "elastic" window of sampling can be used to effectively enact (nonuniform) preferential sampling over the lambda domain, and how to stitch the weights from separate one-dimensional NBS runs to produce a eta surface over a two-dimensional domain.
Proton optical potential and scattering matrix for tin nuclei at sub-coulomb energies
International Nuclear Information System (INIS)
Guzhovskij, B.Ya.; Dzyuba, B.M.
1981-01-01
A unified set of parameters of the proton optical potential (OP) for the n nuclei is searched for in the below-Coulomb-barrier energy range. The set must describe well the experimental data on the pn-reaction total cross sections and on the angular distributions of elastically scattered protons at E [ru
The structure of alkali silicate gel by total scattering methods
Benmore, C.J.
2010-06-01
The structure of the alkali silicate gel (ASR) collected from the galleries of Furnas Dam in Brazil was determined by a pair distribution function (PDF) analysis of high energy X-ray diffraction data. Since this method is relatively new to concrete structure analysis a detailed introduction on the PDF method is given for glassy SiO2. The bulk amorphous structure of the dam material is confirmed as no Bragg peaks are observed in the scattered intensity. The real space results show that the local structure of the amorphous material is similar to kanemite (KHSi2O5:3H2O) however the long range layer structure of the crystal is broken up in the amorphous state, so that ordering only persists of the length scale of a few polyhedra. The silicate layer structure is a much more disordered than predicted by molecular dynamics models. The X-ray results are consistent with the molecular dynamics model of Kirkpatrick et al. (2005) [1] which predicts that most of the water resides in pores within the amorphous network rather than in layers. The total scattering data provide a rigorous basis against which other models may also be tested. © 2010.
The structure of alkali silicate gel by total scattering methods
Benmore, C.J.; Monteiro, Paulo J.M.
2010-01-01
The structure of the alkali silicate gel (ASR) collected from the galleries of Furnas Dam in Brazil was determined by a pair distribution function (PDF) analysis of high energy X-ray diffraction data. Since this method is relatively new to concrete structure analysis a detailed introduction on the PDF method is given for glassy SiO2. The bulk amorphous structure of the dam material is confirmed as no Bragg peaks are observed in the scattered intensity. The real space results show that the local structure of the amorphous material is similar to kanemite (KHSi2O5:3H2O) however the long range layer structure of the crystal is broken up in the amorphous state, so that ordering only persists of the length scale of a few polyhedra. The silicate layer structure is a much more disordered than predicted by molecular dynamics models. The X-ray results are consistent with the molecular dynamics model of Kirkpatrick et al. (2005) [1] which predicts that most of the water resides in pores within the amorphous network rather than in layers. The total scattering data provide a rigorous basis against which other models may also be tested. © 2010.
FAIR-DDX, Double Diffusion Cross-Sections Scattering Matrix Generated from ENDF/B-4 or JENDL-2
International Nuclear Information System (INIS)
Minami, Kazuyoshi; Yamano, Naoki
2001-01-01
1 - Description of program or function: FAIR-DDX produces double differential (energy and angle) cross sections (DDX) in the form of group-to-group scattering matrices using the evaluated nuclear data libraries JENDL-2 or ENDF/B-IV. The DDX form is useful for verification of the evaluated data, such as the inelastic scattering, through comparison with the experimental DDX values. 2 - Method of solution: DDX uses the file 4 data (angular distribution of secondary neutrons) and the energy and momentum conservation laws. For continuum region reactions, file 5 (energy spectrum of secondary neutrons) is used. To express the angular distribution of secondary neutrons in group-to-group scattering matrices FAIR-DDX adopts a direct angular representation method. 3 - Restrictions on the complexity of the problem: The maximum number of energy groups is 200
International Nuclear Information System (INIS)
Kumar, V.; Sahni, D.C.
1983-01-01
In this paper, the authors present the mathematical techniques that were developed for solving the integral transport equation for the criticality of a homogeneous cylinder of finite height with general anisotropic scattering. They present the integral transport equations for the Fourier transformed spherical harmonic moments of the angular flux. These moments are also represented by a series of products of spherical Bessel functions. The criticality problem is, then, posed by the matrix eigenvalue problem whose eigenvector is composed of the expansion coefficients mentioned above. An methodology of calculating the general matrix element is discussed by using the recursion relations derived in this paper. Finally, for the one-group criticality of finite cylinders, the benchmark results are generated when scattering is linearly anisotropic. Also, these benchmarks are solved and compared with the S/sub N/ method of TWOTRAN
DEFF Research Database (Denmark)
Wagner, Stephan; Legros, Samuel; Löschner, Katrin
2015-01-01
content by asymmetric flow-field flow fractionation coupled to a multi-angle light scattering detector and an inductively coupled plasma mass spectrometer. Following the proposed generic procedure SiO2-ENPs were separated from a tomato soup. Two potential sample preparation methods were tested these being...... quality criteria for method development is urgently needed for standardized and systematic development of procedures for separation of ENPs from a complex matrix. The chosen analytical technique was shown to be suitable for detecting SiO2-ENPs in a complex food matrix like tomato soup and may therefore...
DANTE, Activation Analysis Neutron Spectra Unfolding by Covariance Matrix Method
International Nuclear Information System (INIS)
Petilli, M.
1981-01-01
1 - Description of problem or function: The program evaluates activation measurements of reactor neutron spectra and unfolds the results for dosimetry purposes. Different evaluation options are foreseen: absolute or relative fluxes and different iteration algorithms. 2 - Method of solution: A least-square fit method is used. A correlation between available data and their uncertainties has been introduced by means of flux and activity variance-covariance matrices. Cross sections are assumed to be constant, i.e. with variance-covariance matrix equal to zero. The Lagrange multipliers method has been used for calculating the solution. 3 - Restrictions on the complexity of the problem: 9 activation experiments can be analyzed. 75 energy groups are accepted
Simplified solutions of the Cox-Thompson inverse scattering method at fixed energy
International Nuclear Information System (INIS)
Palmai, Tamas; Apagyi, Barnabas; Horvath, Miklos
2008-01-01
Simplified solutions of the Cox-Thompson inverse quantum scattering method at fixed energy are derived if a finite number of partial waves with only even or odd angular momenta contribute to the scattering process. Based on new formulae various approximate methods are introduced which also prove applicable to the generic scattering events
Campagnola, Paul J.; Tilbury, Karissa B.; Campbell, Kirby R.; Eliceiri, Kevin W.; Patankar, Manish
2017-02-01
Ovarian cancer remains the most deadly gynecological cancer with a poor aggregate survival rate. To improve upon this situation, we utilized collagen-specific Second Harmonic Generation (SHG) imaging microscopy and optical scattering measurements to probe structural differences in the extracellular matrix of normal stroma, benign tumors, endometrioid tumors, and low and high-grade serous (LGS and HGS) tumors. The SHG signatures of the emission directionality and conversion efficiency as well as the optical scattering are related to the organization of collagen on the sub-micron size. The wavelength dependence of these readouts adds additional characterization of the size and distribution of collagen fibrils/fibers relative to the interrogating wavelengths. We found strong wavelength dependent dependencies of these metrics that were different between the different tumors that are related to respective structural attributes in the collagen organization. These sub-resolution determinations are consistent with the dualistic classification of type I and II serous tumors. However, type I endometrioid tumors have strongly differing ECM architecture than the serous malignancies. Moreover, our analyses are further consistent with LGS and benign tumors having similar etiology. We identified optimal wavelengths for the SHG metrics as well as optical scattering measurements. The SHG metrics and optical scattering measurements were then used to form a linear discriminant model to classify the tissues, and we obtained high accuracy ( 90%) between the tissue types. This delineation is superior to current clinical performance and has potential applicability in supplementing histological analysis, understanding the etiology, as well as development of an in vivo screening tool.
Character expansion methods for matrix models of dually weighted graphs
International Nuclear Information System (INIS)
Kazakov, V.A.; Staudacher, M.; Wynter, T.
1996-01-01
We consider generalized one-matrix models in which external fields allow control over the coordination numbers on both the original and dual lattices. We rederive in a simple fashion a character expansion formula for these models originally due to Itzykson and Di Francesco, and then demonstrate how to take the large N limit of this expansion. The relationship to the usual matrix model resolvent is elucidated. Our methods give as a by-product an extremely simple derivation of the Migdal integral equation describing the large N limit of the Itzykson-Zuber formula. We illustrate and check our methods by analysing a number of models solvable by traditional means. We then proceed to solve a new model: a sum over planar graphs possessing even coordination numbers on both the original and the dual lattice. We conclude by formulating equations for the case of arbitrary sets of even, self-dual coupling constants. This opens the way for studying the deep problem of phase transitions from random to flat lattices. (orig.). With 4 figs
POLLA-NESC, Resonance Parameter R-Matrix to S-Matrix Conversion by Reich-Moore Method
International Nuclear Information System (INIS)
Saussure, G. de; Perez, R.B.
1975-01-01
1 - Description of problem or function: The program transforms a set of r-matrix nuclear resonance parameters into a set of equivalent s-matrix (or Kapur-Peierls) resonance parameters. 2 - Method of solution: The program utilizes the multilevel formalism of Reich and Moore and avoids diagonalization of the level matrix. The parameters are obtained by a direct partial fraction expansion of the Reich-Moore expression of the collision matrix. This approach appears simpler and faster when the number of fission channels is known and small. The method is particularly useful when a large number of levels must be considered because it does not require diagonalization of a large level matrix. 3 - Restrictions on the complexity of the problem: By DIMENSION statements, the program is limited to maxima of 100 levels and 5 channels
Improved parallel solution techniques for the integral transport matrix method
Energy Technology Data Exchange (ETDEWEB)
Zerr, R. Joseph, E-mail: rjz116@psu.edu [Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, PA (United States); Azmy, Yousry Y., E-mail: yyazmy@ncsu.edu [Department of Nuclear Engineering, North Carolina State University, Burlington Engineering Laboratories, Raleigh, NC (United States)
2011-07-01
Alternative solution strategies to the parallel block Jacobi (PBJ) method for the solution of the global problem with the integral transport matrix method operators have been designed and tested. The most straightforward improvement to the Jacobi iterative method is the Gauss-Seidel alternative. The parallel red-black Gauss-Seidel (PGS) algorithm can improve on the number of iterations and reduce work per iteration by applying an alternating red-black color-set to the subdomains and assigning multiple sub-domains per processor. A parallel GMRES(m) method was implemented as an alternative to stationary iterations. Computational results show that the PGS method can improve on the PBJ method execution time by up to 10´ when eight sub-domains per processor are used. However, compared to traditional source iterations with diffusion synthetic acceleration, it is still approximately an order of magnitude slower. The best-performing cases are optically thick because sub-domains decouple, yielding faster convergence. Further tests revealed that 64 sub-domains per processor was the best performing level of sub-domain division. An acceleration technique that improves the convergence rate would greatly improve the ITMM. The GMRES(m) method with a diagonal block pre conditioner consumes approximately the same time as the PBJ solver but could be improved by an as yet undeveloped, more efficient pre conditioner. (author)
Improved parallel solution techniques for the integral transport matrix method
International Nuclear Information System (INIS)
Zerr, R. Joseph; Azmy, Yousry Y.
2011-01-01
Alternative solution strategies to the parallel block Jacobi (PBJ) method for the solution of the global problem with the integral transport matrix method operators have been designed and tested. The most straightforward improvement to the Jacobi iterative method is the Gauss-Seidel alternative. The parallel red-black Gauss-Seidel (PGS) algorithm can improve on the number of iterations and reduce work per iteration by applying an alternating red-black color-set to the subdomains and assigning multiple sub-domains per processor. A parallel GMRES(m) method was implemented as an alternative to stationary iterations. Computational results show that the PGS method can improve on the PBJ method execution time by up to 10´ when eight sub-domains per processor are used. However, compared to traditional source iterations with diffusion synthetic acceleration, it is still approximately an order of magnitude slower. The best-performing cases are optically thick because sub-domains decouple, yielding faster convergence. Further tests revealed that 64 sub-domains per processor was the best performing level of sub-domain division. An acceleration technique that improves the convergence rate would greatly improve the ITMM. The GMRES(m) method with a diagonal block pre conditioner consumes approximately the same time as the PBJ solver but could be improved by an as yet undeveloped, more efficient pre conditioner. (author)
Empirical method for matrix effects correction in liquid samples
International Nuclear Information System (INIS)
Vigoda de Leyt, Dora; Vazquez, Cristina
1987-01-01
A simple method for the determination of Cr, Ni and Mo in stainless steels is presented. In order to minimize the matrix effects, the conditions of liquid system to dissolve stainless steels chips has been developed. Pure element solutions were used as standards. Preparation of synthetic solutions with all the elements of steel and also mathematic corrections are avoided. It results in a simple chemical operation which simplifies the method of analysis. The variance analysis of the results obtained with steel samples show that the three elements may be determined from the comparison with the analytical curves obtained with the pure elements if the same parameters in the calibration curves are used. The accuracy and the precision were checked against other techniques using the British Chemical Standards of the Bureau of Anlysed Samples Ltd. (England). (M.E.L.) [es
Matrix transformation relation for the radial integrals of lepton scattering processes
International Nuclear Information System (INIS)
Sud, K.K.; Soto Vargas, C.W.; Sharma, D.K.
1988-01-01
The radial integrals of many physical problems involving products of initial- and final-state wave functions and the Coulomb interaction are expressible in terms of special cases of generalized hypergeometric functions. In the present work, the generalized hypergeometric functions become elements of a gamma vector which, by means of a partial differential equation and a matrix transformation relation, can be used in calculating the gamma vector in physical regions where the hypergeometric functions are nonconvergent or very slowly converging. Our matrix transformation relation contains the special cases of Gauss' hypergeometric functions 2 F 1 , Appell's hypergeometric functions F 2 , and Lauricella's functions L F transformation relations. The use of contiguous relations along with the transformation relations presented in this paper will facilitate the calculation of physical processes involving such radial integrals
Aspects of fabrication aluminium matrix heterophase composites by suspension method
Dolata, A. J.; Dyzia, M.
2012-05-01
Composites with an aluminium alloy matrix (AlMMC) exhibit several advantageous properties such as good strength, stiffness, low density, resistance and dimensional stability to elevated temperatures, good thermal expansion coefficient and particularly high resistance to friction wear. Therefore such composites are more and more used in modern engineering constructions. Composites reinforced with hard ceramic particles (Al2O3, SiC) are gradually being implemented into production in automotive or aircraft industries. Another application of AlMMC is in the electronics industry, where the dimensional stability and capacity to absorb and remove heat is used in radiators. However the main problems are still: a reduction of production costs, developing methods of composite material tests and final product quality assessment, standardisation, development of recycling and mechanical processing methods. AlMMC production technologies, based on liquid-phase methods, and the shaping of products by casting methods, belong to the cheapest production methods. Application of a suspension method for the production of composites with heterophase reinforcement may turn out to be a new material and technological solution. The article presents the material and technological aspects of the transfer procedures for the production of composite suspensions from laboratory scale to a semi-industrial scale.
Aspects of fabrication aluminium matrix heterophase composites by suspension method
International Nuclear Information System (INIS)
Dolata, A J; Dyzia, M
2012-01-01
Composites with an aluminium alloy matrix (AlMMC) exhibit several advantageous properties such as good strength, stiffness, low density, resistance and dimensional stability to elevated temperatures, good thermal expansion coefficient and particularly high resistance to friction wear. Therefore such composites are more and more used in modern engineering constructions. Composites reinforced with hard ceramic particles (Al 2 O 3 , SiC) are gradually being implemented into production in automotive or aircraft industries. Another application of AlMMC is in the electronics industry, where the dimensional stability and capacity to absorb and remove heat is used in radiators. However the main problems are still: a reduction of production costs, developing methods of composite material tests and final product quality assessment, standardisation, development of recycling and mechanical processing methods. AlMMC production technologies, based on liquid-phase methods, and the shaping of products by casting methods, belong to the cheapest production methods. Application of a suspension method for the production of composites with heterophase reinforcement may turn out to be a new material and technological solution. The article presents the material and technological aspects of the transfer procedures for the production of composite suspensions from laboratory scale to a semi-industrial scale.
Teaching Improvement Model Designed with DEA Method and Management Matrix
Montoneri, Bernard
2014-01-01
This study uses student evaluation of teachers to design a teaching improvement matrix based on teaching efficiency and performance by combining management matrix and data envelopment analysis. This matrix is designed to formulate suggestions to improve teaching. The research sample consists of 42 classes of freshmen following a course of English…
Response matrix method for neutron transport in reactor lattices using group symmetry properties
International Nuclear Information System (INIS)
Mund, E.H.
1991-01-01
This paper describes a response matrix method for the approximate solution of one-velocity, multi-dimensional transport problems in reactor lattices, with isotropic neutron scattering. The transport equation is solved on a homogeneous cell by using a Petrov-Galerkin technique based on a set of trial and test functions (including polynomials and exponential functions) closely related to transport problems in infinite media. The number of non-zero elements of the response matrices reduces to a minimum when the symmetry properties of the cell are included ab initio in the span of the basis functions. To include these properties, use is made of projection operations which are performed very efficiently on symbolic manipulation programs. Numerical results of model problems in square geometry show a good agreement with reference solutions
Vibration analysis of pipes conveying fluid by transfer matrix method
International Nuclear Information System (INIS)
Li, Shuai-jun; Liu, Gong-min; Kong, Wei-tao
2014-01-01
Highlights: • A theoretical study on vibration analysis of pipes with FSI is presented. • Pipelines with high fluid pressure and velocity can be solved by developed method. • Several pipeline schemes are discussed to illustrate the application of the method. • The proposed method is easier to apply compared to most existing procedures. • Influence laws of structural and fluid parameters on FSI of pipe are analyzed. -- Abstract: Considering the effects of pipe wall thickness, fluid pressure and velocity, a developed 14-equation model is presented, which describes the fluid–structure interaction behavior of pipelines. The transfer matrix method has been used for numerical modeling of both hydraulic and structural equations. Based on these models and algorithms, several pipeline schemes are presented to illustrate the application of the proposed method. Furthermore, the influence laws of supports, structural properties and fluid parameters on the dynamic response and natural frequencies of pipeline are analyzed, which shows using the optimal supports and structural properties is beneficial to reduce vibration of pipelines
Comparison of matrix exponential methods for fuel burnup calculations
International Nuclear Information System (INIS)
Oh, Hyung Suk; Yang, Won Sik
1999-01-01
Series expansion methods to compute the exponential of a matrix have been compared by applying them to fuel depletion calculations. Specifically, Taylor, Pade, Chebyshev, and rational Chebyshev approximations have been investigated by approximating the exponentials of bum matrices by truncated series of each method with the scaling and squaring algorithm. The accuracy and efficiency of these methods have been tested by performing various numerical tests using one thermal reactor and two fast reactor depletion problems. The results indicate that all the four series methods are accurate enough to be used for fuel depletion calculations although the rational Chebyshev approximation is relatively less accurate. They also show that the rational approximations are more efficient than the polynomial approximations. Considering the computational accuracy and efficiency, the Pade approximation appears to be better than the other methods. Its accuracy is better than the rational Chebyshev approximation, while being comparable to the polynomial approximations. On the other hand, its efficiency is better than the polynomial approximations and is similar to the rational Chebyshev approximation. In particular, for fast reactor depletion calculations, it is faster than the polynomial approximations by a factor of ∼ 1.7. (author). 11 refs., 4 figs., 2 tabs
An inter-crystal scatter correction method for DOI PET image reconstruction
International Nuclear Information System (INIS)
Lam, Chih Fung; Hagiwara, Naoki; Obi, Takashi; Yamaguchi, Masahiro; Yamaya, Taiga; Murayama, Hideo
2006-01-01
New positron emission tomography (PET) scanners utilize depth-of-interaction (DOI) information to improve image resolution, particularly at the edge of field-of-view while maintaining high detector sensitivity. However, the inter-crystal scatter (ICS) effect cannot be neglected in DOI scanners due to the use of smaller crystals. ICS is the phenomenon wherein there are multiple scintillations for irradiation of a gamma photon due to Compton scatter in detecting crystals. In the case of ICS, only one scintillation position is approximated for detectors with Anger-type logic calculation. This causes an error in position detection and ICS worsens the image contrast, particularly for smaller hotspots. In this study, we propose to model an ICS probability by using a Monte Carlo simulator. The probability is given as a statistical relationship between the gamma photon first interaction crystal pair and the detected crystal pair. It is then used to improve the system matrix of a statistical image reconstruction algorithm, such as maximum likehood expectation maximization (ML-EM) in order to correct for the position error caused by ICS. We apply the proposed method to simulated data of the jPET-D4, which is a four-layer DOI PET being developed at the National Institute of Radiological Sciences. Our computer simulations show that image contrast is recovered successfully by the proposed method. (author)
Directory of Open Access Journals (Sweden)
Li Mianquan
2016-04-01
Full Text Available The polarization feature of a fully Polarimetric Phased-Array Radar (PPAR antenna varies according to the beam-scanning angle, thereby introducing two problems on the target Polarization Scattering Matrix (PSM measurement. First, the antenna polarization basis is defined within the vertical cross-section of an electromagnetic wave propagation direction, and the polarization basis of each beam direction angle is not identical, resulting in the PSM of a fixed-posture target observed by PPAR being not identical for different beam-scanning angles. Second, the cross polarization of the PPAR antenna increases with increasing beamscanning angle, resulting in a crosstalk among the elements of PSM observed by PPAR. This study focuses on the analysis of the abovementioned two aspects of the effect of beam scanning on target PSM observed by PPAR. The results will establish a more accurate observation of the equation for the precision PSM measurement of PPAR.
Practical methods to define scattering coefficients in a room acoustics computer model
DEFF Research Database (Denmark)
Zeng, Xiangyang; Christensen, Claus Lynge; Rindel, Jens Holger
2006-01-01
of obtaining the data becomes quite time consuming thus increasing the cost of design. In this paper, practical methods to define scattering coefficients, which is based on an approach of modeling surface scattering and scattering caused by limited size of surface as well as edge diffraction are presented...
New method for imaging epicardial motion with scattered radiation
International Nuclear Information System (INIS)
Tilley, D.G.
1976-01-01
A new method for monitoring cardiac motion is described which employs the secondary radiation emerging from the thorax during fluoroscopic x-ray examination of the heart. The motion of selected points on the heart's epicardial surface can be investigated by detecting the intensity variations of radiation scattered in the local vicinity of the heart-lung border. Also discussed are the radiation detectors and signal processing electronics used to produce a voltage analog depicting the periodic displacements of the heart surface. Digital data processing methods are described which are used to accomplish a transformation from a time scale for representing surface motion, to a frequency scale that is better suited for the quantitative analysis of the heart's myocardial dynamics. The dynamic radiographic technique is compared to other methods such as electrocardiography, phonocardiography, radarkymography, and echocardiography; which are also used to sense the dynamic state of the heart. A three-dimensional Monte Carlo computer code is used to investigate the transport of x-radiation in the canine thorax. The Monte Carlo computer studies are used to explore the capabilities and limitations of the dynamic radiograph as it is used to sense motions of the canine heart. Animal studies were conducted with the dynamic radiograph to determine the reproducibility of the examination procedure. Canine case studies are reported showing the effects of increased myocardial contractility resulting from intervention with these inotropic agents
Methods for converging correlation energies within the dielectric matrix formalism
Dixit, Anant; Claudot, Julien; Gould, Tim; Lebègue, Sébastien; Rocca, Dario
2018-03-01
Within the dielectric matrix formalism, the random-phase approximation (RPA) and analogous methods that include exchange effects are promising approaches to overcome some of the limitations of traditional density functional theory approximations. The RPA-type methods however have a significantly higher computational cost, and, similarly to correlated quantum-chemical methods, are characterized by a slow basis set convergence. In this work we analyzed two different schemes to converge the correlation energy, one based on a more traditional complete basis set extrapolation and one that converges energy differences by accounting for the size-consistency property. These two approaches have been systematically tested on the A24 test set, for six points on the potential-energy surface of the methane-formaldehyde complex, and for reaction energies involving the breaking and formation of covalent bonds. While both methods converge to similar results at similar rates, the computation of size-consistent energy differences has the advantage of not relying on the choice of a specific extrapolation model.
A new version of transfer matrix method for multibody systems
Energy Technology Data Exchange (ETDEWEB)
Rui, Xiaoting, E-mail: ruixt@163.net [Nanjing University of Science and Technology, Institute of Launch Dynamics (China); Bestle, Dieter, E-mail: bestle@b-tu.de [Brandenburg University of Technology, Engineering Mechanics and Vehicle Dynamics (Germany); Zhang, Jianshu, E-mail: zhangdracpa@sina.com; Zhou, Qinbo, E-mail: zqb912-new@163.com [Nanjing University of Science and Technology, Institute of Launch Dynamics (China)
2016-10-15
In order to avoid the global dynamics equations and increase the computational efficiency for multibody system dynamics (MSD), the transfer matrix method of multibody system (MSTMM) has been developed and applied very widely in research and engineering in recent 20 years. It differs from ordinary methods in multibody system dynamics with respect to the feature that there is no need for a global dynamics equation, and it uses low-order matrices for high computational efficiency. For linear systems, MSTMM is exact even if continuous elements like beams are involved. The discrete time MSTMM, however, has to use local linearization. In order to release the method from such approximations, a new version of MSTMM is presented in this paper where translational and angular accelerations, on the one hand, and internal forces and moments, on the other hand, are used as state variables. Already linear relationships among these quantities are utilized, which results in new element transfer matrices and algorithms making the study of multibody systems as simple as the study of single bodies. The proposed approach also allows combining MSTMM with any general numerical integration procedure. Some numerical examples of MSD are given to demonstrate the proposed method.
Study of the multiple scattering effect in TEBENE using the Monte Carlo method
International Nuclear Information System (INIS)
Singkarat, Somsorn.
1990-01-01
The neutron time-of-flight and energy spectra, from the TEBENE set-up, have been calculated by a computer program using the Monte Carlo method. The neutron multiple scattering within the polyethylene scatterer ring is closely investigated. The results show that multiple scattering has a significant effect on the detected neutron yield. They also indicate that the thickness of the scatterer ring has to be carefully chosen. (author)
Polarized micro-Raman scattering characterization of Mg2Si nanolayers in (001) Si matrix
International Nuclear Information System (INIS)
Zlateva, G; Atanassov, A; Baleva, M; Nikolova, L; Abrashev, M V
2007-01-01
An orientational growth of the Mg 2 Si lattice relative to the Si lattice is considered assuming minimum mismatch of their lattice parameters. The Raman scattering cross-sections are calculated for the four possible orientations of the Mg 2 Si lattice positioned in this way. The integral intensity ratios for the F 2g mode of Mg 2 Si in different polarization configurations, obtained from the experimental spectra, are compared with the calculated ratios. It is found that the Mg 2 Si nanolayer's morphology is sensitive to the implantation energy, which determines both the peak Mg concentration in the initial implantation profile and its position in the sample depth. At a peak concentration of the order of the stoichiometric concentration, the layers are highly oriented. When the peak concentration is higher and the peak is placed closer to the surface, the layers are polycrystalline
International Nuclear Information System (INIS)
Bando, H.; Krenciglowa, E.M.
1976-01-01
The role of 2p1h correlations in 17 O is studied within a multiple-scattering formalism. An accurate, energy-dependent reaction matrix with orthogonalized plane-wave intermediate states is used to assess the relative importance of particle-particle and particle-hole correlations in the 17 O energies. The effect of energy dependence of the reaction matrix is closely examined. (Auth.)
International Nuclear Information System (INIS)
Shidahara, Miho; Kato, Takashi; Kawatsu, Shoji; Yoshimura, Kumiko; Ito, Kengo; Watabe, Hiroshi; Kim, Kyeong Min; Iida, Hidehiro; Kato, Rikio
2005-01-01
An image-based scatter correction (IBSC) method was developed to convert scatter-uncorrected into scatter-corrected SPECT images. The purpose of this study was to validate this method by means of phantom simulations and human studies with 99m Tc-labeled tracers, based on comparison with the conventional triple energy window (TEW) method. The IBSC method corrects scatter on the reconstructed image I AC μb with Chang's attenuation correction factor. The scatter component image is estimated by convolving I AC μb with a scatter function followed by multiplication with an image-based scatter fraction function. The IBSC method was evaluated with Monte Carlo simulations and 99m Tc-ethyl cysteinate dimer SPECT human brain perfusion studies obtained from five volunteers. The image counts and contrast of the scatter-corrected images obtained by the IBSC and TEW methods were compared. Using data obtained from the simulations, the image counts and contrast of the scatter-corrected images obtained by the IBSC and TEW methods were found to be nearly identical for both gray and white matter. In human brain images, no significant differences in image contrast were observed between the IBSC and TEW methods. The IBSC method is a simple scatter correction technique feasible for use in clinical routine. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Shidahara, Miho; Kato, Takashi; Kawatsu, Shoji; Yoshimura, Kumiko; Ito, Kengo [National Center for Geriatrics and Gerontology Research Institute, Department of Brain Science and Molecular Imaging, Obu, Aichi (Japan); Watabe, Hiroshi; Kim, Kyeong Min; Iida, Hidehiro [National Cardiovascular Center Research Institute, Department of Investigative Radiology, Suita (Japan); Kato, Rikio [National Center for Geriatrics and Gerontology, Department of Radiology, Obu (Japan)
2005-10-01
An image-based scatter correction (IBSC) method was developed to convert scatter-uncorrected into scatter-corrected SPECT images. The purpose of this study was to validate this method by means of phantom simulations and human studies with {sup 99m}Tc-labeled tracers, based on comparison with the conventional triple energy window (TEW) method. The IBSC method corrects scatter on the reconstructed image I{sub AC}{sup {mu}}{sup b} with Chang's attenuation correction factor. The scatter component image is estimated by convolving I{sub AC}{sup {mu}}{sup b} with a scatter function followed by multiplication with an image-based scatter fraction function. The IBSC method was evaluated with Monte Carlo simulations and {sup 99m}Tc-ethyl cysteinate dimer SPECT human brain perfusion studies obtained from five volunteers. The image counts and contrast of the scatter-corrected images obtained by the IBSC and TEW methods were compared. Using data obtained from the simulations, the image counts and contrast of the scatter-corrected images obtained by the IBSC and TEW methods were found to be nearly identical for both gray and white matter. In human brain images, no significant differences in image contrast were observed between the IBSC and TEW methods. The IBSC method is a simple scatter correction technique feasible for use in clinical routine. (orig.)
Shidahara, Miho; Watabe, Hiroshi; Kim, Kyeong Min; Kato, Takashi; Kawatsu, Shoji; Kato, Rikio; Yoshimura, Kumiko; Iida, Hidehiro; Ito, Kengo
2005-10-01
An image-based scatter correction (IBSC) method was developed to convert scatter-uncorrected into scatter-corrected SPECT images. The purpose of this study was to validate this method by means of phantom simulations and human studies with 99mTc-labeled tracers, based on comparison with the conventional triple energy window (TEW) method. The IBSC method corrects scatter on the reconstructed image I(mub)AC with Chang's attenuation correction factor. The scatter component image is estimated by convolving I(mub)AC with a scatter function followed by multiplication with an image-based scatter fraction function. The IBSC method was evaluated with Monte Carlo simulations and 99mTc-ethyl cysteinate dimer SPECT human brain perfusion studies obtained from five volunteers. The image counts and contrast of the scatter-corrected images obtained by the IBSC and TEW methods were compared. Using data obtained from the simulations, the image counts and contrast of the scatter-corrected images obtained by the IBSC and TEW methods were found to be nearly identical for both gray and white matter. In human brain images, no significant differences in image contrast were observed between the IBSC and TEW methods. The IBSC method is a simple scatter correction technique feasible for use in clinical routine.
Gamma-ray scatter methods applied to industrial measurement systems
Energy Technology Data Exchange (ETDEWEB)
Holstad, Marie Bueie
2004-09-01
Throughout the work presented in this dissertation it has been confirmed that the use of scattered gamma-radiation is a complex but useful tool in industrial measurement science. Scattered radiation has shown to be useful both when traditional measurement principles cannot be used (Chapter 4) and when more information about a system is needed than what is obtained with transmission measurements (Chapter 6). All three main projects (Chapters 4, 5 and 6) confirm that the sensitivity and accuracy of systems based on scattered gamma-radiation depends strongly on the geometry of the setup and that that presence of multiple scattered radiation makes the problems complex. Chapter 4 shows that multiple scattered gamma-radiation can be used for detection of changes in density where the dimensions are too large to use transmitted radiation. There is, however, an upper limit on the thickness of the absorbing medium also when scattered radiation is utilized. As seen in Chapter 5, multiple scattered gamma-radiation can in principle also be used in level gauges with very compact measurement geometries. The main challenges are the sensitivity to interfaces between materials with similar densities and low count rate. These challenges could not be overcome for level measurements in gravitational separator tanks. The results presented in Chapter 6 show that it is feasible to combine transmission and scatter measurements to characterize produced water in the oil and gas industry. (Author)
Methods and apparatus for transparent display using scattering nanoparticles
Hsu, Chia Wei; Qiu, Wenjun; Zhen, Bo; Shapira, Ofer; Soljacic, Marin
2016-05-10
Transparent displays enable many useful applications, including heads-up displays for cars and aircraft as well as displays on eyeglasses and glass windows. Unfortunately, transparent displays made of organic light-emitting diodes are typically expensive and opaque. Heads-up displays often require fixed light sources and have limited viewing angles. And transparent displays that use frequency conversion are typically energy inefficient. Conversely, the present transparent displays operate by scattering visible light from resonant nanoparticles with narrowband scattering cross sections and small absorption cross sections. More specifically, projecting an image onto a transparent screen doped with nanoparticles that selectively scatter light at the image wavelength(s) yields an image on the screen visible to an observer. Because the nanoparticles scatter light at only certain wavelengths, the screen is practically transparent under ambient light. Exemplary transparent scattering displays can be simple, inexpensive, scalable to large sizes, viewable over wide angular ranges, energy efficient, and transparent simultaneously.
Rapid surface enhanced Raman scattering detection method for chloramphenicol residues
Ji, Wei; Yao, Weirong
2015-06-01
Chloramphenicol (CAP) is a widely used amide alcohol antibiotics, which has been banned from using in food producing animals in many countries. In this study, surface enhanced Raman scattering (SERS) coupled with gold colloidal nanoparticles was used for the rapid analysis of CAP. Density functional theory (DFT) calculations were conducted with Gaussian 03 at the B3LYP level using the 3-21G(d) and 6-31G(d) basis sets to analyze the assignment of vibrations. Affirmatively, the theoretical Raman spectrum of CAP was in complete agreement with the experimental spectrum. They both exhibited three strong peaks characteristic of CAP at 1104 cm-1, 1344 cm-1, 1596 cm-1, which were used for rapid qualitative analysis of CAP residues in food samples. The use of SERS as a method for the measurements of CAP was explored by comparing use of different solvents, gold colloidal nanoparticles concentration and absorption time. The method of the detection limit was determined as 0.1 μg/mL using optimum conditions. The Raman peak at 1344 cm-1 was used as the index for quantitative analysis of CAP in food samples, with a linear correlation of R2 = 0.9802. Quantitative analysis of CAP residues in foods revealed that the SERS technique with gold colloidal nanoparticles was sensitive and of a good stability and linear correlation, and suited for rapid analysis of CAP residue in a variety of food samples.
Bhatia, A. K.; Temkin, A.; Fisher, Richard R. (Technical Monitor)
2001-01-01
We report on the first part of a study of electron-hydrogen scattering, using a method which allows for the ab initio calculation of total and elastic cross sections at higher energies. In its general form the method uses complex 'radial' correlation functions, in a (Kohn) T-matrix formalism. The titled method, abbreviated Complex Correlation Kohn T (CCKT) method, is reviewed, in the context of electron-hydrogen scattering, including the derivation of the equation for the (complex) scattering function, and the extraction of the scattering information from the latter. The calculation reported here is restricted to S-waves in the elastic region, where the correlation functions can be taken, without loss of generality, to be real. Phase shifts are calculated using Hylleraas-type correlation functions with up to 95 terms. Results are rigorous lower bounds; they are in general agreement with those of Schwartz, but they are more accurate and outside his error bounds at a couple of energies,
Inverse Scattering Method and Soliton Solution Family for String Effective Action
International Nuclear Information System (INIS)
Ya-Jun, Gao
2009-01-01
A modified Hauser–Ernst-type linear system is established and used to develop an inverse scattering method for solving the motion equations of the string effective action describing the coupled gravity, dilaton and Kalb–Ramond fields. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the proposed inverse scattering method applied fine and effective. As an application, a concrete family of soliton solutions for the considered theory is obtained
On matrix diffusion: formulations, solution methods and qualitative effects
Carrera, Jesús; Sánchez-Vila, Xavier; Benet, Inmaculada; Medina, Agustín; Galarza, Germán; Guimerà, Jordi
Matrix diffusion has become widely recognized as an important transport mechanism. Unfortunately, accounting for matrix diffusion complicates solute-transport simulations. This problem has led to simplified formulations, partly motivated by the solution method. As a result, some confusion has been generated about how to properly pose the problem. One of the objectives of this work is to find some unity among existing formulations and solution methods. In doing so, some asymptotic properties of matrix diffusion are derived. Specifically, early-time behavior (short tests) depends only on φm2RmDm / Lm2, whereas late-time behavior (long tracer tests) depends only on φmRm, and not on matrix diffusion coefficient or block size and shape. The latter is always true for mean arrival time. These properties help in: (a) analyzing the qualitative behavior of matrix diffusion; (b) explaining one paradox of solute transport through fractured rocks (the apparent dependence of porosity on travel time); (c) discriminating between matrix diffusion and other problems (such as kinetic sorption or heterogeneity); and (d) describing identifiability problems and ways to overcome them. RésuméLa diffusion matricielle est un phénomène reconnu maintenant comme un mécanisme de transport important. Malheureusement, la prise en compte de la diffusion matricielle complique la simulation du transport de soluté. Ce problème a conduit à des formulations simplifiées, en partie à cause de la méthode de résolution. Il s'en est suivi une certaine confusion sur la façon de poser correctement le problème. L'un des objectifs de ce travail est de trouver une certaine unité parmi les formulations et les méthodes de résolution. C'est ainsi que certaines propriétés asymptotiques de la diffusion matricielle ont été dérivées. En particulier, le comportement à l'origine (expériences de traçage courtes) dépend uniquement du terme φm2RmDm / Lm2, alors que le comportement à long terme
Reactor calculation in coarse mesh by finite element method applied to matrix response method
International Nuclear Information System (INIS)
Nakata, H.
1982-01-01
The finite element method is applied to the solution of the modified formulation of the matrix-response method aiming to do reactor calculations in coarse mesh. Good results are obtained with a short running time. The method is applicable to problems where the heterogeneity is predominant and to problems of evolution in coarse meshes where the burnup is variable in one same coarse mesh, making the cross section vary spatially with the evolution. (E.G.) [pt
An Efficient Method for Electron-Atom Scattering Using Ab-initio Calculations
Energy Technology Data Exchange (ETDEWEB)
Xu, Yuan; Yang, Yonggang; Xiao, Liantuan; Jia, Suotang [Shanxi University, Taiyuan (China)
2017-02-15
We present an efficient method based on ab-initio calculations to investigate electron-atom scatterings. Those calculations profit from methods implemented in standard quantum chemistry programs. The new approach is applied to electron-helium scattering. The results are compared with experimental and other theoretical references to demonstrate the efficiency of our method.
Bourlier, Christophe; Kubické, Gildas; Déchamps, Nicolas
2008-04-01
A fast, exact numerical method based on the method of moments (MM) is developed to calculate the scattering from an object below a randomly rough surface. Déchamps et al. [J. Opt. Soc. Am. A23, 359 (2006)] have recently developed the PILE (propagation-inside-layer expansion) method for a stack of two one-dimensional rough interfaces separating homogeneous media. From the inversion of the impedance matrix by block (in which two impedance matrices of each interface and two coupling matrices are involved), this method allows one to calculate separately and exactly the multiple-scattering contributions inside the layer in which the inverses of the impedance matrices of each interface are involved. Our purpose here is to apply this method for an object below a rough surface. In addition, to invert a matrix of large size, the forward-backward spectral acceleration (FB-SA) approach of complexity O(N) (N is the number of unknowns on the interface) proposed by Chou and Johnson [Radio Sci.33, 1277 (1998)] is applied. The new method, PILE combined with FB-SA, is tested on perfectly conducting circular and elliptic cylinders located below a dielectric rough interface obeying a Gaussian process with Gaussian and exponential height autocorrelation functions.
A New On-the-Fly Sampling Method for Incoherent Inelastic Thermal Neutron Scattering Data in MCNP6
Energy Technology Data Exchange (ETDEWEB)
Pavlou, Andrew Theodore [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Brown, Forrest B. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Ji, Wei [Rensselaer Polytechnic Inst., Troy, NY (United States)
2014-09-02
At thermal energies, the scattering of neutrons in a system is complicated by the comparable velocities of the neutron and target, resulting in competing upscattering and downscattering events. The neutron wavelength is also similar in size to the target's interatomic spacing making the scattering process a quantum mechanical problem. Because of the complicated nature of scattering at low energies, the thermal data files in ACE format used in continuous-energy Monte Carlo codes are quite large { on the order of megabytes for a single temperature and material. In this paper, a new storage and sampling method is introduced that is orders of magnitude less in size and is used to sample scattering parameters at any temperature on-the-fly. In addition to the reduction in storage, the need to pre-generate thermal scattering data tables at fine temperatures has been eliminated. This is advantageous for multiphysics simulations which may involve temperatures not known in advance. A new module was written for MCNP6 that bypasses the current S(α,β) table lookup in favor of the new format. The new on-the-fly sampling method was tested for graphite for two benchmark problems at ten temperatures: 1) an eigenvalue test with a fuel compact of uranium oxycarbide fuel homogenized into a graphite matrix, 2) a surface current test with a \\broomstick" problem with a monoenergetic point source. The largest eigenvalue difference was 152pcm for T= 1200K. For the temperatures and incident energies chosen for the broomstick problem, the secondary neutron spectrum showed good agreement with the traditional S(α,β) sampling method. These preliminary results show that sampling thermal scattering data on-the-fly is a viable option to eliminate both the storage burden of keeping thermal data at discrete temperatures and the need to know temperatures before simulation runtime.
Application of the Method Risk Matrix to Radiotherapy. Main Principles
International Nuclear Information System (INIS)
2012-08-01
The published fundamental principles of security, and basic international standards of security for ionizing radiation safety, contain requirements of protection for patients undergoing medical exposure. In accordance with these requirements and fulfilling its responsibility to provide for the application of these rules, the IAEA has been working intensively in the prevention of accidental exposures in radiotherapy, and this has resulted in a series of technical reports on the lessons learned from the research done in very serious events, and also in teaching materials shared for regional courses and accessible on the website for the protection of patients. The lessons learned are necessary but not sufficient, as we continue receiving information about new types of accidental exposures and not all may have been published. We need a more proactive approach, with a systematic, comprehensive and structured manner, to try to find out in advance what other errors may happen, to prevent or detect them early. Among these approaches are the method of the 'risk matrix', which by its relative simplicity can be applied to all radiotherapy service.
Jo, Byung-Du; Lee, Young-Jin; Kim, Dae-Hong; Jeon, Pil-Hyun; Kim, Hee-Joung
2014-03-01
In conventional digital radiography (DR) using a dual energy subtraction technique, a significant fraction of the detected photons are scattered within the body, resulting in the scatter component. Scattered radiation can significantly deteriorate image quality in diagnostic X-ray imaging systems. Various methods of scatter correction, including both measurement and non-measurement-based methods have been proposed in the past. Both methods can reduce scatter artifacts in images. However, non-measurement-based methods require a homogeneous object and have insufficient scatter component correction. Therefore, we employed a measurement-based method to correct for the scatter component of inhomogeneous objects from dual energy DR (DEDR) images. We performed a simulation study using a Monte Carlo simulation with a primary modulator, which is a measurement-based method for the DEDR system. The primary modulator, which has a checkerboard pattern, was used to modulate primary radiation. Cylindrical phantoms of variable size were used to quantify imaging performance. For scatter estimation, we used Discrete Fourier Transform filtering. The primary modulation method was evaluated using a cylindrical phantom in the DEDR system. The scatter components were accurately removed using a primary modulator. When the results acquired with scatter correction and without correction were compared, the average contrast-to-noise ratio (CNR) with the correction was 1.35 times higher than that obtained without correction, and the average root mean square error (RMSE) with the correction was 38.00% better than that without correction. In the subtraction study, the average CNR with correction was 2.04 (aluminum subtraction) and 1.38 (polymethyl methacrylate (PMMA) subtraction) times higher than that obtained without the correction. The analysis demonstrated the accuracy of scatter correction and the improvement of image quality using a primary modulator and showed the feasibility of
Computational method for an axisymmetric laser beam scattered by a body of revolution
International Nuclear Information System (INIS)
Combis, P.; Robiche, J.
2005-01-01
An original hybrid computational method to solve the 2-D problem of the scattering of an axisymmetric laser beam by an arbitrary-shaped inhomogeneous body of revolution is presented. This method relies on a domain decomposition of the scattering zone into concentric spherical radially homogeneous sub-domains and on an expansion of the angular dependence of the fields on the Legendre polynomials. Numerical results for the fields obtained for various scatterers geometries are presented and analyzed. (authors)
International Nuclear Information System (INIS)
Amos, K.; Allen, L.J.; Steward, C.; Hodgson, P.E.; Sofianos, S.A.
1995-01-01
Direct solution of the Schroedinger equation and inversion methods of analysis of elastic scattering data are considered to evaluate the information that they can provide about the physical interaction between colliding nuclear particles. It was found that both optical model and inversion methods based upon inverse scattering theories are subject to ambiguities. Therefore, it is essential that elastic scattering data analyses are consistent with microscopic calculations of the potential. 25 refs
Energy Technology Data Exchange (ETDEWEB)
Amos, K.; Allen, L.J.; Steward, C. [Melbourne Univ., Parkville, VIC (Australia). School of Physics; Hodgson, P.E. [Oxford Univ. (United Kingdom). Dept. of Physics; Sofianos, S.A. [University of South Africa (UNISA), Pretoria (South Africa). Dept. of Physics
1995-10-01
Direct solution of the Schroedinger equation and inversion methods of analysis of elastic scattering data are considered to evaluate the information that they can provide about the physical interaction between colliding nuclear particles. It was found that both optical model and inversion methods based upon inverse scattering theories are subject to ambiguities. Therefore, it is essential that elastic scattering data analyses are consistent with microscopic calculations of the potential. 25 refs.
Modern Nondestructive Test Methods for Army Ceramic Matrix Composites
National Research Council Canada - National Science Library
Strand, Douglas J
2008-01-01
.... Ceramic matrix composites (CMC) are potentially good high-temperature structural materials because of their low density, high elastic moduli, high strength, and for those with weak interfaces, surprisingly good damage tolerance...
On the processes of generation of particles in the extended S-matrix method
International Nuclear Information System (INIS)
Dushutin, N.K.; Mal'tsev, V.M.; Sinegovskij, S.I.
1975-01-01
In order to understand the processes of hadron multiple production very important are integral characteristics, such as the multiplicity distribution function Psub(n)=sigmasub(n)/sigmasub(inel) and correlation parameters of fsub(K). From the shape of distribution and the energy dependence of correlation parameters one may arrive at definite conclusions about the interaction dynamics. In the paper a possibility is studied of obtaining integral characteristics in the S matrix formulation of the quantum field theory. This technique is based on principles of the scattering matrix expanding beyond the energy surface (ES). This follows from the fact that the predetermination of the scattering matrix on the ES does not permit strict to determinate the condition for causality. The expansion of S matrix is performed by introducing some object described by a substantial function rho(x) and interacting with a quantum system, properties of rho(x) being such that the space of asymptotic states remains complete for the expanded matrix also, i.e., the unitarity condition is fulfilled for S(rho) too. The expansion of S-matrix over the function of the interaction insertion g(x) and the transition to the differential equations for the coupling constant allowed investigation of hadron inelastic processes at some simplifying suppositions. Experimental data do not contradict in the main the proposed picture of interactions [ru
Wang, An; Cao, Yang; Shi, Quan
2018-01-01
In this paper, we demonstrate a complete version of the convergence theory of the modulus-based matrix splitting iteration methods for solving a class of implicit complementarity problems proposed by Hong and Li (Numer. Linear Algebra Appl. 23:629-641, 2016). New convergence conditions are presented when the system matrix is a positive-definite matrix and an [Formula: see text]-matrix, respectively.
Czech Academy of Sciences Publication Activity Database
Axelsson, Owe
2010-01-01
Roč. 5910, - (2010), s. 76-83 ISSN 0302-9743. [International Conference on Large-Scale Scientific Computations, LSSC 2009 /7./. Sozopol, 04.06.2009-08.06.2009] R&D Projects: GA AV ČR 1ET400300415 Institutional research plan: CEZ:AV0Z30860518 Keywords : additive matrix * condition number * domain decomposition Subject RIV: BA - General Mathematics www.springerlink.com
Calculating massive 3-loop graphs for operator matrix elements by the method of hyperlogarithms
International Nuclear Information System (INIS)
Ablinger, Jakob; Schneider, Carsten; Bluemlein, Johannes; Raab, Clemens; Wissbrock, Fabian
2014-02-01
We calculate convergent 3-loop Feynman diagrams containing a single massive loop equipped with twist τ=2 local operator insertions corresponding to spin N. They contribute to the massive operator matrix elements in QCD describing the massive Wilson coefficients for deep-inelastic scattering at large virtualities. Diagrams of this kind can be computed using an extended version to the method of hyperlogarithms, originally being designed for massless Feynman diagrams without operators. The method is applied to Benz- and V-type graphs, belonging to the genuine 3-loop topologies. In case of the V-type graphs with five massive propagators new types of nested sums and iterated integrals emerge. The sums are given in terms of finite binomially and inverse binomially weighted generalized cyclotomic sums, while the 1-dimensionally iterated integrals are based on a set of ∝30 square-root valued letters. We also derive the asymptotic representations of the nested sums and present the solution for N element of C. Integrals with a power-like divergence in N-space∝a N , a element of R, a>1, for large values of N emerge. They still possess a representation in x-space, which is given in terms of root-valued iterated integrals in the present case. The method of hyperlogarithms is also used to calculate higher moments for crossed box graphs with different operator insertions.
Matrix-product-state method with local basis optimization for nonequilibrium electron-phonon systems
Heidrich-Meisner, Fabian; Brockt, Christoph; Dorfner, Florian; Vidmar, Lev; Jeckelmann, Eric
We present a method for simulating the time evolution of quasi-one-dimensional correlated systems with strongly fluctuating bosonic degrees of freedom (e.g., phonons) using matrix product states. For this purpose we combine the time-evolving block decimation (TEBD) algorithm with a local basis optimization (LBO) approach. We discuss the performance of our approach in comparison to TEBD with a bare boson basis, exact diagonalization, and diagonalization in a limited functional space. TEBD with LBO can reduce the computational cost by orders of magnitude when boson fluctuations are large and thus it allows one to investigate problems that are out of reach of other approaches. First, we test our method on the non-equilibrium dynamics of a Holstein polaron and show that it allows us to study the regime of strong electron-phonon coupling. Second, the method is applied to the scattering of an electronic wave packet off a region with electron-phonon coupling. Our study reveals a rich physics including transient self-trapping and dissipation. Supported by Deutsche Forschungsgemeinschaft (DFG) via FOR 1807.
Calculating massive 3-loop graphs for operator matrix elements by the method of hyperlogarithms
Energy Technology Data Exchange (ETDEWEB)
Ablinger, Jakob; Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Reserach Inst. for Symbolic Computation (RISC); Bluemlein, Johannes; Raab, Clemens [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Wissbrock, Fabian [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Johannes Kepler Univ., Linz (Austria). Reserach Inst. for Symbolic Computation (RISC)
2014-02-15
We calculate convergent 3-loop Feynman diagrams containing a single massive loop equipped with twist τ=2 local operator insertions corresponding to spin N. They contribute to the massive operator matrix elements in QCD describing the massive Wilson coefficients for deep-inelastic scattering at large virtualities. Diagrams of this kind can be computed using an extended version to the method of hyperlogarithms, originally being designed for massless Feynman diagrams without operators. The method is applied to Benz- and V-type graphs, belonging to the genuine 3-loop topologies. In case of the V-type graphs with five massive propagators new types of nested sums and iterated integrals emerge. The sums are given in terms of finite binomially and inverse binomially weighted generalized cyclotomic sums, while the 1-dimensionally iterated integrals are based on a set of ∝30 square-root valued letters. We also derive the asymptotic representations of the nested sums and present the solution for N element of C. Integrals with a power-like divergence in N-space∝a{sup N}, a element of R, a>1, for large values of N emerge. They still possess a representation in x-space, which is given in terms of root-valued iterated integrals in the present case. The method of hyperlogarithms is also used to calculate higher moments for crossed box graphs with different operator insertions.
Calculating massive 3-loop graphs for operator matrix elements by the method of hyperlogarithms
Energy Technology Data Exchange (ETDEWEB)
Ablinger, Jakob [Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenbergerstraße 69, A-4040 Linz (Austria); Blümlein, Johannes; Raab, Clemens [Deutsches Elektronen-Synchrotron, DESY, Platanenallee 6, D-15738 Zeuthen (Germany); Schneider, Carsten [Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenbergerstraße 69, A-4040 Linz (Austria); Wißbrock, Fabian [Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenbergerstraße 69, A-4040 Linz (Austria); Deutsches Elektronen-Synchrotron, DESY, Platanenallee 6, D-15738 Zeuthen (Germany)
2014-08-15
We calculate convergent 3-loop Feynman diagrams containing a single massive loop equipped with twist τ=2 local operator insertions corresponding to spin N. They contribute to the massive operator matrix elements in QCD describing the massive Wilson coefficients for deep-inelastic scattering at large virtualities. Diagrams of this kind can be computed using an extended version of the method of hyperlogarithms, originally being designed for massless Feynman diagrams without operators. The method is applied to Benz- and V-type graphs, belonging to the genuine 3-loop topologies. In case of the V-type graphs with five massive propagators, new types of nested sums and iterated integrals emerge. The sums are given in terms of finite binomially and inverse binomially weighted generalized cyclotomic sums, while the 1-dimensionally iterated integrals are based on a set of ∼30 square-root valued letters. We also derive the asymptotic representations of the nested sums and present the solution for N∈C. Integrals with a power-like divergence in N-space ∝a{sup N},a∈R,a>1, for large values of N emerge. They still possess a representation in x-space, which is given in terms of root-valued iterated integrals in the present case. The method of hyperlogarithms is also used to calculate higher moments for crossed box graphs with different operator insertions.
Calculating massive 3-loop graphs for operator matrix elements by the method of hyperlogarithms
International Nuclear Information System (INIS)
Ablinger, Jakob; Blümlein, Johannes; Raab, Clemens; Schneider, Carsten; Wißbrock, Fabian
2014-01-01
We calculate convergent 3-loop Feynman diagrams containing a single massive loop equipped with twist τ=2 local operator insertions corresponding to spin N. They contribute to the massive operator matrix elements in QCD describing the massive Wilson coefficients for deep-inelastic scattering at large virtualities. Diagrams of this kind can be computed using an extended version of the method of hyperlogarithms, originally being designed for massless Feynman diagrams without operators. The method is applied to Benz- and V-type graphs, belonging to the genuine 3-loop topologies. In case of the V-type graphs with five massive propagators, new types of nested sums and iterated integrals emerge. The sums are given in terms of finite binomially and inverse binomially weighted generalized cyclotomic sums, while the 1-dimensionally iterated integrals are based on a set of ∼30 square-root valued letters. We also derive the asymptotic representations of the nested sums and present the solution for N∈C. Integrals with a power-like divergence in N-space ∝a N ,a∈R,a>1, for large values of N emerge. They still possess a representation in x-space, which is given in terms of root-valued iterated integrals in the present case. The method of hyperlogarithms is also used to calculate higher moments for crossed box graphs with different operator insertions
Theoretical treatment of molecular photoionization based on the R-matrix method
International Nuclear Information System (INIS)
Tashiro, Motomichi
2012-01-01
The R-matrix method was implemented to treat molecular photoionization problem based on the UK R-matrix codes. This method was formulated to treat photoionization process long before, however, its application has been mostly limited to photoionization of atoms. Application of the method to valence photoionization as well as inner-shell photoionization process will be presented.
An Analytical Method of Auxiliary Sources Solution for Plane Wave Scattering by Impedance Cylinders
DEFF Research Database (Denmark)
Larsen, Niels Vesterdal; Breinbjerg, Olav
2004-01-01
Analytical Method of Auxiliary Sources solutions for plane wave scattering by circular impedance cylinders are derived by transformation of the exact eigenfunction series solutions employing the Hankel function wave transformation. The analytical Method of Auxiliary Sources solution thus obtained...
International Nuclear Information System (INIS)
Mickael, M.; Gardner, R.P.; Verghese, K.
1988-01-01
An improved method for calculating the total probability of particle scattering within the solid angle subtended by finite detectors is developed, presented, and tested. The limiting polar and azimuthal angles subtended by the detector are measured from the direction that most simplifies their calculation rather than from the incident particle direction. A transformation of the particle scattering probability distribution function (pdf) is made to match the transformation of the direction from which the limiting angles are measured. The particle scattering probability to the detector is estimated by evaluating the integral of the transformed pdf over the range of the limiting angles measured from the preferred direction. A general formula for transforming the particle scattering pdf is derived from basic principles and applied to four important scattering pdf's; namely, isotropic scattering in the Lab system, isotropic neutron scattering in the center-of-mass system, thermal neutron scattering by the free gas model, and gamma-ray Klein-Nishina scattering. Some approximations have been made to these pdf's to enable analytical evaluations of the final integrals. These approximations are shown to be valid over a wide range of energies and for most elements. The particle scattering probability to spherical, planar circular, and right circular cylindrical detectors has been calculated using the new and previously reported direct approach. Results indicate that the new approach is valid and is computationally faster by orders of magnitude
Transformation Matrix for Time Discretization Based on Tustin’s Method
Directory of Open Access Journals (Sweden)
Yiming Jiang
2014-01-01
Full Text Available This paper studies rules in transformation of transfer function through time discretization. A method of using transformation matrix to realize bilinear transform (also known as Tustin’s method is presented. This method can be described as the conversion between the coefficients of transfer functions, which are expressed as transform by certain matrix. For a polynomial of degree n, the corresponding transformation matrix of order n exists and is unique. Furthermore, the transformation matrix can be decomposed into an upper triangular matrix multiplied with another lower triangular matrix. And both have obvious regularity. The proposed method can achieve rapid bilinear transform used in automatic design of digital filter. The result of numerical simulation verifies the correctness of the theoretical results. Moreover, it also can be extended to other similar problems. Example in the last throws light on this point.
The algebraic method of the scattering inverse problem solution under untraditional statements
Popushnoj, M N
2001-01-01
The algebraic method of the scattering inverse problem solution under untraditional statements is proposed consistently in this review, in the framework of which some quantum theory od scattering charged particles problem were researched afterwards. The inverse problem of scattering theory of charged particles on the complex plane of the Coulomb coupling constant (CCC) is considered. A procedure of interaction potential restoration is established for the case when the energy, orbital moment quadrate and CCC are linearly dependent. The relation between one-parametric problems of the potential scattering of charged particles is investigated
Evaluation of a method for correction of scatter radiation in thorax cone beam CT
International Nuclear Information System (INIS)
Rinkel, J.; Dinten, J.M.; Esteve, F.
2004-01-01
Purpose: Cone beam CT (CBCT) enables three-dimensional imaging with isotropic resolution. X-ray scatter estimation is a big challenge for quantitative CBCT imaging of thorax: scatter level is significantly higher on cone beam systems compared to collimated fan beam systems. The effects of this scattered radiation are cupping artefacts, streaks, and quantification inaccuracies. The beam stops conventional scatter estimation approach can be used for CBCT but leads to a significant increase in terms of dose and acquisition time. At CEA-LETI has been developed an original scatter management process without supplementary acquisition. Methods and Materials: This Analytical Plus Indexing-based method (API) of scatter correction in CBCT is based on scatter calibration through offline acquisitions with beam stops on lucite plates, combined to an analytical transformation issued from physical equations. This approach has been applied with success in bone densitometry and mammography. To evaluate this method in CBCT, acquisitions from a thorax phantom with and without beam stops have been performed. To compare different scatter correction approaches, Feldkamp algorithm has been applied on rough data corrected from scatter by API and by beam stops approaches. Results: The API method provides results in good agreement with the beam stops array approach, suppressing cupping artefact. Otherwise influence of the scatter correction method on the noise in the reconstructed images has been evaluated. Conclusion: The results indicate that the API method is effective for quantitative CBCT imaging of thorax. Compared to a beam stops array method it needs a lower x-ray dose and shortens acquisition time. (authors)
Transverse impedance measurement using response matrix fit method at APS
International Nuclear Information System (INIS)
Sajaev, V.
2007-01-01
of an accelerator. The orbit bump method was done at BINP, APS, and ESRF. All these methods have one common feature: they employ the fact that the beam sees the impedance as an additional defocusing quadrupole whose strength depends on the beam current. At APS we use an orbit response matrix fit to determine the distribution of focusing errors around the machine, and then use these errors to calculate beta functions. Since the beam sees the impedance as a quadrupole whose strength depends on the beam current, the measurement of the beta functions with different currents could be used to determine the impedance distribution around the machine. This approach was first used at APS and reported in.
Convergent close-coupling method: a `complete scattering theory`?
Energy Technology Data Exchange (ETDEWEB)
Bray, I; Fursa, D V
1995-09-01
It is demonstrated that a single convergent close-coupling (CCC) calculation of 100 eV electron impact on the ground state of helium is able to provide accurate elastic and inelastic (n {<=} 3 levels) differential cross sections, as well as singly-, doubly-, and triply-, differential ionization cross sections. Hence, it is suggested that the CCC theory deserve the title of a `complete scattering theory`. 28 refs., 5 figs.
Determinantal method for complex angular momenta in potential scattering
Energy Technology Data Exchange (ETDEWEB)
Lee, B. W. [University of Pennsylvania, Philadelphia, PA (United States)
1963-01-15
In this paper I would like do describe a formulation of the complex angular momenta in potential scattering based on the Lippmann-Schwinger integral equation rather than on the Schrödinger differential equation. This is intended as a preliminary to the paper by SAWYER on the Regge poles and high energy limits in field theory (Bethe-Salpeter amplitudes), where the integral formulation is definitely more advantageous than the differential formulation.
The slab albedo problem for the triplet scattering kernel with modified F{sub N} method
Energy Technology Data Exchange (ETDEWEB)
Tuereci, Demet [Ministry of Education, 75th year Anatolia High School, Ankara (Turkey)
2016-12-15
One speed, time independent neutron transport equation for a slab geometry with the quadratic anisotropic scattering kernel is considered. The albedo and transmission factor are calculated by the modified F{sub N} method. The obtained numerical results are listed for different scattering coefficients.
International Nuclear Information System (INIS)
Takahashi, Akito; Yamamoto, Junji; Ebisuya, Mituo; Sumita, Kenji
1979-01-01
A new method for calculating the anisotropic neutron transport is proposed for the angular spectral analysis of D-T fusion reactor neutronics. The method is based on the transport equation with new type of anisotropic scattering kernels formulated by a single function I sub(i) (μ', μ) instead of polynomial expansion, for instance, Legendre polynomials. In the calculation of angular flux spectra by using scattering kernels with the Legendre polynomial expansion, we often observe the oscillation with negative flux. But in principle this oscillation disappears by this new method. In this work, we discussed anisotropic scattering kernels of the elastic scattering and the inelastic scatterings which excite discrete energy levels. The other scatterings were included in isotropic scattering kernels. An approximation method, with use of the first collision source written by the I sub(i) (μ', μ) function, was introduced to attenuate the ''oscillations'' when we are obliged to use the scattering kernels with the Legendre polynomial expansion. Calculated results with this approximation showed remarkable improvement for the analysis of the angular flux spectra in a slab system of lithium metal with the D-T neutron source. (author)
A Workshop on Methods for Neutron Scattering Instrument Design. Introduction and Summary
International Nuclear Information System (INIS)
Hjelm, Rex P.
1996-09-01
The future of neutron and x-ray scattering instrument development and international cooperation was the focus of the workshop on ''Methods for Neutron Scattering Instrument Design'' September 23-25 at the E.O. Lawrence Berkeley National Laboratory. These proceedings are a collection of a portion of the invited and contributed presentations
DEFF Research Database (Denmark)
Karamehmedovic, Mirza; Breinbjerg, Olav
2002-01-01
The Method of Auxiliary Sources (MAS) is applied to 3D scattering problems involving spherical impedance scatterers. The MAS results are compared with the reference spherical wave expansion (SWE) solution. It is demonstrated that good agreement is achieved between the MAS and SWE results....
Energy Technology Data Exchange (ETDEWEB)
Tuereci, R. Goekhan [Kirikkale Univ. (Turkey). Kirikkale Vocational School; Tuereci, D. [Ministry of Education, Ankara (Turkey). 75th year Anatolia High School
2017-11-15
One speed, time independent and homogeneous medium neutron transport equation is solved with the anisotropic scattering which includes both the linearly and the quadratically anisotropic scattering kernel. Having written Case's eigenfunctions and the orthogonality relations among of these eigenfunctions, slab albedo problem is investigated as numerically by using Modified F{sub N} method. Selected numerical results are presented in tables.
Matrix methods applied to engineering rigid body mechanics
Crouch, T.
The purpose of this book is to present the solution of a range of rigorous body mechanics problems using a matrix formulation of vector algebra. Essential theory concerning kinematics and dynamics is formulated in terms of matrix algebra. The solution of kinematics and dynamics problems is discussed, taking into account the velocity and acceleration of a point moving in a circular path, the velocity and acceleration determination for a linkage, the angular velocity and angular acceleration of a roller in a taper-roller thrust race, Euler's theroem on the motion of rigid bodies, an automotive differential, a rotating epicyclic, the motion of a high speed rotor mounted in gimbals, and the vibration of a spinning projectile. Attention is given to the activity of a force, the work done by a conservative force, the work and potential in a conservative system, the equilibrium of a mechanism, bearing forces due to rotor misalignment, and the frequency of vibrations of a constrained rod.
Inverse mass matrix via the method of localized lagrange multipliers
Czech Academy of Sciences Publication Activity Database
González, José A.; Kolman, Radek; Cho, S.S.; Felippa, C.A.; Park, K.C.
2018-01-01
Roč. 113, č. 2 (2018), s. 277-295 ISSN 0029-5981 R&D Projects: GA MŠk(CZ) EF15_003/0000493; GA ČR GA17-22615S Institutional support: RVO:61388998 Keywords : explicit time integration * inverse mass matrix * localized Lagrange multipliers * partitioned analysis Subject RIV: BI - Acoustics OBOR OECD: Applied mechanics Impact factor: 2.162, year: 2016 https://onlinelibrary.wiley.com/doi/10.1002/nme.5613
Energy Technology Data Exchange (ETDEWEB)
Behring, A.; Bluemlein, J.; Freitas, A. de [Deutsches Elektronen Synchrotron, DESY, Zeuthen (Germany); Bierenbaum, I. [Universitaet Hamburg, II. Institut fuer Theoretische Physik, Hamburg (Germany); Klein, S. [RWTH Aachen University, Institut fuer Theoretische Teilchenphysik und Kosmologie, Aachen (Germany); Wissbrock, F. [Deutsches Elektronen Synchrotron, DESY, Zeuthen (Germany); Johannes Kepler University, Research Institute for Symbolic Computation (RISC), Linz (Austria); IHES, Bures-sur-Yvette (France)
2014-09-15
We calculate the logarithmic contributions to the massive Wilson coefficients for deep-inelastic scattering in the asymptotic region Q{sup 2} >> m{sup 2} to 3-loop order in the fixed flavor number scheme and present the corresponding expressions for the massive operator matrix elements needed in the variable flavor number scheme. Explicit expressions are given in Mellin N-space. (orig.)
International Nuclear Information System (INIS)
Descouvemont, P; Baye, D
2010-01-01
The different facets of the R-matrix method are presented pedagogically in a general framework. Two variants have been developed over the years: (i) The 'calculable' R-matrix method is a calculational tool to derive scattering properties from the Schroedinger equation in a large variety of physical problems. It was developed rather independently in atomic and nuclear physics with too little mutual influence. (ii) The 'phenomenological' R-matrix method is a technique to parametrize various types of cross sections. It was mainly (or uniquely) used in nuclear physics. Both directions are explained by starting from the simple problem of scattering by a potential. They are illustrated by simple examples in nuclear and atomic physics. In addition to elastic scattering, the R-matrix formalism is applied to inelastic and radiative-capture reactions. We also present more recent and more ambitious applications of the theory in nuclear physics.
Li, Ping
2014-05-01
A scheme hybridizing discontinuous Galerkin time-domain (DGTD) and time-domain boundary integral (TDBI) methods for accurately analyzing transient electromagnetic scattering is proposed. Radiation condition is enforced using the numerical flux on the truncation boundary. The fields required by the flux are computed using the TDBI from equivalent currents introduced on a Huygens\\' surface enclosing the scatterer. The hybrid DGTDBI ensures that the radiation condition is mathematically exact and the resulting computation domain is as small as possible since the truncation boundary conforms to scatterer\\'s shape and is located very close to its surface. Locally truncated domains can also be defined around each disconnected scatterer additionally reducing the size of the overall computation domain. Numerical examples demonstrating the accuracy and versatility of the proposed method are presented. © 2014 IEEE.
Finite element and finite difference methods in electromagnetic scattering
Morgan, MA
2013-01-01
This second volume in the Progress in Electromagnetic Research series examines recent advances in computational electromagnetics, with emphasis on scattering, as brought about by new formulations and algorithms which use finite element or finite difference techniques. Containing contributions by some of the world's leading experts, the papers thoroughly review and analyze this rapidly evolving area of computational electromagnetics. Covering topics ranging from the new finite-element based formulation for representing time-harmonic vector fields in 3-D inhomogeneous media using two coupled sca
International Nuclear Information System (INIS)
Ljungberg, M.
1990-05-01
Quantitative scintigrafic images, obtained by NaI(Tl) scintillation cameras, are limited by photon attenuation and contribution from scattered photons. A Monte Carlo program was developed in order to evaluate these effects. Simple source-phantom geometries and more complex nonhomogeneous cases can be simulated. Comparisons with experimental data for both homogeneous and nonhomogeneous regions and with published results have shown good agreement. The usefulness for simulation of parameters in scintillation camera systems, stationary as well as in SPECT systems, has also been demonstrated. An attenuation correction method based on density maps and build-up functions has been developed. The maps were obtained from a transmission measurement using an external 57 Co flood source and the build-up was simulated by the Monte Carlo code. Two scatter correction methods, the dual-window method and the convolution-subtraction method, have been compared using the Monte Carlo method. The aim was to compare the estimated scatter with the true scatter in the photo-peak window. It was concluded that accurate depth-dependent scatter functions are essential for a proper scatter correction. A new scatter and attenuation correction method has been developed based on scatter line-spread functions (SLSF) obtained for different depths and lateral positions in the phantom. An emission image is used to determine the source location in order to estimate the scatter in the photo-peak window. Simulation studies of a clinically realistic source in different positions in cylindrical water phantoms were made for three photon energies. The SLSF-correction method was also evaluated by simulation studies for 1. a myocardial source, 2. uniform source in the lungs and 3. a tumour located in the lungs in a realistic, nonhomogeneous computer phantom. The results showed that quantitative images could be obtained in nonhomogeneous regions. (67 refs.)
Scatter measurement and correction method for cone-beam CT based on single grating scan
Huang, Kuidong; Shi, Wenlong; Wang, Xinyu; Dong, Yin; Chang, Taoqi; Zhang, Hua; Zhang, Dinghua
2017-06-01
In cone-beam computed tomography (CBCT) systems based on flat-panel detector imaging, the presence of scatter significantly reduces the quality of slices. Based on the concept of collimation, this paper presents a scatter measurement and correction method based on single grating scan. First, according to the characteristics of CBCT imaging, the scan method using single grating and the design requirements of the grating are analyzed and figured out. Second, by analyzing the composition of object projection images and object-and-grating projection images, the processing method for the scatter image at single projection angle is proposed. In addition, to avoid additional scan, this paper proposes an angle interpolation method of scatter images to reduce scan cost. Finally, the experimental results show that the scatter images obtained by this method are accurate and reliable, and the effect of scatter correction is obvious. When the additional object-and-grating projection images are collected and interpolated at intervals of 30 deg, the scatter correction error of slices can still be controlled within 3%.
Analytic continuation of scattering data as a method of obtaining characteristics of bound states
International Nuclear Information System (INIS)
Blokhintsev, L.; Savin, D.
2014-01-01
An asymptotic normalization coefficient (ANC) determines the asymptotics of a wave function of a nucleus a in a binary channel b + c. ANCs are proportional to nuclear vertex constants (NVCs), which are on-shell matrix elements of the virtual processes a ↔ b+c. The method of the analytic continuation of the effective range function is applied to obtain the asymptotic normalization coefficients for 6 Li nucleus in the α+ d channel. Several sets of scattering phases obtained from the phase-shift analyses as well as from Faddeev calculations are used as an input. Since the α+d system possesses the low-lying inelastic threshold due to the dissociation of a deuteron, the approach used is generalized to include inelastic channels. The sensitivity of the obtained values of asymptotic normalization coefficients to the elastic channels coupling and to account of the inelastic channel is investigated. In summary, we can say that employing the analytic continuation of the effective range expansion to determine the ANCs and NVCs for the 6 Li → α + d channel turns out to be successful
A New Method of Creating Technology/Function Matrix for Systematic Innovation without Expert
Directory of Open Access Journals (Sweden)
Tien-Yuan Cheng
2012-02-01
Full Text Available The technology/function matrix is comprised by specific technologies and functions, and through the technology/function matrix we can known what the technologies with functions have opportunities for innovation of product or technology. However, the technology/function matrix is very difficult to create, because the patents need to be read, analyzed and categorized into the technology/function matrix always more than hundreds or thousands. In this research, I propose a method to create a technology/function matrix just need to execute patent search without reading and analyzing patents. Through the proposed method anyone can create a technology/function matrix in a short time without experts’ help even if there are thousands of thousands of patents need to be read and analyzed.
Interpolation methods for creating a scatter radiation exposure map
Energy Technology Data Exchange (ETDEWEB)
Gonçalves, Elicardo A. de S., E-mail: elicardo.goncalves@ifrj.edu.br [Instituto Federal do Rio de Janeiro (IFRJ), Paracambi, RJ (Brazil); Gomes, Celio S.; Lopes, Ricardo T. [Coordenacao de Pos-Graduacao e Pesquisa de Engenharia (PEN/COPPE/UFRJ), Rio de Janeiro, RJ (Brazil). Programa de Engenharia Nuclear; Oliveira, Luis F. de; Anjos, Marcelino J. dos; Oliveira, Davi F. [Universidade do Estado do Rio de Janeiro (UFRJ), RJ (Brazil). Instituto de Física
2017-07-01
A well know way for best comprehension of radiation scattering during a radiography is to map exposure over the space around the source and sample. This map is done measuring exposure in points regularly spaced, it means, measurement will be placed in localization chosen by increasing a regular steps from a starting point, along the x, y and z axes or even radial and angular coordinates. However, it is not always possible to maintain the accuracy of the steps throughout the entire space, or there will be regions of difficult access where the regularity of the steps will be impaired. This work intended to use some interpolation techniques that work with irregular steps, and to compare their results and their limits. It was firstly done angular coordinates, and tested in lack of some points. Later, in the same data was performed the Delaunay tessellation interpolation ir order to compare. Computational and graphic treatments was done with the GNU OCTAVE software and its image-processing package. Real data was acquired from a bunker where a 6 MeV betatron can be used to produce radiation scattering. (author)
Membrane Characterization by Microscopic and Scattering Methods: Multiscale Structure
Directory of Open Access Journals (Sweden)
Philippe Moulin
2011-04-01
Full Text Available Several microscopic and scattering techniques at different observation scales (from atomic to macroscopic were used to characterize both surface and bulk properties of four new flat-sheet polyethersulfone (PES membranes (10, 30, 100 and 300 kDa and new 100 kDa hollow fibers (PVDF. Scanning Electron Microscopy (SEM with “in lens” detection was used to obtain information on the pore sizes of the skin layers at the atomic scale. White Light Interferometry (WLI and Atomic Force Microscopy (AFM using different scales (for WLI: windows: 900 × 900 µm2 and 360 × 360 µm2; number of points: 1024; for AFM: windows: 50 × 50 µm2 and 5 × 5 µm2; number of points: 512 showed that the membrane roughness increases markedly with the observation scale and that there is a continuity between the different scan sizes for the determination of the RMS roughness. High angular resolution ellipsometric measurements were used to obtain the signature of each cut-off and the origin of the scattering was identified as coming from the membrane bulk.
Interpolation methods for creating a scatter radiation exposure map
International Nuclear Information System (INIS)
Gonçalves, Elicardo A. de S.; Gomes, Celio S.; Lopes, Ricardo T.; Oliveira, Luis F. de; Anjos, Marcelino J. dos; Oliveira, Davi F.
2017-01-01
A well know way for best comprehension of radiation scattering during a radiography is to map exposure over the space around the source and sample. This map is done measuring exposure in points regularly spaced, it means, measurement will be placed in localization chosen by increasing a regular steps from a starting point, along the x, y and z axes or even radial and angular coordinates. However, it is not always possible to maintain the accuracy of the steps throughout the entire space, or there will be regions of difficult access where the regularity of the steps will be impaired. This work intended to use some interpolation techniques that work with irregular steps, and to compare their results and their limits. It was firstly done angular coordinates, and tested in lack of some points. Later, in the same data was performed the Delaunay tessellation interpolation ir order to compare. Computational and graphic treatments was done with the GNU OCTAVE software and its image-processing package. Real data was acquired from a bunker where a 6 MeV betatron can be used to produce radiation scattering. (author)
International Nuclear Information System (INIS)
Abdolsalami, F.; Abdolsalami, M.; Perez, L.; Gomez, P.
1995-01-01
The authors have applied the finite-element method to electron-molecule collision with the exchange effect implemented rigorously. All the calculations are done in the body-frame within the fixed-nuclei approximation, where the exact treatment of exchange as a nonlocal effect results in a set of coupled integro-differential equations. The method is applied to e-H 2 and e-N 2 scatterings and the cross sections obtained are in very good agreement with the corresponding results the authors have generated from the linear-algebraic approach. This confirms the significant difference observed between their results generated by linear-algebraic method and the previously published e-N 2 cross sections. Their studies show that the finite-element method is clearly superior to the linear-algebraic approach in both memory usage and CPU time especially for large systems such as e-N 2 . The system coefficient matrix obtained from the finite-element method is often sparse and smaller in size by a factor of 12 to 16, compared to the linear-algebraic technique. Moreover, the CPU time required to obtain stable results with the finite-element method is significantly smaller than the linear-algebraic approach for one incident electron energy. The usage of computer resources in the finite-element method can even be reduced much further when (1) scattering calculations involving multiple electron energies are performed in one computer run and (2) exchange, which is a short range effect, is approximated by a sparse matrix. 17 refs., 7 figs., 5 tabs
Rayleigh-wave scattering by shallow cracks using the indirect boundary element method
International Nuclear Information System (INIS)
Ávila-Carrera, R; Rodríguez-Castellanos, A; Ortiz-Alemán, C; Sánchez-Sesma, F J
2009-01-01
The scattering and diffraction of Rayleigh waves by shallow cracks using the indirect boundary element method (IBEM) are investigated. The detection of cracks is of interest because their presence may compromise structural elements, put technological devices at risk or represent economical potential in reservoir engineering. Shallow cracks may give rise to scattered body and surface waves. These waves are sensitive to the crack's geometry, size and orientation. Under certain conditions, amplitude spectra clearly show conspicuous resonances that are associated with trapped waves. Several applications based on the scattering of surface waves (e.g. Rayleigh and Stoneley waves), such as non-destructive testing or oil well exploration, have shown that the scattered fields may provide useful information to detect cracks and other heterogeneities. The subject is not new and several analytical and numerical techniques have been applied for the last 50 years to understand the basis of multiple scattering phenomena. In this work, we use the IBEM to calculate the scattered fields produced by single or multiple cracks near a free surface. This method is based upon an integral representation of the scattered displacement fields, which is derived from Somigliana's identity. Results are given in both frequency and time domains. The analyses of the displacement field using synthetic seismograms and snapshots reveal some important effects from various configurations of cracks. The study of these simple cases may provide an archetype to geoscientists and engineers to understand the fundamental aspects of multiple scattering and diffraction by cracks
Radiative heat transfer in strongly forward scattering media using the discrete ordinates method
Granate, Pedro; Coelho, Pedro J.; Roger, Maxime
2016-03-01
The discrete ordinates method (DOM) is widely used to solve the radiative transfer equation, often yielding satisfactory results. However, in the presence of strongly forward scattering media, this method does not generally conserve the scattering energy and the phase function asymmetry factor. Because of this, the normalization of the phase function has been proposed to guarantee that the scattering energy and the asymmetry factor are conserved. Various authors have used different normalization techniques. Three of these are compared in the present work, along with two other methods, one based on the finite volume method (FVM) and another one based on the spherical harmonics discrete ordinates method (SHDOM). In addition, the approximation of the Henyey-Greenstein phase function by a different one is investigated as an alternative to the phase function normalization. The approximate phase function is given by the sum of a Dirac delta function, which accounts for the forward scattering peak, and a smoother scaled phase function. In this study, these techniques are applied to three scalar radiative transfer test cases, namely a three-dimensional cubic domain with a purely scattering medium, an axisymmetric cylindrical enclosure containing an emitting-absorbing-scattering medium, and a three-dimensional transient problem with collimated irradiation. The present results show that accurate predictions are achieved for strongly forward scattering media when the phase function is normalized in such a way that both the scattered energy and the phase function asymmetry factor are conserved. The normalization of the phase function may be avoided using the FVM or the SHDOM to evaluate the in-scattering term of the radiative transfer equation. Both methods yield results whose accuracy is similar to that obtained using the DOM along with normalization of the phase function. Very satisfactory predictions were also achieved using the delta-M phase function, while the delta
Desmal, Abdulla; Bagci, Hakan
2014-01-01
A numerical framework that incorporates recently developed iterative shrinkage thresholding (IST) algorithms within the Born iterative method (BIM) is proposed for solving the two-dimensional inverse electromagnetic scattering problem. IST
Li, Ping
2014-07-01
This paper presents an algorithm hybridizing discontinuous Galerkin time domain (DGTD) method and time domain boundary integral (BI) algorithm for 3-D open region electromagnetic scattering analysis. The computational domain of DGTD is rigorously truncated by analytically evaluating the incoming numerical flux from the outside of the truncation boundary through BI method based on the Huygens\\' principle. The advantages of the proposed method are that it allows the truncation boundary to be conformal to arbitrary (convex/ concave) scattering objects, well-separated scatters can be truncated by their local meshes without losing the physics (such as coupling/multiple scattering) of the problem, thus reducing the total mesh elements. Furthermore, low frequency waves can be efficiently absorbed, and the field outside the truncation domain can be conveniently calculated using the same BI formulation. Numerical examples are benchmarked to demonstrate the accuracy and versatility of the proposed method.
Measuring method to impulse neutron scattering background in complicated ambient condition
International Nuclear Information System (INIS)
Tang Zhangkui; Peng Taiping; Tang Zhengyuan; Liu Hangang; Hu Mengchun; Fan Juan
2004-01-01
This paper introduced a measuring method and calculative formula about impulse neutron scattering background in complicated ambient condition. The experiment had been done in the lab, and the factors to affect measurement conclusion were analysised. (authors)
Light scattering properties of bovine muscle tissue in vitro, a comparison of methods
Zijp, J.R.; ten Bosch, JJ; Benaron, DA; Chance, B; Ferrari, M; Kohl, M
1998-01-01
We measured the light scattering properties of muscular tissue using several methods, and compared the obtained results. Calculation of the extinction coefficient by using collimated transmission measurements and applying Beer's law is not appropriate. Probably surface roughness of the sample
A least squares calculational method: application to e±-H elastic scattering
International Nuclear Information System (INIS)
Das, J.N.; Chakraborty, S.
1989-01-01
The least squares calcualtional method proposed by Das has been applied for the e ± -H elastic scattering problems for intermediate energies. Some important conclusions are made on the basis of the calculation. (author). 7 refs ., 2 tabs
A software-based x-ray scatter correction method for breast tomosynthesis
Jia Feng, Steve Si; Sechopoulos, Ioannis
2011-01-01
Purpose: To develop a software-based scatter correction method for digital breast tomosynthesis (DBT) imaging and investigate its impact on the image quality of tomosynthesis reconstructions of both phantoms and patients.
Synthetic acceleration methods for linear transport problems with highly anisotropic scattering
International Nuclear Information System (INIS)
Khattab, K.M.; Larsen, E.W.
1992-01-01
The diffusion synthetic acceleration (DSA) algorithm effectively accelerates the iterative solution of transport problems with isotropic or mildly anisotropic scattering. However, DSA loses its effectiveness for transport problems that have strongly anisotropic scattering. Two generalizations of DSA are proposed, which, for highly anisotropic scattering problems, converge at least an order of magnitude (clock time) faster than the DSA method. These two methods are developed, the results of Fourier analysis that theoretically predict their efficiency are described, and numerical results that verify the theoretical predictions are presented. (author). 10 refs., 7 figs., 5 tabs
Synthetic acceleration methods for linear transport problems with highly anisotropic scattering
International Nuclear Information System (INIS)
Khattab, K.M.; Larsen, E.W.
1991-01-01
This paper reports on the diffusion synthetic acceleration (DSA) algorithm that effectively accelerates the iterative solution of transport problems with isotropic or mildly anisotropic scattering. However, DSA loses its effectiveness for transport problems that have strongly anisotropic scattering. Two generalizations of DSA are proposed, which, for highly anisotropic scattering problems, converge at least an order of magnitude (clock time) faster than the DSA method. These two methods are developed, the results of Fourier analyses that theoretically predict their efficiency are described, and numerical results that verify the theoretical predictions are presented
Point kernels and superposition methods for scatter dose calculations in brachytherapy
International Nuclear Information System (INIS)
Carlsson, A.K.
2000-01-01
Point kernels have been generated and applied for calculation of scatter dose distributions around monoenergetic point sources for photon energies ranging from 28 to 662 keV. Three different approaches for dose calculations have been compared: a single-kernel superposition method, a single-kernel superposition method where the point kernels are approximated as isotropic and a novel 'successive-scattering' superposition method for improved modelling of the dose from multiply scattered photons. An extended version of the EGS4 Monte Carlo code was used for generating the kernels and for benchmarking the absorbed dose distributions calculated with the superposition methods. It is shown that dose calculation by superposition at and below 100 keV can be simplified by using isotropic point kernels. Compared to the assumption of full in-scattering made by algorithms currently in clinical use, the single-kernel superposition method improves dose calculations in a half-phantom consisting of air and water. Further improvements are obtained using the successive-scattering superposition method, which reduces the overestimates of dose close to the phantom surface usually associated with kernel superposition methods at brachytherapy photon energies. It is also shown that scatter dose point kernels can be parametrized to biexponential functions, making them suitable for use with an effective implementation of the collapsed cone superposition algorithm. (author)
International Nuclear Information System (INIS)
Kuznichenko, A.V.; Onishchenko, G.M.; Pilipenko, V.V.; Dem'yanova, A.S.; Burtebaev, N.
2003-01-01
The analysis of the cross sections of the 16 O + 16 O nuclei elastic scattering by the energy of 124, 145, 250, 350, 480, 704 and 1120 MeV is carried out on the basis of the phenomenological S-matrix model. It is shown, that by high energy the refraction behavior of the opalescent-type cross sections is well described by the simple smooth dependence of the S-matrix on the angular moment and by the energy E ≤ 480 MeV the opalescent-type structures are strongly effected by the Regge poles and S-matrix zeroes, close to the actual axis. The comparison with the results of the cross sections by the optical model is carried out [ru
A semiclassical method in the theory of light scattering by semiconductor quantum dots
International Nuclear Information System (INIS)
Lang, I. G.; Korovin, L. I.; Pavlov, S. T.
2008-01-01
A semiclassical method is proposed for the theoretical description of elastic light scattering by arbitrary semiconductor quantum dots under conditions of size quantization. This method involves retarded potentials and allows one to dispense with boundary conditions for electric and magnetic fields. Exact results for the Umov-Poynting vector at large distances from quantum dots in the case of monochromatic and pulsed irradiation and formulas for differential scattering cross sections are obtained
Wu, Binlin
New near-infrared (NIR) diffuse optical tomography (DOT) approaches were developed to detect, locate, and image small targets embedded in highly scattering turbid media. The first approach, referred to as time reversal optical tomography (TROT), is based on time reversal (TR) imaging and multiple signal classification (MUSIC). The second approach uses decomposition methods of non-negative matrix factorization (NMF) and principal component analysis (PCA) commonly used in blind source separation (BSS) problems, and compare the outcomes with that of optical imaging using independent component analysis (OPTICA). The goal is to develop a safe, affordable, noninvasive imaging modality for detection and characterization of breast tumors in early growth stages when those are more amenable to treatment. The efficacy of the approaches was tested using simulated data, and experiments involving model media and absorptive, scattering, and fluorescent targets, as well as, "realistic human breast model" composed of ex vivo breast tissues with embedded tumors. The experimental arrangements realized continuous wave (CW) multi-source probing of samples and multi-detector acquisition of diffusely transmitted signal in rectangular slab geometry. A data matrix was generated using the perturbation in the transmitted light intensity distribution due to the presence of absorptive or scattering targets. For fluorescent targets the data matrix was generated using the diffusely transmitted fluorescence signal distribution from the targets. The data matrix was analyzed using different approaches to detect and characterize the targets. The salient features of the approaches include ability to: (a) detect small targets; (b) provide three-dimensional location of the targets with high accuracy (~within a millimeter or 2); and (c) assess optical strength of the targets. The approaches are less computation intensive and consequently are faster than other inverse image reconstruction methods that
International Nuclear Information System (INIS)
Armour, E.A.G.; Plummer, M.
1989-01-01
An explanation is given of why it is necessary to include long-range polarisation functions in the trial function when carrying out Kohn calculations of low-energy positron (and electron) scattering by atoms and simple molecules. The asymptotic form of these functions in low-energy e + -H 2 scattering is deduced. Appropriate functions with this asymptotic form are used to represent the closed-channel part of the wavefunction in a Kohn calculation of the lowest partial wave of Σ u + symmetry in e + -H 2 scattering at very low energies. For k≤0.03a 0 -1 , the results obtained are in good agreement with those obtained using the Born approximation and the asymptotic forms of the static and polarisation potentials. The relationship is pointed out between this method of taking into account long-range polarisation and the polarised pseudostate method used in R-matrix calculations. (author)
Methods for reduction of scattered x-ray in measuring MTF with the square chart
International Nuclear Information System (INIS)
Hatagawa, Masakatsu; Yoshida, Rie
1982-01-01
A square wave chart has been used to measure the MTF of a screen-film system. The problem is that the scattered X-ray from the chart may give rise to measurement errors. In this paper, the authors proposed two methods to reduce the scattered X-ray: the first method is the use of a Pb mask and second is to provide for an air gap between the chart and the screen-film system. In these methods, the scattered X-ray from the chart was reduced. MTFs were measured by both of the new methods and the conventional method, and MTF values of the new methods were in good agreement while that of the conventional method was not. It was concluded that these new methods are able to reduce errors in the measurement of MTF. (author)
Inversion assuming weak scattering
DEFF Research Database (Denmark)
Xenaki, Angeliki; Gerstoft, Peter; Mosegaard, Klaus
2013-01-01
due to the complex nature of the field. A method based on linear inversion is employed to infer information about the statistical properties of the scattering field from the obtained cross-spectral matrix. A synthetic example based on an active high-frequency sonar demonstrates that the proposed...
Another method for a global fit of the Cabibbo-Kobayashi-Maskawa matrix
International Nuclear Information System (INIS)
Dita, Petre
2005-01-01
Recently we proposed a novel method for doing global fits on the entries of the Cabibbo-Kobayashi-Maskawa matrix. The new used ingredients were a clear relationship between the entries of the CKM matrix and the experimental data, as well as the use of the necessary and sufficient condition the data have to satisfy in order to find a unitary matrix compatible with them. This condition writes as -1 ≤ cosδ ≤1 where δ is the phase that accounts for CP violation. Numerical results are provided for the CKM matrix entries, the mixing angles between generations and all the angles of the standard unitarity triangle. (author)
International Nuclear Information System (INIS)
Blais, N.; Podgorsak, E.B.
1992-01-01
A method for determining the kinetic energy of clinical electron beams is described, based on the measurement in air of the spatial spread of a pencil electron beam which is produced from the broad clinical electron beam. As predicted by the Fermi-Eyges theory, the dose distribution measured in air on a plane, perpendicular to the incident direction of the initial pencil electron beam, is Gaussian. The square of its spatial spread is related to the mass angular scattering power which in turn is related to the kinetic energy of the electron beam. The measured spatial spread may thus be used to determine the mass angular scattering power, which is then used to determine the kinetic energy of the electron beam from the known relationship between mass angular scattering power and kinetic energy. Energies obtained with the mass angular scattering power method agree with those obtained with the electron range method. (author)
A method for determination mass absorption coefficient of gamma rays by Compton scattering.
El Abd, A
2014-12-01
A method was proposed for determination mass absorption coefficient of gamma rays for compounds, alloys and mixtures. It is based on simulating interaction processes of gamma rays with target elements having atomic numbers from Z=1 to Z=92 using the MCSHAPE software. Intensities of Compton scattered gamma rays at saturation thicknesses and at a scattering angle of 90° were calculated for incident gamma rays of different energies. The obtained results showed that the intensity of Compton scattered gamma rays at saturations and mass absorption coefficients can be described by mathematical formulas. These were used to determine mass absorption coefficients for compound, alloys and mixtures with the knowledge of their Compton scattered intensities. The method was tested by calculating mass absorption coefficients for some compounds, alloys and mixtures. There is a good agreement between obtained results and calculated ones using WinXom software. The advantages and limitations of the method were discussed. Copyright © 2014 Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Khattab, K.M.
1998-01-01
The diffusion synthetic acceleration (DSA) method has been known to be an effective tool for accelerating the iterative solution of transport equations with isotopic or mildly anisotropic scattering. However, the DSA method is not effective for transport equations that have strongly anisotropic scattering. A generalization of the modified DSA (MDSA) methods is proposed. This method converges (Clock time) faster than the MDSA method. It is developed, the results of a Fourier analysis that theoretically predicts its efficiency are described, and numerical results that verify the theoretical prediction are presented. (author). 9 refs., 2 tabs., 5 figs
International Nuclear Information System (INIS)
Khattab, K.M.
1997-01-01
The diffusion synthetic acceleration (DSA) method has been known to be an effective tool for accelerating the iterative solution of transport equations with isotropic or mildly anisotropic scattering. However, the DSA method is not effective for transport equations that have strongly anisotropic scattering. A generalization of the modified DSA (MDSA) method is proposed that converges (clock time) faster than the MDSA method. This method is developed, the results of a Fourier analysis that theoretically predicts its efficiency are described, and numerical results that verify the theoretical prediction are presented
International Nuclear Information System (INIS)
Abdolsalami, F.; Abdolsalami, M.; Gomez, P.
1994-01-01
We have applied the finite-element method to electron-molecule collisions. All the calculations are done in the body frame within the fixed-nuclei approximation. A model potential, which is added to the static and polarization potential, has been used to represent the exchange effect. The method is applied to electron-H 2 scattering and the eigenphase sums and the cross sections obtained are in very good agreement with the corresponding results from the linear-algebraic approach. Finite-element calculations of the R matrix in the region where the static and exchange interactions are strong, however, has about one-half to one-fourth of the memory requirement of the linear-algebraic technique
An algebraic approach to the scattering equations
Energy Technology Data Exchange (ETDEWEB)
Huang, Rijun; Rao, Junjie [Zhejiang Institute of Modern Physics, Zhejiang University,Hangzhou, 310027 (China); Feng, Bo [Zhejiang Institute of Modern Physics, Zhejiang University,Hangzhou, 310027 (China); Center of Mathematical Science, Zhejiang University,Hangzhou, 310027 (China); He, Yang-Hui [School of Physics, NanKai University,Tianjin, 300071 (China); Department of Mathematics, City University,London, EC1V 0HB (United Kingdom); Merton College, University of Oxford,Oxford, OX14JD (United Kingdom)
2015-12-10
We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using simple linear algebra and is amenable to an algorithmic approach. Certain identities in the amplitudes as well as rationality of the final integrand become immediate in this formalism.
An algebraic approach to the scattering equations
International Nuclear Information System (INIS)
Huang, Rijun; Rao, Junjie; Feng, Bo; He, Yang-Hui
2015-01-01
We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using simple linear algebra and is amenable to an algorithmic approach. Certain identities in the amplitudes as well as rationality of the final integrand become immediate in this formalism.
International Nuclear Information System (INIS)
Sanchez, Richard.
1975-11-01
The Integral Transform Method for the neutron transport equation has been developed in last years by Asaoka and others. The method uses Fourier transform techniques in solving isotropic one-dimensional transport problems in homogeneous media. The method has been extended to linearly anisotropic transport in one-dimensional homogeneous media. Series expansions were also obtained using Hembd techniques for the new anisotropic matrix elements in cylindrical geometry. Carlvik spatial-spherical harmonics method was generalized to solve the same problem. By applying a relation between the isotropic and anisotropic one-dimensional kernels, it was demonstrated that anisotropic matrix elements can be calculated by a linear combination of a few isotropic matrix elements. This means in practice that the anisotropic problem of order N with the N+2 isotropic matrix for the plane and spherical geometries, and N+1 isotropic matrix for cylindrical geometries can be solved. A method of solving linearly anisotropic one-dimensional transport problems in homogeneous media was defined by applying Mika and Stankiewicz observations: isotropic matrix elements were computed by Hembd series and anisotropic matrix elements then calculated from recursive relations. The method has been applied to albedo and critical problems in cylindrical geometries. Finally, a number of results were computed with 12-digit accuracy for use as benchmarks [fr
International Nuclear Information System (INIS)
Laletin, N.I.; Sultanov, N.V.; Boyarinov, V.F.
1992-01-01
Estimation is fulfilled of an influence of scattering anisotropy on K ef the TRX and BAPL assemblies by the WIMS-D4 program in the transport (TA) and linear-anisotropic (LAA) approximations. It is shown that account for the scattering anisotropy in the LAA in comparison with TA decreases K ef by 0.8% for TRX assemblies and by 0.5-0.6% for BAPL ones. For more detailed account for the scattering anisotropy in calculations of cylindrical and cluster cells in the one-velocity approximation is developed a technique for account for the anisotropy in the methods of surface pseudosources
Li, Ping; Shi, Yifei; Jiang, Lijun; Bagci, Hakan
2014-01-01
A scheme hybridizing discontinuous Galerkin time-domain (DGTD) and time-domain boundary integral (TDBI) methods for accurately analyzing transient electromagnetic scattering is proposed. Radiation condition is enforced using the numerical flux on the truncation boundary. The fields required by the flux are computed using the TDBI from equivalent currents introduced on a Huygens' surface enclosing the scatterer. The hybrid DGTDBI ensures that the radiation condition is mathematically exact and the resulting computation domain is as small as possible since the truncation boundary conforms to scatterer's shape and is located very close to its surface. Locally truncated domains can also be defined around each disconnected scatterer additionally reducing the size of the overall computation domain. Numerical examples demonstrating the accuracy and versatility of the proposed method are presented. © 2014 IEEE.
Directory of Open Access Journals (Sweden)
Sergiu Ciprian Catinas
2015-07-01
Full Text Available A detailed theoretical and practical investigation of the reinforced concrete elements is due to recent techniques and method that are implemented in the construction market. More over a theoretical study is a demand for a better and faster approach nowadays due to rapid development of the calculus technique. The paper above will present a study for implementing in a static calculus the direct stiffness matrix method in order capable to address phenomena related to different stages of loading, rapid change of cross section area and physical properties. The method is a demand due to the fact that in our days the FEM (Finite Element Method is the only alternative to such a calculus and FEM are considered as expensive methods from the time and calculus resources point of view. The main goal in such a method is to create the moment-curvature diagram in the cross section that is analyzed. The paper above will express some of the most important techniques and new ideas as well in order to create the moment curvature graphic in the cross sections considered.
A cluster approximation for the transfer-matrix method
International Nuclear Information System (INIS)
Surda, A.
1990-08-01
A cluster approximation for the transfer-method is formulated. The calculation of the partition function of lattice models is transformed to a nonlinear mapping problem. The method yields the free energy, correlation functions and the phase diagrams for a large class of lattice models. The high accuracy of the method is exemplified by the calculation of the critical temperature of the Ising model. (author). 14 refs, 2 figs, 1 tab
Water management in sandy soil using neutron scattering method
International Nuclear Information System (INIS)
Mohamed, K.M.
2011-01-01
This study was carried out during 2008/2009 at the Experimental Field of Soil and Water Research Department, Nuclear Research Center, Atomic Energy Authority, Inshas in a newly reclaimed sandy soil. The aims of this work are,- determine soil moisture tension within the active root zone and - detecting the behavior of soil moisture within the active root zoon by defines the total hydraulic potential within the soil profile to predict both of actual evapotranspiration and rate of moisture depletion This work also is aimed to study soil water distribution under drip irrigation system.- reducing water deep percolation under the active root depth.This study included two factors, the first one is the irrigation intervals, and the second one is the application rate of organic manure. Irrigation intervals were 5, 10 and 15 days, besides three application rates of organic manure (0 m 3 /fed, 20 m 3 /fed. and 30 m 3 /fed.) in -three replicates under drip irrigation system, Onion was used as an indicator plant. Obtained data show, generally, that neutron scattering technique and soil moisture retention curve model helps more to study the water behavior in the soil profile.Application of organic manure and irrigation to field capacity is a good way to minimize evapotranspiration and deep percolation, which was zero mm/day in the treated treatments.The best irrigation interval for onion plant, in the studied soil, was 5 days with 30m 3 /fad. an application rate of organic manure.Parameter α of van Genuchent's 1980 model was affected by the additions of organic manure, which was decreased by addition of organic manure decreased it. Data also showed that n parameter was decreased by addition of organic manure Using surfer program is a good tool to describe the water distribution in two directions (vertical and horizontal) through soil profile.
Detection of structural defects in lecithin membranes by the small-angle neutron scattering method
International Nuclear Information System (INIS)
Bezzabotnov, V.Yu.; Gordelij, V.I.; Ostanevich, Yu.M.; Yaguzhinskij, L.S.
1989-01-01
Irregularities interpreted as interdomain defects have been detected in model lipid membranes of dipalmitoil lecithin in liquid L α -phase by the method of small-angle scattering (lateral diffraction). The dimensions and concentrations of the defects were about those supposed within the dynamic cluster model of bilayer (Ivkov, 1984). No irregularities were detected in the solid Lβ ' -phase (the diffusion scattering intensity was at least ten times less)
Novel image analysis methods for quantification of in situ 3-D tendon cell and matrix strain.
Fung, Ashley K; Paredes, J J; Andarawis-Puri, Nelly
2018-01-23
Macroscopic tendon loads modulate the cellular microenvironment leading to biological outcomes such as degeneration or repair. Previous studies have shown that damage accumulation and the phases of tendon healing are marked by significant changes in the extracellular matrix, but it remains unknown how mechanical forces of the extracellular matrix are translated to mechanotransduction pathways that ultimately drive the biological response. Our overarching hypothesis is that the unique relationship between extracellular matrix strain and cell deformation will dictate biological outcomes, prompting the need for quantitative methods to characterize the local strain environment. While 2-D methods have successfully calculated matrix strain and cell deformation, 3-D methods are necessary to capture the increased complexity that can arise due to high levels of anisotropy and out-of-plane motion, particularly in the disorganized, highly cellular, injured state. In this study, we validated the use of digital volume correlation methods to quantify 3-D matrix strain using images of naïve tendon cells, the collagen fiber matrix, and injured tendon cells. Additionally, naïve tendon cell images were used to develop novel methods for 3-D cell deformation and 3-D cell-matrix strain, which is defined as a quantitative measure of the relationship between matrix strain and cell deformation. The results support that these methods can be used to detect strains with high accuracy and can be further extended to an in vivo setting for observing temporal changes in cell and matrix mechanics during degeneration and healing. Copyright © 2017. Published by Elsevier Ltd.
A method for determination mass absorption coefficient of gamma rays by Compton scattering
International Nuclear Information System (INIS)
El Abd, A.
2014-01-01
A method was proposed for determination mass absorption coefficient of gamma rays for compounds, alloys and mixtures. It is based on simulating interaction processes of gamma rays with target elements having atomic numbers from Z=1 to Z=92 using the MCSHAPE software. Intensities of Compton scattered gamma rays at saturation thicknesses and at a scattering angle of 90° were calculated for incident gamma rays of different energies. The obtained results showed that the intensity of Compton scattered gamma rays at saturations and mass absorption coefficients can be described by mathematical formulas. These were used to determine mass absorption coefficients for compound, alloys and mixtures with the knowledge of their Compton scattered intensities. The method was tested by calculating mass absorption coefficients for some compounds, alloys and mixtures. There is a good agreement between obtained results and calculated ones using WinXom software. The advantages and limitations of the method were discussed. - Highlights: • Compton scattering of γ−rays was used for determining mass absorption coefficient. • Scattered intensities were determined by the MCSHAPE software. • Mass absorption coefficients were determined for some compounds, mixtures and alloys. • Mass absorption coefficients were calculated by Winxcom software. • Good agreements were found between determined and calculated results
Discrete-ordinate method with matrix exponential for a pseudo-spherical atmosphere: Scalar case
International Nuclear Information System (INIS)
Doicu, A.; Trautmann, T.
2009-01-01
We present a discrete-ordinate algorithm using the matrix-exponential solution for pseudo-spherical radiative transfer. Following the finite-element technique we introduce the concept of layer equation and formulate the discrete radiative transfer problem in terms of the level values of the radiance. The layer quantities are expressed by means of matrix exponentials, which are computed by using the matrix eigenvalue method and the Pade approximation. These solution methods lead to a compact and versatile formulation of the radiative transfer. Simulated nadir and limb radiances for an aerosol-loaded atmosphere and a cloudy atmosphere are presented along with a discussion of the model intercomparisons and timings
International Nuclear Information System (INIS)
Hategan, Cornel; Comisel, Horia; Ionescu, Remus A.
2004-01-01
The quasiresonant scattering consists from a single channel resonance coupled by direct interaction transitions to some competing reaction channels. A description of quasiresonant Scattering, in terms of generalized reduced K-, R- and S- Matrix, is developed in this work. The quasiresonance's decay width is, due to channels coupling, smaller than the width of the ancestral single channel resonance (resonance's direct compression). (author)
Barkeshli, Kasra; Volakis, John L.
1991-01-01
The theoretical and computational aspects related to the application of the Conjugate Gradient FFT (CGFFT) method in computational electromagnetics are examined. The advantages of applying the CGFFT method to a class of large scale scattering and radiation problems are outlined. The main advantages of the method stem from its iterative nature which eliminates a need to form the system matrix (thus reducing the computer memory allocation requirements) and guarantees convergence to the true solution in a finite number of steps. Results are presented for various radiators and scatterers including thin cylindrical dipole antennas, thin conductive and resistive strips and plates, as well as dielectric cylinders. Solutions of integral equations derived on the basis of generalized impedance boundary conditions (GIBC) are also examined. The boundary conditions can be used to replace the profile of a material coating by an impedance sheet or insert, thus, eliminating the need to introduce unknown polarization currents within the volume of the layer. A general full wave analysis of 2-D and 3-D rectangular grooves and cavities is presented which will also serve as a reference for future work.
A pedagogical derivation of the matrix element method in particle physics data analysis
Sumowidagdo, Suharyo
2018-03-01
The matrix element method provides a direct connection between the underlying theory of particle physics processes and detector-level physical observables. I am presenting a pedagogically-oriented derivation of the matrix element method, drawing from elementary concepts in probability theory, statistics, and the process of experimental measurements. The level of treatment should be suitable for beginning research student in phenomenology and experimental high energy physics.
Small angle scattering methods to study porous materials under high uniaxial strain
Energy Technology Data Exchange (ETDEWEB)
Le Floch, Sylvie, E-mail: sylvie.le-floch@univ-lyon1.fr; Balima, Félix; Pischedda, Vittoria; Legrand, Franck; San-Miguel, Alfonso [Institut Lumière Matière, UMR5306 Université Lyon 1-CNRS, Université de Lyon, 69622 Villeurbanne Cedex (France)
2015-02-15
We developed a high pressure cell for the in situ study of the porosity of solids under high uniaxial strain using neutron small angle scattering. The cell comprises a hydraulically actioned piston and a main body equipped with two single-crystal sapphire windows allowing for the neutron scattering of the sample. The sample cavity is designed to allow for a large volume variation as expected when compressing highly porous materials. We also implemented a loading protocol to adapt an existing diamond anvil cell for the study of porous materials by X-ray small angle scattering under high pressure. The two techniques are complementary as the radiation beam and the applied pressure are in one case perpendicular to each other (neutron cell) and in the other case parallel (X-ray cell). We will illustrate the use of these two techniques in the study of lamellar porous systems up to a maximum pressure of 0.1 GPa and 0.3 GPa for the neutron and X-ray cells, respectively. These devices allow obtaining information on the evolution of porosity with pressure in the pore dimension subdomain defined by the wave-numbers explored in the scattering process. The evolution with the applied load of such parameters as the fractal dimension of the pore-matrix interface or the apparent specific surface in expanded graphite and in expanded vermiculite is used to illustrate the use of the high pressure cells.
Prinari, Barbara; Demontis, Francesco; Li, Sitai; Horikis, Theodoros P.
2018-04-01
The inverse scattering transform (IST) with non-zero boundary conditions at infinity is developed for an m × m matrix nonlinear Schrödinger-type equation which, in the case m = 2, has been proposed as a model to describe hyperfine spin F = 1 spinor Bose-Einstein condensates with either repulsive interatomic interactions and anti-ferromagnetic spin-exchange interactions (self-defocusing case), or attractive interatomic interactions and ferromagnetic spin-exchange interactions (self-focusing case). The IST for this system was first presented by Ieda et al. (2007) , using a different approach. In our formulation, both the direct and the inverse problems are posed in terms of a suitable uniformization variable which allows to develop the IST on the standard complex plane, instead of a two-sheeted Riemann surface or the cut plane with discontinuities along the cuts. Analyticity of the scattering eigenfunctions and scattering data, symmetries, properties of the discrete spectrum, and asymptotics are derived. The inverse problem is posed as a Riemann-Hilbert problem for the eigenfunctions, and the reconstruction formula of the potential in terms of eigenfunctions and scattering data is provided. In addition, the general behavior of the soliton solutions is analyzed in detail in the 2 × 2 self-focusing case, including some special solutions not previously discussed in the literature.
Phase retrieval with the reverse projection method in the presence of object's scattering
International Nuclear Information System (INIS)
Wang, Zhili; Gao, Kun; Wang, Dajiang
2017-01-01
X-ray grating interferometry can provide substantially increased contrast over traditional attenuation-based techniques in biomedical applications, and therefore novel and complementary information. Recently, special attention has been paid to quantitative phase retrieval in X-ray grating interferometry, which is mandatory to perform phase tomography, to achieve material identification, etc. An innovative approach, dubbed “Reverse Projection” (RP), has been developed for quantitative phase retrieval. The RP method abandons grating scanning completely, and is thus advantageous in terms of higher efficiency and reduced radiation damage. Therefore, it is expected that this novel method would find its potential in preclinical and clinical implementations. Strictly speaking, the reverse projection method is applicable for objects exhibiting only absorption and refraction. In this contribution, we discuss the phase retrieval with the reverse projection method for general objects with absorption, refraction and scattering simultaneously. Especially, we investigate the influence of the object's scattering on the retrieved refraction signal. Both theoretical analysis and numerical experiments are performed. The results show that the retrieved refraction signal is the product of object's refraction and scattering signals for small values. In the case of a strong scattering, the reverse projection method cannot provide reliable phase retrieval. Those presented results will guide the use of the reverse projection method for future practical applications, and help to explain some possible artifacts in the retrieved images and/or reconstructed slices. - Highlights: • Accurate phase retrieval by the reverse projection method without object's scattering. • Retrieved refraction signal contaminated by the object's scattering. • Refraction signal underestimated by the reverse projection method. • Guide the use of the reverse projection method for
The Visual Matrix Method: Imagery and Affect in a Group-Based Research Setting
Directory of Open Access Journals (Sweden)
Lynn Froggett
2015-07-01
Full Text Available The visual matrix is a method for researching shared experience, stimulated by sensory material relevant to a research question. It is led by imagery, visualization and affect, which in the matrix take precedence over discourse. The method enables the symbolization of imaginative and emotional material, which might not otherwise be articulated and allows "unthought" dimensions of experience to emerge into consciousness in a participatory setting. We describe the process of the matrix with reference to the study "Public Art and Civic Engagement" (FROGGETT, MANLEY, ROY, PRIOR & DOHERTY, 2014 in which it was developed and tested. Subsequently, examples of its use in other contexts are provided. Both the matrix and post-matrix discussions are described, as is the interpretive process that follows. Theoretical sources are highlighted: its origins in social dreaming; the atemporal, associative nature of the thinking during and after the matrix which we describe through the Deleuzian idea of the rhizome; and the hermeneutic analysis which draws from object relations theory and the Lorenzerian tradition of scenic understanding. The matrix has been conceptualized as a "scenic rhizome" to account for its distinctive quality and hybrid origins in research practice. The scenic rhizome operates as a "third" between participants and the "objects" of contemplation. We suggest that some of the drawbacks of other group-based methods are avoided in the visual matrix—namely the tendency for inter-personal dynamics to dominate the event. URN: http://nbn-resolving.de/urn:nbn:de:0114-fqs150369
A New Method to Extract CSP Gather of Topography for Scattered Wave Imaging
Directory of Open Access Journals (Sweden)
Zhao Pan
2017-01-01
Full Text Available The seismic method is one of the major geophysical tools to study the structure of the earth. The extraction of the common scatter point (CSP gather is a critical step to accomplish the seismic imaging with a scattered wave. Conventionally, the CSP gather is obtained with the assumption that the earth surface is horizontal. However, errors are introduced to the final imaging result if the seismic traces obtained at the rugged surface are processed using the conventional method. Hence, we propose the method of the extraction of the CSP gather for the seismic data collected at the rugged surface. The proposed method is validated by two numerical examples and expected to reduce the effect of the topography on the scattered wave imaging.
Investigation of Compton scattering correction methods in cardiac SPECT by Monte Carlo simulations
International Nuclear Information System (INIS)
Silva, A.M. Marques da; Furlan, A.M.; Robilotta, C.C.
2001-01-01
The goal of this work was the use of Monte Carlo simulations to investigate the effects of two scattering correction methods: dual energy window (DEW) and dual photopeak window (DPW), in quantitative cardiac SPECT reconstruction. MCAT torso-cardiac phantom, with 99m Tc and non-uniform attenuation map was simulated. Two different photopeak windows were evaluated in DEW method: 15% and 20%. Two 10% wide subwindows centered symmetrically within the photopeak were used in DPW method. Iterative ML-EM reconstruction with modified projector-backprojector for attenuation correction was applied. Results indicated that the choice of the scattering and photopeak windows determines the correction accuracy. For the 15% window, fitted scatter fraction gives better results than k = 0.5. For the 20% window, DPW is the best method, but it requires parameters estimation using Monte Carlo simulations. (author)
Gurrala, Praveen; Downs, Andrew; Chen, Kun; Song, Jiming; Roberts, Ron
2018-04-01
Full wave scattering models for ultrasonic waves are necessary for the accurate prediction of voltage signals received from complex defects/flaws in practical nondestructive evaluation (NDE) measurements. We propose the high-order Nyström method accelerated by the multilevel fast multipole algorithm (MLFMA) as an improvement to the state-of-the-art full-wave scattering models that are based on boundary integral equations. We present numerical results demonstrating improvements in simulation time and memory requirement. Particularly, we demonstrate the need for higher order geom-etry and field approximation in modeling NDE measurements. Also, we illustrate the importance of full-wave scattering models using experimental pulse-echo data from a spherical inclusion in a solid, which cannot be modeled accurately by approximation-based scattering models such as the Kirchhoff approximation.
Scatter correction method for x-ray CT using primary modulation: Phantom studies
International Nuclear Information System (INIS)
Gao Hewei; Fahrig, Rebecca; Bennett, N. Robert; Sun Mingshan; Star-Lack, Josh; Zhu Lei
2010-01-01
Purpose: Scatter correction is a major challenge in x-ray imaging using large area detectors. Recently, the authors proposed a promising scatter correction method for x-ray computed tomography (CT) using primary modulation. Proof of concept was previously illustrated by Monte Carlo simulations and physical experiments on a small phantom with a simple geometry. In this work, the authors provide a quantitative evaluation of the primary modulation technique and demonstrate its performance in applications where scatter correction is more challenging. Methods: The authors first analyze the potential errors of the estimated scatter in the primary modulation method. On two tabletop CT systems, the method is investigated using three phantoms: A Catphan(c)600 phantom, an anthropomorphic chest phantom, and the Catphan(c)600 phantom with two annuli. Two different primary modulators are also designed to show the impact of the modulator parameters on the scatter correction efficiency. The first is an aluminum modulator with a weak modulation and a low modulation frequency, and the second is a copper modulator with a strong modulation and a high modulation frequency. Results: On the Catphan(c)600 phantom in the first study, the method reduces the error of the CT number in the selected regions of interest (ROIs) from 371.4 to 21.9 Hounsfield units (HU); the contrast to noise ratio also increases from 10.9 to 19.2. On the anthropomorphic chest phantom in the second study, which represents a more difficult case due to the high scatter signals and object heterogeneity, the method reduces the error of the CT number from 327 to 19 HU in the selected ROIs and from 31.4% to 5.7% on the overall average. The third study is to investigate the impact of object size on the efficiency of our method. The scatter-to-primary ratio estimation error on the Catphan(c)600 phantom without any annulus (20 cm in diameter) is at the level of 0.04, it rises to 0.07 and 0.1 on the phantom with an
Directory of Open Access Journals (Sweden)
Fabian Zeitvogel
2016-02-01
Full Text Available We present ScatterJn, an ImageJ (and Fiji plugin for scatterplot-based exploration and analysis of analytical microscopy data. In contrast to commonly used scatterplot tools, it handles more than two input images (or image stacks, respectively by creating a matrix of pairwise scatterplots. The tool offers the possibility to manually classify pixels by selecting regions of datapoints in the scatterplots as well as in the spatial domain. We demonstrate its functioning using a set of elemental maps acquired by SEM-EDX mapping of a soil sample. The plugin is available at https://savannah.nongnu.org/projects/scatterjn.
International Nuclear Information System (INIS)
Pascual, J.
1987-01-01
An X-ray fluorescence method for determining trace elements in silicate rock samples was studied. The procedure focused on the application of the pertinent matrix corrections. Either the Compton peak or the reciprocal of the mass absorption coefficient of the sample was used as internal standard for this purpose. X-ray tubes with W or Cr anodes were employed, and the W Lβ and Cr Kα Compton intensities scattered by the sample were measured. The mass absorption coefficients at both sides of the absorption edge for Fe (1.658 and 1.936 A) were calculated. The elements Zr, Y, Rb, Zn, Ni, Cr and V were determined in 15 international reference rocks covering wide ranges of concentration. Relative mean errors were in many cases less than 10%. (author)
American Society for Testing and Materials. Philadelphia
2004-01-01
1.1 This test method covers the determination of translaminar fracture toughness, KTL, for laminated and pultruded polymer matrix composite materials of various ply orientations using test results from monotonically loaded notched specimens. 1.2 This test method is applicable to room temperature laboratory air environments. 1.3 Composite materials that can be tested by this test method are not limited by thickness or by type of polymer matrix or fiber, provided that the specimen sizes and the test results meet the requirements of this test method. This test method was developed primarily from test results of various carbon fiber – epoxy matrix laminates and from additional results of glass fiber – epoxy matrix, glass fiber-polyester matrix pultrusions and carbon fiber – bismaleimide matrix laminates (1-4, 6, 7). 1.4 A range of eccentrically loaded, single-edge-notch tension, ESE(T), specimen sizes with proportional planar dimensions is provided, but planar size may be variable and adjusted, with asso...
Emergy Algebra: Improving Matrix Methods for Calculating Tranformities
Transformity is one of the core concepts in Energy Systems Theory and it is fundamental to the calculation of emergy. Accurate evaluation of transformities and other emergy per unit values is essential for the broad acceptance, application and further development of emergy method...
Convergence of an L2-approach in the coupled-channels optical potential method for e-H scattering
International Nuclear Information System (INIS)
Bray, I.; Konovalov, D.A.; McCarthy, I.E.
1990-08-01
An L 2 approach to the coupled-channels optical method is studied. The investigation is done for electron-hydrogen elastic scattering at projectile energies of 30, 50, 100 and 200 eV. Weak coupling, free-particle Green's function and no exchange in Q-space are appoximations used to calculate the polarization potential. This model problem is solved exactly using actual hydrogen discrete and continuum functions. The convergence of an L 2 approach with the Laguerre basis to the exact result is investigated. It is found that a basis of 10 Laguerre functions is sufficient for convergence of approximately 5% in the polarization potential matrix elements and 2% in the differential cross sections for non-large angles. The convergence is faster for smaller energies. In general, the convergence to the exact result is slow. 12 refs., 2 tabs., 2 figs
Telfeyan, Katherine; Ware, S. Doug; Reimus, Paul W.; Birdsell, Kay H.
2018-02-01
Diffusion cell and diffusion wafer experiments were conducted to compare methods for estimating effective matrix diffusion coefficients in rock core samples from Pahute Mesa at the Nevada Nuclear Security Site (NNSS). A diffusion wafer method, in which a solute diffuses out of a rock matrix that is pre-saturated with water containing the solute, is presented as a simpler alternative to the traditional through-diffusion (diffusion cell) method. Both methods yielded estimates of effective matrix diffusion coefficients that were within the range of values previously reported for NNSS volcanic rocks. The difference between the estimates of the two methods ranged from 14 to 30%, and there was no systematic high or low bias of one method relative to the other. From a transport modeling perspective, these differences are relatively minor when one considers that other variables (e.g., fracture apertures, fracture spacings) influence matrix diffusion to a greater degree and tend to have greater uncertainty than effective matrix diffusion coefficients. For the same relative random errors in concentration measurements, the diffusion cell method yields effective matrix diffusion coefficient estimates that have less uncertainty than the wafer method. However, the wafer method is easier and less costly to implement and yields estimates more quickly, thus allowing a greater number of samples to be analyzed for the same cost and time. Given the relatively good agreement between the methods, and the lack of any apparent bias between the methods, the diffusion wafer method appears to offer advantages over the diffusion cell method if better statistical representation of a given set of rock samples is desired.
Chosen interval methods for solving linear interval systems with special type of matrix
Szyszka, Barbara
2013-10-01
The paper is devoted to chosen direct interval methods for solving linear interval systems with special type of matrix. This kind of matrix: band matrix with a parameter, from finite difference problem is obtained. Such linear systems occur while solving one dimensional wave equation (Partial Differential Equations of hyperbolic type) by using the central difference interval method of the second order. Interval methods are constructed so as the errors of method are enclosed in obtained results, therefore presented linear interval systems contain elements that determining the errors of difference method. The chosen direct algorithms have been applied for solving linear systems because they have no errors of method. All calculations were performed in floating-point interval arithmetic.
Energy Technology Data Exchange (ETDEWEB)
Calloo, A.; Vidal, J.F.; Le Tellier, R.; Rimpault, G., E-mail: ansar.calloo@cea.fr, E-mail: jean-francois.vidal@cea.fr, E-mail: romain.le-tellier@cea.fr, E-mail: gerald.rimpault@cea.fr [CEA, DEN, DER/SPRC/LEPh, Saint-Paul-lez-Durance (France)
2011-07-01
This paper deals with the solving of the multigroup integro-differential form of the transport equation for fine energy group structure. In that case, multigroup transfer cross sections display strongly peaked shape for light scatterers and the current Legendre polynomial expansion is not well-suited to represent them. Furthermore, even if considering an exact scattering cross sections representation, the scattering source in the discrete ordinates method (also known as the Sn method) being calculated by sampling the angular flux at given directions, may be wrongly computed due to lack of angular support for the angular flux. Hence, following the work of Gerts and Matthews, an angular finite volume solver has been developed for 2D Cartesian geometries. It integrates the multigroup transport equation over discrete volume elements obtained by meshing the unit sphere with a product grid over the polar and azimuthal coordinates and by considering the integrated flux per solid angle element. The convergence of this method has been compared to the S{sub n} method for a highly anisotropic benchmark. Besides, piecewise-average scattering cross sections have been produced for non-bound Hydrogen atoms using a free gas model for thermal neutrons. LWR lattice calculations comparing Legendre representations of the Hydrogen scattering multigroup cross section at various orders and piecewise-average cross sections for this same atom are carried out (while keeping a Legendre representation for all other isotopes). (author)
Monte Carlo evaluation of scattering correction methods in 131I studies using pinhole collimator
International Nuclear Information System (INIS)
López Díaz, Adlin; San Pedro, Aley Palau; Martín Escuela, Juan Miguel; Rodríguez Pérez, Sunay; Díaz García, Angelina
2017-01-01
Scattering is quite important for image activity quantification. In order to study the scattering factors and the efficacy of 3 multiple window energy scatter correction methods during 131 I thyroid studies with a pinhole collimator (5 mm hole) a Monte Carlo simulation (MC) was developed. The GAMOS MC code was used to model the gamma camera and the thyroid source geometry. First, to validate the MC gamma camera pinhole-source model, sensibility in air and water of the simulated and measured thyroid phantom geometries were compared. Next, simulations to investigate scattering and the result of triple energy (TEW), Double energy (DW) and Reduced double (RDW) energy windows correction methods were performed for different thyroid sizes and depth thicknesses. The relative discrepancies to MC real event were evaluated. Results: The accuracy of the GAMOS MC model was verified and validated. The image’s scattering contribution was significant, between 27-40 %. The discrepancies between 3 multiple window energy correction method results were significant (between 9-86 %). The Reduce Double Window methods (15%) provide discrepancies of 9-16 %. Conclusions: For the simulated thyroid geometry with pinhole, the RDW (15 %) was the most effective. (author)
International Nuclear Information System (INIS)
Calloo, A.; Vidal, J.F.; Le Tellier, R.; Rimpault, G.
2011-01-01
This paper deals with the solving of the multigroup integro-differential form of the transport equation for fine energy group structure. In that case, multigroup transfer cross sections display strongly peaked shape for light scatterers and the current Legendre polynomial expansion is not well-suited to represent them. Furthermore, even if considering an exact scattering cross sections representation, the scattering source in the discrete ordinates method (also known as the Sn method) being calculated by sampling the angular flux at given directions, may be wrongly computed due to lack of angular support for the angular flux. Hence, following the work of Gerts and Matthews, an angular finite volume solver has been developed for 2D Cartesian geometries. It integrates the multigroup transport equation over discrete volume elements obtained by meshing the unit sphere with a product grid over the polar and azimuthal coordinates and by considering the integrated flux per solid angle element. The convergence of this method has been compared to the S_n method for a highly anisotropic benchmark. Besides, piecewise-average scattering cross sections have been produced for non-bound Hydrogen atoms using a free gas model for thermal neutrons. LWR lattice calculations comparing Legendre representations of the Hydrogen scattering multigroup cross section at various orders and piecewise-average cross sections for this same atom are carried out (while keeping a Legendre representation for all other isotopes). (author)
Quantum scattering theory of a single-photon Fock state in three-dimensional spaces.
Liu, Jingfeng; Zhou, Ming; Yu, Zongfu
2016-09-15
A quantum scattering theory is developed for Fock states scattered by two-level systems in three-dimensional free space. It is built upon the one-dimensional scattering theory developed in waveguide quantum electrodynamics. The theory fully quantizes the incident light as Fock states and uses a non-perturbative method to calculate the scattering matrix.
Sharpening methods for images captured through Bayer matrix
Kalevo, Ossi; Rantanen, Henry, Jr.
2003-05-01
Image resolution and sharpness are essential criteria for a human observer when estimating the image quality. Typically cheap small-sized, low-resolution CMOS-camera sensors do not provide sharp enough images, at least when comparing to high-end digital cameras. Sharpening function can be used to increase the subjective sharpness seen by the observer. In this paper, few methods to apply sharpening for images captured by CMOS imaging sensors through color filter array (CFA) are compared. The sharpening easily adds also the visibility of noise, pixel-cross talk and interpolation artifacts. Necessary arrangements to avoid the amplification of these unwanted phenomenon are discussed. By applying the sharpening only to the green component the processing power requirements can be clearly reduced. By adjusting the red and blue component sharpness, according to the green component sharpening, creation of false colors are reduced highly. Direction search sharpening method can be used to reduce the amplification of the artifacts caused by the CFA interpolation (CFAI). The comparison of the presented methods is based mainly on subjective image quality. Also the processing power and memory requirements are considered.
A method for the generation of random multiple Coulomb scattering angles
International Nuclear Information System (INIS)
Campbell, J.R.
1995-06-01
A method for the random generation of spatial angles drawn from non-Gaussian multiple Coulomb scattering distributions is presented. The method employs direct numerical inversion of cumulative probability distributions computed from the universal non-Gaussian angular distributions of Marion and Zimmerman. (author). 12 refs., 3 figs
A Comparison of Methods for Estimating the Determinant of High-Dimensional Covariance Matrix
Hu, Zongliang
2017-09-27
The determinant of the covariance matrix for high-dimensional data plays an important role in statistical inference and decision. It has many real applications including statistical tests and information theory. Due to the statistical and computational challenges with high dimensionality, little work has been proposed in the literature for estimating the determinant of high-dimensional covariance matrix. In this paper, we estimate the determinant of the covariance matrix using some recent proposals for estimating high-dimensional covariance matrix. Specifically, we consider a total of eight covariance matrix estimation methods for comparison. Through extensive simulation studies, we explore and summarize some interesting comparison results among all compared methods. We also provide practical guidelines based on the sample size, the dimension, and the correlation of the data set for estimating the determinant of high-dimensional covariance matrix. Finally, from a perspective of the loss function, the comparison study in this paper may also serve as a proxy to assess the performance of the covariance matrix estimation.
A Comparison of Methods for Estimating the Determinant of High-Dimensional Covariance Matrix.
Hu, Zongliang; Dong, Kai; Dai, Wenlin; Tong, Tiejun
2017-09-21
The determinant of the covariance matrix for high-dimensional data plays an important role in statistical inference and decision. It has many real applications including statistical tests and information theory. Due to the statistical and computational challenges with high dimensionality, little work has been proposed in the literature for estimating the determinant of high-dimensional covariance matrix. In this paper, we estimate the determinant of the covariance matrix using some recent proposals for estimating high-dimensional covariance matrix. Specifically, we consider a total of eight covariance matrix estimation methods for comparison. Through extensive simulation studies, we explore and summarize some interesting comparison results among all compared methods. We also provide practical guidelines based on the sample size, the dimension, and the correlation of the data set for estimating the determinant of high-dimensional covariance matrix. Finally, from a perspective of the loss function, the comparison study in this paper may also serve as a proxy to assess the performance of the covariance matrix estimation.
A Comparison of Methods for Estimating the Determinant of High-Dimensional Covariance Matrix
Hu, Zongliang; Dong, Kai; Dai, Wenlin; Tong, Tiejun
2017-01-01
The determinant of the covariance matrix for high-dimensional data plays an important role in statistical inference and decision. It has many real applications including statistical tests and information theory. Due to the statistical and computational challenges with high dimensionality, little work has been proposed in the literature for estimating the determinant of high-dimensional covariance matrix. In this paper, we estimate the determinant of the covariance matrix using some recent proposals for estimating high-dimensional covariance matrix. Specifically, we consider a total of eight covariance matrix estimation methods for comparison. Through extensive simulation studies, we explore and summarize some interesting comparison results among all compared methods. We also provide practical guidelines based on the sample size, the dimension, and the correlation of the data set for estimating the determinant of high-dimensional covariance matrix. Finally, from a perspective of the loss function, the comparison study in this paper may also serve as a proxy to assess the performance of the covariance matrix estimation.
NewIn-situ synthesis method of magnesium matrix composites reinforced with TiC particulates
Directory of Open Access Journals (Sweden)
Zhang Xiuqing
2006-12-01
Full Text Available Magnesium matrix composites reinforced with TiC particulates was prepared using a new in-situ synthesis method of remelting and dilution technique. And measurements were performed on the composites. The results of x ray diffraction (XRD analysis confirmed that TiC particulates were synthesized during the sintering process, and they retained in magnesium matrix composites after the remelting and dilution processing. From the microstructure characterization and electron probe microanalysis (EPMA, we could see that fine TiC particulates distributed uniformly in the matrix material.
Discrete-ordinate method with matrix exponential for a pseudo-spherical atmosphere: Vector case
International Nuclear Information System (INIS)
Doicu, A.; Trautmann, T.
2009-01-01
The paper is devoted to the extension of the matrix-exponential formalism for the scalar radiative transfer to the vector case. Using basic results of the theory of matrix-exponential functions we provide a compact and versatile formulation of the vector radiative transfer. As in the scalar case, we operate with the concept of the layer equation incorporating the level values of the Stokes vector. The matrix exponentials which enter in the expression of the layer equation are computed by using the matrix eigenvalue method and the Pade approximation. A discussion of the computational efficiency of the proposed method for both an aerosol-loaded atmosphere as well as a cloudy atmosphere is also provided
Studies of coherent/Compton scattering method for bone mineral content measurement
International Nuclear Information System (INIS)
Sakurai, Kiyoko; Iwanami, Shigeru; Nakazawa, Keiji; Matsubayashi, Takashi; Imamura, Keiko.
1980-01-01
A measurement of bone mineral content by a coherent/Compton scattering method was described. A bone sample was irradiated by a collimated narrow beam of 59.6 keV gamma-rays emitted from a 300 mCi 241 Am source, and the scattered radiations were detected using a collimated pure germanium detector placed at 90 0 to the incident beam. The ratio of coherent to Compton peaks in a spectrum of the scattered radiations depends on the bone mineral content of the bone sample. The advantage of this method is that bone mineral content of a small region in a bone can be accurately measured. Assuming that bone consists of two components, protein and bone mineral, and that the mass absorption coefficient for Compton scattering is independent of material, the coherent to Compton scattering ratio is linearly related to the percentage in weight of bone mineral. A calibration curve was obtained by measuring standard samples which were mixed with Ca 3 (PO 4 ) 2 and H 2 O. The error due to the assumption about the mass absorption coefficient for Compton scattering and to the difference between true bone and standard samples was estimated to be less than 3% within the range from 10 to 60% in weight of bone mineral. The fat in bone affects an estimated value by only 1.5% when it is 20% in weight. For the clinical application of this method, the location to be analyzed should be selected before the measurement with two X-ray images viewed from the source and the detector. These views would be also used to correct the difference in absorption between coherent and Compton scattered radiations whose energies are slightly different from each other. The absorbed dose to the analyzed region was approximately 150 mrad. The time required for one measurement in this study was about 10 minutes. (author)
A software-based x-ray scatter correction method for breast tomosynthesis
International Nuclear Information System (INIS)
Jia Feng, Steve Si; Sechopoulos, Ioannis
2011-01-01
Purpose: To develop a software-based scatter correction method for digital breast tomosynthesis (DBT) imaging and investigate its impact on the image quality of tomosynthesis reconstructions of both phantoms and patients. Methods: A Monte Carlo (MC) simulation of x-ray scatter, with geometry matching that of the cranio-caudal (CC) view of a DBT clinical prototype, was developed using the Geant4 toolkit and used to generate maps of the scatter-to-primary ratio (SPR) of a number of homogeneous standard-shaped breasts of varying sizes. Dimension-matched SPR maps were then deformed and registered to DBT acquisition projections, allowing for the estimation of the primary x-ray signal acquired by the imaging system. Noise filtering of the estimated projections was then performed to reduce the impact of the quantum noise of the x-ray scatter. Three dimensional (3D) reconstruction was then performed using the maximum likelihood-expectation maximization (MLEM) method. This process was tested on acquisitions of a heterogeneous 50/50 adipose/glandular tomosynthesis phantom with embedded masses, fibers, and microcalcifications and on acquisitions of patients. The image quality of the reconstructions of the scatter-corrected and uncorrected projections was analyzed by studying the signal-difference-to-noise ratio (SDNR), the integral of the signal in each mass lesion (integrated mass signal, IMS), and the modulation transfer function (MTF). Results: The reconstructions of the scatter-corrected projections demonstrated superior image quality. The SDNR of masses embedded in a 5 cm thick tomosynthesis phantom improved 60%-66%, while the SDNR of the smallest mass in an 8 cm thick phantom improved by 59% (p < 0.01). The IMS of the masses in the 5 cm thick phantom also improved by 15%-29%, while the IMS of the masses in the 8 cm thick phantom improved by 26%-62% (p < 0.01). Some embedded microcalcifications in the tomosynthesis phantoms were visible only in the scatter
On the evolution equations, solvable through the inverse scattering method
International Nuclear Information System (INIS)
Gerdjikov, V.S.; Khristov, E.Kh.
1979-01-01
The nonlinear evolution equations (NLEE), related to the one-parameter family of Dirac operators are considered in a uniform manner. The class of NLEE solvable through the inverse scatterina method and their conservation laws are described. The description of the hierarchy of Hamiltonian structures and the proof of complete integrability of the NLEE is presented. The class of Baecklund transformations for these NLEE is derived. The general formulae are illustrated by two important examples: the nonlinear Schroedinger equation and the sine-Gordon equation
A finite element conjugate gradient FFT method for scattering
Collins, Jeffery D.; Ross, Dan; Jin, J.-M.; Chatterjee, A.; Volakis, John L.
1991-01-01
Validated results are presented for the new 3D body of revolution finite element boundary integral code. A Fourier series expansion of the vector electric and mangnetic fields is employed to reduce the dimensionality of the system, and the exact boundary condition is employed to terminate the finite element mesh. The mesh termination boundary is chosen such that is leads to convolutional boundary operatores of low O(n) memory demand. Improvements of this code are discussed along with the proposed formulation for a full 3D implementation of the finite element boundary integral method in conjunction with a conjugate gradiant fast Fourier transformation (CGFFT) solution.
Application of the R-matrix method to photoionization of molecules.
Tashiro, Motomichi
2010-04-07
The R-matrix method has been used for theoretical calculation of electron collision with atoms and molecules for long years. The method was also formulated to treat photoionization process, however, its application has been mostly limited to photoionization of atoms. In this work, we implement the R-matrix method to treat molecular photoionization problem based on the UK R-matrix codes. This method can be used for diatomic as well as polyatomic molecules, with multiconfigurational description for electronic states of both target neutral molecule and product molecular ion. Test calculations were performed for valence electron photoionization of nitrogen (N(2)) as well as nitric oxide (NO) molecules. Calculated photoionization cross sections and asymmetry parameters agree reasonably well with the available experimental results, suggesting usefulness of the method for molecular photoionization.
Imagining transitions in old age through the Visual Matrix method
DEFF Research Database (Denmark)
Liveng, Anne; Ramvi, Ellen; Froggett, Lynn
2017-01-01
Dominant discourses of ageing are often confined to what is less painful to think about and therefore idealise or denigrate ageing and later life. We present findings from an exploratory psychosocial study, in a Nordic context, into three later-life transitions: from working life to retirement, f......-generational continuity, which together link life and death, hope and despair, separation and connectedness.......Dominant discourses of ageing are often confined to what is less painful to think about and therefore idealise or denigrate ageing and later life. We present findings from an exploratory psychosocial study, in a Nordic context, into three later-life transitions: from working life to retirement......, from mental health to dementia and from life to death. Because, for some, these topics are hard to bear and therefore defended against and routinely excluded from everyday awareness, we used a method led by imagery and affect–the Visual Matrix–to elicit participant s’ free associative personal...
The matrix method for radiological characterization of radioactive waste
Magistris, M
2007-01-01
Beam losses are responsible for material activation in some of the components of particle accelerators. The activation is caused by several nuclear processes and varies with the irradiation history and the characteristics of the material (namely chemical composition and size). Once at the end of their operational lifetime, these materials require radiological characterization. The radionuclide inventory depends on the particle spectrum, the irradiation history and the chemical composition of the material. As long as these factors are known and the material cross-sections are available, the induced radioactivity can be calculated analytically. However, these factors vary widely among different items of waste and sometimes they are only partially known. The European Laboratory for Particle Physics (CERN, Geneva) has been operating accelerators for high-energy physics for 50 years. Different methods for the evaluation of the radionuclide inventory are currently under investigation at CERN, including the so-calle...
The scattering properties of anisotropic dielectric spheres on electromagnetic waves
International Nuclear Information System (INIS)
Chen Hui; Zhang Weiyi; Wang Zhenlin; Ming Naiben
2004-01-01
The scattering coefficients of spheres with dielectric anisotropy are calculated analytically in this paper using the perturbation method. It is found that the different modes of vector spherical harmonics and polarizations are coupled together in the scattering coefficients (c-matrix) in contrast to the isotropic case where all modes are decoupled from each other. The generalized c-matrix is then incorporated into our codes for a vector wave multiple scattering program; the preliminary results on face centred cubic structure show that dielectric anisotropy reduces the symmetry of the scattering c-matrix and removes the degeneracy in photonic band structures composed of isotropic dielectric spheres
Pascual Pañach, Josep
2010-01-01
Leaks are present in all water distribution systems. In this paper a method for leakage detection and localisation is presented. It uses pressure measurements and simulation models. Leakage localisation methodology is based on pressure sensitivity matrix. Sensitivity is normalised and binarised using a common threshold for all nodes, so a signatures matrix is obtained. A pressure sensor optimal distribution methodology is developed too, but it is not used in the real test. To validate this...
Preliminary application of maximum likelihood method in HL-2A Thomson scattering system
International Nuclear Information System (INIS)
Yao Ke; Huang Yuan; Feng Zhen; Liu Chunhua; Li Enping; Nie Lin
2010-01-01
Maximum likelihood method to process the data of HL-2A Thomson scattering system is presented. Using mathematical statistics, this method maximizes the possibility of the likeness between the theoretical data and the observed data, so that we could get more accurate result. It has been proved to be applicable in comparison with that of the ratios method, and some of the drawbacks in ratios method do not exist in this new one. (authors)
Comparison of approximate methods for multiple scattering in high-energy collisions. II
International Nuclear Information System (INIS)
Nolan, A.M.; Tobocman, W.; Werby, M.F.
1976-01-01
The scattering in one dimension of a particle by a target of N like particles in a bound state has been studied. The exact result for the transmission probability has been compared with the predictions of the Glauber theory, the Watson optical potential model, and the adiabatic (or fixed scatterer) approximation. The approximate methods optical potential model is second best. The Watson method is found to work better when the kinematics suggested by Foldy and Walecka are used rather than that suggested by Watson, that is to say, when the two-body of the nucleon-nucleon reduced mass
Application of the method of continued fractions for electron scattering by linear molecules
International Nuclear Information System (INIS)
Lee, M.-T.; Iga, I.; Fujimoto, M.M.; Lara, O.; Brasilia Univ., DF
1995-01-01
The method of continued fractions (MCF) of Horacek and Sasakawa is adapted for the first time to study low-energy electron scattering by linear molecules. Particularly, we have calculated the reactance K-matrices for an electron scattered by hydrogen molecule and hydrogen molecular ion as well as by a polar LiH molecule in the static-exchange level. For all the applications studied herein. the calculated physical quantities converge rapidly, even for a strongly polar molecule such as LiH, to the correct values and in most cases the convergence is monotonic. Our study suggests that the MCF could be an efficient method for studying electron-molecule scattering and also photoionization of molecules. (Author)
Three-body forces for electrons by the S-matrix method
International Nuclear Information System (INIS)
Margaritelli, R.
1989-01-01
A electromagnetic three-body potential between eletrons is derived by the S-matrix method. This potential can be compared up to a certain point with other electromagnetic potentials (obtained by other methods) encountered in the literature. However, since the potential derived here is far more complete than others, this turns direct comparison with the potentials found in the literature somewhat difficult. These calculations allow a better understanding of the S-matrix method as applied to problems which involve the calculations of three-body nuclear forces (these calculations are performed in order to understand the 3 He form factor). Furthermore, these results enable us to decide between two discrepant works which derive the two-pion exchange three-body potential, both by the S-matrix method. (author) [pt
A New Pseudoinverse Matrix Method For Balancing Chemical Equations And Their Stability
International Nuclear Information System (INIS)
Risteski, Ice B.
2008-01-01
In this work is given a new pseudoniverse matrix method for balancing chemical equations. Here offered method is founded on virtue of the solution of a Diophantine matrix equation by using of a Moore-Penrose pseudoinverse matrix. The method has been tested on several typical chemical equations and found to be very successful for the all equations in our extensive balancing research. This method, which works successfully without any limitations, also has the capability to determine the feasibility of a new chemical reaction, and if it is feasible, then it will balance the equation. Chemical equations treated here possess atoms with fractional oxidation numbers. Also, in the present work are introduced necessary and sufficient criteria for stability of chemical equations over stability of their extended matrices
Novel Direction Of Arrival Estimation Method Based on Coherent Accumulation Matrix Reconstruction
Directory of Open Access Journals (Sweden)
Li Lei
2015-04-01
Full Text Available Based on coherent accumulation matrix reconstruction, a novel Direction Of Arrival (DOA estimation decorrelation method of coherent signals is proposed using a small sample. First, the Signal to Noise Ratio (SNR is improved by performing coherent accumulation operation on an array of observed data. Then, according to the structure characteristics of the accumulated snapshot vector, the equivalent covariance matrix, whose rank is the same as the number of array elements, is constructed. The rank of this matrix is proved to be determined just by the number of incident signals, which realize the decorrelation of coherent signals. Compared with spatial smoothing method, the proposed method performs better by effectively avoiding aperture loss with high-resolution characteristics and low computational complexity. Simulation results demonstrate the efficiency of the proposed method.
Synthetic acceleration methods for linear transport problems with highly anisotropic scattering
International Nuclear Information System (INIS)
Khattab, K.M.
1989-01-01
One of the iterative methods which is used to solve the discretized transport equation is called the Source Iteration Method (SI). The SI method converges very slowly for problems with optically thick regions and scattering ratios (σ s /σ t ) near unity. The Diffusion-Synthetic Acceleration method (DSA) is one of the methods which has been devised to improve the convergence rate of the SI method. The DSA method is a good tool to accelerate the SI method, if the particle which is being dealt with is a neutron. This is because the scattering process for neutrons is not severely anisotropic. However, if the particle is a charged particle (electron), DSA becomes ineffective as an acceleration device because here the scattering process is severely anisotropic. To improve the DSA algorithm for electron transport, the author approaches the problem in two different ways in this thesis. He develops the first approach by accelerating more angular moments (φ 0 , φ 1 , φ 2 , φ 3 ,...) than is done in DSA; he calls this approach the Modified P N Synthetic Acceleration (MPSA) method. In the second approach he modifies the definition of the transport sweep, using the physics of the scattering; he calls this approach the Modified Diffusion Synthetic Acceleration (MDSA) method. In general, he has developed, analyzed, and implemented the MPSA and MDSA methods in this thesis and has shown that for a high order quadrature set and mesh widths about 1.0 cm, they are each about 34 times faster (clock time) than the DSA method. Also, he has found that the MDSA spectral radius decreases as the mesh size increases. This makes the MDSA method a better choice for large spatial meshes
A study on basic theory for CDCC method for three-body model of deuteron scattering
International Nuclear Information System (INIS)
Kawai, Mitsuji
1988-01-01
Recent studies have revealed that the CDCC method is valid for treating the decomposition process involved in deuteron scattering on the basis of a three-body model. However, theoretical support has not been developed for this method. The present study is aimed at determining whether a solution by the CDCC method can be obtained 'correctly' from a 'realistic' model Hamiltonian for deuteron scattering. Some researchers have recently pointed out that there are some problems with the conventional CDCC calculation procedure in view of the general scattering theory. These problems are associated with asymptotic froms of the wave functions, convergence of calculations, and boundary conditions. Considerations show that the problem with asymptotic forms of the wave function is not a fatal defect, though some compromise is necessary. The problem with the convergence of calculations is not very serious either. Discussions are made of the handling of boundary conditions. Thus, the present study indicates that the CDCC method can be applied satisfactorily to actual deuteron scattering, and that the model wave function for the CDCC method is consistent with the model Hamiltonian. (Nogami, K.)
International Nuclear Information System (INIS)
Das, Avik; Mazumder, S.; Sen, D.; Yalmali, V.; Shah, J.G.
2014-01-01
Nuclear power plants generate many kinds of hazardous nuclear waste which are needed to be disposed in an eco-friendly manner. Many different waste incarceration techniques have been adapted for managing the nuclear waste of different category of radioactivity. Immobilisation of low and intermediate level radioactive wastes in cement matrix is one of the widely used and cost-effective techniques in waste management. However, loading of nuclear waste in cement matrix can alter the mesoscopic structure of the hydrated cement and hence, it is very important to set the maximum limit of waste loading in cement for providing proper physical isolation to the nuclear waste
On the generalized eigenvalue method for energies and matrix elements in lattice field theory
Energy Technology Data Exchange (ETDEWEB)
Blossier, Benoit [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)]|[Paris-XI Univ., 91 - Orsay (France). Lab. de Physique Theorique; Morte, Michele della [CERN, Geneva (Switzerland). Physics Dept.]|[Mainz Univ. (Germany). Inst. fuer Kernphysik; Hippel, Georg von; Sommer, Rainer [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Mendes, Tereza [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)]|[Sao Paulo Univ. (Brazil). IFSC
2009-02-15
We discuss the generalized eigenvalue problem for computing energies and matrix elements in lattice gauge theory, including effective theories such as HQET. It is analyzed how the extracted effective energies and matrix elements converge when the time separations are made large. This suggests a particularly efficient application of the method for which we can prove that corrections vanish asymptotically as exp(-(E{sub N+1}-E{sub n}) t). The gap E{sub N+1}-E{sub n} can be made large by increasing the number N of interpolating fields in the correlation matrix. We also show how excited state matrix elements can be extracted such that contaminations from all other states disappear exponentially in time. As a demonstration we present numerical results for the extraction of ground state and excited B-meson masses and decay constants in static approximation and to order 1/m{sub b} in HQET. (orig.)
A Lexicographic Method for Matrix Games with Payoffs of Triangular Intuitionistic Fuzzy Numbers
Directory of Open Access Journals (Sweden)
Jiang-Xia Nan
2010-09-01
Full Text Available The intuitionistic fuzzy set (IF-set has not been applied to matrix game problems yet since it was introduced by K.T.Atanassov. The aim of this paper is to develop a methodology for solving matrix games with payoffs of triangular intuitionistic fuzzy numbers (TIFNs. Firstly the concept of TIFNs and their arithmetic operations and cut sets are introduced as well as the ranking order relations. Secondly the concept of solutions for matrix games with payoffs of TIFNs is defined. A lexicographic methodology is developed to determine the solutions of matrix games with payoffs of TIFNs for both Players through solving a pair of bi-objective linear programming models derived from two new auxiliary intuitionistic fuzzy programming models. The proposed method is illustrated with a numerical example.
On the generalized eigenvalue method for energies and matrix elements in lattice field theory
International Nuclear Information System (INIS)
Blossier, Benoit; Mendes, Tereza; Sao Paulo Univ.
2009-02-01
We discuss the generalized eigenvalue problem for computing energies and matrix elements in lattice gauge theory, including effective theories such as HQET. It is analyzed how the extracted effective energies and matrix elements converge when the time separations are made large. This suggests a particularly efficient application of the method for which we can prove that corrections vanish asymptotically as exp(-(E N+1 -E n ) t). The gap E N+1 -E n can be made large by increasing the number N of interpolating fields in the correlation matrix. We also show how excited state matrix elements can be extracted such that contaminations from all other states disappear exponentially in time. As a demonstration we present numerical results for the extraction of ground state and excited B-meson masses and decay constants in static approximation and to order 1/m b in HQET. (orig.)
A Synthetic Approach to the Transfer Matrix Method in Classical and Quantum Physics
Pujol, O.; Perez, J. P.
2007-01-01
The aim of this paper is to propose a synthetic approach to the transfer matrix method in classical and quantum physics. This method is an efficient tool to deal with complicated physical systems of practical importance in geometrical light or charged particle optics, classical electronics, mechanics, electromagnetics and quantum physics. Teaching…
Evaluation of the streaming-matrix method for discrete-ordinates duct-streaming calculations
International Nuclear Information System (INIS)
Clark, B.A.; Urban, W.T.; Dudziak, D.J.
1983-01-01
A new deterministic streaming technique called the Streaming Matrix Hybrid Method (SMHM) is applied to two realistic duct-shielding problems. The results are compared to standard discrete-ordinates and Monte Carlo calculations. The SMHM shows promise as an alternative deterministic streaming method to standard discrete-ordinates
International Nuclear Information System (INIS)
Leymarie, E.
2002-11-01
In this thesis we study the theoretical and experimental aspects of Contrast Variation by Nuclear Polarization (CVNP) applied to small-angle neutron scattering. The basics of neutron scattering theory is developed by highlighting the origin of the CVNP method: the strong spin dependence of thermal neutron scattering, especially on protons. We also present the principles of NMR with a special attention on the method of dynamic nuclear polarization by the solid effect which makes it possible to control the proton polarization and therefore the contrast for neutron scattering. We present a theoretical study of the CVNP method called static which supposes that the nuclear polarization is homogeneous in the sample and constant during the experiment. We show that it allows one to obtain partial structure functions of systems with multiple components, by carrying out several acquisitions with different polarizations on a single sample. For this purpose, we tested a simple device to stabilize the nuclear polarization. We describe finally a new application of the CVNP method called dynamic. In a solution of deuterated glycerol-water containing a small concentration of paramagnetic centres, we showed the existence of domains of polarized protons at the onset of dynamic polarization. This reinforces considerably the coherent scattering of paramagnetic centres. We describe the theoretical reasons explaining the appearance of these domains of polarization, as well as the various techniques used to observe them by neutron scattering. (author)
The Crossed-Beam Scattering Method in Studies of Ion-Molecule Reaction Dynamics
Czech Academy of Sciences Publication Activity Database
Herman, Zdeněk
2001-01-01
Roč. 212, - (2001), s. 413-443 ISSN 1387-3806 R&D Projects: GA ČR GA203/00/0632 Institutional research plan: CEZ:AV0Z4040901 Keywords : ion-molecule reaction dynamics * ion scattering * experimental methods Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 2.176, year: 2001
Integrating the Toda Lattice with Self-Consistent Source via Inverse Scattering Method
International Nuclear Information System (INIS)
Urazboev, Gayrat
2012-01-01
In this work, there is shown that the solutions of Toda lattice with self-consistent source can be found by the inverse scattering method for the discrete Sturm-Liuville operator. For the considered problem the one-soliton solution is obtained.
Perego, R.C.
2004-01-01
Two novel neutron-based analytical techniques have been treated in this thesis, Neutron Resonance Capture Analysis (NRCA), employing a pulsed neutron source, and Neutron Incoherent Scattering (NIS), making use of a cold neutron source. With the NRCA method isotopes are identified by the
International Nuclear Information System (INIS)
Chaichian, M.; Kulish, P. P.
1978-04-01
Supersymmetric Liouville and sine-Gordon equations are studied. We write down for these models the system of linear equations for which the method of inverse scattering problem should be applicable. Expressions for an infinite set of conserved currents are explicitly given. Supersymmetric Baecklund transformations and generalized conservation laws are constructed. (author)
Inverse scattering transform method and soliton solutions for Davey-Stewartson II equation
International Nuclear Information System (INIS)
Arkadiev, V.A.; Pogrebkov, A.K.; Polivanov, M.C.
1989-01-01
The inverse scattering method for Davey-Stewartson II (DS-II) equation including both soliton and continuous spectrum solutions is developed. The explicit formulae for N-soliton solutions are given. Note that our solitons decrease as |z| -2 with z tending to infinity. (author). 8 refs
DTF4-J, 1-D Neutron Transport with Anisotropic Scattering by Sn Method
International Nuclear Information System (INIS)
Nishimura, Hideo
1971-01-01
Nature of physical problem solved: DTF-4-J solves the one-dimensional multi-group transport equation with anisotropic scattering by Sn method. It is a FORTRAN adaptation of the Los Alamos DTF-IV program written by K.D. Lathrop, and it is combined with the JAERI SIMPLED-4 program written by H. Nishimura
Method of computer algebraic calculation of the matrix elements in the second quantization language
International Nuclear Information System (INIS)
Gotoh, Masashi; Mori, Kazuhide; Itoh, Reikichi
1995-01-01
An automated method by the algebraic programming language REDUCE3 for specifying the matrix elements expressed in second quantization language is presented and then applied to the case of the matrix elements in the TDHF theory. This program works in a very straightforward way by commuting the electron creation and annihilation operator (a † and a) until these operators have completely vanished from the expression of the matrix element under the appropriate elimination conditions. An improved method using singlet generators of unitary transformations in the place of the electron creation and annihilation operators is also presented. This improvement reduces the time and memory required for the calculation. These methods will make programming in the field of quantum chemistry much easier. 11 refs., 1 tab
Directory of Open Access Journals (Sweden)
Ayşe Betül Koç
2014-01-01
Full Text Available A pseudospectral method based on the Fibonacci operational matrix is proposed to solve generalized pantograph equations with linear functional arguments. By using this method, approximate solutions of the problems are easily obtained in form of the truncated Fibonacci series. Some illustrative examples are given to verify the efficiency and effectiveness of the proposed method. Then, the numerical results are compared with other methods.
Apparatus and method for detection and characterization of particles using light scattered therefrom
Johnston, R.G.
1987-03-23
Apparatus and method for detection and characterization of particles using light scattered therefrom. Differential phase measurements on scattered light from particles are possible using the two-frequency Zeeman effect laser which emits two frequencies of radiation 250 kHz apart. Excellent discrimination and reproducibility for various pure pollen and bacterial samples in suspension have been observed with a single polarization element. Additionally, a 250 kHz beat frequency was recorded from an individual particle traversing the focused output from the laser in a flow cytometer. 13 figs.
International Nuclear Information System (INIS)
Hoffmann, T H; Ruf, M-W; Hotop, H; Zatsarinny, O; Bartschat, K; Allan, M
2010-01-01
In a joint experimental and theoretical effort, we carried out a detailed study of electron scattering from Kr atoms in the energy range of the low-lying Kr - (4p 5 5s 2 ) Feshbach resonances. Absolute angle-differential cross sections for elastic electron scattering were measured over the energy range 9.3-10.3 eV with an energy width of about 13 meV at scattering angles between 10 deg. and 180 deg. Using several sets of elastic scattering phase shifts, a detailed analysis of the sharp Kr - (4p 5 5s 2 2 P 3/2 ) resonance was carried out, resulting in a resonance width of Γ 3/2 3.6(2) meV. By direct comparison with the position of the Ar - (3p 5 4s 2 2 P 3/2 ) resonance, the energy for the Kr - (4p 5 5s 2 2 P 3/2 ) resonance was determined as E 3/2 = 9.489(3) eV. A Fano-type fit of the higher lying Kr - (4p 5 5s 2 2 P 1/2 ) resonance yielded the resonance parameters Γ 1/2 = 33(5) meV and E 1/2 = 10.126(4) eV. In order to obtain additional insights, B-spline R-matrix calculations were performed for both the elastic and the inelastic cross sections above the threshold for 4p 5 5s excitation. They provide the total and angle-differential cross sections for excitation of long-lived and short-lived levels of the 4p 5 5s configuration in Kr and branching ratios for the decay of the Kr - (4p 5 5s 2 2 P 1/2 ) resonance into the three available exit channels. The results are compared with selected experimental data.
Soltanmoradi, Elmira; Shokri, Babak
2017-05-01
In this article, the electromagnetic wave scattering from plasma columns with inhomogeneous electron density distribution is studied by the Green's function volume integral equation method. Due to the ready production of such plasmas in the laboratories and their practical application in various technological fields, this study tries to find the effects of plasma parameters such as the electron density, radius, and pressure on the scattering cross-section of a plasma column. Moreover, the incident wave frequency influence of the scattering pattern is demonstrated. Furthermore, the scattering cross-section of a plasma column with an inhomogeneous collision frequency profile is calculated and the effect of this inhomogeneity is discussed first in this article. These results are especially used to determine the appropriate conditions for radar cross-section reduction purposes. It is shown that the radar cross-section of a plasma column reduces more for a larger collision frequency, for a relatively lower plasma frequency, and also for a smaller radius. Furthermore, it is found that the effect of the electron density on the scattering cross-section is more obvious in comparison with the effect of other plasma parameters. Also, the plasma column with homogenous collision frequency can be used as a better shielding in contrast to its inhomogeneous counterpart.
Nakamura, Yusuke; Hoshizawa, Taku; Takashima, Yuzuru
2017-09-01
A new method, wavelength diversity detection (WDD), for improving signal quality is proposed and its effectiveness is numerically confirmed. We consider that WDD is especially effective for high-capacity systems having low hologram diffraction efficiencies. In such systems, the signal quality is primarily limited by coherent scattering noise; thus, effective improvement of the signal quality under a scattering-limited system is of great interest. WDD utilizes a new degree of freedom, the spectrum width, and scattering by molecules to improve the signal quality of the system. We found that WDD improves the quality by counterbalancing the degradation of the quality due to Bragg mismatch. With WDD, a higher-scattering-coefficient medium can improve the quality. The result provides an interesting insight into the requirements for material characteristics, especially for a large-M/# material. In general, a larger-M/# material contains more molecules; thus, the system is subject to more scattering, which actually improves the quality with WDD. We propose a pathway for a future holographic data storage system (HDSS) using WDD, which can record a larger amount of data than a conventional HDSS.
International Nuclear Information System (INIS)
Klose, G.
1999-01-01
Lyotropic mesophases possess lattice dimensions of the order of magnitude of the length of their molecules. Consequently, the first Bragg reflections of such systems appear at small scattering angles (small angle scattering). A combination of scattering and NMR methods was applied to study structural properties of POPC/C 12 E n mixtures. Generally, the ranges of existence of the liquid crystalline lamellar phase, the dimension of the unit-cell of the lamellae and important structural parameters of the lipid and surfactant molecules in the mixed bilayers were determined. With that the POPC/C 12 E 4 bilayer represents one of the best structurally characterized mixed model membranes. It is a good starting system for studying the interrelation with other e.g. dynamic or thermodynamic properties. (K.A.)
A Globally Convergent Matrix-Free Method for Constrained Equations and Its Linear Convergence Rate
Directory of Open Access Journals (Sweden)
Min Sun
2014-01-01
Full Text Available A matrix-free method for constrained equations is proposed, which is a combination of the well-known PRP (Polak-Ribière-Polyak conjugate gradient method and the famous hyperplane projection method. The new method is not only derivative-free, but also completely matrix-free, and consequently, it can be applied to solve large-scale constrained equations. We obtain global convergence of the new method without any differentiability requirement on the constrained equations. Compared with the existing gradient methods for solving such problem, the new method possesses linear convergence rate under standard conditions, and a relax factor γ is attached in the update step to accelerate convergence. Preliminary numerical results show that it is promising in practice.
International Nuclear Information System (INIS)
Gu Yi; Xiong Shengqing; Zhou Jianxin; Fan Zhengguo; Ge Liangquan
2014-01-01
γ-ray released by the radon daughter has severe impact on airborne γ-ray spectrometry. The spectral-ratio method is one of the best mathematical methods for radon background deduction in airborne γ-ray spectrometry. In this paper, an advanced spectral-ratio method was proposed which deducts Compton scattering ray by the fast Fourier transform rather than tripping ratios, the relationship between survey height and correction coefficient of the advanced spectral-ratio radon background correction method was studied, the advanced spectral-ratio radon background correction mathematic model was established, and the ground saturation model calibrating technology for correction coefficient was proposed. As for the advanced spectral-ratio radon background correction method, its applicability and correction efficiency are improved, and the application cost is saved. Furthermore, it can prevent the physical meaning lost and avoid the possible errors caused by matrix computation and mathematical fitting based on spectrum shape which is applied in traditional correction coefficient. (authors)
A Predictive-Control-Based Over-Modulation Method for Conventional Matrix Converters
DEFF Research Database (Denmark)
Zhang, Guanguan; Yang, Jian; Sun, Yao
2018-01-01
To increase the voltage transfer ratio of the matrix converter and improve the input/output current performance simultaneously, an over-modulation method based on predictive control is proposed in this paper, where the weighting factor is selected by an automatic adjusting mechanism, which is able...... to further enhance the system performance promptly. This method has advantages like the maximum voltage transfer ratio can reach 0.987 in the experiments; the total harmonic distortion of the input and output current are reduced, and the losses in the matrix converter are decreased. Moreover, the specific...
Directory of Open Access Journals (Sweden)
Tamer Ahmed El-Sayed
2017-01-01
Full Text Available The exact solution for multistepped Timoshenko beam is derived using a set of fundamental solutions. This set of solutions is derived to normalize the solution at the origin of the coordinates. The start, end, and intermediate boundary conditions involve concentrated masses and linear and rotational elastic supports. The beam start, end, and intermediate equations are assembled using the present normalized transfer matrix (NTM. The advantage of this method is that it is quicker than the standard method because the size of the complete system coefficient matrix is 4 × 4. In addition, during the assembly of this matrix, there are no inverse matrix steps required. The validity of this method is tested by comparing the results of the current method with the literature. Then the validity of the exact stepped analysis is checked using experimental and FE(3D methods. The experimental results for stepped beams with single step and two steps, for sixteen different test samples, are in excellent agreement with those of the three-dimensional finite element FE(3D. The comparison between the NTM method and the finite element method results shows that the modal percentage deviation is increased when a beam step location coincides with a peak point in the mode shape. Meanwhile, the deviation decreases when a beam step location coincides with a straight portion in the mode shape.
Matrix-based system reliability method and applications to bridge networks
International Nuclear Information System (INIS)
Kang, W.-H.; Song Junho; Gardoni, Paolo
2008-01-01
Using a matrix-based system reliability (MSR) method, one can estimate the probabilities of complex system events by simple matrix calculations. Unlike existing system reliability methods whose complexity depends highly on that of the system event, the MSR method describes any general system event in a simple matrix form and therefore provides a more convenient way of handling the system event and estimating its probability. Even in the case where one has incomplete information on the component probabilities and/or the statistical dependence thereof, the matrix-based framework enables us to estimate the narrowest bounds on the system failure probability by linear programming. This paper presents the MSR method and applies it to a transportation network consisting of bridge structures. The seismic failure probabilities of bridges are estimated by use of the predictive fragility curves developed by a Bayesian methodology based on experimental data and existing deterministic models of the seismic capacity and demand. Using the MSR method, the probability of disconnection between each city/county and a critical facility is estimated. The probability mass function of the number of failed bridges is computed as well. In order to quantify the relative importance of bridges, the MSR method is used to compute the conditional probabilities of bridge failures given that there is at least one city disconnected from the critical facility. The bounds on the probability of disconnection are also obtained for cases with incomplete information
Fall, Mandiaye; Boutami, Salim; Glière, Alain; Stout, Brian; Hazart, Jerome
2013-06-01
A combination of the multilevel fast multipole method (MLFMM) and boundary element method (BEM) can solve large scale photonics problems of arbitrary geometry. Here, MLFMM-BEM algorithm based on a scalar and vector potential formulation, instead of the more conventional electric and magnetic field formulations, is described. The method can deal with multiple lossy or lossless dielectric objects of arbitrary geometry, be they nested, in contact, or dispersed. Several examples are used to demonstrate that this method is able to efficiently handle 3D photonic scatterers involving large numbers of unknowns. Absorption, scattering, and extinction efficiencies of gold nanoparticle spheres, calculated by the MLFMM, are compared with Mie's theory. MLFMM calculations of the bistatic radar cross section (RCS) of a gold sphere near the plasmon resonance and of a silica coated gold sphere are also compared with Mie theory predictions. Finally, the bistatic RCS of a nanoparticle gold-silver heterodimer calculated with MLFMM is compared with unmodified BEM calculations.
International Nuclear Information System (INIS)
Resler, D.A.
1987-03-01
The specific purpose of this work is to provide a better understanding of the 14 C level structure; the general purpose is to provide the details for using shell model calculations in R-matrix analyses. Using the TOF facilities of the Ohio University Accelerator Laboratory, the elastic and first 3 inelastic differential scattering cross sections for 13 C + n were measured at 69 energies for 4.5 ≤ E/sub n/ ≤ 11 MeV. A multiple scattering code was developed which provided a simulation of the experimental scattering process allowing accurate corrections to the small inelastic data. The integrated 13 C(n,α) 10 Be cross section is estimated. The sequential 2n-decay of 14 C states populated by 13 C + n was observed. A shell model code was developed. Normal and nonnormal parity calculations were made for the lithium isotopes using a new two-body interaction. The results for 5 Li predict the 2s/sub 1/2/ and 1d/sub 5/2/ single-particle states to be located below the 3/2 + state. Similar calculations were made for 13 C, 13 N, and 14 C. Results for 13 C and 13 N show for E/sub x/ 7 Li and 14 C, 2 h-barω calculations were done. Shell model calculations generated the R-matrix parameters for the elastic and first 3 inelastic channels of 13 C + n. After adjusting some energies, the predicted structure generally agrees with experiment for E/sub n/ 13 C + n data were refit to replace R 0 background terms by more realistic broad states and to get better agreement with model calculations. R-matrix fitting of the full data set produced new 14 C level information. For E/sub n/ > 4 MeV (E/sub x/ > 12 MeV), 5 states are given definite J/sup π/ assignments; 3, tentative assignments. 122 refs., 91 figs., 30 tabs
Energy Technology Data Exchange (ETDEWEB)
Telfeyan, Katherine Christina [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Ware, Stuart Douglas [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Reimus, Paul William [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Birdsell, Kay Hanson [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-11-06
Diffusion cell and diffusion wafer experiments were conducted to compare methods for estimating matrix diffusion coefficients in rock core samples from Pahute Mesa at the Nevada Nuclear Security Site (NNSS). A diffusion wafer method, in which a solute diffuses out of a rock matrix that is pre-saturated with water containing the solute, is presented as a simpler alternative to the traditional through-diffusion (diffusion cell) method. Both methods yielded estimates of matrix diffusion coefficients that were within the range of values previously reported for NNSS volcanic rocks. The difference between the estimates of the two methods ranged from 14 to 30%, and there was no systematic high or low bias of one method relative to the other. From a transport modeling perspective, these differences are relatively minor when one considers that other variables (e.g., fracture apertures, fracture spacings) influence matrix diffusion to a greater degree and tend to have greater uncertainty than diffusion coefficients. For the same relative random errors in concentration measurements, the diffusion cell method yields diffusion coefficient estimates that have less uncertainty than the wafer method. However, the wafer method is easier and less costly to implement and yields estimates more quickly, thus allowing a greater number of samples to be analyzed for the same cost and time. Given the relatively good agreement between the methods, and the lack of any apparent bias between the methods, the diffusion wafer method appears to offer advantages over the diffusion cell method if better statistical representation of a given set of rock samples is desired.
The Split Coefficient Matrix method for hyperbolic systems of gasdynamic equations
Chakravarthy, S. R.; Anderson, D. A.; Salas, M. D.
1980-01-01
The Split Coefficient Matrix (SCM) finite difference method for solving hyperbolic systems of equations is presented. This new method is based on the mathematical theory of characteristics. The development of the method from characteristic theory is presented. Boundary point calculation procedures consistent with the SCM method used at interior points are explained. The split coefficient matrices that define the method for steady supersonic and unsteady inviscid flows are given for several examples. The SCM method is used to compute several flow fields to demonstrate its accuracy and versatility. The similarities and differences between the SCM method and the lambda-scheme are discussed.
Linear programming models and methods of matrix games with payoffs of triangular fuzzy numbers
Li, Deng-Feng
2016-01-01
This book addresses two-person zero-sum finite games in which the payoffs in any situation are expressed with fuzzy numbers. The purpose of this book is to develop a suite of effective and efficient linear programming models and methods for solving matrix games with payoffs in fuzzy numbers. Divided into six chapters, it discusses the concepts of solutions of matrix games with payoffs of intervals, along with their linear programming models and methods. Furthermore, it is directly relevant to the research field of matrix games under uncertain economic management. The book offers a valuable resource for readers involved in theoretical research and practical applications from a range of different fields including game theory, operational research, management science, fuzzy mathematical programming, fuzzy mathematics, industrial engineering, business and social economics. .
Graphene-Reinforced Aluminum Matrix Composites: A Review of Synthesis Methods and Properties
Chen, Fei; Gupta, Nikhil; Behera, Rakesh K.; Rohatgi, Pradeep K.
2018-06-01
Graphene-reinforced aluminum (Gr-Al) matrix nanocomposites (NCs) have attracted strong interest from both research and industry in high-performance weight-sensitive applications. Due to the vastly different bonding characteristics of the Al matrix (metallic) and graphene (in-plane covalent + inter-plane van der Waals), the graphene phase has a general tendency to agglomerate and phase separate in the metal matrix, which is detrimental for the mechanical and chemical properties of the composite. Thus, synthesis of Gr-Al NCs is extremely challenging. This review summarizes the different methods available to synthesize Gr-Al NCs and the resulting properties achieved in these NCs. Understanding the effect of processing parameters on the realized properties opens up the possibility of tailoring the synthesis methods to achieve the desired properties for a given application.
Graphene-Reinforced Aluminum Matrix Composites: A Review of Synthesis Methods and Properties
Chen, Fei; Gupta, Nikhil; Behera, Rakesh K.; Rohatgi, Pradeep K.
2018-03-01
Graphene-reinforced aluminum (Gr-Al) matrix nanocomposites (NCs) have attracted strong interest from both research and industry in high-performance weight-sensitive applications. Due to the vastly different bonding characteristics of the Al matrix (metallic) and graphene (in-plane covalent + inter-plane van der Waals), the graphene phase has a general tendency to agglomerate and phase separate in the metal matrix, which is detrimental for the mechanical and chemical properties of the composite. Thus, synthesis of Gr-Al NCs is extremely challenging. This review summarizes the different methods available to synthesize Gr-Al NCs and the resulting properties achieved in these NCs. Understanding the effect of processing parameters on the realized properties opens up the possibility of tailoring the synthesis methods to achieve the desired properties for a given application.
Solution of the Multigroup-Diffusion equation by the response matrix method
International Nuclear Information System (INIS)
Oliveira, C.R.E.
1980-10-01
A preliminary analysis of the response matrix method is made, considering its application to the solution of the multigroup diffusion equations. The one-dimensional formulation is presented and used to test some flux expansions, seeking the application of the method to the two-dimensional problem. This formulation also solves the equations that arise from the integro-differential synthesis algorithm. The slow convergence of the power method, used to solve the eigenvalue problem, and its acceleration by means of the Chebyshev polynomial method, are also studied. An algorithm for the estimation of the dominance ratio is presented, based on the residues of two successive iteration vectors. This ratio, which is not known a priori, is fundamental for the efficiency of the method. Some numerical problems are solved, testing the 1D formulation of the response matrix method, its application to the synthesis algorithm and also, at the same time, the algorithm to accelerate the source problem. (Author) [pt
International Nuclear Information System (INIS)
Wang Huaiying; Zhang Yujin; Yang Lirui; Li Dong
2011-01-01
As for X-ray Compton Back-Scattering (CBS) body scanner, image clearness is very important for the performance of detecting the contraband hidden on the body. A new image combination enhancement method is provided based on characteristics of CBS body images and points of human vision. After processed by this method, the CBS image will be obviously improved with clear levels, distinct outline and uniform background. (authors)
International Nuclear Information System (INIS)
Arzumanov, S.S; Bondarenko, L.N.; Gel'tenbort, P.; Morozov, V.I.; Nesvizhevskij, V.V.; Panin, Yu.N.; Strepetov, A.N.
2007-01-01
The experimental setup and the method of measuring the neutron lifetime with a precision less then 1 s is described. The measurements will be carried out by storage of ultracold neutrons (UCN) into vessels with inner walls coated with fluorine polymer oil with simultaneous registration of inelastically scattered UCN leaving storage vessels. The analysis of statistical and methodical errors is carried out. The calculated estimation of the measurement accuracy is presented [ru
On the kinematic reconstruction of deep inelastic scattering at HERA: the Σmethod
International Nuclear Information System (INIS)
Bassler, U.; Bernardi, G.
1994-12-01
We review and compare the reconstruction methods of the inclusive deep inelastic scattering variables used at HERA. We introduce a new prescription, the Sigma (Σ) method, which allows to measure the structure function of the proton F 2 (x, Q 2 ) in a large kinematic domain, and in particular in the low x-low Q 2 region, with small systematic errors and small radiative corrections. A detailed comparison between the Σ method and the other methods is shown. Extensions of the Σ method are presented. The effect of QED radiation on the kinematic reconstruction and on the structure function measurement is discussed. (orig.)
Study on Scattered Data Points Interpolation Method Based on Multi-line Structured Light
International Nuclear Information System (INIS)
Fan, J Y; Wang, F G; W, Y; Zhang, Y L
2006-01-01
Aiming at the range image obtained through multi-line structured light, a regional interpolation method is put forward in this paper. This method divides interpolation into two parts according to the memory format of the scattered data, one is interpolation of the data on the stripes, and the other is interpolation of data between the stripes. Trend interpolation method is applied to the data on the stripes, and Gauss wavelet interpolation method is applied to the data between the stripes. Experiments prove regional interpolation method feasible and practical, and it also promotes the speed and precision
A matrix structured LED backlight system with 2D-DHT local dimming method
Liu, Jia; Li, Yang; Du, Sidan
To reduce the number of the drivers in the conventional local dimming method for LCDs, a novel LED backlight local dimming system is proposed in this paper. The backlight of this system is generated by 2D discrete Hadamard transform and its matrix structured LED modules. Compared with the conventional 2D local dimming method, the proposed method costs much fewer drivers but with little degradation.
Adaptation of chemical methods of analysis to the matrix of pyrite-acidified mining lakes
International Nuclear Information System (INIS)
Herzsprung, P.; Friese, K.
2000-01-01
Owing to the unusual matrix of pyrite-acidified mining lakes, the analysis of chemical parameters may be difficult. A number of methodological improvements have been developed so far, and a comprehensive validation of methods is envisaged. The adaptation of the available methods to small-volume samples of sediment pore waters and the adaptation of sensitivity to the expected concentration ranges is an important element of the methods applied in analyses of biogeochemical processes in mining lakes [de
The response-matrix based AFEN method for the hexagonal geometry
International Nuclear Information System (INIS)
Noh, Jae Man; Kim, Keung Koo; Zee, Sung Quun; Joo, Hyung Kook; Cho, Byng Oh; Jeong, Hyung Guk; Cho, Jin Young
1998-03-01
The analytic function expansion nodal (AFEN) method, developed to overcome the limitations caused by the transverse integration, has been successfully to predict the neutron behavior in the hexagonal core as well as rectangular core. In the hexagonal node, the transverse leakage resulted from the transverse integration has some singular terms such as delta-function and step-functions near the node center line. In most nodal methods using the transverse integration, the accuracy of nodal method is degraded because the transverse leakage is approximated as a smooth function across the node center line by ignoring singular terms. However, the AFEN method in which there is no transverse leakage term in deriving nodal coupling equations keeps good accuracy for hexagonal node. In this study, the AFEN method which shows excellent accuracy in the hexagonal core analyses is reformulated as a response matrix form. This form of the AFEN method can be implemented easily to nodal codes based on the response matrix method. Therefore, the Coarse Mesh Rebalance (CMR) acceleration technique which is one of main advantages of the response matrix method can be utilized for the AFEN method. The response matrix based AFEN method has been successfully implemented into the MASTER code and its accuracy and computational efficiency were examined by analyzing the two- and three- dimensional benchmark problem of VVER-440. Based on the results, it can be concluded that the newly formulated AFEN method predicts accurately the assembly powers (within 0.2% average error) as well as the effective multiplication factor (within 0.2% average error) as well as the effective multiplication factor (within 20 pcm error). In addition, the CMR acceleration technique is quite efficient in reducing the computation time of the AFEN method by 8 to 10 times. (author). 22 refs., 1 tab., 4 figs
Directory of Open Access Journals (Sweden)
Jun Zhang
2018-01-01
Full Text Available The single scattering of P- and SV-waves by a cylindrical fiber with a partially imperfect bonding to the surrounding matrix is investigated, which benefits the characterization of the behavior of elastic waves in composite materials. The imperfect interface is modelled by the spring model. To solve the corresponding single scattering problem, a collocation point (CP method is introduced. Based on this method, influence of various aspects of the imperfect interface on the scattering of P- and SV-waves is studied. Results indicate that (i the total scattering cross section (SCS is almost symmetric about the axis α=π/2 with respect to the location (α of the imperfect interface, (ii imperfect interfaces located at α=0 and α=π highly reduce the total SCS under a P-wave incidence and imperfect interfaces located at α=π/2 reduce the total SCS most significantly under SV-incidence, and (iii under a P-wave incidence the SCS has a high sensitivity to the bonding level of imperfect interfaces when α is small, while it becomes more sensitive to the bonding level when α is larger under SV-wave incidence.
Korkin, Sergey V.; Lyapustin, Alexei I.; Rozanov, Vladimir V.
2012-01-01
A numerical accuracy analysis of the radiative transfer equation (RTE) solution based on separation of the diffuse light field into anisotropic and smooth parts is presented. The analysis uses three different algorithms based on the discrete ordinate method (DOM). Two methods, DOMAS and DOM2+, that do not use the truncation of the phase function, are compared against the TMS-method. DOMAS and DOM2+ use the Small-Angle Modification of RTE and the single scattering term, respectively, as an anisotropic part. The TMS method uses Delta-M method for truncation of the phase function along with the single scattering correction. For reference, a standard discrete ordinate method, DOM, is also included in analysis. The obtained results for cases with high scattering anisotropy show that at low number of streams (16, 32) only DOMAS provides an accurate solution in the aureole area. Outside of the aureole, the convergence and accuracy of DOMAS, and TMS is found to be approximately similar: DOMAS was found more accurate in cases with coarse aerosol and liquid water cloud models, except low optical depth, while the TMS showed better results in case of ice cloud.
Attenuation correction of myocardial SPECT by scatter-photopeak window method in normal subjects
International Nuclear Information System (INIS)
Okuda, Koichi; Nakajima, Kenichi; Matsuo, Shinro; Kinuya, Seigo; Motomura, Nobutoku; Kubota, Masahiro; Yamaki, Noriyasu; Maeda, Hisato
2009-01-01
Segmentation with scatter and photopeak window data using attenuation correction (SSPAC) method can provide a patient-specific non-uniform attenuation coefficient map only by using photopeak and scatter images without X-ray computed tomography (CT). The purpose of this study is to evaluate the performance of attenuation correction (AC) by the SSPAC method on normal myocardial perfusion database. A total of 32 sets of exercise-rest myocardial images with Tc-99m-sestamibi were acquired in both photopeak (140 keV±10%) and scatter (7% of lower side of the photopeak window) energy windows. Myocardial perfusion databases by the SSPAC method and non-AC (NC) were created from 15 female and 17 male subjects with low likelihood of cardiac disease using quantitative perfusion SPECT software. Segmental myocardial counts of a 17-segment model from these databases were compared on the basis of paired t test. AC average myocardial perfusion count was significantly higher than that in NC in the septal and inferior regions (P<0.02). On the contrary, AC average count was significantly lower in the anterolateral and apical regions (P<0.01). Coefficient variation of the AC count in the mid, apical and apex regions was lower than that of NC. The SSPAC method can improve average myocardial perfusion uptake in the septal and inferior regions and provide uniform distribution of myocardial perfusion. The SSPAC method could be a practical method of attenuation correction without X-ray CT. (author)
Studies of oxide-based thin-layered heterostructures by X-ray scattering methods
Energy Technology Data Exchange (ETDEWEB)
Durand, O. [Thales Research and Technology France, Route Departementale 128, F-91767 Palaiseau Cedex (France)]. E-mail: olivier.durand@thalesgroup.com; Rogers, D. [Nanovation SARL, 103 bis rue de Versailles 91400 Orsay (France); Universite de Technologie de Troyes, 10-12 rue Marie Curie, 10010 (France); Teherani, F. Hosseini [Nanovation SARL, 103 bis rue de Versailles 91400 Orsay (France); Andrieux, M. [LEMHE, ICMMOCNRS-UMR 8182, Universite d' Orsay, Batiment 410, 91410 Orsay (France); Modreanu, M. [Tyndall National Institute, Lee Maltings, Prospect Row, Cork (Ireland)
2007-06-04
Some X-ray scattering methods (X-ray reflectometry and Diffractometry) dedicated to the study of thin-layered heterostructures are presented with a particular focus, for practical purposes, on the description of fast, accurate and robust techniques. The use of X-ray scattering metrology as a routinely working non-destructive testing method, particularly by using procedures simplifying the data-evaluation, is emphasized. The model-independent Fourier-inversion method applied to a reflectivity curve allows a fast determination of the individual layer thicknesses. We demonstrate the capability of this method by reporting X-ray reflectometry study on multilayered oxide structures, even when the number of the layers constitutive of the stack is not known a-priori. Fast Fourier transform-based procedure has also been employed successfully on high resolution X-ray diffraction profiles. A study of the reliability of the integral-breadth methods in diffraction line-broadening analysis applied to thin layers, in order to determine coherent domain sizes, is also reported. Examples from studies of oxides-based thin-layers heterostructures will illustrate these methods. In particular, X-ray scattering studies performed on high-k HfO{sub 2} and SrZrO{sub 3} thin-layers, a (GaAs/AlOx) waveguide, and a ZnO thin-layer are reported.
Jarlebring, E.; Hochstenbach, M.E.
2009-01-01
Several recent methods used to analyze asymptotic stability of delay-differential equations (DDEs) involve determining the eigenvalues of a matrix, a matrix pencil or a matrix polynomial constructed by Kronecker products. Despite some similarities between the different types of these so-called
Determining Complex Structures using Docking Method with Single Particle Scattering Data
Directory of Open Access Journals (Sweden)
Haiguang Liu
2017-04-01
Full Text Available Protein complexes are critical for many molecular functions. Due to intrinsic flexibility and dynamics of complexes, their structures are more difficult to determine using conventional experimental methods, in contrast to individual subunits. One of the major challenges is the crystallization of protein complexes. Using X-ray free electron lasers (XFELs, it is possible to collect scattering signals from non-crystalline protein complexes, but data interpretation is more difficult because of unknown orientations. Here, we propose a hybrid approach to determine protein complex structures by combining XFEL single particle scattering data with computational docking methods. Using simulations data, we demonstrate that a small set of single particle scattering data collected at random orientations can be used to distinguish the native complex structure from the decoys generated using docking algorithms. The results also indicate that a small set of single particle scattering data is superior to spherically averaged intensity profile in distinguishing complex structures. Given the fact that XFEL experimental data are difficult to acquire and at low abundance, this hybrid approach should find wide applications in data interpretations.
A Control Method of Current Type Matrix Converter for Plasma Control Coil Power Supply
International Nuclear Information System (INIS)
Shimada, K.; Matsukawa, M.; Kurihara, K.; Jun-ichi Itoh
2006-01-01
In exploration to a tokamak fusion reactor, the control of plasma instabilities of high β plasma such as neoclassical tearing mode (NTM), resistive wall mode (RWM) etc., is the key issue for steady-state sustainment. One of the proposed methods to avoid suppressing RWM is that AC current having a phase to work for reduction the RWM growth is generated in a coil (sector coil) equipped spirally on the plasma vacuum vessel. To stabilize RWM, precise and fast real-time feedback control of magnetic field with proper amplitude and frequency is necessary. This implies that an appropriate power supply dedicated for such an application is expected to be developed. A matrix converter as one of power supply candidates for this purpose could provide a solution The matrix converter, categorized in an AC/AC direct converter composed of nine bi-directional current switches, has a great feature that a large energy storage element is unnecessary in comparison with a standard existing AC/AC indirect converter, which is composed of an AC/DC converter and a DC/AC inverter. It is also advantageous in cost and size of its applications. Fortunately, a voltage type matrix converter has come to be available at the market recently, while a current type matrix converter, which is advantageous for fast control of the large-inductance coil current, has been unavailable. On the background above mentioned, we proposed a new current type matrix converter and its control method applicable to a power supply with fast response for suppressing plasma instabilities. Since this converter is required with high accuracy control, the gate control method is adopted to three-phase switching method using middle phase to reduce voltage and current waveforms distortion. The control system is composed of VME-bus board with DSP (Digital Signal Processor) and FPGA (Field Programmable Gate Array) for high speed calculation and control. This paper describes the control method of a current type matrix converter
Relativistic convergent close-coupling method applied to electron scattering from mercury
International Nuclear Information System (INIS)
Bostock, Christopher J.; Fursa, Dmitry V.; Bray, Igor
2010-01-01
We report on the extension of the recently formulated relativistic convergent close-coupling (RCCC) method to accommodate two-electron and quasi-two-electron targets. We apply the theory to electron scattering from mercury and obtain differential and integrated cross sections for elastic and inelastic scattering. We compared with previous nonrelativistic convergent close-coupling (CCC) calculations and for a number of transitions obtained significantly better agreement with the experiment. The RCCC method is able to resolve structure in the integrated cross sections for the energy regime in the vicinity of the excitation thresholds for the (6s6p) 3 P 0,1,2 states. These cross sections are associated with the formation of negative ion (Hg - ) resonances that could not be resolved with the nonrelativistic CCC method. The RCCC results are compared with the experiment and other relativistic theories.
International Nuclear Information System (INIS)
Armour, E.A.G.; Baker, D.J.; Plummer, M.
1990-01-01
Above incident energies of about 2 eV, the contribution to the total cross section in positron+H2 scattering from the sigma g+ symmetry is insufficient to account for the experimental value. Calculations carried out of the lowest partial waves of sigma u+ symmetry and Pion u symmetry using the Kohn variational method are described. The contributions to the total cross section from the two equivalent partial waves of Pion u symmetry significantly reduce the discrepancy with experiment up to incident energies of 4 to 5 eV. Comparisons are made with recent R-matrix calculations performed by Danby and Tennyson
Weng, Fuzhong
1992-01-01
A theory is developed for discretizing the vector integro-differential radiative transfer equation including both solar and thermal radiation. A complete solution and boundary equations are obtained using the discrete-ordinate method. An efficient numerical procedure is presented for calculating the phase matrix and achieving computational stability. With natural light used as a beam source, the Stokes parameters from the model proposed here are compared with the analytical solutions of Chandrasekhar (1960) for a Rayleigh scattering atmosphere. The model is then applied to microwave frequencies with a thermal source, and the brightness temperatures are compared with those from Stamnes'(1988) radiative transfer model.
Armour, E. A. G.; Baker, D. J.; Plummer, M.
1990-01-01
Above incident energies of about 2 eV, the contribution to the total cross section in positron+H2 scattering from the sigma g+ symmetry is insufficient to account for the experimental value. Calculations carried out of the lowest partial waves of sigma u+ symmetry and Pion u symmetry using the Kohn variational method are described. The contributions to the total cross section from the two equivalent partial waves of Pion u symmetry significantly reduce the discrepancy with experiment up to incident energies of 4 to 5 eV. Comparisons are made with recent R-matrix calculations performed by Danby and Tennyson.
International Nuclear Information System (INIS)
Maekawa, T.; Tanaka, H.; Uchida, M.; Igami, H.
2003-01-01
General properties of scattering matrix, which governs the mode conversion process between electron Bernstein (B) waves and external electromagnetic (EM) waves in the presence of steep density gradient, are theoretically analyzed. Based on the analysis, polarization adjustment of incident EM waves for optimal mode conversion to B waves is possible and effective for a range of density gradient near the upper hybrid resonance, which are not covered by the previously proposed schemes of perpendicular injection of X mode and oblique injection of O mode. Furthermore, the analysis shows that the polarization of the externally emitted EM waves from B waves is uniquely related to the optimized polarization of incident EM waves for B wave heating and that the mode conversion rate is the same for the both processes of emission and the injection with the optimized polarization
The Dirac operator on a finite domain and the R-matrix method
International Nuclear Information System (INIS)
Grant, I P
2008-01-01
Relativistic effects in electron-atom collisions and photo-excitation and -ionization processes increase in importance as the atomic number of the target atom grows and spin-dependent effects increase. A relativistic treatment in which electron motion is described using the Dirac Hamiltonian is then desirable. A version of the popular nonrelativistic R-matrix package incorporating terms from the Breit-Pauli Hamiltonian has been used for modelling such processes for some years. The fully relativistic Dirac R-matrix method has been less popular, but is becoming increasingly relevant for applications to heavy ion targets, where the need to use relativistic wavefunctions is more obvious. The Dirac R-matrix method has been controversial ever since it was first proposed by Goertzel (1948 Phys. Rev. 73 1463-6), and it is therefore important to confirm that recent elaborate and costly applications of the method, such as, Badnell et al (2004 J. Phys. B: At. Mol. Phys. 37 4589) and Ballance and Griffin (2007 J. Phys. B: At. Mol. Opt. Phys. 40 247-58), rest on secure foundations. The first part of this paper analyses the structure of the two-point boundary-value problem for the Dirac operator on a finite domain, from which we construct a unified derivation of the Schroedinger (nonrelativistic) and Dirac (relativistic) R-matrix methods. Suggestions that the usual relativistic theory is not well founded are shown to be without foundation
Algebraic method for analysis of nonlinear systems with a normal matrix
International Nuclear Information System (INIS)
Konyaev, Yu.A.; Salimova, A.F.
2014-01-01
A promising method has been proposed for analyzing a class of quasilinear nonautonomous systems of differential equations whose matrix can be represented as a sum of nonlinear normal matrices, which makes it possible to analyze stability without using the Lyapunov functions [ru
A Simple DTC-SVM method for Matrix Converter Drives Using a Deadbeat Scheme
DEFF Research Database (Denmark)
Lee, Kyo-Beum; Blaabjerg, Frede; Lee, Kwang-Won
2005-01-01
In this paper, a simple direct torque control (DTC) method for sensorless matrix converter drives is proposed, which is characterized by a simple structure, minimal torque ripple and unity input power factor. Also a good sensorless speed-control performance in the low speed operation is obtained,...
On the Numerical Behavior of Matrix Splitting Iteration Methods for Solving Linear Systems
Czech Academy of Sciences Publication Activity Database
Bai, Z.-Z.; Rozložník, Miroslav
2015-01-01
Roč. 53, č. 4 (2015), s. 1716-1737 ISSN 0036-1429 R&D Projects: GA ČR GA13-06684S Institutional support: RVO:67985807 Keywords : matrix splitting * stationary iteration method * backward error * rounding error analysis Subject RIV: BA - General Mathematics Impact factor: 1.899, year: 2015
A matrix-inversion method for gamma-source mapping from gamma-count data - 59082
International Nuclear Information System (INIS)
Bull, Richard K.; Adsley, Ian; Burgess, Claire
2012-01-01
Gamma ray counting is often used to survey the distribution of active waste material in various locations. Ideally the output from such surveys would be a map of the activity of the waste. In this paper a simple matrix-inversion method is presented. This allows an array of gamma-count data to be converted to an array of source activities. For each survey area the response matrix is computed using the gamma-shielding code Microshield [1]. This matrix links the activity array to the count array. The activity array is then obtained via matrix inversion. The method was tested on artificially-created arrays of count-data onto which statistical noise had been added. The method was able to reproduce, quite faithfully, the original activity distribution used to generate the dataset. The method has been applied to a number of practical cases, including the distribution of activated objects in a hot cell and to activated Nimonic springs amongst fuel-element debris in vaults at a nuclear plant. (authors)
Large-N limit of the two-Hermitian-matrix model by the hidden BRST method
International Nuclear Information System (INIS)
Alfaro, J.
1993-01-01
This paper discusses the large-N limit of the two-Hermitian-matrix model in zero dimensions, using the hidden Becchi-Rouet-Stora-Tyutin method. A system of integral equations previously found is solved, showing that it contained the exact solution of the model in leading order of large N
Discrete ordinates transport methods for problems with highly forward-peaked scattering
International Nuclear Information System (INIS)
Pautz, S.D.
1998-04-01
The author examines the solutions of the discrete ordinates (S N ) method for problems with highly forward-peaked scattering kernels. He derives conditions necessary to obtain reasonable solutions in a certain forward-peaked limit, the Fokker-Planck (FP) limit. He also analyzes the acceleration of the iterative solution of such problems and offer improvements to it. He extends the analytic Fokker-Planck limit analysis to the S N equations. This analysis shows that in this asymptotic limit the S N solution satisfies a pseudospectral discretization of the FP equation, provided that the scattering term is handled in a certain way (which he describes) and that the analytic transport solution satisfies an analytic FP equation. Similar analyses of various spatially discretized S N equations reveal that they too produce solutions that satisfy discrete FP equations, given the same provisions. Numerical results agree with these theoretical predictions. He defines a multidimensional angular multigrid (ANMG) method to accelerate the iterative solution of highly forward-peaked problems. The analyses show that a straightforward application of this scheme is subject to high-frequency instabilities. However, by applying a diffusive filter to the ANMG corrections he is able to stabilize this method. Fourier analyses of model problems show that the resulting method is effective at accelerating the convergence rate when the scattering is forward-peaked. The numerical results demonstrate that these analyses are good predictors of the actual performance of the ANMG method
Electron-impact study of PO2 using the R-matrix method
Bharadvaja, Anand; Kaur, Savinder; Baluja, K. L.
2013-06-01
The R-matrix approach is used to study the electron scattering from PO2 radical at low electron impact energies. The elastic scattering phenomenon is studied in static-exchange, one-state and many-states close-coupling approximation. The elastic differential cross sections, corresponding momentum-transfer cross sections, and collision frequency are calculated in the one-state configuration interaction approximation only. Calculations reveal a stable bound state of PO2- having symmetry 1A1, a configuration of ⋯8a12,⋯2b12,⋯5b22,⋯1a22, and vertical electron affinity of 2.94 eV. The excited state of anion PO2- having symmetry 3B1 is also just bound relative to the ground state of PO2 at its equilibrium geometry. The shape, core-excited, and Feshbach resonances are analyzed in different symmetries up to 7 eV. The partial waves up to l=4 are used to represent continuum electron. The converged cross sections are obtained for the partial waves having l greater than 4 by applying Born correction. Certain interesting spectroscopic properties of radical are also reported.
Calculating Relativistic Transition Matrix Elements for Hydrogenic Atoms Using Monte Carlo Methods
Alexander, Steven; Coldwell, R. L.
2015-03-01
The nonrelativistic transition matrix elements for hydrogen atoms can be computed exactly and these expressions are given in a number of classic textbooks. The relativistic counterparts of these equations can also be computed exactly but these expressions have been described in only a few places in the literature. In part, this is because the relativistic equations lack the elegant simplicity of the nonrelativistic equations. In this poster I will describe how variational Monte Carlo methods can be used to calculate the energy and properties of relativistic hydrogen atoms and how the wavefunctions for these systems can be used to calculate transition matrix elements.
Legendre Wavelet Operational Matrix Method for Solution of Riccati Differential Equation
Directory of Open Access Journals (Sweden)
S. Balaji
2014-01-01
Full Text Available A Legendre wavelet operational matrix method (LWM is presented for the solution of nonlinear fractional-order Riccati differential equations, having variety of applications in quantum chemistry and quantum mechanics. The fractional-order Riccati differential equations converted into a system of algebraic equations using Legendre wavelet operational matrix. Solutions given by the proposed scheme are more accurate and reliable and they are compared with recently developed numerical, analytical, and stochastic approaches. Comparison shows that the proposed LWM approach has a greater performance and less computational effort for getting accurate solutions. Further existence and uniqueness of the proposed problem are given and moreover the condition of convergence is verified.
International Nuclear Information System (INIS)
Constantinescu, V.; Orban, R.; Colan, H.
1993-01-01
Starting from the observation that Sintering by Infiltration of Loose Mixture of Powders confers large possibilities for both complex shaped and of large dimensions Particulate Reinforced Metal Matrix Composite components elaboration, its mechanism comparative with those of the classical melt infiltration was investigated. Appropriate measures in order to prevent an excessive hydrostatic flow of the melt and, consequently, reinforcement particle dispersion, as well as to promote wetting in both infiltration and liquid phase sintering stages of the process were established as necessary. Some experimental results in the method application to the fusion tungsten carbide and diamond reinforced metal matrix composite elaboration are, also, presented. (orig.)
Evaluation of the ICS and DEW scatter correction methods for low statistical content scans in 3D PET
International Nuclear Information System (INIS)
Sossi, V.; Oakes, T.R.; Ruth, T.J.
1996-01-01
The performance of the Integral Convolution and the Dual Energy Window scatter correction methods in 3D PET has been evaluated over a wide range of statistical content of acquired data (1M to 400M events) The order in which scatter correction and detector normalization should be applied has also been investigated. Phantom and human neuroreceptor studies were used with the following figures of merit: axial and radial uniformity, sinogram and image noise, contrast accuracy and contrast accuracy uniformity. Both scatter correction methods perform reliably in the range of number of events examined. Normalization applied after scatter correction yields better radial uniformity and fewer image artifacts
International Nuclear Information System (INIS)
Jat, R.L.; Das, D.K.; Naskar, G.C.
1975-01-01
Water content of a sandy clay loam soil was measured by neutron scattering, gravimetric and tensiometric methods. Tensiometric measurement based on laboratory moisture retention curve gave comparatively higher moisture content than those obtained by other methods. No significant differences were observed among neutron meter, gravimetric and tensiometric measurement based on field calibration curve. Though for irrigation purposes all the methods can be used equally, use of tensiometric method with field calibration curve is suggested for easy and more accurate soil water content measurement where neutron meter is not available. (author)
International Nuclear Information System (INIS)
Maurer-Spurej, Elisabeth; Brown, Keddie; Labrie, Audrey; Marziali, Andre; Glatter, Otto
2006-01-01
No routine test exists to determine the quality of blood platelet transfusions although every year millions of patients require platelet transfusions to survive cancer chemotherapy, surgery or trauma. A new, portable dynamic light scattering instrument is described that is suitable for the measurement of turbid solutions of large particles under temperature-controlled conditions. The challenges of small sample size, short light path through the sample and accurate temperature control have been solved with a specially designed temperature-controlled sample holder for small diameter, disposable capillaries. Efficient heating and cooling is achieved with Peltier elements in direct contact with the sample capillary. Focusing optical fibres are used for light delivery and collection of scattered light. The practical use of this new technique was shown by the reproducible measurement of latex microspheres and the temperature-induced morphological changes of human blood platelets. The measured parameters for platelet transfusions are platelet size, number of platelet-derived microparticles and the response of platelets to temperature changes. This three-dimensional analysis provides a high degree of confidence for the determination of platelet quality. The experimental data are compared to a matrix and facilitate automated, unbiased quality testing
Directory of Open Access Journals (Sweden)
Thomas Gomez
2018-04-01
Full Text Available Atomic structure of N-electron atoms is often determined by solving the Hartree-Fock equations, which are a set of integro-differential equations. The integral part of the Hartree-Fock equations treats electron exchange, but the Hartree-Fock equations are not often treated as an integro-differential equation. The exchange term is often approximated as an inhomogeneous or an effective potential so that the Hartree-Fock equations become a set of ordinary differential equations (which can be solved using the usual shooting methods. Because the Hartree-Fock equations are an iterative-refinement method, the inhomogeneous term relies on the previous guess of the wavefunction. In addition, there are numerical complications associated with solving inhomogeneous differential equations. This work uses matrix methods to solve the Hartree-Fock equations as an integro-differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using linear-algebra packages. The integral (exchange part of the Hartree-Fock equation can be approximated as a sum and written as a matrix. The Hartree-Fock equations can be solved as a matrix that is the sum of the differential and integral matrices. We compare calculations using this method against experiment and standard atomic structure calculations. This matrix method can also be used to solve for free-electron wavefunctions, thus improving how the atoms and free electrons interact. This technique is important for spectral line broadening in two ways: it improves the atomic structure calculations, and it improves the motion of the plasma electrons that collide with the atom.
Synthesizing (ZrAl3 + AlN)/Mg-Al composites by a 'matrix exchange' method
Gao, Tong; Li, Zengqiang; Hu, Kaiqi; Han, Mengxia; Liu, Xiangfa
2018-06-01
A method named 'matrix exchange' to synthesize ZrAl3 and AlN reinforced Mg-Al composite was developed in this paper. By inserting Al-10ZrN master alloy into Mg matrix and reheating the cooled ingot to 550 °C, Al and Mg atoms diffuse to the opposite side. As a result, liquid melt occurs once the interface areas reach to proper compositions. Then dissolved Al atoms react with ZrN, leading to the in-situ formation of ZrAl3 and AlN particles, while the Al matrix is finally replaced by Mg. This study provides a new insight for preparing Mg composites.
Hesford, Andrew J.; Waag, Robert C.
2010-10-01
The fast multipole method (FMM) is applied to the solution of large-scale, three-dimensional acoustic scattering problems involving inhomogeneous objects defined on a regular grid. The grid arrangement is especially well suited to applications in which the scattering geometry is not known a priori and is reconstructed on a regular grid using iterative inverse scattering algorithms or other imaging techniques. The regular structure of unknown scattering elements facilitates a dramatic reduction in the amount of storage and computation required for the FMM, both of which scale linearly with the number of scattering elements. In particular, the use of fast Fourier transforms to compute Green's function convolutions required for neighboring interactions lowers the often-significant cost of finest-level FMM computations and helps mitigate the dependence of FMM cost on finest-level box size. Numerical results demonstrate the efficiency of the composite method as the number of scattering elements in each finest-level box is increased.
International Nuclear Information System (INIS)
Ishikawa, H.; Nakano, S.; Yuuki, R.; Chung, N.Y.
1991-01-01
In the virtual crack extension method, the stress intensity factor, K, is obtained from the converged value of the energy release rate by the difference of the finite element stiffness matrix when some crack extension are taken. Instead of the numerical difference of the finite element stiffness, a new method to use a direct dirivative of the finite element stiffness matrix with respect to crack length is proposed. By the present method, the results of some example problems, such as uniform tension problems of a square plate with a center crack and a rectangular plate with an internal slant crack, are obtained with high accuracy and good efficiency. Comparing with analytical results, the present values of the stress intensity factors of the problems are obtained with the error that is less than 0.6%. This shows the numerical assurance of the usefulness of the present method. A personal computer program for the analysis is developed
Determination of Dispersion Curves for Composite Materials with the Use of Stiffness Matrix Method
Directory of Open Access Journals (Sweden)
Barski Marek
2017-06-01
Full Text Available Elastic waves used in Structural Health Monitoring systems have strongly dispersive character. Therefore it is necessary to determine the appropriate dispersion curves in order to proper interpretation of a received dynamic response of an analyzed structure. The shape of dispersion curves as well as number of wave modes depends on mechanical properties of layers and frequency of an excited signal. In the current work, the relatively new approach is utilized, namely stiffness matrix method. In contrast to transfer matrix method or global matrix method, this algorithm is considered as numerically unconditionally stable and as effective as transfer matrix approach. However, it will be demonstrated that in the case of hybrid composites, where mechanical properties of particular layers differ significantly, obtaining results could be difficult. The theoretical relationships are presented for the composite plate of arbitrary stacking sequence and arbitrary direction of elastic waves propagation. As a numerical example, the dispersion curves are estimated for the lamina, which is made of carbon fibers and epoxy resin. It is assumed that elastic waves travel in the parallel, perpendicular and arbitrary direction to the fibers in lamina. Next, the dispersion curves are determined for the following laminate [0°, 90°, 0°, 90°, 0°, 90°, 0°, 90°] and hybrid [Al, 90°, 0°, 90°, 0°, 90°, 0°], where Al is the aluminum alloy PA38 and the rest of layers are made of carbon fibers and epoxy resin.
International Nuclear Information System (INIS)
Gamba, Irene M.; Haack, Jeffrey R.
2014-01-01
We present the formulation of a conservative spectral method for the Boltzmann collision operator with anisotropic scattering cross-sections. The method is an extension of the conservative spectral method of Gamba and Tharkabhushanam [17,18], which uses the weak form of the collision operator to represent the collisional term as a weighted convolution in Fourier space. The method is tested by computing the collision operator with a suitably cut-off angular cross section and comparing the results with the solution of the Landau equation. We analytically study the convergence rate of the Fourier transformed Boltzmann collision operator in the grazing collisions limit to the Fourier transformed Landau collision operator under the assumption of some regularity and decay conditions of the solution to the Boltzmann equation. Our results show that the angular singularity which corresponds to the Rutherford scattering cross section is the critical singularity for which a grazing collision limit exists for the Boltzmann operator. Additionally, we numerically study the differences between homogeneous solutions of the Boltzmann equation with the Rutherford scattering cross section and an artificial cross section, which give convergence to solutions of the Landau equation at different asymptotic rates. We numerically show the rate of the approximation as well as the consequences for the rate of entropy decay for homogeneous solutions of the Boltzmann equation and Landau equation
Monte Carlo evaluation of accuracy and noise properties of two scatter correction methods
International Nuclear Information System (INIS)
Narita, Y.; Eberl, S.; Nakamura, T.
1996-01-01
Two independent scatter correction techniques, transmission dependent convolution subtraction (TDCS) and triple-energy window (TEW) method, were evaluated in terms of quantitative accuracy and noise properties using Monte Carlo simulation (EGS4). Emission projections (primary, scatter and scatter plus primary) were simulated for 99m Tc and 201 Tl for numerical chest phantoms. Data were reconstructed with ordered-subset ML-EM algorithm including attenuation correction using the transmission data. In the chest phantom simulation, TDCS provided better S/N than TEW, and better accuracy, i.e., 1.0% vs -7.2% in myocardium, and -3.7% vs -30.1% in the ventricular chamber for 99m Tc with TDCS and TEW, respectively. For 201 Tl, TDCS provided good visual and quantitative agreement with simulated true primary image without noticeably increasing the noise after scatter correction. Overall TDCS proved to be more accurate and less noisy than TEW, facilitating quantitative assessment of physiological functions with SPECT
Experimental validation of a multi-energy x-ray adapted scatter separation method
Sossin, A.; Rebuffel, V.; Tabary, J.; Létang, J. M.; Freud, N.; Verger, L.
2016-12-01
Both in radiography and computed tomography (CT), recently emerged energy-resolved x-ray photon counting detectors enable the identification and quantification of individual materials comprising the inspected object. However, the approaches used for these operations require highly accurate x-ray images. The accuracy of the images is severely compromised by the presence of scattered radiation, which leads to a loss of spatial contrast and, more importantly, a bias in radiographic material imaging and artefacts in CT. The aim of the present study was to experimentally evaluate a recently introduced partial attenuation spectral scatter separation approach (PASSSA) adapted for multi-energy imaging. For this purpose, a prototype x-ray system was used. Several radiographic acquisitions of an anthropomorphic thorax phantom were performed. Reference primary images were obtained via the beam-stop (BS) approach. The attenuation images acquired from PASSSA-corrected data showed a substantial increase in local contrast and internal structure contour visibility when compared to uncorrected images. A substantial reduction of scatter induced bias was also achieved. Quantitatively, the developed method proved to be in relatively good agreement with the BS data. The application of the proposed scatter correction technique lowered the initial normalized root-mean-square error (NRMSE) of 45% between the uncorrected total and the reference primary spectral images by a factor of 9, thus reducing it to around 5%.
A self-consistent nodal method in response matrix formalism for the multigroup diffusion equations
International Nuclear Information System (INIS)
Malambu, E.M.; Mund, E.H.
1996-01-01
We develop a nodal method for the multigroup diffusion equations, based on the transverse integration procedure (TIP). The efficiency of the method rests upon the convergence properties of a high-order multidimensional nodal expansion and upon numerical implementation aspects. The discrete 1D equations are cast in response matrix formalism. The derivation of the transverse leakage moments is self-consistent i.e. does not require additional assumptions. An outstanding feature of the method lies in the linear spatial shape of the local transverse leakage for the first-order scheme. The method is described in the two-dimensional case. The method is validated on some classical benchmark problems. (author)
Alternating optimization method based on nonnegative matrix factorizations for deep neural networks
Sakurai, Tetsuya; Imakura, Akira; Inoue, Yuto; Futamura, Yasunori
2016-01-01
The backpropagation algorithm for calculating gradients has been widely used in computation of weights for deep neural networks (DNNs). This method requires derivatives of objective functions and has some difficulties finding appropriate parameters such as learning rate. In this paper, we propose a novel approach for computing weight matrices of fully-connected DNNs by using two types of semi-nonnegative matrix factorizations (semi-NMFs). In this method, optimization processes are performed b...
Efficient Tridiagonal Preconditioner for the Matrix-Free Truncated Newton Method
Czech Academy of Sciences Publication Activity Database
Lukšan, Ladislav; Vlček, Jan
2014-01-01
Roč. 235, 25 May (2014), s. 394-407 ISSN 0096-3003 R&D Projects: GA ČR GA13-06684S Institutional support: RVO:67985807 Keywords : unconstrained optimization * large scale optimization * matrix-free truncated Newton method * preconditioned conjugate gradient method * preconditioners obtained by the directional differentiation * numerical algorithms Subject RIV: BA - General Mathematics Impact factor: 1.551, year: 2014
Mueller matrix polarimetry for the characterization of complex ...
Indian Academy of Sciences (India)
Scattering; polarization; Mueller matrix; wave propagation in random media; ... Initial biomedical applications of this novel general method for polarimetry analysis in random media are also presented. ... Pramana – Journal of Physics | News.
A domain derivative-based method for solving elastodynamic inverse obstacle scattering problems
International Nuclear Information System (INIS)
Le Louër, Frédérique
2015-01-01
The present work is concerned with the shape reconstruction problem of isotropic elastic inclusions from far-field data obtained by the scattering of a finite number of time-harmonic incident plane waves. This paper aims at completing the theoretical framework which is necessary for the application of geometric optimization tools to the inverse transmission problem in elastodynamics. The forward problem is reduced to systems of boundary integral equations following the direct and indirect methods initially developed for solving acoustic transmission problems. We establish the Fréchet differentiability of the boundary to far-field operator and give a characterization of the first Fréchet derivative and its adjoint operator. Using these results we propose an inverse scattering algorithm based on the iteratively regularized Gauß–Newton method and show numerical experiments in the special case of star-shaped obstacles. (paper)
Neutron Scattering in Hydrogenous Moderators, Studied by Time Dependent Reaction Rate Method
Energy Technology Data Exchange (ETDEWEB)
Larsson, L G; Moeller, E; Purohit, S N
1966-03-15
The moderation and absorption of a neutron burst in water, poisoned with the non-1/v absorbers cadmium and gadolinium, has been followed on the time scale by multigroup calculations, using scattering kernels for the proton gas and the Nelkin model. The time dependent reaction rate curves for each absorber display clear differences for the two models, and the separation between the curves does not depend much on the absorber concentration. An experimental method for the measurement of infinite medium reaction rate curves in a limited geometry has been investigated. This method makes the measurement of the time dependent reaction rate generally useful for thermalization studies in a small geometry of a liquid hydrogenous moderator, provided that the experiment is coupled to programs for the calculation of scattering kernels and time dependent neutron spectra. Good agreement has been found between the reaction rate curve, measured with cadmium in water, and a calculated curve, where the Haywood kernel has been used.
A new shielding calculation method for X-ray computed tomography regarding scattered radiation.
Watanabe, Hiroshi; Noto, Kimiya; Shohji, Tomokazu; Ogawa, Yasuyoshi; Fujibuchi, Toshioh; Yamaguchi, Ichiro; Hiraki, Hitoshi; Kida, Tetsuo; Sasanuma, Kazutoshi; Katsunuma, Yasushi; Nakano, Takurou; Horitsugi, Genki; Hosono, Makoto
2017-06-01
The goal of this study is to develop a more appropriate shielding calculation method for computed tomography (CT) in comparison with the Japanese conventional (JC) method and the National Council on Radiation Protection and Measurements (NCRP)-dose length product (DLP) method. Scattered dose distributions were measured in a CT room with 18 scanners (16 scanners in the case of the JC method) for one week during routine clinical use. The radiation doses were calculated for the same period using the JC and NCRP-DLP methods. The mean (NCRP-DLP-calculated dose)/(measured dose) ratios in each direction ranged from 1.7 ± 0.6 to 55 ± 24 (mean ± standard deviation). The NCRP-DLP method underestimated the dose at 3.4% in fewer shielding directions without the gantry and a subject, and the minimum (NCRP-DLP-calculated dose)/(measured dose) ratio was 0.6. The reduction factors were 0.036 ± 0.014 and 0.24 ± 0.061 for the gantry and couch directions, respectively. The (JC-calculated dose)/(measured dose) ratios ranged from 11 ± 8.7 to 404 ± 340. The air kerma scatter factor κ is expected to be twice as high as that calculated with the NCRP-DLP method and the reduction factors are expected to be 0.1 and 0.4 for the gantry and couch directions, respectively. We, therefore, propose a more appropriate method, the Japanese-DLP method, which resolves the issues of possible underestimation of the scattered radiation and overestimation of the reduction factors in the gantry and couch directions.
International Nuclear Information System (INIS)
Badalov, S.A.; Filippov, G.F.
1983-01-01
All the basic calculation formulas of an algebraic version of the resonating-group method for a pultichannel problem of the scattering of a nucleon by 7 Li and 7 Be taking into account α+α channel are derived. The spin-orbital and the Coulomb interactions are taken into consideration. The procedure enabling an exact projection into the states with the given values of the channel quantum numbers is proposed
International Nuclear Information System (INIS)
Glavata, D.; Pleshtil, I.; Kunchenko, A.B.; Ostanevich, Yu.M.
1982-01-01
Neutron experiments performed by the contrast (background) variation method allows to understand better the role that hydration plays in the study of macromolecules and to draw the connection between the excess scattering amplitude of hydrated molecule with its partial volume. The observed dependence of the compensation point on the degree of neutralization apparently plays an important role in the investigation of polyelectrolytes of biological origin
Three-group albedo method applied to the diffusion phenomenon with up-scattering of neutrons
International Nuclear Information System (INIS)
Terra, Andre M. Barge Pontes Torres; Silva, Jorge A. Valle da; Cabral, Ronaldo G.
2007-01-01
The main objective of this research is to develop a three-group neutron Albedo algorithm considering the up-scattering of neutrons in order to analyse the diffusion phenomenon in nonmultiplying media. The neutron Albedo method is an analytical method that does not try to solve describing explicit equations for the neutron fluxes. Thus the neutron Albedo methodology is very different from the conventional methodology, as the neutron diffusion theory model. Graphite is analyzed as a model case. One major application is in the determination of the nonleakage probabilities with more understandable results in physical terms than conventional radiation transport method calculations. (author)
The factorization method for inverse acoustic scattering in a layered medium
International Nuclear Information System (INIS)
Bondarenko, Oleksandr; Kirsch, Andreas; Liu, Xiaodong
2013-01-01
In this paper, we consider a problem of inverse acoustic scattering by an impenetrable obstacle embedded in a layered medium. We will show that the factorization method can be applied to recover the embedded obstacle; that is, the equation F-tilde g =φ z is solvable if and only if the sampling point z is in the interior of the unknown obstacle. Here, F-tilde is a self-adjoint operator related to the far field operator and ϕ z is the far field pattern of the Green function with respect to the problem of scattering by the background medium for point z. The validity of the factorization method is proven with the help of a mixed reciprocity principle and an application of the scattering operator. Due to the established mixed reciprocity principle, knowledge of the Green function for the background medium is no longer required, which makes the method attractive from the computational point of view. The paper is only concerned with sound-soft obstacles, but the analysis can be easily extended for sound-hard obstacles, or obstacles with separated sound-soft and sound-hard parts. Finally, we provide an explicit example for a radially symmetric case and present some numerical examples. (paper)
Improvements in in-situ filter test methods using a total light-scattering detector
International Nuclear Information System (INIS)
Marshall, M.; Stevens, D.C.
1986-01-01
This paper presents research aimed at providing useful data on a commonly used technique; a DOP (di-2-ethylhexyl phthalate) aerosol and a total light-scattering photometer. Methods of increasing the sensitivity of this technique are described. Alternative methods of in-situ filter testing are also considered. The sensitivity of a typical, modern, total light-scattering photometer, as a function of particle diameter, has a broad maximum in mass terms between 0.1 and 0.4 um. At its maximum usable sensitivity the instrument can detect approx. 1 particle/cm 3 . This response can be explained by light scattering theory and particle loss in the instrument inlet. The mass median diameter of the aerosols produced by various DOP generators varies from 0.2 to 1.0μm. Experiments with good quality HEPA filters indicate a maximum penetration for particles of 0.15 - 0.2μm. Details of the studies are given and the consequences discussed. It is shown that filter penetration of -3 % can be measured in-situ with existing equipment. Methods of extending the sensitivity to measure a penetration of approx.10 -5 % are described. (author)
International Nuclear Information System (INIS)
Yamamoto, Akio; Tatsumi, Masahiro
2006-01-01
In this paper, the scattered source subtraction (SSS) method is newly proposed to improve the spatial discretization error of the semi-analytic nodal method with the flat-source approximation. In the SSS method, the scattered source is subtracted from both side of the diffusion or the transport equation to make spatial variation of the source term to be small. The same neutron balance equation is still used in the SSS method. Since the SSS method just modifies coefficients of node coupling equations (those used in evaluation for the response of partial currents), its implementation is easy. Validity of the present method is verified through test calculations that are carried out in PWR multi-assemblies configurations. The calculation results show that the SSS method can significantly improve the spatial discretization error. Since the SSS method does not have any negative impact on execution time, convergence behavior and memory requirement, it will be useful to reduce the spatial discretization error of the semi-analytic nodal method with the flat-source approximation. (author)
Multiple resonance compensation for betatron coupling and its equivalence with matrix method
De Ninno, G
1999-01-01
Analyses of betatron coupling can be broadly divided into two categories: the matrix approach that decouples the single-turn matrix to reveal the normal modes and the hamiltonian approach that evaluates the coupling in terms of the action of resonances in perturbation theory. The latter is often regarded as being less exact but good for physical insight. The common opinion is that the correction of the two closest sum and difference resonances to the working point is sufficient to reduce the off-axis terms in the 4X4 single-turn matrix, but this is only partially true. The reason for this is explained, and a method is developed that sums to infinity all coupling resonances and, in this way, obtains results equivalent to the matrix approach. The two approaches is discussed with reference to the dynamic aperture. Finally, the extension of the summation method to resonances of all orders is outlined and the relative importance of a single resonance compared to all resonances of a given order is analytically desc...
Comparison of the spatial landmark scatter of various 3D digitalization methods.
Boldt, Florian; Weinzierl, Christian; Hertrich, Klaus; Hirschfelder, Ursula
2009-05-01
The aim of this study was to compare four different three-dimensional digitalization methods on the basis of the complex anatomical surface of a cleft lip and palate plaster cast, and to ascertain their accuracy when positioning 3D landmarks. A cleft lip and palate plaster cast was digitalized with the SCAN3D photo-optical scanner, the OPTIX 400S laser-optical scanner, the Somatom Sensation 64 computed tomography system and the MicroScribe MLX 3-axis articulated-arm digitizer. First, four examiners appraised by individual visual inspection the surface detail reproduction of the three non-tactile digitalization methods in comparison to the reference plaster cast. The four examiners then localized the landmarks five times at intervals of 2 weeks. This involved simply copying, or spatially tracing, the landmarks from a reference plaster cast to each model digitally reproduced by each digitalization method. Statistical analysis of the landmark distribution specific to each method was performed based on the 3D coordinates of the positioned landmarks. Visual evaluation of surface detail conformity assigned the photo-optical digitalization method an average score of 1.5, the highest subjectively-determined conformity (surpassing computer tomographic and laser-optical methods). The tactile scanning method revealed the lowest degree of 3D landmark scatter, 0.12 mm, and at 1.01 mm the lowest maximum 3D landmark scatter; this was followed by the computer tomographic, photo-optical and laser-optical methods (in that order). This study demonstrates that the landmarks' precision and reproducibility are determined by the complexity of the reference-model surface as well as the digital surface quality and individual ability of each evaluator to capture 3D spatial relationships. The differences in the 3D-landmark scatter values and lowest maximum 3D-landmark scatter between the best and the worst methods showed minor differences. The measurement results in this study reveal that it
A method to compute the inverse of a complex n-block tridiagonal quasi-hermitian matrix
International Nuclear Information System (INIS)
Godfrin, Elena
1990-01-01
This paper presents a method to compute the inverse of a complex n-block tridiagonal quasi-hermitian matrix using adequate partitions of the complete matrix. This type of matrix is very usual in quantum mechanics and, more specifically, in solid state physics (e.g., interfaces and superlattices), when the tight-binding approximation is used. The efficiency of the method is analyzed comparing the required CPU time and work-area for different usual techniques. (Author)
t matrix of metallic wire structures
International Nuclear Information System (INIS)
Zhan, T. R.; Chui, S. T.
2014-01-01
To study the electromagnetic resonance and scattering properties of complex structures of which metallic wire structures are constituents within multiple scattering theory, the t matrix of individual structures is needed. We have recently developed a rigorous and numerically efficient equivalent circuit theory in which retardation effects are taken into account for metallic wire structures. Here, we show how the t matrix can be calculated analytically within this theory. We illustrate our method with the example of split ring resonators. The density of states and cross sections for scattering and absorption are calculated, which are shown to be remarkably enhanced at resonant frequencies. The t matrix serves as the basic building block to evaluate the interaction of wire structures within the framework of multiple scattering theory. This will open the door to efficient design and optimization of assembly of wire structures
A comparison of companion matrix methods to find roots of a trigonometric polynomial
Boyd, John P.
2013-08-01
A trigonometric polynomial is a truncated Fourier series of the form fN(t)≡∑j=0Naj cos(jt)+∑j=1N bj sin(jt). It has been previously shown by the author that zeros of such a polynomial can be computed as the eigenvalues of a companion matrix with elements which are complex valued combinations of the Fourier coefficients, the "CCM" method. However, previous work provided no examples, so one goal of this new work is to experimentally test the CCM method. A second goal is introduce a new alternative, the elimination/Chebyshev algorithm, and experimentally compare it with the CCM scheme. The elimination/Chebyshev matrix (ECM) algorithm yields a companion matrix with real-valued elements, albeit at the price of usefulness only for real roots. The new elimination scheme first converts the trigonometric rootfinding problem to a pair of polynomial equations in the variables (c,s) where c≡cos(t) and s≡sin(t). The elimination method next reduces the system to a single univariate polynomial P(c). We show that this same polynomial is the resultant of the system and is also a generator of the Groebner basis with lexicographic ordering for the system. Both methods give very high numerical accuracy for real-valued roots, typically at least 11 decimal places in Matlab/IEEE 754 16 digit floating point arithmetic. The CCM algorithm is typically one or two decimal places more accurate, though these differences disappear if the roots are "Newton-polished" by a single Newton's iteration. The complex-valued matrix is accurate for complex-valued roots, too, though accuracy decreases with the magnitude of the imaginary part of the root. The cost of both methods scales as O(N3) floating point operations. In spite of intimate connections of the elimination/Chebyshev scheme to two well-established technologies for solving systems of equations, resultants and Groebner bases, and the advantages of using only real-valued arithmetic to obtain a companion matrix with real-valued elements
DEFF Research Database (Denmark)
Karamehmedovic, Mirza; Breinbjerg, Olav
2002-01-01
The Method of Auxiliary Sources (MAS) is applied to 3D scattering problems involving spherical impedance scatterers. The MAS results are compared with the reference spherical wave expansion (SWE) solution. It is demonstrated that good agreement is achieved between the MAS and SWE results....
IMPACT OF MATRIX INVERSION ON THE COMPLEXITY OF THE FINITE ELEMENT METHOD
Directory of Open Access Journals (Sweden)
M. Sybis
2016-04-01
Full Text Available Purpose. The development of a wide construction market and a desire to design innovative architectural building constructions has resulted in the need to create complex numerical models of objects having increasingly higher computational complexity. The purpose of this work is to show that choosing a proper method for solving the set of equations can improve the calculation time (reduce the complexity by a few levels of magnitude. Methodology. The article presents an analysis of the impact of matrix inversion algorithm on the deflection calculation in the beam, using the finite element method (FEM. Based on the literature analysis, common methods of calculating set of equations were determined. From the found solutions the Gaussian elimination, LU and Cholesky decomposition methods have been implemented to determine the effect of the matrix inversion algorithm used for solving the equations set on the number of computational operations performed. In addition, each of the implemented method has been further optimized thereby reducing the number of necessary arithmetic operations. Findings. These optimizations have been performed on the use of certain properties of the matrix, such as symmetry or significant number of zero elements in the matrix. The results of the analysis are presented for the division of the beam to 5, 50, 100 and 200 nodes, for which the deflection has been calculated. Originality. The main achievement of this work is that it shows the impact of the used methodology on the complexity of solving the problem (or equivalently, time needed to obtain results. Practical value. The difference between the best (the less complex and the worst (the most complex is in the row of few orders of magnitude. This result shows that choosing wrong methodology may enlarge time needed to perform calculation significantly.
Online monitoring of a belt grinding process by using a light scattering method
International Nuclear Information System (INIS)
Boehm, Johannes; Vernes, Andras; Vorlaufer, Georg; Vellekoop, Michael
2010-01-01
Industrially ground surfaces often have a characteristic surface topography known as chatter marks. The surface finishing is mainly monitored by optical measurement techniques. In this work, the monitoring of an industrial belt grinding process with a light scattering sensor is presented. Although this technique is primarily applied for parametric surface roughness analysis, here it is shown that it enables also the measurement of the surface topography, i.e., the chatter marks occurring during the belt grinding process. In particular, it is proven that the light scattering method is appropriate to measure online the topography of chatter marks. Furthermore, the frequency analysis of the data reveals that the wavelength of chatter marks strongly depends on process parameters, such as the grinding speed.
Windows pollution problems of the dust concentration measurement based on scattering method
International Nuclear Information System (INIS)
Zhao Yanjun; Zhang Yongtao; Shi Xinyue; Xu Chuanlong; Wang Shimin
2009-01-01
The windows are separated the measurement system from the dust space in the light Scattering dust concentration measurement system. The windows are polluted unavoidably by the dust and the measurement error is produced. Based on the Mie Scattering theory, the measurement error is researched in this paper. The numerical simulation results show that the measurement error is related to the particles diameter distribution and the refractive index, but is independent of the particles average diameter. A novel photoelectricity sensor is developed in this paper in order to solve the measurement error by the windows pollution. The calculated method is brought out which can amend the measurement errors by the windows pollution and improve the measurement accuracy.
International Nuclear Information System (INIS)
Tyas-Djuhariningrum
2004-01-01
The gold sample analysis can be deviated more than >10% to those thrue value caused by the matrix element. So that the matrix element character need to be study in order to reduce the deviation. In rock samples, the matrix elements can cause self quenching, self absorption and ionization process, so there is a result analysis error. In the rock geochemical process, the elements of the same group at the periodic system have the tendency to be together because of their same characteristic. In absorption Atomic Spectroscopy analysis, the elements associate can absorb primer energy with similar wave length so that it can cause deviation in the result interpretation. The aim of study is to predict matrix element influences from rock sample with application standard method for reducing deviation. In quantitative way, assessment of primer light intensity that will be absorbed is proportional to the concentration atom in the sample that relationship between photon intensity with concentration in part per million is linier (ppm). These methods for eliminating matrix elements influence consist of three methods : external standard method, internal standard method, and addition standard method. External standard method for all matrix element, internal standard method for elimination matrix element that have similar characteristics, addition standard methods for elimination matrix elements in Au, Pt samples. The third of standard posess here accuracy are about 95-97%. (author)