Bouwkamp, C.J.
1954-01-01
A critical review is presented of recent progress in classical diffraction theory. Both scalar and electromagnetic problems are discussed. The report may serve as an introduction to general diffraction theory although the main emphasis is on diffraction by plane obstacles. Various modifications of
Contribution to diffraction theory
International Nuclear Information System (INIS)
Chako, N.
1966-11-01
In a first part, we have given a general and detailed treatment of the modern theory of diffraction. The rigorous theory is formulated as a boundary value problem of the wave equation or Maxwell equations. However, up to the present time, such a program of treating diffraction by optical systems, even for simple optical instruments, has not been realized due to the complicated character of the boundary conditions. The recent developments show clearly the nature of the approximation of the classical theories originally due to Fresnel and Young, later formulated in a rigorous manner by Kirchhoff and Rubinowicz, respectively and, at the same time the insufficiency of these theories in explaining a number of diffraction phenomena. Furthermore, we have made a study of the limitations of the approximate theories and the recent attempts to improve these. The second part is devoted to a general mathematical treatment of the theory of diffraction of optical systems including aberrations. After a general and specific analysis of geometrical and wave aberrations along classical and modern (Nijboer) lines, we have been able to evaluate the diffraction integrals representing the image field at any point in image space explicitly, when the aberrations are small. Our formulas are the generalisations of all anterior results obtained by previous investigators. Moreover, we have discussed the Zernike-Nijboer theory of aberration and generalised it not only for rotational systems, but also for non-symmetric systems as well, including the case of non circular apertures. The extension to non-circular apertures is done by introducing orthogonal functions or polynomials over such aperture shapes. So far the results are valid for small aberrations, that is to say, where the deformation of the real wave front emerging from the optical system is less than a wave length of light or of the electromagnetic wave from the ideal wave front. If the aberrations are large, then one must employ the
Dynamical theory of neutron diffraction
International Nuclear Information System (INIS)
Sears, V.F.
1978-01-01
We present a review of the dynamical theory of neutron diffraction by macroscopic bodies which provides the theoretical basis for the study of neutron optics. We consider both the theory of dispersion, in which it is shown that the coherent wave in the medium satisfies a macroscopic one-body Schroedinger equation, and the theory of reflection, refraction, and diffraction in which the above equation is solved for a number of special cases of interest. The theory is illustrated with the help of experimental results obtained over the past 10 years by a number of new techniques such as neutron gravity refractometry. Pendelloesung interference, and neutron interferometry. (author)
Extended vector-tensor theories
Energy Technology Data Exchange (ETDEWEB)
Kimura, Rampei; Naruko, Atsushi; Yoshida, Daisuke, E-mail: rampei@th.phys.titech.ac.jp, E-mail: naruko@th.phys.titech.ac.jp, E-mail: yoshida@th.phys.titech.ac.jp [Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551 (Japan)
2017-01-01
Recently, several extensions of massive vector theory in curved space-time have been proposed in many literatures. In this paper, we consider the most general vector-tensor theories that contain up to two derivatives with respect to metric and vector field. By imposing a degeneracy condition of the Lagrangian in the context of ADM decomposition of space-time to eliminate an unwanted mode, we construct a new class of massive vector theories where five degrees of freedom can propagate, corresponding to three for massive vector modes and two for massless tensor modes. We find that the generalized Proca and the beyond generalized Proca theories up to the quartic Lagrangian, which should be included in this formulation, are degenerate theories even in curved space-time. Finally, introducing new metric and vector field transformations, we investigate the properties of thus obtained theories under such transformations.
Gauge Theories of Vector Particles
Glashow, S. L.; Gell-Mann, M.
1961-04-24
The possibility of generalizing the Yang-Mills trick is examined. Thus we seek theories of vector bosons invariant under continuous groups of coordinate-dependent linear transformations. All such theories may be expressed as superpositions of certain "simple" theories; we show that each "simple theory is associated with a simple Lie algebra. We may introduce mass terms for the vector bosons at the price of destroying the gauge-invariance for coordinate-dependent gauge functions. The theories corresponding to three particular simple Lie algebras - those which admit precisely two commuting quantum numbers - are examined in some detail as examples. One of them might play a role in the physics of the strong interactions if there is an underlying super-symmetry, transcending charge independence, that is badly broken. The intermediate vector boson theory of weak interactions is discussed also. The so-called "schizon" model cannot be made to conform to the requirements of partial gauge-invariance.
Generating and measuring non-diffracting vector Bessel beams
CSIR Research Space (South Africa)
Dudley, Angela L
2014-03-01
Full Text Available We demonstrate how to create non-diffracting vector Bessel beams by implementing a spatial light modulator (SLM) to generate scalar Bessel beams which are then converted into vector fields by the use of an azimuthally-varying birefringent plate...
Theory of edge diffraction in electromagnetics
Ufimtsev, Pyotr
2009-01-01
This book is an essential resource for researchers involved in designing antennas and RCS calculations. It is also useful for students studying high frequency diffraction techniques. It contains basic original ideas of the Physical Theory of Diffraction (PTD), examples of its practical application, and its validation by the mathematical theory of diffraction. The derived analytic expressions are convenient for numerical calculations and clearly illustrate the physical structure of the scattered field.
Uniform asymptotic theory of edge diffraction
Lewis, R.M.; Boersma, J.; Oughstun, K.E.
1992-01-01
Geometrical optics fails to account for the phenomenon of diffraction, i.e., the existence of nonzero fields in the geometrical shadow. Keller's geometrical theory of diffraction accounts for this phenomenon by providing correction terms to the geometrical optics field, in the form of a
Uniform asymptotic theory of edge diffraction
Lewis, R.M.; Boersma, J.
1969-01-01
Geometrical optics fails to account for the phenomenon of diffraction, i.e., the existence of nonzero fields in the geometrical shadow. Keller's geometrical theory of diffraction accounts for this phenomenon by providing correction terms to the geometrical optics field, in the form of a
Light-scattering theory of diffraction.
Guo, Wei
2010-03-01
Since diffraction is a scattering process in principle, light propagation through one aperture in a screen is discussed in the light-scattering theory. Through specific calculation, the expression of the electric field observed at an observation point is obtained and is used not only to explain why Kirchhoff's diffraction theory is a good approximation when the screen is both opaque and sufficiently thin but also to demonstrate that the mathematical and physical problems faced by Kirchhoff's theory are avoided in the light-scattering theory.
Exclusive central diffractive production of scalar, pseudoscalar and vector mesons
Directory of Open Access Journals (Sweden)
Lebiedowicz P.
2014-01-01
Full Text Available We discuss exclusive central diffractive production of scalar (ƒ0(980, ƒ0(1370, ƒ0(1500, pseudoscalar (η, η′(958, and vector (ρ0 mesons in proton-proton collisions. The amplitudes are formulated in terms of effective vertices required to respect standard rules of Quantum Field Theory and propagators for the exchanged pomeron and reggeons. Different pomeron-pomeron-meson tensorial (vectorial coupling structures are possible in general. In most cases two lowest orbital angular momentum - spin couplings are necessary to describe experimental differential distributions. For the ƒ0(980 and η production the reggeon-pomeron, pomeron-reggeon, and reggeon-reggeon exchanges are included in addition, which seems to be necessary at relatively low energies. The theoretical results are compared with the WA102 experimental data, in order to determine the model parameters. For the ρ0 production the photon-pomeron and pomeron-photon exchanges are considered. The coupling parameters of tensor pomeron and/or reggeon are fixed from the H1 and ZEUS experimental data of the γp → ρ0 p reaction. We present first predictions of this mechanism for pp → ppπ+π− reaction being studied at COMPASS, RHIC, Tevatron, and LHC. Correlation in azimuthal angle between outgoing protons and distribution in pion rapidities at √s = 7 TeV are presented. We show that high-energy central production of mesons could provide crucial information on the spin structure of the soft pomeron.
Fundamentals of the physical theory of diffraction
Ufimtsev, Pyotr Ya
2014-01-01
A complete presentation of the modern physical theory of diffraction and its applications, by the world's leading authority on the topicExtensive revisions and additions to the first edition yield a second edition that is 492 pages in length, with 122 figuresNew sections examine the nature of polarization coupling, and extend the theory of shadow radiation and reflection to opaque objectsThis book features end-of-chapter problems and a solutions manual for university professors and graduate studentsMATLAB codes presented in appendices allow for quick numeric calculations of diffracted waves
Diffractive vector meson production in deep inelastic scattering
International Nuclear Information System (INIS)
Kamps, M. de.
1997-01-01
This thesis seeks to bring comfort to those who are appalled by the usual high level of violence in high energy physics. Although also here we engage in the customary vandalistic smashing together of two particles, the reaction we will study has a happy end in store for both of them. The subject of this thesis will be the reaction: e + p→e + pV where V is one of the vector mesons ρ, ω, φ, J/ψ. We will investigate the situation where the final state positron enters the ZEUS main detector, which indicates that a violent reaction has taken place between the initial state particles, but nevertheless the proton does not break up. The violence with which the positron is scattered characterises the reaction as a Deep Inelastic Scattering (DIS), the fact that the proton does not break up characterises the reaction as diffractive which explains the title of the thesis. Both DIS and diffractive physics will be defined and discussed in the context of this thesis. (orig./WL)
Vector optimization theory, applications, and extensions
Jahn, Johannes
2011-01-01
This new edition of a key monograph has fresh sections on the work of Edgeworth and Pareto in its presentation in a general setting of the fundamentals and important results of vector optimization. It examines background material, applications and theories.
Vector supersymmetry in topological field theories
International Nuclear Information System (INIS)
Gieres, F.; Grimstrup, J.; Pisar, T.; Schweda, M.
2000-01-01
We present a simple derivation of vector supersymmetry transformations for topological field theories of Schwarz- and Witten-type. Our method is similar to the derivation of BRST-transformations from the so-called horizontality conditions or Russian formulae. We show that this procedure reproduces in a concise way the known vector supersymmetry transformations of various topological models and we use it to obtain some new transformations of this type for 4d topological YM-theories in different gauges. (author)
Quantum theory in vector bundles
International Nuclear Information System (INIS)
Mayer, M.E.
1986-01-01
This paper describes a framework capable of accomodating quantum gauge theory (QGT), based on recent insights on the cohomological interpretation of ghosts, BRS-transformations, anomalies, and Schwinger terms. The hope is that the approach will lead to a trial marriage of quantum theory and gravity. Some points that are stressed are: nonabelian QGT is subtler than QED; in spite of their BRS-variance, the Yang-Mills potential together with the ghost-form are needed in addition to the field theory; the ghost form together with their Lagrange multiplier in a Lagrangian formalism makes its appearance through the BRS cohomology; and, in QGT one can treat the connection form, the curvature form and the ghost form in one of several ways
Contribution to diffraction theory; Contribution a la theorie de la diffraction
Energy Technology Data Exchange (ETDEWEB)
Chako, N [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1966-11-01
In a first part, we have given a general and detailed treatment of the modern theory of diffraction. The rigorous theory is formulated as a boundary value problem of the wave equation or Maxwell equations. However, up to the present time, such a program of treating diffraction by optical systems, even for simple optical instruments, has not been realized due to the complicated character of the boundary conditions. The recent developments show clearly the nature of the approximation of the classical theories originally due to Fresnel and Young, later formulated in a rigorous manner by Kirchhoff and Rubinowicz, respectively and, at the same time the insufficiency of these theories in explaining a number of diffraction phenomena. Furthermore, we have made a study of the limitations of the approximate theories and the recent attempts to improve these. The second part is devoted to a general mathematical treatment of the theory of diffraction of optical systems including aberrations. After a general and specific analysis of geometrical and wave aberrations along classical and modern (Nijboer) lines, we have been able to evaluate the diffraction integrals representing the image field at any point in image space explicitly, when the aberrations are small. Our formulas are the generalisations of all anterior results obtained by previous investigators. Moreover, we have discussed the Zernike-Nijboer theory of aberration and generalised it not only for rotational systems, but also for non-symmetric systems as well, including the case of non circular apertures. The extension to non-circular apertures is done by introducing orthogonal functions or polynomials over such aperture shapes. So far the results are valid for small aberrations, that is to say, where the deformation of the real wave front emerging from the optical system is less than a wave length of light or of the electromagnetic wave from the ideal wave front. If the aberrations are large, then one must employ the
Contribution to diffraction theory; Contribution a la theorie de la diffraction
Energy Technology Data Exchange (ETDEWEB)
Chako, N. [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1966-11-01
In a first part, we have given a general and detailed treatment of the modern theory of diffraction. The rigorous theory is formulated as a boundary value problem of the wave equation or Maxwell equations. However, up to the present time, such a program of treating diffraction by optical systems, even for simple optical instruments, has not been realized due to the complicated character of the boundary conditions. The recent developments show clearly the nature of the approximation of the classical theories originally due to Fresnel and Young, later formulated in a rigorous manner by Kirchhoff and Rubinowicz, respectively and, at the same time the insufficiency of these theories in explaining a number of diffraction phenomena. Furthermore, we have made a study of the limitations of the approximate theories and the recent attempts to improve these. The second part is devoted to a general mathematical treatment of the theory of diffraction of optical systems including aberrations. After a general and specific analysis of geometrical and wave aberrations along classical and modern (Nijboer) lines, we have been able to evaluate the diffraction integrals representing the image field at any point in image space explicitly, when the aberrations are small. Our formulas are the generalisations of all anterior results obtained by previous investigators. Moreover, we have discussed the Zernike-Nijboer theory of aberration and generalised it not only for rotational systems, but also for non-symmetric systems as well, including the case of non circular apertures. The extension to non-circular apertures is done by introducing orthogonal functions or polynomials over such aperture shapes. So far the results are valid for small aberrations, that is to say, where the deformation of the real wave front emerging from the optical system is less than a wave length of light or of the electromagnetic wave from the ideal wave front. If the aberrations are large, then one must employ the
Null vectors in superconformal quantum field theory
International Nuclear Information System (INIS)
Huang Chaoshang
1993-01-01
The superspace formulation of the N=1 superconformal field theory and superconformal Ward identities are used to give a precise definition of fusion. Using the fusion procedure, superconformally covariant differential equations are derived and consequently a complete and straightforward algorithm for finding null vectors in Verma modules of the Neveu-Schwarz algebra is given. (orig.)
Theory of hard diffraction and rapidity gaps
International Nuclear Information System (INIS)
Del Duca, V.
1995-06-01
In this talk we review the models describing the hard diffractive production of jets or more generally high-mass states in presence of rapidity gaps in hadron-hadron and lepton-hadron collisions. By rapidity gaps we mean regions on the lego plot in (pseudo)-rapidity and azimuthal angle where no hadrons are produced, between the jet(s) and an elastically scattered hadron (single hard diffraction) or between two jets (double hard diffraction). (orig.)
Theory of hard diffraction and rapidity gaps
International Nuclear Information System (INIS)
Del Duca, V.
1996-01-01
In this talk we review the models describing the hard diffractive production of jets or more generally high-mass states in presence of rapidity gaps in hadron-hadron and lepton-hadron collisions. By rapidity gaps we mean regions on the lego plot in (pseudo)-rapidity and azimuthal angle where no hadrons are produced, between the jet(s) and an elastically scattered hadron (single hard diffraction) or between two jets (double hard diffraction). copyright 1996 American Institute of Physics
Black holes in vector-tensor theories
Energy Technology Data Exchange (ETDEWEB)
Heisenberg, Lavinia [Institute for Theoretical Studies, ETH Zurich, Clausiusstrasse 47, 8092 Zurich (Switzerland); Kase, Ryotaro; Tsujikawa, Shinji [Department of Physics, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan); Minamitsuji, Masato, E-mail: lavinia.heisenberg@eth-its.ethz.ch, E-mail: r.kase@rs.tus.ac.jp, E-mail: masato.minamitsuji@tecnico.ulisboa.pt, E-mail: shinji@rs.kagu.tus.ac.jp [Centro Multidisciplinar de Astrofisica—CENTRA, Departamento de Fisica, Instituto Superior Tecnico—IST, Universidade de Lisboa—UL, Avenida Rovisco Pais 1, 1049-001 Lisboa (Portugal)
2017-08-01
We study static and spherically symmetric black hole (BH) solutions in second-order generalized Proca theories with nonminimal vector field derivative couplings to the Ricci scalar, the Einstein tensor, and the double dual Riemann tensor. We find concrete Lagrangians which give rise to exact BH solutions by imposing two conditions of the two identical metric components and the constant norm of the vector field. These exact solutions are described by either Reissner-Nordström (RN), stealth Schwarzschild, or extremal RN solutions with a non-trivial longitudinal mode of the vector field. We then numerically construct BH solutions without imposing these conditions. For cubic and quartic Lagrangians with power-law couplings which encompass vector Galileons as the specific cases, we show the existence of BH solutions with the difference between two non-trivial metric components. The quintic-order power-law couplings do not give rise to non-trivial BH solutions regular throughout the horizon exterior. The sixth-order and intrinsic vector-mode couplings can lead to BH solutions with a secondary hair. For all the solutions, the vector field is regular at least at the future or past horizon. The deviation from General Relativity induced by the Proca hair can be potentially tested by future measurements of gravitational waves in the nonlinear regime of gravity.
Vector wave diffraction pattern of slits masked by polarizing devices
Indian Academy of Sciences (India)
This calls for a systematic study of diffraction properties of different apertures using polarization-sensitive devices. In the present paper, we have studied the Fraunhofer diffraction pattern of slits masked by different kinds of polarizing devices which introduce a phase difference between the two orthogonal components of the ...
International Nuclear Information System (INIS)
Macrander, A.T.; Blasdell, R.C.
1993-09-01
Dynamical x-ray diffraction theory can be cast in matrix form. In recent years, an 8x8 matrix theory was developed that treated asymmetric reflections from strained crystals. The polarization of the incident, specularly reflected, reflected diffracted, transmitted diffracted, and transmitted electromagnetic wave fields were all defined as s or p. That is, polarizations were defined with respect to the plane containing the incident beam direction and the surface normal. The authors present modifications of the theory to treat σ and π polarizations for Bragg diffraction from asymmetric planes, that is, for polarizations defined with respect to the plane containing the incident beam direction and the reciprocal lattice vector for Bragg diffraction. They present results of this theory for unstrained crystals in the inclined geometry. In this geometry the incident beam wavevector, the reciprocal lattice vector, and the surface normal are not coplanar. The inclined crystal geometry appears promising for use in a high-heat-load monochromator for undulator radiation at the Advanced Photon Source. As expected, they find a weak π-polarization component in the diffracted beam when the polarization of the incident beam is pure σ
Ono, Hiroshi; Kuzuwata, Mitsuru; Sasaki, Tomoyuki; Noda, Kohei; Kawatsuki, Nobuhiro
2014-03-01
The blazed vector grating possessing antisymmetric distributions of the birefringence were fabricated by exposing the line-focused linearly polarized ultraviolet light on the photosensitive polymer liquid crystals. The polarization states of the diffraction beams can be highly and widely controlled by designing the blazed structures, and the diffraction properties were well-explained by Jones calculus.
Anisotropic cosmological solutions in massive vector theories
Energy Technology Data Exchange (ETDEWEB)
Heisenberg, Lavinia [Institute for Theoretical Studies, ETH Zurich, Clausiusstrasse 47, 8092 Zurich (Switzerland); Kase, Ryotaro; Tsujikawa, Shinji, E-mail: Lavinia.heisenberg@googlemail.com, E-mail: r.kase@rs.tus.ac.jp, E-mail: shinji@rs.kagu.tus.ac.jp [Department of Physics, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan)
2016-11-01
In beyond-generalized Proca theories including the extension to theories higher than second order, we study the role of a spatial component v of a massive vector field on the anisotropic cosmological background. We show that, as in the case of the isotropic cosmological background, there is no additional ghostly degrees of freedom associated with the Ostrogradski instability. In second-order generalized Proca theories we find the existence of anisotropic solutions on which the ratio between the anisotropic expansion rate Σ and the isotropic expansion rate H remains nearly constant in the radiation-dominated epoch. In the regime where Σ/ H is constant, the spatial vector component v works as a dark radiation with the equation of state close to 1/3. During the matter era, the ratio Σ/ H decreases with the decrease of v . As long as the conditions |Σ| || H and v {sup 2} || φ{sup 2} are satisfied around the onset of late-time cosmic acceleration, where φ is the temporal vector component, we find that the solutions approach the isotropic de Sitter fixed point (Σ = 0 = v ) in accordance with the cosmic no-hair conjecture. In the presence of v and Σ the early evolution of the dark energy equation of state w {sub DE} in the radiation era is different from that in the isotropic case, but the approach to the isotropic value w {sub DE}{sup (iso)} typically occurs at redshifts z much larger than 1. Thus, apart from the existence of dark radiation, the anisotropic cosmological dynamics at low redshifts is similar to that in isotropic generalized Proca theories. In beyond-generalized Proca theories the only consistent solution to avoid the divergence of a determinant of the dynamical system corresponds to v = 0, so Σ always decreases in time.
Anisotropic cosmological solutions in massive vector theories
International Nuclear Information System (INIS)
Heisenberg, Lavinia; Kase, Ryotaro; Tsujikawa, Shinji
2016-01-01
In beyond-generalized Proca theories including the extension to theories higher than second order, we study the role of a spatial component v of a massive vector field on the anisotropic cosmological background. We show that, as in the case of the isotropic cosmological background, there is no additional ghostly degrees of freedom associated with the Ostrogradski instability. In second-order generalized Proca theories we find the existence of anisotropic solutions on which the ratio between the anisotropic expansion rate Σ and the isotropic expansion rate H remains nearly constant in the radiation-dominated epoch. In the regime where Σ/ H is constant, the spatial vector component v works as a dark radiation with the equation of state close to 1/3. During the matter era, the ratio Σ/ H decreases with the decrease of v . As long as the conditions |Σ| || H and v 2 || φ 2 are satisfied around the onset of late-time cosmic acceleration, where φ is the temporal vector component, we find that the solutions approach the isotropic de Sitter fixed point (Σ = 0 = v ) in accordance with the cosmic no-hair conjecture. In the presence of v and Σ the early evolution of the dark energy equation of state w DE in the radiation era is different from that in the isotropic case, but the approach to the isotropic value w DE (iso) typically occurs at redshifts z much larger than 1. Thus, apart from the existence of dark radiation, the anisotropic cosmological dynamics at low redshifts is similar to that in isotropic generalized Proca theories. In beyond-generalized Proca theories the only consistent solution to avoid the divergence of a determinant of the dynamical system corresponds to v = 0, so Σ always decreases in time.
Gu, Bing; Xu, Danfeng; Pan, Yang; Cui, Yiping
2014-07-01
Based on the vectorial Rayleigh-Sommerfeld integrals, the analytical expressions for azimuthal-variant vector fields diffracted by an annular aperture are presented. This helps us to investigate the propagation behaviors and the focusing properties of apertured azimuthal-variant vector fields under nonparaxial and paraxial approximations. The diffraction by a circular aperture, a circular disk, or propagation in free space can be treated as special cases of this general result. Simulation results show that the transverse intensity, longitudinal intensity, and far-field divergence angle of nonparaxially apertured azimuthal-variant vector fields depend strongly on the azimuthal index, the outer truncation parameter and the inner truncation parameter of the annular aperture, as well as the ratio of the waist width to the wavelength. Moreover, the multiple-ring-structured intensity pattern of the focused azimuthal-variant vector field, which originates from the diffraction effect caused by an annular aperture, is experimentally demonstrated.
Relativistic stars in vector-tensor theories
Kase, Ryotaro; Minamitsuji, Masato; Tsujikawa, Shinji
2018-04-01
We study relativistic star solutions in second-order generalized Proca theories characterized by a U (1 )-breaking vector field with derivative couplings. In the models with cubic and quartic derivative coupling, the mass and radius of stars become larger than those in general relativity for negative derivative coupling constants. This phenomenon is mostly attributed to the increase of star radius induced by a slower decrease of the matter pressure compared to general relativity. There is a tendency that the relativistic star with a smaller mass is not gravitationally bound for a low central density and hence is dynamically unstable, but that with a larger mass is gravitationally bound. On the other hand, we show that the intrinsic vector-mode couplings give rise to general relativistic solutions with a trivial field profile, so the mass and radius are not modified from those in general relativity.
The geometrical theory of diffraction for axially symmetric reflectors
DEFF Research Database (Denmark)
Rusch, W.; Sørensen, O.
1975-01-01
The geometrical theory of diffraction (GTD) (cf. [1], for example) may be applied advantageously to many axially symmetric reflector antenna geometries. The material in this communication presents analytical, computational, and experimental results for commonly encountered reflector geometries...
Generating and analyzing non-diffracting vector vortex beams
CSIR Research Space (South Africa)
Li, Y
2013-08-01
Full Text Available single order Bessel beam and superposition cases are studied. The polarization and the azimuthal modes of the generated beams are analyzed. The results of modal decompositions on polarization components are in good agreement with theory. We demonstrate...
A new theory for X-ray diffraction.
Fewster, Paul F
2014-05-01
This article proposes a new theory of X-ray scattering that has particular relevance to powder diffraction. The underlying concept of this theory is that the scattering from a crystal or crystallite is distributed throughout space: this leads to the effect that enhanced scatter can be observed at the `Bragg position' even if the `Bragg condition' is not satisfied. The scatter from a single crystal or crystallite, in any fixed orientation, has the fascinating property of contributing simultaneously to many `Bragg positions'. It also explains why diffraction peaks are obtained from samples with very few crystallites, which cannot be explained with the conventional theory. The intensity ratios for an Si powder sample are predicted with greater accuracy and the temperature factors are more realistic. Another consequence is that this new theory predicts a reliability in the intensity measurements which agrees much more closely with experimental observations compared to conventional theory that is based on `Bragg-type' scatter. The role of dynamical effects (extinction etc.) is discussed and how they are suppressed with diffuse scattering. An alternative explanation for the Lorentz factor is presented that is more general and based on the capture volume in diffraction space. This theory, when applied to the scattering from powders, will evaluate the full scattering profile, including peak widths and the `background'. The theory should provide an increased understanding of the reliability of powder diffraction measurements, and may also have wider implications for the analysis of powder diffraction data, by increasing the accuracy of intensities predicted from structural models.
Introduction to the theory of low-energy electron diffraction
International Nuclear Information System (INIS)
Fingerland, A.; Tomasek, M.
1975-01-01
An elementary introduction to the basic principles of the theory of low-energy electron diffraction is presented. General scattering theory is used to classify the hitherto known approaches to the problem (optical potential and one-electron approximation; formal scattering theory: Born expansion and multiple scattering; translational symmetry: Ewald construction; classification of LEED theories by means of the T matrix; pseudokinematical theory for crystal with clean surface and with an adsorbed monomolecular layer; dynamical theory; inclusion of inelastic collisions; discussion of a simple example by means of the band-structure approach)
Diffraction theory in QCD and beyond
International Nuclear Information System (INIS)
White, A.R.
1987-01-01
A study of the Pomeron in QCD is briefly outlined. Implications for the production of W + W - and Z 0 Z 0 pairs are described and the possibility that the electroweak scale is a major strong-interaction threshold discussed. The application of Pomeron phase-transition theory to SU(5) dynamical symmetry breaking is suggested and the related ''strong-interaction'' properties of the photon briefly mentioned
Dynamic theory of neutron diffraction from a moving grating
Energy Technology Data Exchange (ETDEWEB)
Bushuev, V. A., E-mail: vabushuev@yandex.ru [Moscow State University (Russian Federation); Frank, A. I.; Kulin, G. V. [Joint Institute for Nuclear Research (Russian Federation)
2016-01-15
A multiwave dynamic theory of diffraction of ultracold neutrons from a moving phase grating has been developed in the approximation of coupled slowly varying amplitudes of wavefunctions. The effect of the velocity, period, and height of grooves of the grating, as well as the spectral angular distribution of the intensity of incident neurons, on the discrete energy spectrum and the intensity of diffraction reflections of various orders has been analyzed.
Theory of time-resolved inelastic x-ray diffraction
DEFF Research Database (Denmark)
Lorenz, Ulf; Møller, Klaus Braagaard; Henriksen, Niels Engholm
2010-01-01
Starting from a general theory of time-resolved x-ray scattering, we derive a convenient expression for the diffraction signal based on a careful analysis of the relevant inelastic scattering processes. We demonstrate that the resulting inelastic limit applies to a wider variety of experimental...... conditions than similar, previously derived formulas, and it directly allows the application of selection rules when interpreting diffraction signals. Furthermore, we present a simple extension to systems simultaneously illuminated by x rays and a laser beam....
Compact stars in vector-tensor-Horndeski theory of gravity
Energy Technology Data Exchange (ETDEWEB)
Momeni, Davood; Myrzakulov, Kairat; Myrzakulov, Ratbay [Eurasian National University, Department of General and Theoretical Physics, Eurasian International Center for Theoretical Physics, Astana (Kazakhstan); Faizal, Mir [University of British Columbia-Okanagan, Irving K. Barber School of Arts and Sciences, Kelowna, BC (Canada); University of Lethbridge, Department of Physics and Astronomy, Lethbridge, AB (Canada)
2017-01-15
In this paper, we will analyze a theory of modified gravity, in which the field content of general relativity will be increased to include a vector field. We will use the Horndeski formalism to non-minimally couple this vector field to the metric. As we will be using the Horndeski formalism, this theory will not contain Ostrogradsky ghost degree of freedom. We will analyze compact stars using this vector-tensor-Horndeski theory. (orig.)
Support vector machines optimization based theory, algorithms, and extensions
Deng, Naiyang; Zhang, Chunhua
2013-01-01
Support Vector Machines: Optimization Based Theory, Algorithms, and Extensions presents an accessible treatment of the two main components of support vector machines (SVMs)-classification problems and regression problems. The book emphasizes the close connection between optimization theory and SVMs since optimization is one of the pillars on which SVMs are built.The authors share insight on many of their research achievements. They give a precise interpretation of statistical leaning theory for C-support vector classification. They also discuss regularized twi
Semiclassical perturbation theory for diffraction in heavy atom surface scattering.
Miret-Artés, Salvador; Daon, Shauli; Pollak, Eli
2012-05-28
The semiclassical perturbation theory formalism of Hubbard and Miller [J. Chem. Phys. 78, 1801 (1983)] for atom surface scattering is used to explore the possibility of observation of heavy atom diffractive scattering. In the limit of vanishing ℏ the semiclassical theory is shown to reduce to the classical perturbation theory. The quantum diffraction pattern is sensitive to the characteristics of the beam of incoming particles. Necessary conditions for observation of quantum diffraction are derived for the angular width of the incoming beam. An analytic expression for the angular distribution as a function of the angular and momentum variance of the incoming beam is obtained. We show both analytically and through some numerical results that increasing the angular width of the incident beam leads to decoherence of the quantum diffraction peaks and one approaches the classical limit. However, the incoherence of the beam in the parallel direction does not destroy the diffraction pattern. We consider the specific example of Ar atoms scattered from a rigid LiF(100) surface.
Problems of vector Lagrangians in field theories
International Nuclear Information System (INIS)
Krivsky, I.Yu.; Simulik, V.M.
1997-01-01
A vector Lagrange approach to the Dirac spinor field and the relationship between the vector Lagrangians for the spinor and electromagnetic fields are considered. A vector Lagrange approach for the system of interacting electromagnetic B=(B μ υ)=(E-bar,H-bar) and spinor Ψ fields is constructed. New Lagrangians (scalar and vector) for electromagnetic field in terms of field strengths are found. The foundations of two new QED models are formulated
50 years with J. B. Keller's Geometrical Theory of Diffraction in Denmark - Revisiting the Theory
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Albertsen, N. Chr.; Breinbjerg, Olav
2013-01-01
In the introduction, Danish contributions to J. B. Keller's Geometrical Theory of Diffraction are surveyed. The edge diffraction coefficient in the case of scattering by a half-plane with an impedance surface is then analyzed. In short-wavelength scattering theory, the amplitudes of the incident...
Inverse scattering theory foundations of tomography with diffracting wavefields
International Nuclear Information System (INIS)
Devaney, A.J.
1987-01-01
The underlying mathematical models employed in reflection and transmission computed tomography using diffracting wavefields (called diffraction tomography) are reviewed and shown to have a rigorous basis in inverse scattering theory. In transmission diffraction tomography the underlying wave model is shown to be the Rytov approximation to the complex phase of the wavefield transmitted by the object being probed while in reflection diffraction tomography the underlying wave model is shown to be the Born approximation to the backscattered wavefield from the object. In both cases the goal of the reconstruction process is the determination of the objects's complex index of refraction as a function of position r/sup →/ and, possibly, the frequency ω of the probing wavefield. By use of these approximations the reconstruction problem for both transmission and reflection diffraction tomography can be cast into the simple and elegant form of linearized inverse scattering theory. Linearized inverse scattering theory is shown to lead directly to generalized projection-slice theorems for both reflection and transmission diffraction tomography that provide a simple mathematical relationship between the object's complex index of refraction (the unknown) and the data (the complex phase of the transmitted wave or the complex amplitude of the reflected wave). The conventional projection-slice theorem of X-ray CT is shown to result from the generalized projection-slice theorem for transmission diffraction tomography in the limit of vanishing wavelength (in the absence of wave effects). Fourier based and back-projection type reconstruction algorithms are shown to be directly derivable from the generalized projection-slice theorems
Cosmological Solutions of Tensor–Vector Theories of Gravity by ...
Indian Academy of Sciences (India)
We consider tensor–vector theories by varying the space- time–matter coupling ... solutions by considering the character of critical points of the theory and their stability .... light (Magueijo 2003) that has arisen from the possibility of varying fine structure constant. ... Vector-like dark energy displays a series of properties that.
Transition operators in electromagnetic-wave diffraction theory - General theory
Hahne, G. E.
1992-01-01
A formal theory is developed for the scattering of time-harmonic electromagnetic waves from impenetrable immobile obstacles with given linear, homogeneous, and generally nonlocal boundary conditions of Leontovich (impedance) type for the wave of the obstacle's surface. The theory is modeled on the complete Green's function and the transition (T) operator in time-independent formal scattering theory of nonrelativistic quantum mechanics. An expression for the differential scattering cross section for plane electromagnetic waves is derived in terms of certain matrix elements of the T operator for the obstacle.
A foundation for the statistical dynamical theory of diffraction
International Nuclear Information System (INIS)
Kato, Norio
1991-01-01
The statistical dynamical theory is reformulated on a sounder basis. The starting wave equation is free from the so-called Takagi-Taupin (T-T) approximation. Functional calculus, an operational technique and the concept of the Green function are used as mathematical tools. Integro-differential equations are derived for the coherent (averaged) wave field and the energy flow vector of the incoherent intensity field. The formulae are exact except for assuming a model in which the fluctuation of the lattice phase is a set of Gaussian random variables defined in three-dimensional space. The general framework of the previous theory is justified within the T-T approximation. In general, however, new terms must be added and some terms have to be revised by introducing a Green function matrix. The theory may be used as a starting point when any approximate theory is developed for practical purposes. (orig.)
Statistical Theory of the Vector Random Decrement Technique
DEFF Research Database (Denmark)
Asmussen, J. C.; Brincker, Rune; Ibrahim, S. R.
1999-01-01
decays. Due to the speed and/or accuracy of the Vector Random Decrement technique, it was introduced as an attractive alternative to the Random Decrement technique. In this paper, the theory of the Vector Random Decrement technique is extended by applying a statistical description of the stochastic...
Diffraction and angular momentum effects in semiclassical atomic scattering theory
International Nuclear Information System (INIS)
Russek, A.
1979-01-01
The semiclassical scattering theory of Mott and Massey and Ford and Wheeler is here extended to multichannel scattering as occurs at a crossing or pseudocrossing of the transient molecule formed by the colliding atoms. The generalized theory incorporates both interference and diffraction phenomena, but the emphasis in this work is on diffraction. For small-angle scattering, diffraction effects become broader, not narrower, as the collision energy increases: ΔbΔtau > or = h[E/sub inc//(2m)]/sup 1/2/ relates the uncertainties in impact parameter b and reduced scattering angle tau = E/sub inc/theta, and determines the range in b required to resolve a structure in the deflection function of height Δtau. In the kilovolt range of collision energies, the effects of local maxima and minima in the deflection function are washed out, and the Airy-function approximation of Ford and Wheeler is inappropriate to describe the differential cross section. More generally, it is shown that at keV collision energies the stationary-phase approximation, heretofore essential in the reduction to the semiclassical limit, breaks down in the vicinity of a level crossing. An approximate theorem is proposed which remains valid in this region and elsewhere reduces to the standard stationary-phase approximation. Several illustrative examples are considered. A separate development treats the effect on the differential scattering cross section of a change in electronic angular momentum when electronic excitation occurs
Cosmological evolution in vector-tensor theories of gravity
International Nuclear Information System (INIS)
Beltran Jimenez, Jose; Maroto, Antonio L.
2009-01-01
We present a detailed study of the cosmological evolution in general vector-tensor theories of gravity without potential terms. We consider the evolution of the vector field throughout the expansion history of the Universe and carry out a classification of models according to the behavior of the vector field in each cosmological epoch. We also analyze the case in which the Universe is dominated by the vector field, performing a complete analysis of the system phase map and identifying those attracting solutions which give rise to accelerated expansion. Moreover, we consider the evolution in a universe filled with a pressureless fluid in addition to the vector field and study the existence of attractors in which we can have a transition from matter domination to vector domination with accelerated expansion so that the vector field may play the role of dark energy. We find that the existence of solutions with late-time accelerated expansion is a generic prediction of vector-tensor theories and that such solutions typically lead to the presence of future singularities. Finally, limits from local gravity tests are used to get constraints on the value of the vector field at small (Solar System) scales.
Renormalization in theories with strong vector forces
International Nuclear Information System (INIS)
Kocic, A.
1991-01-01
There are not many field theories in four dimensions that have sensible ultraviolet and interesting (non-trivial) infrared behavior. At present, asymptotically free theories seem to have deserved their legitimacy and there is a strong prejudice that they might be the only ones to have such a distinction. This belief stems mostly from the fact that most of the knowledge of field theory in four dimensions comes from perturbation theory. However, nonperturbative studies of the lower dimensional theories reveal a host of interesting phenomena that are perturbative studies of the lower dimensional theories reveal a host of interesting phenomena that perturbatively inaccessible. The lack of asymptotic freedom implies that the coupling constant grows at short distances and perturbation theory breaks down. Thus, in such theories, ultraviolet behavior requires nonperturbative treatment. Recently, the interest in strongly coupled gauge theories has been revived. In particularly, four dimensional quantum electrodynamics has received considerable attention. This was motivated by the discovery of an ultraviolet stable fixed point at strong couplings. If this fixed point would turn out to be non-gaussian, then QED would be the first nontrivial nonasymptotically free theory in four dimensions. The importance of such a result would be twofold. First, the old question of the existence of QED could be settled. Of course, this would be the case provided that the low energy limit of the theory actually describes photons and electrons; apriori, there is no reason to assume this. Second, the discovery of a nontrivial nonasymptotically free theory would be of great paradigmatic value. The theories which quenched QED resembles the most are nonabelian gauge theories with many flavors with beta-function positive or vanishing at weak couplings. These theories are at present considered as viable candidates for technicolor unification schemes
Design of structurally colored surfaces based on scalar diffraction theory
DEFF Research Database (Denmark)
Johansen, Villads Egede; Andkjær, Jacob Anders; Sigmund, Ole
2014-01-01
In this paper we investigate the possibility of controlling the color and appearance of surfaces simply by modifying the height profile of the surface on a nanoscale level. The applications for such methods are numerous: new design possibilities for high-end products, color engraving on any highly...... reflective surface, paint-free text and coloration, UV-resistant coloring, etc. In this initial study, the main focus is on finding a systematic way to obtain these results. For now the simulation and optimization is based on a simple scalar diffraction theory model. From the results, several design issues...
Theory of net analyte signal vectors in inverse regression
DEFF Research Database (Denmark)
Bro, R.; Andersen, Charlotte Møller
2003-01-01
The. net analyte signal and the net analyte signal vector are useful measures in building and optimizing multivariate calibration models. In this paper a theory for their use in inverse regression is developed. The theory of net analyte signal was originally derived from classical least squares...
Singular vectors of Malikov-Fagin-Fux in topological theories
International Nuclear Information System (INIS)
Semikhatov, A.M.
1993-01-01
Coincidence of singular vectors in relation to the sl(2) Katza-Mudi algebra and the algebra of the N=2 (twisted) supersymmetry is established. On the base of the Kazama-Suzuki simplest model is obtained a representation for the sl(2) currents in terms of an interacting with mater gravitation. From the Malikov-Fagin-Fux formulae for the sl(2) singular currents is obtained the general expression for singular vectors in topological theories
Gauge structure of neutral-vector field theory. [Massive vector fields, massless limits
Energy Technology Data Exchange (ETDEWEB)
Kubo, R; Yokoyama, [Hiroshima univ., Takehara (Japan). Research Inst. for Theoretical Physics
1975-03-01
General aspects of gauge structure of neutral-vector field theory are investigated from an extended standpoint, where massive vector fields are treated in a form corresponding to the electromagnetic fields in a general gauge formalism reported previously. All results obtained are shown to have unique massless limits. It is shown that a generalized q-number gauge transformation for fields makes the theory invariant in cooperation with a simultaneous transformation for relevant gauge parameters. A method of differentiation with respect to a gauge variable is found to clarify some essential features of the gauge structure. Two possible types of gauge structure also emerge correspondingly to the massless case. A neutral-vector field theory proposed in a preceding paper is included in the present framework as the most preferable case.
International Nuclear Information System (INIS)
Schaerpf, O.
1978-01-01
Two ways are given for solving the problem of the dependence of the refraction on the direction of magnetization on both sides of the refractive boundary, one applying the Halpern magnetic scattering vector, the other applying the dynamical theory of diffraction. They lead to different results. Experimental investigation of refraction by magnetic boundaries shows no dependence of the angle of deflection on the relative angles of magnetization in adjacent domains. This behaviour is only described correctly by the dynamical theory, which far from Laue reflections leads to a treatment by the Schoedinger equation with a spin-dependent potential dependent on the average continuous homogenous magnetic induction, both for the law of refraction and for the precession of the spin. The results of this treatment are discussed as a consequence of the behaviour of the spin of the neutrons. This gives some insight about how and why, with refraction, the intensities of the direct and deflected beams depend on the magnetization directions in adjacent domains. The dynamical theory also shows that the Halpern magnetic scattering vector applies only with Laue or Bragg reflections and not with transmission far from those reflections. (Auth.)
Bridging Economic Theory Models and the Cointegrated Vector Autoregressive Model
DEFF Research Database (Denmark)
Møller, Niels Framroze
2008-01-01
Examples of simple economic theory models are analyzed as restrictions on the Cointegrated VAR (CVAR). This establishes a correspondence between basic economic concepts and the econometric concepts of the CVAR: The economic relations correspond to cointegrating vectors and exogeneity in the econo......Examples of simple economic theory models are analyzed as restrictions on the Cointegrated VAR (CVAR). This establishes a correspondence between basic economic concepts and the econometric concepts of the CVAR: The economic relations correspond to cointegrating vectors and exogeneity...... are related to expectations formation, market clearing, nominal rigidities, etc. Finally, the general-partial equilibrium distinction is analyzed....
Bridging Economic Theory Models and the Cointegrated Vector Autoregressive Model
DEFF Research Database (Denmark)
Møller, Niels Framroze
2008-01-01
Examples of simple economic theory models are analyzed as restrictions on the Cointegrated VAR (CVAR). This establishes a correspondence between basic economic concepts and the econometric concepts of the CVAR: The economic relations correspond to cointegrating vectors and exogeneity in the econo......Examples of simple economic theory models are analyzed as restrictions on the Cointegrated VAR (CVAR). This establishes a correspondence between basic economic concepts and the econometric concepts of the CVAR: The economic relations correspond to cointegrating vectors and exogeneity...... parameters of the CVAR are shown to be interpretable in terms of expectations formation, market clearing, nominal rigidities, etc. The general-partial equilibrium distinction is also discussed....
Renormalized multiple-scattering theory of photoelectron diffraction
International Nuclear Information System (INIS)
Biagini, M.
1993-01-01
The current multiple-scattering cluster techniques for the calculation of x-ray photoelectron and Auger-electron diffraction patterns consume much computer time in the intermediate-energy range (200--1000 eV); in fact, because of the large value of the electron mean free path and of the large forward-scattering amplitude at such energies, the electron samples a relatively large portion of the crystal, so that the number of paths to be considered becomes dramatically high. An alternative method is developed in the present paper: instead of calculating the individual contribution from each single path, the scattering matrix of each plane parallel to the surface is calculated with a renormalization process that calculates every scattering event in the plane up to infinite order. Similarly the scattering between two planes is calculated up to infinite order, and the double-plane scattering matrix is introduced. The process may then be applied to the calculation of a larger set of atomic layers. The advantage of the method is that a relatively small number of internuclear vectors have been used to obtain convergence in the calculation
Cosmological Solutions of Tensor–Vector Theories of Gravity by ...
Indian Academy of Sciences (India)
We consider tensor–vector theories by varying the space-time–matter coupling constant (varying Einstein velocity) in a spatially flat FRW universe.We examine the dynamics of this model by dynamical system method assuming a CDM background and we find some exact solutions by considering the character of critical ...
Black holes in vector-tensor theories and their thermodynamics
Energy Technology Data Exchange (ETDEWEB)
Fan, Zhong-Ying [Guangzhou University, Center for Astrophysics, School of Physics and Electronic Engineering, Guangzhou (China)
2018-01-15
In this paper, we study Einstein gravity either minimally or non-minimally coupled to a vector field which breaks the gauge symmetry explicitly in general dimensions. We first consider a minimal theory which is simply the Einstein-Proca theory extended with a quartic self-interaction term for the vector field. We obtain its general static maximally symmetric black hole solution and study the thermodynamics using Wald formalism. The aspects of the solution are much like a Reissner-Nordstroem black hole in spite of that a global charge cannot be defined for the vector. For non-minimal theories, we obtain a lot of exact black hole solutions, depending on the parameters of the theories. In particular, many of the solutions are general static and have maximal symmetry. However, there are some subtleties and ambiguities in the derivation of the first laws because the existence of an algebraic degree of freedom of the vector in general invalids the Wald entropy formula. The thermodynamics of these solutions deserves further studies. (orig.)
Mineralogical applications of electron diffraction. 1. Theory and techniques
Ross, Malcolm; Christ, C.L.
1958-01-01
The small wavelengths used in electron-diffraction experiments and the thinness of the crystals necessary for the transmission of the electron beam combine to require a somewhat different diffraction geometry for the interpretation of electron-diffraction patterns than is used in the interpretation of X-ray diffraction patterns. This geometry, based on the reciprocal lattice concept and geometrical construction of Ewald, needed for the interpretation.
Constraints and stability in vector theories with spontaneous Lorentz violation
International Nuclear Information System (INIS)
Bluhm, Robert; Gagne, Nolan L.; Potting, Robertus; Vrublevskis, Arturs
2008-01-01
Vector theories with spontaneous Lorentz violation, known as bumblebee models, are examined in flat spacetime using a Hamiltonian constraint analysis. In some of these models, Nambu-Goldstone modes appear with properties similar to photons in electromagnetism. However, depending on the form of the theory, additional modes and constraints can appear that have no counterparts in electromagnetism. An examination of these constraints and additional degrees of freedom, including their nonlinear effects, is made for a variety of models with different kinetic and potential terms, and the results are compared with electromagnetism. The Hamiltonian constraint analysis also permits an investigation of the stability of these models. For certain bumblebee theories with a timelike vector, suitable restrictions of the initial-value solutions are identified that yield ghost-free models with a positive Hamiltonian. In each case, the restricted phase space is found to match that of electromagnetism in a nonlinear gauge
Stealth configurations in vector-tensor theories of gravity
Chagoya, Javier; Tasinato, Gianmassimo
2018-01-01
Studying the physics of compact objects in modified theories of gravity is important for understanding how future observations can test alternatives to General Relativity. We consider a subset of vector-tensor Galileon theories of gravity characterized by new symmetries, which can prevent the propagation of the vector longitudinal polarization, even in absence of Abelian gauge invariance. We investigate new spherically symmetric and slowly rotating solutions for these systems, including an arbitrary matter Lagrangian. We show that, under certain conditions, there always exist stealth configurations whose geometry coincides with solutions of Einstein gravity coupled with the additional matter. Such solutions have a non-trivial profile for the vector field, characterized by independent integration constants, which extends to asymptotic infinity. We interpret our findings in terms of the symmetries and features of the original vector-tensor action, and on the number of degrees of freedom that it propagates. These results are important to eventually describe gravitationally bound configurations in modified theories of gravity, such as black holes and neutron stars, including realistic matter fields forming or surrounding the object.
Vector entropy imaging theory with application to computerized tomography
International Nuclear Information System (INIS)
Wang Yuanmei; Cheng Jianping; Heng, Pheng Ann
2002-01-01
Medical imaging theory for x-ray CT and PET is based on image reconstruction from projections. In this paper a novel vector entropy imaging theory under the framework of multiple criteria decision making is presented. We also study the most frequently used image reconstruction methods, namely, least square, maximum entropy, and filtered back-projection methods under the framework of the single performance criterion optimization. Finally, we introduce some of the results obtained by various reconstruction algorithms using computer-generated noisy projection data from the Hoffman phantom and real CT scanner data. Comparison of the reconstructed images indicates that the vector entropy method gives the best in error (difference between the original phantom data and reconstruction), smoothness (suppression of noise), grey value resolution and is free of ghost images. (author)
The method of the generalised eikonal new approaches in the diffraction theory
Vesnik, Michael V
2015-01-01
The diffraction theory describes scattering mechanism for waves of various physical nature, scattered on objects of different shapes and composed of different materials. Using the diffraction theory, one can study a number of important effects connected with wave propagation, and create objects with given properties.
Analytic theory of soft x-ray diffraction by lamellar multilayer gratings
Kozhevnikov, I.V.; van der Meer, R.; Bastiaens, Hubertus M.J.; Boller, Klaus J.; Bijkerk, Frederik
2011-01-01
An analytic theory describing soft x-ray diffraction by Lamellar Multilayer Gratings (LMG) has been developed. The theory is derived from a coupled waves approach for LMGs operating in the single-order regime, where an incident plane wave can only excite a single diffraction order. The results from
Fermi interaction. Conservation of vector current and modified perturbation theory
International Nuclear Information System (INIS)
Rochev, V.E.
1983-01-01
The Fermi interaction (anti psi ysub(n) psi)sup(2) is investigated with the method of auxilary field. The analogues of the Ward-Takahashi electrodynamical identities and the gauge transformations of Green functions, that are the consequence of the conservation of vector current, have been obtained. The gauge function for the spinor propagator is the exponential superpropagator. The arguments are given in favour of the existence of a modified perturbation theory, which is finite in every order and non-analytical over its coupling constant, for the four-fermion interaction. The non-analytical part is defined unambiguously, and the analytical part contains a set of finite dimensionless constants to define which non-perturbative information is needed. The simplest model (the chain approximation) for the non-stable vector bound state is considered
Effective field theory and unitarity in vector boson scattering
International Nuclear Information System (INIS)
Sekulla, Marco; Kilian, Wolfgang; Ohl, Thorsten; Reuter, Juergen
2016-10-01
Weak vector boson scattering at high energies will be one of the key measurements in current and upcoming LHC runs. It is most sensitive to any new physics associated with electroweak symmetry breaking. However, a conventional EFT analysis will fail at high energies. To address this problem, we present a parameter-free prescription valid for arbitrary perturbative and non-perturbative models: the T-matrix unitarization. We describe its implementation as an asymptotically consistent reference model matched to the low-energy effective theory. We show examples of typical observables of vector-boson scattering at the LHC in our unitarized framework. For many strongly-coupled models like composite Higgs models, dimension-8 operators might be actually the leading operators. In addition to those longitudinal and transversal dimension eight EFT operators, the effects of generic tensor and scalar resonances within simplified models are considered.
On the cosmology of scalar-tensor-vector gravity theory
Jamali, Sara; Roshan, Mahmood; Amendola, Luca
2018-01-01
We consider the cosmological consequences of a special scalar-tensor-vector theory of gravity, known as MOG (for MOdified Gravity), proposed to address the dark matter problem. This theory introduces two scalar fields G(x) and μ(x), and one vector field phiα(x), in addition to the metric tensor. We set the corresponding self-interaction potentials to zero, as in the standard form of MOG. Then using the phase space analysis in the flat Friedmann-Robertson-Walker background, we show that the theory possesses a viable sequence of cosmological epochs with acceptable time dependency for the cosmic scale factor. We also investigate MOG's potential as a dark energy model and show that extra fields in MOG cannot provide a late time accelerated expansion. Furthermore, using a dynamical system approach to solve the non-linear field equations numerically, we calculate the angular size of the sound horizon, i.e. θs, in MOG. We find that 8× 10‑3rad<θs<8.2× 10‑3 rad which is way outside the current observational bounds. Finally, we generalize MOG to a modified form called mMOG, and we find that mMOG passes the sound-horizon constraint. However, mMOG also cannot be considered as a dark energy model unless one adds a cosmological constant, and more importantly, the matter dominated era is still slightly different from the standard case.
Theory of charged vector mesons interacting with the electromagnetic field
International Nuclear Information System (INIS)
Lee, T.D.; Yang, C.N.
1983-01-01
It is shown that starting from the usual canonical formalism for the electromagnetic interaction of a charged vector meson with arbitrary magnetic moment one is led to a set of rules for Feynman diagrams, which appears to contain terms that are both infinite and noncovariant. These difficulties, however, can be circumvented by introducing a xi-limiting process which depends on a dimensionless positive parameter xi → 0. Furthermore, by using the mathematical artifice of a negative metric the theory becomes renormalizable (for xi > 0)
Dynamical theory of neutron diffraction. [One-body Schroedinger equation, review
Energy Technology Data Exchange (ETDEWEB)
Sears, V F [Atomic Energy of Canada Ltd., Chalk River, Ontario. Chalk River Nuclear Labs.
1978-10-01
We present a review of the dynamical theory of neutron diffraction by macroscopic bodies which provides the theoretical basis for the study of neutron optics. We consider both the theory of dispersion, in which it is shown that the coherent wave in the medium satisfies a macroscopic one-body Schroedinger equation, and the theory of reflection, refraction, and diffraction in which the above equation is solved for a number of special cases of interest. The theory is illustrated with the help of experimental results obtained over the past 10 years by a number of new techniques such as neutron gravity refractometry. Pendelloesung interference, and neutron interferometry.
International Nuclear Information System (INIS)
Tint, M.
The contribution of the mesonic exchange effect to the conserved vector current in the first forbidden β-decay of Ra E is estimated under the headings: (1) The conserved vector current. (2) The CVC theory and the first forbidden β-decays. (3) Shell model calculations of some matrix-elements. (4) Direct calculation of the exchange term. Considering the mesonic exchange effect in the axial vector-current of β-decay the partially conserved axial vector current theory and experimental results of the process p + p → d + π + are examined. (U.K.)
On the Pomeranchuk singularity in massless vector theories
International Nuclear Information System (INIS)
Bartels, J.; Hamburg Univ.
1980-06-01
It is shown that the Pomeron in massless (abelian of nonabelian) vector theories, as derived from a perturbative high energy description which satisfies unitarity, comes as a diffusion problem in the logarithmic scale of transverse momentum. For a realistic theory there are reasons to expect that this diffusion should come to a stop: (a) the long range forces of the massless gluons should be screened, (b) the Pomeranchuk singularity in the j-plane should be t-dependant, and (c) there should not be a discontinuity in the zero mass limit at t = 0 or in the t 0 limit of the massless case. In the third part we outline a scheme for summing all diagrams which are required by unitarity. It uses reggeon field theory in zero transverse dimensions and leads to: (i) the diffusion comes to a stop (zero drift and zero diffusion constant); (ii) the total cross section is constant (up to powers of lns); (iii) in order to give a meaning to the divergent perturbation expansion, one has to add a nonperturbative term of the order exp(-const/g 2 ). (orig.)
Primer Vector Optimization: Survey of Theory, new Analysis and Applications
Guzman
This paper presents a preliminary study in developing a set of optimization tools for orbit rendezvous, transfer and station keeping. This work is part of a large scale effort undergoing at NASA Goddard Space Flight Center and a.i. solutions, Inc. to build generic methods, which will enable missions with tight fuel budgets. Since no single optimization technique can solve efficiently all existing problems, a library of tools where the user could pick the method most suited for the particular mission is envisioned. The first trajectory optimization technique explored is Lawden's primer vector theory [Ref. 1]. Primer vector theory can be considered as a byproduct of applying Calculus of Variations (COV) techniques to the problem of minimizing the fuel usage of impulsive trajectories. For an n-impulse trajectory, it involves the solution of n-1 two-point boundary value problems. In this paper, we look at some of the different formulations of the primer vector (dependent on the frame employed and on the force model). Also, the applicability of primer vector theory is examined in effort to understand when and why the theory can fail. Specifically, since COV is based on "small variations", singularities in the linearized (variational) equations of motion along the arcs must be taken into account. These singularities are a recurring problem in analyzes that employ "small variations" [Refs. 2, 3]. For example, singularities in the (2-body problem) variational equations along elliptic arcs occur when [Ref. 4], 1) the difference between the initial and final times is a multiple of the reference orbit period, 2) the difference between the initial and final true anomalies are given by k, for k= 0, 1, 2, 3,..., note that this cover the 3) the time of flight is a minimum for the given difference in true anomaly. For the N-body problem, the situation is more complex and is still under investigation. Several examples, such as the initialization of an orbit (ascent trajectory) and
Variational formulation of covariant eikonal theory for vector waves
International Nuclear Information System (INIS)
Kaufman, A.N.; Ye, H.; Hui, Y.
1986-10-01
The eikonal theory of wave propagation is developed by means of a Lorentz-covariant variational principle, involving functions defined on the natural eight-dimensional phase space of rays. The wave field is a four-vector representing the electromagnetic potential, while the medium is represented by an anisotropic, dispersive nonuniform dielectric tensor D/sup μν/(k,x). The eikonal expansion yields, to lowest order, the Hamiltonian ray equations, which define the Lagrangian manifold k(x), and the wave-action conservation law, which determines the wave-amplitude transport along the rays. The first-order contribution to the variational principle yields a concise expression for the transport of the polarization phase. The symmetry between k-space and x-space allows for a simple implementation of the Maslov transform, which avoids the difficulties of caustic singularities
Theory and Application of Photoelectron Diffraction for Complex Oxide Systems
Chassé, Angelika; Chassé, Thomas
2018-06-01
X-ray photoelectron diffraction (XPD) has been used to investigate film structures and local sites of surface and dopant atoms in complex oxide materials. We have performed angular-resolved measurements of intensity distribution curves (ADCs) and patterns (ADPs) of elemental core level intensities from binary to quaternary mixed oxide samples and compared them to multiple-scattering cluster (MSC) calculations in order to derive information on structural models and related parameters. MSC calculations permitted to describe both bulk diffraction features of binary oxide MnO(001) and the thickness-dependence of the tetragonal distortion of epitaxial MnO films on Ag(001). XPD was further used to investigate the surface termination of perovskite SrTiO3 and BaTiO3 substrates in order to evaluate influence of different ex situ and in situ preparation procedures on the surface layers, which are crucial for quality of following film growth. Despite the similarity of local environments of Sr (Ba) and Ti atoms in the perovskite film structure an angular region in the ADCs was identified as a fingerprint with the help of MSC simulations which provided clear conclusions on the perovskite oxide surfaces. Dopant sites in quaternary perovskite manganites La1-xCaxMnO3, La1-xSrxMnO3, and La1-xCexMnO3 were studied with polar angle scans of the photoemission intensities of host and dopant atoms. Both direct comparison of experimental ADCs and to the simulations within MSC models confirm the occupation of A sites by the dopants and the structural quality of the complex oxide films.
More about a successful vector-tensor theory of gravitation
Energy Technology Data Exchange (ETDEWEB)
Dale, R. [Departamento de Estadísica, Matemática e Informática, Universidad Miguel Hernandez, Elche, Alicante (Spain); Sáez, D., E-mail: rdale@umh.es, E-mail: diego.saez@uv.es [Departamento de Astronomía y Astrofísica, Universidad de Valencia, Burjassot, Valencia (Spain)
2017-01-01
The vector-tensor (VT) theory of gravitation revisited in this article was studied in previous papers, where it was proved that VT works and deserves attention. New observational data and numerical codes have motivated further development which is presented here. New research has been planed with the essential aim of proving that current cosmological observations, including Planck data, baryon acoustic oscillations (BAO), and so on, may be explained with VT, a theory which accounts for a kind of dark energy which has the same equation of state as vacuum. New versions of the codes CAMB and COSMOMC have been designed for applications to VT, and the resulting versions have been used to get the cosmological parameters of the VT model at suitable confidence levels. The parameters to be estimated are the same as in general relativity (GR), plus a new parameter D . For D = 0, VT linear cosmological perturbations reduces to those of GR, but the VT background may explain dark energy. The fits between observations and VT predictions lead to non vanishing | D | upper limits at the 1σ confidence level. The value D = 0 is admissible at this level, but this value is not that of the best fit in any case. Results strongly suggest that VT may explain current observations, at least, as well as GR; with the advantage that, as it is proved in this paper, VT has an additional parameter which facilitates adjustments to current observational data.
Energy Technology Data Exchange (ETDEWEB)
Kubo, R; Takahashi, Y; Yokoyama, K
1975-01-01
In a wide class of neutral vector field theories, in which massive and massless fields are described in a unified way and a unique massless limit exists to quantum electrodynamics in covariant gauges, the commutability of the scale transformation and the massless limit is examined. It is shown that there occurs no anomaly with respect to the assignment for scale dimensions of relevant fields. Connection of scale transformation and gauge transformation is also discussed.
Djakou, Audrey Kamta; Darmon, Michel; Fradkin, Larissa; Potel, Catherine
2015-11-01
Diffraction phenomena studied in electromagnetism, acoustics, and elastodynamics are often modeled using integrals, such as the well-known Sommerfeld integral. The far field asymptotic evaluation of such integrals obtained using the method of steepest descent leads to the classical Geometrical Theory of Diffraction (GTD). It is well known that the method of steepest descent is inapplicable when the integrand's stationary phase point coalesces with its pole, explaining why GTD fails in zones where edge diffracted waves interfere with incident or reflected waves. To overcome this drawback, the Uniform geometrical Theory of Diffraction (UTD) has been developed previously in electromagnetism, based on a ray theory, which is particularly easy to implement. In this paper, UTD is developed for the canonical elastodynamic problem of the scattering of a plane wave by a half-plane. UTD is then compared to another uniform extension of GTD, the Uniform Asymptotic Theory (UAT) of diffraction, based on a more cumbersome ray theory. A good agreement between the two methods is obtained in the far field.
Search for a PHI' vector meson in diffractive photoproduction of K+K-π+π-
International Nuclear Information System (INIS)
Atkinson, M.; Davenport, M.; Flower, P.; Hutton, J.S.; Kumar, B.R.; Morris, J.A.G.; Morris, J.V.; Patrick, G.N.; Sharp, P.H.; Bussey, P.J.; Dainton, J.B.; Paterson, C.; Raine, C.; Skillicorn, I.O.; Smith, K.M.; Brodbeck, T.J.; Clegg, A.B.; Flynn, P.J.; Henderson, R.C.W.; Newton, D.; Axon, T.J.; Barberis, D.; Dickinson, B.; Donnachie, A.; Ellison, R.J.; Hughes-Jones, R.E.; Ibbotson, M.; Lafferty, G.D.; Lane, J.B.; Mercer, D.; Thompson, R.J.; Waite, A.P.; Worsell, M.F.; Levy, J.M.; Laberrigue, J.; La Vaissiere, C. de; Yiou, T.P.; Brookes, G.R.; Bunn, J.J.; Galbraith, W.; McClatchey, R.H.
1986-01-01
A study of photoproduction of K + K - π + π - shows a broad threshold enhancement, about 30% of which is due to Ksup(*)Kπ production. This Ksup(*)Kπ component shows no dynamical features indicative of the existence of a PHI' vector meson in this channel. (orig.)
Effective theory analysis for vector-like quark model
Morozumi, Takuya; Shimizu, Yusuke; Takahashi, Shunya; Umeeda, Hiroyuki
2018-04-01
We study a model with a down-type SU(2) singlet vector-like quark (VLQ) as a minimal extension of the standard model (SM). In this model, flavor-changing neutral currents (FCNCs) arise at tree level and the unitarity of the 3× 3 Cabibbo-Kobayashi-Maskawa (CKM) matrix does not hold. In this paper, we constrain the FCNC coupling from b\\rArr s transitions, especially B_s\\rArr μ^+μ^- and \\bar{B}\\rArr X_sγ processes. In order to analyze these processes we derive an effective Lagrangian that is valid below the electroweak symmetry breaking scale. For this purpose, we first integrate out the VLQ field and derive an effective theory by matching Wilson coefficients up to one-loop level. Using the effective theory, we construct the effective Lagrangian for b\\rArr sγ^{(*)}. It includes the effects of the SM quarks and the violation of CKM unitarity. We show the constraints on the magnitude of the FCNC coupling and its phase by taking account of the current experimental data on Δ M_{B_s}, Br[B_s\\rArrμ^+μ^-], Br[\\bar{B}\\rArr X_sγ], and CKM matrix elements, as well as theoretical uncertainties. We find that the constraint from Br[B_s\\rArrμ^+μ^-] is more stringent than that from Br[\\bar{B}\\rArr X_sγ]. We also obtain a bound for the mass of the VLQ and the strength of the Yukawa couplings related to the FCNC coupling of the b\\rArr s transition. Using the CKM elements that satisfy the above constraints, we show how the unitarity is violated on the complex plane.
Knowledge formalization for vector data matching using belief theory
Directory of Open Access Journals (Sweden)
Ana-Maria Olteanu-Raimond
2015-06-01
Full Text Available Nowadays geographic vector data is produced both by public and private institutions using well defined specifications or crowdsourcing via Web 2.0 mapping portals. As a result, multiple representations of the same real world objects exist, without any links between these different representations. This becomes an issue when integration, updates, or multi-level analysis needs to be performed, as well as for data quality assessment. In this paper a multi-criteria data matching approach allowing the automatic definition of links between identical features is proposed. The originality of the approach is that the process is guided by an explicit representation and fusion of knowledge from various sources. Moreover the imperfection (imprecision, uncertainty, and incompleteness is explicitly modeled in the process. Belief theory is used to represent and fuse knowledge from different sources, to model imperfection, and make a decision. Experiments are reported on real data coming from different producers, having different scales and either representing relief (isolated points or road networks (linear data.
Groiss, Heiko; Glaser, Martin; Marzegalli, Anna; Isa, Fabio; Isella, Giovanni; Miglio, Leo; Schäffler, Friedrich
2015-06-01
By transmission electron microscopy with extended Burgers vector analyses, we demonstrate the edge and screw character of vertical dislocations (VDs) in novel SiGe heterostructures. The investigated pillar-shaped Ge epilayers on prepatterned Si(001) substrates are an attempt to avoid the high defect densities of lattice mismatched heteroepitaxy. The Ge pillars are almost completely strain-relaxed and essentially defect-free, except for the rather unexpected VDs. We investigated both pillar-shaped and unstructured Ge epilayers grown either by molecular beam epitaxy or by chemical vapor deposition to derive a general picture of the underlying dislocation mechanisms. For the Burgers vector analysis we used a combination of dark field imaging and large-angle convergent beam electron diffraction (LACBED). With LACBED simulations we identify ideally suited zeroth and second order Laue zone Bragg lines for an unambiguous determination of the three-dimensional Burgers vectors. By analyzing dislocation reactions we confirm the origin of the observed types of VDs, which can be efficiently distinguished by LACBED. The screw type VDs are formed by a reaction of perfect 60° dislocations, whereas the edge types are sessile dislocations that can be formed by cross-slips and climbing processes. The understanding of these origins allows us to suggest strategies to avoid VDs.
On the theory of diffraction of Maxwellian atomic beams by solid surfaces
International Nuclear Information System (INIS)
Goodman, F.O.
1976-01-01
In the context of diffraction of Maxwellian (thermal) atomic beams by solid surfaces, the usual assumption that the angular position of the maximum in a diffracted beam corresponds to the diffraction angle of atoms with the most probable de Broglie wavelength is examined, and compared with other possible criteria and with the correct result. It is concluded that, although this criterion may be the best simple one available, it is certainly bad in some situations; the reasons why, and the conditions under which, it is expected to be good are discussed. Also, it is shown that considerable care must be taken when shapes of diffracted beams and when angular positions of their maxima are calculated, because certain physical effects (which are always present) may change these shapes and positions in unexpected ways. The theory is compared with two sets of relatively modern experimental data, one set for which the fit is good, and another set for which a fit is impossible
Complex vector triads in spinor theory in Minkowski space
International Nuclear Information System (INIS)
Zhelnorovich, V.A.
1990-01-01
It is shown that tensor equations corresponding to the spinor Dirac equations represent a three-dimensional part of four-dimensional vector equations. The equations are formulated in an evidently invariant form in antisymmetric tensor components and in the corresponding components of a complex vector triad. A complete system of relativistically invariant tensor equations is ascertained
Truncation of the Series Expressions in the Advanced ENZ-Theory of Diffraction Integrals
van Haver, S.; Janssen, A. J. E. M.
2014-09-01
The point-spread function (PSF) is used in optics for design and assessment of the imaging capabilities of an optical system. It is therefore of vital importance that this PSF can be calculated fast and accurately. In the past 12 years, the Extended Nijboer-Zernike (ENZ) approach has been developed for the purpose of semi-analytic evaluation of the PSF, for circularly symmetric optical systems, in the focal region. In the earliest ENZ-years, the Debye approximation of the diffraction integral, by which the PSF is given, was considered for the very basic situation of a low-NA optical system and relatively small defocus values, so that a scalar treatment was allowed with a focal factor comprising a quadratic function in the exponential. At present, the ENZ-method allows calculation of the PSF in low- and high-NA cases, in scalar form and for vector fields (including polarization), for large wave-front aberrations, including amplitude non-uniformities, using a quasi-spherical phase focal factor in a virtually unlimited focal range around the focal plane, and no limitations in the off-axis direction. Additionally, the application range of the method has been broadened and generalized to the calculation of aerial images of extended objects by including the finite distance of the object to the entrance pupil. Also imaging into a multi-layer is now possible by accounting for both forward and backward propagation in the layers. In the advanced ENZ-approach, the generalized, complex-valued pupil function is developed into a series of Zernike circle polynomials, with exponential azimuthal dependence (having cosine/sine azimuthal dependence as special cases). For each Zernike term, the diffraction integral reduces after azimuthal integration to an integral that can be expressed as an infinite double series involving spherical Bessel functions, accounting for the parameters of the optical system and the defocus value, and Jinc functions comprising the radial off-axis value
Application of a particular class of integrals in the theory of diffraction
Energy Technology Data Exchange (ETDEWEB)
Kamishi, Burim, E-mail: burim.kamishi@uni-pr.edu; Bejtullahu, Rasim [Faculty of Natural Sciences and Mathematics, University of Prishtina, Prishtina, Kosovo (Country Unknown); Sykja, Halil [Faculty of Natural Sciences, University of Tirana, Tirana (Albania)
2016-03-25
A particular class of integrals appearing in the problems of diffraction is treated in this paper. For the analysis of the classical sources or lasers, Kirchhoff’s integral can be used only for apertures of a determined shape. So far, the problems are solved and analyzed completely, whenever the geomtry of apertures creates the possibility of using Kirchhoff’s integral, namely for the so-called geometry of rectangular apertures. Other apertures exist for which Kirchhoff’s integral cannot be applied, because of difficulties of mathematical character. In this group of apertures belong all the apertures which are bounded with an inclined line, such as those with triangular form. In this paper, the application of a particular class of integrals is shown to give satisfying results in two problems of diffraction theory: double-diffraction phenomena consisting on separating the interferential-diffractional field from the diffractional field, and the case of near-zone of diffraction in the triangular aperture.
The Scherrer equation and the dynamical theory of X-ray diffraction.
Muniz, Francisco Tiago Leitão; Miranda, Marcus Aurélio Ribeiro; Morilla Dos Santos, Cássio; Sasaki, José Marcos
2016-05-01
The Scherrer equation is a widely used tool to determine the crystallite size of polycrystalline samples. However, it is not clear if one can apply it to large crystallite sizes because its derivation is based on the kinematical theory of X-ray diffraction. For large and perfect crystals, it is more appropriate to use the dynamical theory of X-ray diffraction. Because of the appearance of polycrystalline materials with a high degree of crystalline perfection and large sizes, it is the authors' belief that it is important to establish the crystallite size limit for which the Scherrer equation can be applied. In this work, the diffraction peak profiles are calculated using the dynamical theory of X-ray diffraction for several Bragg reflections and crystallite sizes for Si, LaB6 and CeO2. The full width at half-maximum is then extracted and the crystallite size is computed using the Scherrer equation. It is shown that for crystals with linear absorption coefficients below 2117.3 cm(-1) the Scherrer equation is valid for crystallites with sizes up to 600 nm. It is also shown that as the size increases only the peaks at higher 2θ angles give good results, and if one uses peaks with 2θ > 60° the limit for use of the Scherrer equation would go up to 1 µm.
Diffractive scattering on nuclei in multiple scattering theory with inelastic screening
International Nuclear Information System (INIS)
Zoller, V.R.
1988-01-01
The cross sections for the diffractive scattering of hadrons on nuclei are calculated in the two-channel approximation of multiple scattering theory. In contrast to the standard Glauber approach, it is not assumed that the nucleon scattering profile is a Gaussian or that the Regge radius of the hadron is small compared to the nuclear radius. The AGK Reggeon diagrammatic technique is used to calculate the topological cross sections and the cross sections for coherent and incoherent diffractive dissociation and quasielastic scattering. The features of hadron-nucleus scattering at superhigh energies are discussed
DEFF Research Database (Denmark)
Boeriis, Morten; van Leeuwen, Theo
2017-01-01
should be taken into account in discussing ‘reactions’, which Kress and van Leeuwen link only to eyeline vectors. Finally, the question can be raised as to whether actions are always realized by vectors. Drawing on a re-reading of Rudolf Arnheim’s account of vectors, these issues are outlined......This article revisits the concept of vectors, which, in Kress and van Leeuwen’s Reading Images (2006), plays a crucial role in distinguishing between ‘narrative’, action-oriented processes and ‘conceptual’, state-oriented processes. The use of this concept in image analysis has usually focused...
Algebra of Complex Vectors and Applications in Electromagnetic Theory and Quantum Mechanics
Directory of Open Access Journals (Sweden)
Kundeti Muralidhar
2015-08-01
Full Text Available A complex vector is a sum of a vector and a bivector and forms a natural extension of a vector. The complex vectors have certain special geometric properties and considered as algebraic entities. These represent rotations along with specified orientation and direction in space. It has been shown that the association of complex vector with its conjugate generates complex vector space and the corresponding basis elements defined from the complex vector and its conjugate form a closed complex four dimensional linear space. The complexification process in complex vector space allows the generation of higher n-dimensional geometric algebra from (n — 1-dimensional algebra by considering the unit pseudoscalar identification with square root of minus one. The spacetime algebra can be generated from the geometric algebra by considering a vector equal to square root of plus one. The applications of complex vector algebra are discussed mainly in the electromagnetic theory and in the dynamics of an elementary particle with extended structure. Complex vector formalism simplifies the expressions and elucidates geometrical understanding of the basic concepts. The analysis shows that the existence of spin transforms a classical oscillator into a quantum oscillator. In conclusion the classical mechanics combined with zeropoint field leads to quantum mechanics.
Topological vector spaces admissible in economic equilibrium theory
DEFF Research Database (Denmark)
Keiding, Hans
2009-01-01
In models of economic equilibrium in markets with infinitely many commodities, the commodity space is an ordered topological vector space endowed with additional structure. In the present paper, we consider ordered topological vector spaces which are admissible (for equilibrium analysis) in the s......) in the sense that every economy which is reasonably well behaved posesses an equilibrium. It turns out that this condition may be characterized in terms of topology and order. This characterization implies that the commodity space has the structure of a Kakutani space....
International Nuclear Information System (INIS)
Li Ming; Mai Zhenhong; Li Jianhua; Li Chaorong; Cui Shufan
1995-01-01
Based on the statistical theory of X-ray dynamical diffraction for thin films, the mosaicity of three types of semiconductor epitaxic layers has been investigated by analyzing their rocking curves by the X-ray double-crystal diffraction method. It is shown that the statistical theory can provide quantitative information on the mosaicity of the epitaxic layers such as the mean size and the mean disorientation of mosaic blocks in the layers. Some misunderstandings in interpreting experimental data are cleared up by taking into account the effect of diffuse scattering. It is emphasized that attempts to obtain structural parameters of specimens from their rocking curves by means of the Takagi-Taupin equations for coherent fields only are not strictly correct since diffuse scattering causes additional changes in the tails of the rocking curves. (orig.)
DEFF Research Database (Denmark)
Sørensen, O.; Rusch, W.
1975-01-01
The geometrical theory of diffraction (GTD) as formulated by R. G. Kouyoumjian has been applied to predict the radiation characteristics of hyperboloidal subreflectors with laterally defocused feeds. In caustic or multicaustic directions the scattered fields are determined using an equivalent ring...... current placed along the edge of the subreflector. The theoretical results are compared to measured amplitude and phase data. In order to improve the agreement, the blocking effects of the feed horn have been accounted for using the geometrical theory of diffraction. The calculated subreflector fields...... have been used to illuminate a paraboloid from which the scattered field is determined by physical optics. The results are compared to those obtained using a laterally defocused equivalent paraboloid....
The Scalar, Vector and Tensor Fields in Theory of Elasticity and Plasticity
Directory of Open Access Journals (Sweden)
František FOJTÍK
2014-06-01
Full Text Available This article is devoted to an analysis of scalar, vector and tensor fields, which occur in the loaded and deformed bodies. The aim of this article is to clarify and simplify the creation of an understandable idea of some elementary concepts and quantities in field theories, such as, for example equiscalar levels, scalar field gradient, Hamilton operator, divergence, rotation and gradient of vector or tensor and others. Applications of those mathematical terms are shown in simple elasticity and plasticity tasks. We hope that content of our article might help technicians to make their studies of necessary mathematical chapters of vector and tensor analysis and field theories easier.
Hairy black hole solutions in U(1) gauge-invariant scalar-vector-tensor theories
Heisenberg, Lavinia; Tsujikawa, Shinji
2018-05-01
In U (1) gauge-invariant scalar-vector-tensor theories with second-order equations of motion, we study the properties of black holes (BH) on a static and spherically symmetric background. In shift-symmetric theories invariant under the shift of scalar ϕ → ϕ + c, we show the existence of new hairy BH solutions where a cubic-order scalar-vector interaction gives rise to a scalar hair manifesting itself around the event horizon. In the presence of a quartic-order interaction besides the cubic coupling, there are also regular BH solutions endowed with scalar and vector hairs.
Optical propagators in vector and spinor theories by path integral formalism
International Nuclear Information System (INIS)
Linares, J.
1993-01-01
The construction of an extended parabolic (wide-angle) vector and spinor wave theory is presented. For that, optical propagators in monochromatic vector light optics and monoenergetic spinor electron optics are evaluated by the path integral formalism. The auxiliary parameter method introduced by Fock and the Feynman-Dyson perturbative series are used. The proposed theory supplies, by a generalized Fermat's principle, the Mukunda-Simon-Sudarshan transformation for the passage from scalar to vector light (or spinor electron) optics in an asymptotic approximation. (author). 19 refs
DEFF Research Database (Denmark)
Johansen, Peter Meincke
1996-01-01
New uniform closed-form expressions for physical theory of diffraction equivalent edge currents are derived for truncated incremental wedge strips. In contrast to previously reported expressions, the new expressions are well-behaved for all directions of incidence and observation and take a finite...... value for zero strip length. Consequently, the new equivalent edge currents are, to the knowledge of the author, the first that are well-suited for implementation in general computer codes...
Comments on conformal Killing vector fields and quantum field theory
International Nuclear Information System (INIS)
Brown, M.R.; Ottewill, A.C.; Siklos, S.T.C.
1982-01-01
We give a comprehensive analysis of those vacuums for flat and conformally flat space-times which can be defined by timelike, hypersurface-orthogonal, conformal Killing vector fields. We obtain formulas for the difference in stress-energy density between any two such states and display the correspondence with the renormalized stress tensors. A brief discussion is given of the relevance of these results to quantum-mechanical measurements made by noninertial observers moving through flat space
Algebraic characterization of vector supersymmetry in topological field theories
International Nuclear Information System (INIS)
Vilar, L.C.Q.; Ventura, O.S.; Sasaki, C.A.G.; Sorella, S.P.
1997-01-01
An algebraic cohomological characterization of a class of linearly broken Ward identities is provided. The examples of the topological vector supersymmetry and of the Landau ghost equation are discussed in detail. The existence of such a linearly broken Ward identities turns out to be related to BRST exact anti-field dependent cocycles with negative ghost number, according to the cohomological reformulation of the Noether theorem given by M. Henneaux et al. (author)
Algebraic characterization of vector supersymmetry in topological field theories
Energy Technology Data Exchange (ETDEWEB)
Vilar, L.C.Q.; Ventura, O.S.; Sasaki, C.A.G. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Sorella, S.P. [Universidade do Estado, Rio de Janeiro, RJ (Brazil). Inst. de Fisica. Dept. de Fisica Teorica
1997-01-01
An algebraic cohomological characterization of a class of linearly broken Ward identities is provided. The examples of the topological vector supersymmetry and of the Landau ghost equation are discussed in detail. The existence of such a linearly broken Ward identities turns out to be related to BRST exact anti-field dependent cocycles with negative ghost number, according to the cohomological reformulation of the Noether theorem given by M. Henneaux et al. (author). 32 refs., 5 tabs.
Chern-Simons theory with vector fermion matter
International Nuclear Information System (INIS)
Giombi, Simone; Minwalla, Shiraz; Prakash, Shiroman; Trivedi, Sandip P.; Wadia, Spenta R.; Yin, Xi
2012-01-01
We study three-dimensional conformal field theories described by U(N) Chern-Simons theory at level k coupled to massless fermions in the fundamental representation. By solving a Schwinger-Dyson equation in light-cone gauge, we compute the exact planar free energy of the theory at finite temperature on R 2 as a function of the 't Hooft coupling λ=N/k. Employing a dimensional reduction regularization scheme, we find that the free energy vanishes at vertical stroke λvertical stroke =1; the conformal theory does not exist for vertical stroke λvertical stroke >1. We analyze the operator spectrum via the anomalous conservation relation for higher spin currents, and in particular show that the higher spin currents do not develop anomalous dimensions at leading order in 1/N. We present an integral equation whose solution in principle determines all correlators of these currents at leading order in 1/N and present explicit perturbative results for all three-point functions up to two loops. We also discuss a light-cone Hamiltonian formulation of this theory where a W ∞ algebra arises. The maximally supersymmetric version of our theory is ABJ model with one gauge group taken to be U(1), demonstrating that a pure higher spin gauge theory arises as a limit of string theory. (orig.)
Transition operators in electromagnetic-wave diffraction theory. II - Applications to optics
Hahne, G. E.
1993-01-01
The theory developed by Hahne (1992) for the diffraction of time-harmonic electromagnetic waves from fixed obstacles is briefly summarized and extended. Applications of the theory are considered which comprise, first, a spherical harmonic expansion of the so-called radiation impedance operator in the theory, for a spherical surface, and second, a reconsideration of familiar short-wavelength approximation from the new standpoint, including a derivation of the so-called physical optics method on the basis of quasi-planar approximation to the radiation impedance operator, augmented by the method of stationary phase. The latter includes a rederivation of the geometrical optics approximation for the complete Green's function for the electromagnetic field in the presence of a smooth- and a convex-surfaced perfectly electrically conductive obstacle.
Volakis, John L.
1991-01-01
There are two tasks described in this report. First, an extension of a two dimensional formulation is presented for a three dimensional body of revolution. A Fourier series expansion of the vector electric and magnetic fields is employed to reduce the dimensionality of the system, and an exact boundary condition is employed to terminate the mesh. The mesh termination boundary is chosen such that it leads to convolutional boundary operators for low O(n) memory demand. Second, rigorous uniform geometrical theory of diffraction (UTD) diffraction coefficients are presented for a coated convex cylinder simulated with generalized impedance boundary conditions. Ray solutions are obtained which remain valid in the transition region and reduce uniformly those in the deep lit and shadow regions. A uniform asymptotic solution is also presented for observations in the close vicinity of the cylinder.
Group-theoretical method in the many-beam theory of electron diffraction
International Nuclear Information System (INIS)
Kogiso, Motokazu; Takahashi, Hidewo.
1977-01-01
A group-theoretical method is developed for the many-beam dynamical theory of the symmetric Laue case. When the incident wave is directed so that the Laue point lies on a symmetric position in the reciprocal lattice, the dispersion matrix in the fundamental equation can be reduced to a block diagonal form. The transformation matrix is composed of column vectors belonging to irreducible representations of the group of the incident wave vector. Without performing reduction, the reduced form of the dispersion matrix is determined from characters of representations. Practical application is made to the case of symmorphic crystals, where general reduced forms and all solvable examples are given in terms of some geometrical factors of reciprocal lattice arrangements. (auth.)
Stewart, Terrence C; Eliasmith, Chris
2013-06-01
Quantum probability (QP) theory can be seen as a type of vector symbolic architecture (VSA): mental states are vectors storing structured information and manipulated using algebraic operations. Furthermore, the operations needed by QP match those in other VSAs. This allows existing biologically realistic neural models to be adapted to provide a mechanistic explanation of the cognitive phenomena described in the target article by Pothos & Busemeyer (P&B).
Ghost free dual vector theories in 2+1 dimensions
International Nuclear Information System (INIS)
Dalmazi, Denis
2006-01-01
We explore here the issue of duality versus spectrum equivalence in dual theories generated through the master action approach. Specifically we examine a generalized self-dual (GSD) model where a Maxwell term is added to the self-dual model. A gauge embedding procedure applied to the GSD model leads to a Maxwell-Chern-Simons (MCS) theory with higher derivatives. We show here that the latter contains a ghost mode contrary to the original GSD model. By figuring out the origin of the ghost we are able to suggest a new master action which interpolates between the local GSD model and a nonlocal MCS model. Those models share the same spectrum and are ghost free. Furthermore, there is a dual map between both theories at classical level which survives quantum correlation functions up to contact terms. The remarks made here may be relevant for other applications of the master action approach
Resonance energy transfer: The unified theory via vector spherical harmonics
Energy Technology Data Exchange (ETDEWEB)
Grinter, Roger, E-mail: r.grinter@uea.ac.uk; Jones, Garth A., E-mail: garth.jones@uea.ac.uk [School of Chemistry, University of East Anglia, Norwich NR4 7TJ (United Kingdom)
2016-08-21
In this work, we derive the well-established expression for the quantum amplitude associated with the resonance energy transfer (RET) process between a pair of molecules that are beyond wavefunction overlap. The novelty of this work is that the field of the mediating photon is described in terms of a spherical wave rather than a plane wave. The angular components of the field are constructed in terms of vector spherical harmonics while Hankel functions are used to define the radial component. This approach alleviates the problem of having to select physically correct solution from non-physical solutions, which seems to be inherent in plane wave derivations. The spherical coordinate system allows one to easily decompose the photon’s fields into longitudinal and transverse components and offers a natural way to analyse near-, intermediate-, and far-zone RET within the context of the relative orientation of the transition dipole moments for the two molecules.
Uniform physical theory of diffraction equivalent edge currents for truncated wedge strips
DEFF Research Database (Denmark)
Johansen, Peter Meincke
1996-01-01
New uniform closed-form expressions for physical theory of diffraction equivalent edge currents are derived for truncated incremental wedge strips. In contrast to previously reported expressions, the new expressions are well behaved for all directions of incidence and observation and take a finite...... value for zero strip length. This means that the expressions are well suited for implementation in general computer codes. The new expressions are expressed as the difference between two terms. The first term is obtained by integrating the exact fringe wave current on a wedge along an untruncated...
Fermion frontiers in vector lattice gauge theories: Proceedings. Volume 8
International Nuclear Information System (INIS)
1998-01-01
The inclusion of fermions into simulations of lattice gauge theories is very difficult both theoretically and numerically. With the presence of Teraflops-scale computers for lattice gauge theory, the authors wanted a forum to discuss new approaches to lattice fermions. The workshop concentrated on approaches which are ripe for study on such large machines. Although lattice chiral fermions are vitally important to understand, there is not technique at hand which is viable on these Teraflops-scale machines for real-world problems. The discussion was therefore focused on recent developments and future prospects for QCD-like theories. For the well-known fermion formulations, the Aoki phase in Wilson fermions, novelties of U A (1) symmetry and the η' for staggered fermions and new approaches for simulating the determinant for Wilson fermions were discussed. The newer domain-wall fermion formulation was reviewed, with numerical results given by many speakers. The fermion proposal of Friedberg, Lee and Pang was introduced. They also were able to compare and contrast the dependence of QCD and QCD-like SUSY theories on the number of quark flavors. These proceedings consist of several transparencies and a summary page from each speaker. This should serve to outline the major points made in each talk
Gauge theories of Yang-Mills vector fields coupled to antisymmetric tensor fields
International Nuclear Information System (INIS)
Anco, Stephen C.
2003-01-01
A non-Abelian class of massless/massive nonlinear gauge theories of Yang-Mills vector potentials coupled to Freedman-Townsend antisymmetric tensor potentials is constructed in four space-time dimensions. These theories involve an extended Freedman-Townsend-type coupling between the vector and tensor fields, and a Chern-Simons mass term with the addition of a Higgs-type coupling of the tensor fields to the vector fields in the massive case. Geometrical, field theoretic, and algebraic aspects of the theories are discussed in detail. In particular, the geometrical structure mixes and unifies features of Yang-Mills theory and Freedman-Townsend theory formulated in terms of Lie algebra valued curvatures and connections associated to the fields and nonlinear field strengths. The theories arise from a general determination of all possible geometrical nonlinear deformations of linear Abelian gauge theory for one-form fields and two-form fields with an Abelian Chern-Simons mass term in four dimensions. For this type of deformation (with typical assumptions on the allowed form considered for terms in the gauge symmetries and field equations), an explicit classification of deformation terms at first-order is obtained, and uniqueness of deformation terms at all higher orders is proven. This leads to a uniqueness result for the non-Abelian class of theories constructed here
Directory of Open Access Journals (Sweden)
Diego Tami
2018-01-01
Full Text Available We discuss three sets of heuristic coefficients used in uniform theory of diffraction (UTD to characterize the electromagnetic scattering in realistic urban scenarios and canonical examples of diffraction by lossy conducting wedges using the three sets of heuristic coefficients and the Malyuzhinets solution as reference model. We compare not only the results of the canonical models but also their implementation in real outdoor scenarios. To predict the coverage of mobile networks, we used propagation models for outdoor environments by using a 3D ray-tracing model based on a brute-force algorithm for ray launching and a propagation model based on image theory. To evaluate each set of coefficients, we analyzed the mean and standard deviation of the absolute error between estimates and measured data in Ottawa, Canada; Valencia, Spain; and Cali, Colombia. Finally, we discuss the path loss prediction for each set of heuristic UTD coefficients in outdoor environment, as well as the comparison with the canonical results.
Vector theory of gravity: Universe without black holes and solution of dark energy problem
Svidzinsky, Anatoly A.
2017-12-01
We propose an alternative theory of gravity which assumes that background geometry of the Universe is fixed four dimensional Euclidean space and gravity is a vector field A k in this space which breaks the Euclidean symmetry. Direction of A k gives the time coordinate, while perpendicular directions are spatial coordinates. Vector gravitational field is coupled to matter universally and minimally through the equivalent metric f ik which is a functional of A k . We show that such assumptions yield a unique theory of gravity, it is free of black holes and, to the best of our knowledge, passes all available tests. For cosmology our theory predicts the same evolution of the Universe as general relativity with cosmological constant and zero spatial curvature. However, the present theory provides explanation of the dark energy as energy of longitudinal gravitational field induced by the Universe expansion and yields, with no free parameters, the value of {{{Ω }}}{{Λ }}=2/3≈ 0.67 which is consistent with the recent Planck result {{{Ω }}}{{Λ }}=0.686+/- 0.02. Such close agreement with cosmological data indicates that gravity has a vector, rather than tensor, origin. We demonstrate that gravitational wave signals measured by LIGO are compatible with vector gravity. They are produced by orbital inspiral of massive neutron stars which can exist in the present theory. We also quantize gravitational field and show that quantum vector gravity is equivalent to QED. Vector gravity can be tested by making more accurate measurement of the time delay of radar signal traveling near the Sun; by improving accuracy of the light deflection experiments; or by measuring propagation direction of gravitational waves relative to laser interferometer arms. Resolving the supermassive object at the center of our Galaxy with VLBA could provide another test of gravity and also shed light on the nature of dark matter.
Massive mu pair production in a vector field theory model
Halliday, I G
1976-01-01
Massive electrodynamics is treated as a model for the production of massive mu pairs in high-energy hadronic collisions. The dominant diagrams in perturbation theory are identified and analyzed. These graphs have an eikonal structure which leads to enormous cancellations in the two-particle inclusive cross section but not in the n-particle production cross sections. Under the assumption that these cancellations are complete, a Drell-Yan structure appears in the inclusive cross section but the particles accompanying the mu pairs have a very different structure compared to the parton model. The pionization region is no longer empty of particles as in single parton models. (10 refs).
Parallel/vector algorithms for the spherical SN transport theory method
International Nuclear Information System (INIS)
Haghighat, A.; Mattis, R.E.
1990-01-01
This paper discusses vector and parallel processing of a 1-D curvilinear (i.e. spherical) S N transport theory algorithm on the Cornell National SuperComputer Facility (CNSF) IBM 3090/600E. Two different vector algorithms were developed and parallelized based on angular decomposition. It is shown that significant speedups are attainable. For example, for problems with large granularity, using 4 processors, the parallel/vector algorithm achieves speedups (for wall-clock time) of more than 4.5 relative to the old serial/scalar algorithm. Furthermore, this work has demonstrated the existing potential for the development of faster processing vector and parallel algorithms for multidimensional curvilinear geometries. (author)
Non-Abelian formulation of a vector-tensor gauge theory with topological coupling
International Nuclear Information System (INIS)
Barcelos Neto, J.; Cabo, A.; Silva, M.B.D.
1995-08-01
We obtain a non-Abelian version of a theory involving vector and tensor and tensor gauge fields interacting via a massive topological coupling, besides the nonminimum one. The new fact is that the non-Abelian theory is not reducible and Stuckelberg fields are introduced in order to compatibilize gauge invariance, nontrivial physical degrees of freedom and the limit of the Abelian case. (author). 9 refs
Additional neutral vector boson in the 7-dimensional theory of gravy-electro-weak interactions
International Nuclear Information System (INIS)
Gavrilov, V.R.
1988-01-01
Possibilities of manifestation of an additional neutron vector boson, the existence of which is predicted by the 7-dimensional theory of gravy-electro-weak interactions, are analyzed. A particular case of muon neutrino scattering on a muon is considered. In this case additional neutral current manifests both at high and at relatively low energies of particle collisions
P-odd effects in the e-d scattering in the vector-like theories
International Nuclear Information System (INIS)
Gakh, G.I.
1979-01-01
P-odd effects in elastic electron-deuteron scattering, due to the weak neutral currents, are analyzed in the framework of the vector-like theories. Considered is the case of the most general form of the P-invariance breaking in the elastic e - d scattering amplitude in both the leptonic and hadronic vertices. It is found that in the vector-like theories the parity violation in the electro-deuteron elastic scattering is confined in the hadronic vertex, while in the Weinberg-Salam model it is confined in the leptonic vertex. In the vector-like theories the asymmetry in the scattering of longitudinally polarized electrons by nonpolarized deuterons depends on the electromagnetic and weak form factors of a deuteron, whereas in the Weinberg-Salam model it does not depend on the structure of the deuteron. In the Weinberg-Salam model the asymmetry is independent on the T-violating form factors of the deuteron, whereas such a dependence is present in the vector-like theories
Energy Technology Data Exchange (ETDEWEB)
Gorenflo, Norbert [Beuth Hochschule fuer Technik Berlin (Germany). Fachbereich II; Kunik, Matthias [Magdeburg Univ. (Germany). Inst. fuer Analysis und Numerik
2009-07-01
We present a new and self-contained theory for mapping properties of the boundary operators for slit diffraction occurring in Sommerfeld's diffraction theory, covering two different cases of the polarisation of the light. This theory is entirely developed in the context of the boundary operators with a Hankel kernel and not based on the corresponding mixed boundary value problem for the Helmholtz equation. For a logarithmic approximation of the Hankel kernel we also study the corresponding mapping properties and derive explicit solutions together with certain regularity results. (orig.)
Kharin, Nikolay A.
2000-04-01
In nonlinear ultrasound imaging the images are formed using the second harmonic energy generated due to the nonlinear nature of finite amplitude propagation. This propagation can be modeled using the KZK wave equation. This paper presents further development of nonlinear diffractive field theory based on the KZK equation and its solution by means of the slowly changing profile method for moderate nonlinearity. The analytical expression for amplitudes and phases of sum frequency wave are obtained in addition to the second harmonic wave. Also, the analytical expression for the relative curvature of the wave fronts of fundamental and second harmonic signals are derived. The media with different nonlinear properties and absorption coefficients were investigated to characterize the diffractive field of the transducer at medical frequencies. All expressions demonstrate good agreement with experimental results. The expressions are novel and provide an easy way for prediction of amplitude and phase structure of nonlinearly distorted field of a transducer. The sum frequency signal technique could be implemented as well as second harmonic technique to improve the quality of biomedical images. The results obtained are of importance for medical diagnostic ultrasound equipment design.
Black hole perturbations in vector-tensor theories: the odd-mode analysis
Kase, Ryotaro; Minamitsuji, Masato; Tsujikawa, Shinji; Zhang, Ying-li
2018-02-01
In generalized Proca theories with vector-field derivative couplings, a bunch of hairy black hole solutions have been derived on a static and spherically symmetric background. In this paper, we formulate the odd-parity black hole perturbations in generalized Proca theories by expanding the corresponding action up to second order and investigate whether or not black holes with vector hair suffer ghost or Laplacian instabilities. We show that the models with cubic couplings G3(X), where X=‑AμAμ/2 with a vector field Aμ, do not provide any additional stability condition as in General Relativity. On the other hand, the exact charged stealth Schwarzschild solution with a nonvanishing longitudinal vector component A1, which originates from the coupling to the Einstein tensor GμνAμ Aν equivalent to the quartic coupling G4(X) containing a linear function of X, is unstable in the vicinity of the event horizon. The same instability problem also persists for hairy black holes arising from general quartic power-law couplings G4(X) ⊃ β4 Xn with the nonvanishing A1, while the other branch with A1=0 can be consistent with conditions for the absence of ghost and Laplacian instabilities. We also discuss the case of other exact and numerical black hole solutions associated with intrinsic vector-field derivative couplings and show that there exists a wide range of parameter spaces in which the solutions suffer neither ghost nor Laplacian instabilities against odd-parity perturbations.
Implementation of the CCGM approximation for surface diffraction using Wigner R-matrix theory
International Nuclear Information System (INIS)
Lauderdale, J.G.; McCurdy, C.W.
1983-01-01
The CCGM approximation for surface scattering proposed by Cabrera, Celli, Goodman, and Manson [Surf. Sci. 19, 67 (1970)] is implemented for realistic surface interaction potentials using Wigner R-matrix theory. The resulting procedure is highly efficient computationally and is in no way limited to hard wall or purely repulsive potentials. Comparison is made with the results of close-coupling calculations of other workers which include the same diffraction channels in order to fairly evaluate the CCGM approximation which is an approximation to the coupled channels Lippman--Schwinger equation for the T matrix. The shapes of selective adsorption features, whether maxima or minima, in the scattered intensity are well represented in this approach for cases in which the surface corrugation is not too strong
A new approach to radiative transfer theory using Jones's vectors. I
International Nuclear Information System (INIS)
Fymat, A.L.; Vasudevan, R.
1975-01-01
Radiative transfer of partially polarized radiation in an anisotropically scattering, inhomogeneous atmosphere containing arbitrary polydispersion of particles is described using Jones's amplitude vectors and matrices. This novel approach exploits the close analogy between the quantum mechanical states of spin 1/2 systems and the polarization states of electromagnetic radiation described by Jones's vector, and draws on the methodology of such spin 1/2 systems. The complete equivalence between the transport equation for Jones's vectors and the classical radiative transfer equation for Stokes's intensity vectors is demonstrated in two independent ways after deriving the transport equations for the polarization coherency matrices and for the quaternions corresponding to the Jones's vectors. A compact operator formulation of the theory is provided, and used to derive the necessary equations for both a local and a global description of the transport of Jones's vectors. Lastly, the integro-differential equations for the amplitude reflection and transmission matrices are derived, and related to the usual corresponding equations. The present formulation is the most succinct and the most convenient one for both theoretical and experimental studies. It yields a simpler analysis than the classical formulation since it reduces by a factor of two the dimensionality of transfer problems. It preserves information on phases, and thus can be used directly across the entire electromagnetic spectrum without any further conversion into intensities. (Auth.)
Renormalizable massive charged vector-boson theory without spontaneous symmetry breakdown
International Nuclear Information System (INIS)
Mac, E.
1977-01-01
A renormalizable and unitary theory of massive charged vector bosons is proposed. This theory has a similarity with the Georgi-Glashow theory, the difference being that in the former the Lagrangian does not contain the potential term in the scalar fields necessary in theories with spontaneous symmetry breaking. The mass M > 0 of the charged vector bosons are introduced in the Lagrangian in such a way that the Lagrangian is still invariant under a ''distorted'' local gauge symmetry. This Lagrangian is studied in the generalized renormalizable gauge (gauge R /sub xi/), by means of the Lagrange multiplier formalism. In this way, the fictitious Lagrangian that restores unitarity to the theory can be constructed. The fictitious Lagrangian constructed using the Lagrange multiplier formalism is compared to the one obtained due to the variation of the gauge condition under the gauge transformations. The renormalizability of this theory is studied and the Ward-Takahaski identities are derived; these identities are checked by explicit calculations. Using the Becchi-Rouet-Stora transformation, one can obtain the equation satisfied by the renormalized Lagrangian; solving this equation the most general form of the renormalized Lagrangian is obtained. Also the classical solutions of this kind of theories are studied. Solutions are found suggesting the presence of dyons
Photonic-Doppler-Velocimetry, Paraxial-Scalar Diffraction Theory and Simulation
Energy Technology Data Exchange (ETDEWEB)
Ambrose, W. P. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-07-20
In this report I describe current progress on a paraxial, scalar-field theory suitable for simulating what is measured in Photonic Doppler Velocimetry (PDV) experiments in three dimensions. I have introduced a number of approximations in this work in order to bring the total computation time for one experiment down to around 20 hours. My goals were: to develop an approximate method of calculating the peak frequency in a spectral sideband at an instant of time based on an optical diffraction theory for a moving target, to compare the ‘measured’ velocity to the ‘input’ velocity to gain insights into how and to what precision PDV measures the component of the mass velocity along the optical axis, and to investigate the effects of small amounts of roughness on the measured velocity. This report illustrates the progress I have made in describing how to perform such calculations with a full three dimensional picture including tilted target, tilted mass velocity (not necessarily in the same direction), and small amounts of surface roughness. With the method established for a calculation at one instant of time, measured velocities can be simulated for a sequence of times, similar to the process of sampling velocities in experiments. Improvements in these methods are certainly possible at hugely increased computational cost. I am hopeful that readers appreciate the insights possible at the current level of approximation.
Background Killing vectors and conservation laws in Rosen's bimetric theories of gravitation
International Nuclear Information System (INIS)
Israelit, M.
1979-01-01
The problem of global energy, linear momentum, and angular momentum in Rosen's bimetric theories of gravitation is considered from the point of view of motions of the background space-time. It turns out that by means of background Killing vectors global mechanical integrals for matter and field can be defined in a correct manner. For the flat-background bimetric theory conditions are obtained which have been imposed on the algebraic structure of the matter tensor Tsub(μ)sup(ν) in order to get global mechanical conservation laws. For bimetric gravitation theories based on a cosmological (nonflat) background the set of Killing vectors is found. For these theories the obtained restrictions on the algebraic structure of Tsub(μ)sup(ν) lead to global generation laws (instead of conservation laws in the flat-background theory) for mechanical quantities. In particular cases the generation effect vanishes and then conservation laws exist. By means of the method developed in this paper, Rosen's homogeneous isotropic universe in the framework of the cosmological-background bimetric theory with k = 1 is considered. It turns out that such a universe does not generate globally, but will generate locally. The global energy of this universe is found to be zero. (author)
Locally extracting scalar, vector and tensor modes in cosmological perturbation theory
International Nuclear Information System (INIS)
Clarkson, Chris; Osano, Bob
2011-01-01
Cosmological perturbation theory relies on the decomposition of perturbations into so-called scalar, vector and tensor modes. This decomposition is non-local and depends on unknowable boundary conditions. The non-locality is particularly important at second and higher order because perturbative modes are sourced by products of lower order modes, which must be integrated over all space in order to isolate each mode. However, given a trace-free rank-2 tensor, a locally defined scalar mode may be trivially derived by taking two divergences, which knocks out the vector and tensor degrees of freedom. A similar local differential operation will return a pure vector mode. This means that scalar and vector degrees of freedom have local descriptions. The corresponding local extraction of the tensor mode is unknown however. We give it here. The operators we define are useful for defining gauge-invariant quantities at second order. We perform much of our analysis using an index-free 'vector-calculus' approach which makes manipulating tensor equations considerably simpler. (papers)
Soirat, Arnaud J. A.
Density Matrix Theory is a Quantum Mechanical formalism in which the wavefunction is eliminated and its role taken over by reduced density matrices. The interest of this is that, it allows one, in principle, to calculate any electronic property of a physical system, without having to solve the Schrodinger equation, using only two entities much simpler than an N-body wavefunction: first and second -order reduced density matrices. In practice, though, this very promising possibility faces the tremendous theoretical problem of N-representability, which has been solved for the former, but, until now, voids any hope of theoretically determining the latter. However, it has been shown that single determinant reduced density matrices of any order may be recovered from coherent X-ray diffraction data, if one provides a proper Quantum Mechanical description of the Crystallography experiment. A deeper investigation of this method is the purpose of this work, where we, first, further study the calculation of X-ray reduced density matrices N-representable by a single Slater determinant. In this context, we independently derive necessary and sufficient conditions for the uniqueness of the method. We then show how to account for electron correlation in this model. For the first time, indeed, we derive highly accurate, yet practical, density matrices approximately N-representable by correlated-determinant wavefunctions. The interest of such a result lies in the Quantum Mechanical validity of these density matrices, their property of being entirely obtainable from X-ray coherent diffraction data, their very high accuracy conferred by this known property of the N-representing wavefunction, as well as their definition as explicit functionals of the density. All of these properties are finally used in both a theoretical and a numerical application: in the former, we show that these density matrices may be used in the context of Density Functional Theory to highly accurately determine
DEFF Research Database (Denmark)
van de Streek, Jacco; Neumann, Marcus A
2014-01-01
In 2010 we energy-minimized 225 high-quality single-crystal (SX) structures with dispersion-corrected density functional theory (DFT-D) to establish a quantitative benchmark. For the current paper, 215 organic crystal structures determined from X-ray powder diffraction (XRPD) data and published...
DEFF Research Database (Denmark)
Dridi, Kim; Bjarklev, Anders Overgaard
1999-01-01
An electromagnetic vector-field modle for design of optical components based on the finite-difference-time-domain method and radiation integrals in presented. Its ability to predict the optical electromagnetic dynamics in structures with complex material distribution is demonstrated. Theoretical...
Combining the multilevel fast multipole method with the uniform geometrical theory of diffraction
Directory of Open Access Journals (Sweden)
A. Tzoulis
2005-01-01
Full Text Available The presence of arbitrarily shaped and electrically large objects in the same environment leads to hybridization of the Method of Moments (MoM with the Uniform Geometrical Theory of Diffraction (UTD. The computation and memory complexity of the MoM solution is improved with the Multilevel Fast Multipole Method (MLFMM. By expanding the k-space integrals in spherical harmonics, further considerable amount of memory can be saved without compromising accuracy and numerical speed. However, until now MoM-UTD hybrid methods are restricted to conventional MoM formulations only with Electric Field Integral Equation (EFIE. In this contribution, a MLFMM-UTD hybridization for Combined Field Integral Equation (CFIE is proposed and applied within a hybrid Finite Element - Boundary Integral (FEBI technique. The MLFMM-UTD hybridization is performed at the translation procedure on the various levels of the MLFMM, using a far-field approximation of the corresponding translation operator. The formulation of this new hybrid technique is presented, as well as numerical results.
Electron diffraction from carbon nanotubes
International Nuclear Information System (INIS)
Qin, L-C
2006-01-01
The properties of a carbon nanotube are dependent on its atomic structure. The atomic structure of a carbon nanotube can be defined by specifying its chiral indices (u, v), that specify its perimeter vector (chiral vector), with which the diameter and helicity are also determined. The fine electron beam available in a modern transmission electron microscope (TEM) offers a unique probe to reveal the atomic structure of individual nanotubes. This review covers two aspects related to the use of the electron probe in the TEM for the study of carbon nanotubes: (a) to understand the electron diffraction phenomena for inter-pretation of the electron diffraction patterns of carbon nanotubes and (b) to obtain the chiral indices (u, v), of the carbon nanotubes from the electron diffraction patterns. For a nanotube of a given structure, the electron scattering amplitude from the carbon nanotube is first described analytically in closed form using the helical diffraction theory. From a known structure as given by the chiral indices (u, v), its electron diffraction pattern can be calculated and understood. The reverse problem, i.e. assignment of the chiral indices from an electron diffraction pattern of a carbon nanotube, is approached from the relationship between the electron scattering intensity distribution and the chiral indices (u, v). We show that electron diffraction patterns can provide an accurate and unambiguous assignment of the chiral indices of carbon nanotubes. The chiral indices (u, v) can be read indiscriminately with a high accuracy from the intensity distribution on the principal layer lines in an electron diffraction pattern. The symmetry properties of electron diffraction from carbon nanotubes and the electron diffraction from deformed carbon nanotubes are also discussed in detail. It is shown that 2mm symmetry is always preserved for single-walled carbon nanotubes, but it can break down for multiwalled carbon nanotubes under some special circumstances
International Nuclear Information System (INIS)
Ghirardi, G.C.; Pearle, P.
1991-02-01
The propositions, that what we see around us is real and that reality should be represented by the statevector, conflict with quantum theory. In quantum theory, the statevector can readily become a sum of states of comparable norm, each state representing a different reality. In this paper we present the Continuous Spontaneous Localization (CSL) theory, in which a modified Schroedinger equation, while scarcely affecting the dynamics of a microscopic system, rapidly ''reduces'' the statevector of a macroscopic system to a state appropriate for representing individual reality. (author). Refs
Propagation of gravitational waves in the generalized tensor-vector-scalar theory
International Nuclear Information System (INIS)
Sagi, Eva
2010-01-01
Efforts are underway to improve the design and sensitivity of gravitational wave detectors, with the hope that the next generation of these detectors will observe a gravitational wave signal. Such a signal will not only provide information on dynamics in the strong gravity regime that characterizes potential sources of gravitational waves, but will also serve as a decisive test for alternative theories of gravitation that are consistent with all other current experimental observations. We study the linearized theory of the tensor-vector-scalar theory of gravity with generalized vector action, an alternative theory of gravitation designed to explain the apparent deficit of visible matter in galaxies and clusters of galaxies without postulating yet-undetected dark matter. We find the polarization states and propagation speeds for gravitational waves in vacuum, and show that in addition to the usual transverse-traceless propagation modes, there are two more mixed longitudinal-transverse modes and two trace modes, of which at least one has longitudinal polarization. Additionally, the propagation speeds are different from the speed of light.
Kroes, G J; Wijzenbroek, Mark; Manson, J R
2017-12-28
Specific features of diffractive scattering of H 2 from metal surfaces can serve as fingerprints of the reactivity of the metal towards H 2 , and in principle theory-experiment comparisons for molecular diffraction can help with the validation of semi-empirical functionals fitted to experiments of sticking of H 2 on metals. However, a recent comparison of calculated and Debye-Waller (DW) extrapolated experimental diffraction probabilities, in which the theory was done on the basis of a potential energy surface (PES) accurately describing sticking to Ru(0001), showed substantial discrepancies, with theoretical and experimental probabilities differing by factors of 2 and 3. We demonstrate that assuming a particular amount of random static disorder to be present in the positions of the surface atoms, which can be characterized through a single parameter, removes most of the discrepancies between experiment and theory. Further improvement might be achievable by improving the accuracy of the DW extrapolation, the model of the H 2 rotational state distribution in the experimental beams, and by fine-tuning the PES. However, the question of whether the DW model is applicable to attenuation of diffractive scattering in the presence of a sizable van der Waals well (depth ≈ 50 meV) should also receive attention, in addition to the question of whether the amount of static surface disorder effectively assumed in the modeling by us could have been present in the experiments.
Vershik, A.
2017-01-01
The paper presents a general duality theory for vector measure spaces taking its origin in the author's papers written in the 1960s. The main result establishes a direct correspondence between the geometry of a measure in a vector space and the properties of the space of measurable linear functionals on this space regarded as closed subspaces of an abstract space of measurable functions. An example of useful new features of this theory is the notion of a free measure and its applications.
VECTOR THEORY AND OPTIMAL CHOICE OF ANTIMICROBIAL DRUG FOR LOCAL WOUND TREATMENT
Directory of Open Access Journals (Sweden)
Boyko N. N
2016-12-01
Full Text Available Introduction. One of important problems in the field of medicine and pharmacy is an optimal choice among several alternatives. For example, the choice of drugs for treatment among several analogs, selection of excipients among analogs for development of pharmaceutical forms with optimal pharmacological, technological and economical parameters, etc.The aim of the work is to show the possibility of vector theory use for optimal choice of antimicrobial drugs for local wound treatment among analogs taking into account several criteria at the same time. Materials and methods. For our investigation we have chosen ten drugs with antimicrobial properties for local wound treatment in different pharmaceutical forms (ointment, liniment, water and glycerin solution, tincture. We have determined antibacterial activity of drugs by agar well diffusion method on six test-stain microorganisms: Staphylococcus aureus ATCC 25923, Escherichia coli ATCC 25922, Pseudomonas aeruginosa ATCC 27853, Proteus vulgaris ATCC 4636, Bacillus subtilis ATCC 6633, and Candida albicans ATCC 885-653. Well diameter was 10 mm, the volume of drug in the well was 0.27±0.02 ml, microbial burden of agar upper layer was 107 CFU/ml, and total layer height in Petri dish was 4.0±0.5 mm. In order to integrate various qualitative and quantitative parameters into one index (vector object in multidimensional factors’ space we modify these parameters to non-dimensional normalized values. For this purpose we use a desirability theory. We have chosen the following criteria for optimal choice of the drug: antimicrobial activity (integrated index of drug’s antimicrobial activity, drug’s price, pharmacological and technological index, spectrum of drug’s action on test strains of microorganisms studied. Results and their discussions. Using vector and desirability theory, we have obtained the following range of drugs in decreasing order: Laevomecol ointment, Ioddicerinum, Tincture of Sophora
Linking Simple Economic Theory Models and the Cointegrated Vector AutoRegressive Model
DEFF Research Database (Denmark)
Møller, Niels Framroze
This paper attempts to clarify the connection between simple economic theory models and the approach of the Cointegrated Vector-Auto-Regressive model (CVAR). By considering (stylized) examples of simple static equilibrium models, it is illustrated in detail, how the theoretical model and its stru....... Further fundamental extensions and advances to more sophisticated theory models, such as those related to dynamics and expectations (in the structural relations) are left for future papers......This paper attempts to clarify the connection between simple economic theory models and the approach of the Cointegrated Vector-Auto-Regressive model (CVAR). By considering (stylized) examples of simple static equilibrium models, it is illustrated in detail, how the theoretical model and its......, it is demonstrated how other controversial hypotheses such as Rational Expectations can be formulated directly as restrictions on the CVAR-parameters. A simple example of a "Neoclassical synthetic" AS-AD model is also formulated. Finally, the partial- general equilibrium distinction is related to the CVAR as well...
Parameterized Post-Newtonian Expansion of Scalar-Vector-Tensor Theory of Gravity
International Nuclear Information System (INIS)
Arianto; Zen, Freddy P.; Gunara, Bobby E.; Hartanto, Andreas
2010-01-01
We investigate the weak-field, post-Newtonian expansion to the solution of the field equations in scalar-vector-tensor theory of gravity. In the calculation we restrict ourselves to the first post Newtonian. The parameterized post Newtonian (PPN) parameters are determined by expanding the modified field equations in the metric perturbation. Then, we compare the solution to the PPN formalism in first PN approximation proposed by Will and Nordtvedt and read of the coefficients (the PPN parameters) of post Newtonian potentials of the theory. We find that the values of γ PPN and β PPN are the same as in General Relativity but the coupling functions β 1 , β 2 , and β 3 are the effect of the preferred frame.
On the theory of time-resolved x-ray diffraction
DEFF Research Database (Denmark)
Henriksen, Niels Engholm; Møller, Klaus Braagaard
2008-01-01
We derive the basic theoretical formulation for X-ray diffraction with pulsed fields, using a fully quantized description of light and matter. Relevant time scales are discussed for coherent as well as incoherent X-ray pulses, and we provide expressions to be used for calculation...... of the experimental diffraction signal for both types of X-ray sources. We present a simple analysis of time-resolved X-ray scattering for direct bond breaking in diatomic molecules. This essentially analytical approach highlights the relation between the signal and the time-dependent quantum distribution...
International Nuclear Information System (INIS)
Wojcik, M.; Gaca, J.; Turos, A.; Strupinski, W.
2000-01-01
The method of investigation of the chemical composition for quaternary heterostructures has been developed. To this end X-ray high resolution diffractometry and RBS methods were applied. This method consists in finding a best fit between experimental diffraction pattern and theoretical one calculated, employing Darwin dynamical diffraction theory for a given model of heterostructure. This procedure was applied to determine the chemical profile in the growth direction for InGaAsP/InP superlattices that were grown by MOCVD technology on 001 InP substrate. The relations between the chemical composition of In x Ga 1-x As y P 1-y layer, its lattice parameter, optoelectronic properties and growth conditions were found. (author)
Rahmat-Samii, Yahya
1986-01-01
Both offset and symmetric Cassegrain reflector antennas are used in satellite and ground communication systems. It is known that the subreflector diffraction can degrade the performance of these reflectors. A geometrical theory of diffraction/physical optics analysis technique is used to investigate the effects of the extended subreflector, beyond its optical rim, on the reflector efficiency and far-field patterns. Representative numerical results are shown for an offset Cassegrain reflector antenna with different feed illumination tapers and subreflector extensions. It is observed that for subreflector extensions as small as one wavelength, noticeable improvements in the overall efficiencies can be expected. Useful design data are generated for the efficiency curves and far-field patterns.
Differential Galois theory and non-integrability of planar polynomial vector fields
Acosta-Humánez, Primitivo B.; Lázaro, J. Tomás; Morales-Ruiz, Juan J.; Pantazi, Chara
2018-06-01
We study a necessary condition for the integrability of the polynomials vector fields in the plane by means of the differential Galois Theory. More concretely, by means of the variational equations around a particular solution it is obtained a necessary condition for the existence of a rational first integral. The method is systematic starting with the first order variational equation. We illustrate this result with several families of examples. A key point is to check whether a suitable primitive is elementary or not. Using a theorem by Liouville, the problem is equivalent to the existence of a rational solution of a certain first order linear equation, the Risch equation. This is a classical problem studied by Risch in 1969, and the solution is given by the "Risch algorithm". In this way we point out the connection of the non integrability with some higher transcendent functions, like the error function.
Black hole and cosmos with multiple horizons and multiple singularities in vector-tensor theories
Gao, Changjun; Lu, Youjun; Yu, Shuang; Shen, You-Gen
2018-05-01
A stationary and spherically symmetric black hole (e.g., Reissner-Nordström black hole or Kerr-Newman black hole) has, at most, one singularity and two horizons. One horizon is the outer event horizon and the other is the inner Cauchy horizon. Can we construct static and spherically symmetric black hole solutions with N horizons and M singularities? The de Sitter cosmos has only one apparent horizon. Can we construct cosmos solutions with N horizons? In this article, we present the static and spherically symmetric black hole and cosmos solutions with N horizons and M singularities in the vector-tensor theories. Following these motivations, we also construct the black hole solutions with a firewall. The deviation of these black hole solutions from the usual ones can be potentially tested by future measurements of gravitational waves or the black hole continuum spectrum.
Theory of inner product vector and its application to multi-location damage detection
International Nuclear Information System (INIS)
Wang Le; Yang Zhichun; Zhang Muyu; Waters, T P
2011-01-01
Structural damage detection methods using time domain vibration responses have shown appeal in recent years. In previous papers by the authors, the inner product vector (IPV) was proposed as a damage detection algorithm which uses cross correlation functions between vibration responses under white noise excitation or band pass white noise excitation. The proposed algorithm was verified by some simulative and experimental examples featuring a single damage location. However, damage at multiple locations was not considered. Therefore, this paper extends the application of IPV-based structural damage detection to the problem of multiple damage locations. Firstly, the theory of the IPV and its implementation in a damage detection context is reviewed. Then, two strategies for detecting multiple damages utilizing IPV are proposed. Finally, a damage detection experiment of a honeycomb sandwich composite beam is adopted to illustrate the feasibility and effectiveness of the IPV-based damage detection method.
Process service quality evaluation based on Dempster-Shafer theory and support vector machine.
Pei, Feng-Que; Li, Dong-Bo; Tong, Yi-Fei; He, Fei
2017-01-01
Human involvement influences traditional service quality evaluations, which triggers an evaluation's low accuracy, poor reliability and less impressive predictability. This paper proposes a method by employing a support vector machine (SVM) and Dempster-Shafer evidence theory to evaluate the service quality of a production process by handling a high number of input features with a low sampling data set, which is called SVMs-DS. Features that can affect production quality are extracted by a large number of sensors. Preprocessing steps such as feature simplification and normalization are reduced. Based on three individual SVM models, the basic probability assignments (BPAs) are constructed, which can help the evaluation in a qualitative and quantitative way. The process service quality evaluation results are validated by the Dempster rules; the decision threshold to resolve conflicting results is generated from three SVM models. A case study is presented to demonstrate the effectiveness of the SVMs-DS method.
Process service quality evaluation based on Dempster-Shafer theory and support vector machine.
Directory of Open Access Journals (Sweden)
Feng-Que Pei
Full Text Available Human involvement influences traditional service quality evaluations, which triggers an evaluation's low accuracy, poor reliability and less impressive predictability. This paper proposes a method by employing a support vector machine (SVM and Dempster-Shafer evidence theory to evaluate the service quality of a production process by handling a high number of input features with a low sampling data set, which is called SVMs-DS. Features that can affect production quality are extracted by a large number of sensors. Preprocessing steps such as feature simplification and normalization are reduced. Based on three individual SVM models, the basic probability assignments (BPAs are constructed, which can help the evaluation in a qualitative and quantitative way. The process service quality evaluation results are validated by the Dempster rules; the decision threshold to resolve conflicting results is generated from three SVM models. A case study is presented to demonstrate the effectiveness of the SVMs-DS method.
Neutron powder diffraction and theory-aided structure refinement of rubidium and cesium ureate
Energy Technology Data Exchange (ETDEWEB)
Sterri, Kjersti B.; Deringer, Volker L.; Houben, Andreas; Jacobs, Philipp [RWTH Aachen Univ. (Germany). Inst. of Inorganic Chemistry; Kumar, Chogondahalli M.N. [Forschungszentrum Juelich GmbH, Juelich Centre for Neutron Science (JCNS), Outstation at SNS, Oak Ridge National Laboratory, Oak Ridge, TN (United States); Oak Ridge National Laboratory, TN (United States). Chemical and Engineering Materials Div.; Dronskowski, Richard [RWTH Aachen Univ. (Germany). Inst. of Inorganic Chemistry; RWTH Aachen Univ. (Germany). Juelich-Aachen Research Alliance (JARA-HPC)
2016-08-01
Urea (CN{sub 2}H{sub 4}O) is a fundamental biomolecule whose derivatives are abundant throughout chemistry. Among the latter, rubidium ureate (RbCN{sub 2}H{sub 3}O) and its cesium analog (CsCN{sub 2}H{sub 3}O) have been described only very recently and form the first structurally characterized salts of deprotonated urea. Here, we report on a neutron diffraction study on the aforementioned alkaline-metal ureates, which affords the positions for all hydrogen atoms (including full anisotropic displacement tensors) and thus allows us to gain fundamental insights into the hydrogen-bonding networks in the title compounds. The structure refinements of the experimental neutron data proceeded successfully using starting parameters from ab initio simulations of atomic positions and anisotropic displacement parameters. Such joint experimental-theoretical refinement procedures promise significant practical potential in cases where complex solids (organic, organometallic, framework materials) are studied by powder diffraction.
Low-energy electron diffraction experiment, theory and surface structure determination
Hove, Michel A; Chan, Chi-Ming
1986-01-01
Surface crystallography plays the same fundamental role in surface science which bulk crystallography has played so successfully in solid-state physics and chemistry. The atomic-scale structure is one of the most important aspects in the understanding of the behavior of surfaces in such widely diverse fields as heterogeneous catalysis, microelectronics, adhesion, lubrication, cor rosion, coatings, and solid-solid and solid-liquid interfaces. Low-Energy Electron Diffraction or LEED has become the prime tech nique used to determine atomic locations at surfaces. On one hand, LEED has yielded the most numerous and complete structural results to date (almost 200 structures), while on the other, LEED has been regarded as the "technique to beat" by a variety of other surface crystallographic methods, such as photoemission, SEXAFS, ion scattering and atomic diffraction. Although these other approaches have had impressive successes, LEED has remained the most productive technique and has shown the most versatility...
Computer Simulation of Diffraction Patterns.
Dodd, N. A.
1983-01-01
Describes an Apple computer program (listing available from author) which simulates Fraunhofer and Fresnel diffraction using vector addition techniques (vector chaining) and allows user to experiment with different shaped multiple apertures. Graphics output include vector resultants, phase difference, diffraction patterns, and the Cornu spiral…
Mocella, V; Freund, A K; Hoszowska, J; Zhang, L; Epelboin, Y
2001-01-01
The aim of this work is to generate the rocking curves of monochromators exposed to heat load in synchrotron radiation beams with a computer code performing diffraction calculations based on the theory of Takagi and Taupin. The model study starts with the calculation of deformation by finite element analysis and from an accurate characterization of the incident wave and includes the simulation of the wavefront propagation between the first and the second crystal (analyzer) of a double crystal monochromator. A monochromatic plane wave as well as a polychromatic spherical wave approach is described. The theoretical predictions of both methods are compared with experimental data measured in Bragg geometry and critically discussed.
International Nuclear Information System (INIS)
Mocella, V.; Ferrero, C.; Freund, A.K.; Hoszowska, J.; Zhang, L.; Epelboin, Y.
2001-01-01
The aim of this work is to generate the rocking curves of monochromators exposed to heat load in synchrotron radiation beams with a computer code performing diffraction calculations based on the theory of Takagi and Taupin. The model study starts with the calculation of deformation by finite element analysis and from an accurate characterization of the incident wave and includes the simulation of the wavefront propagation between the first and the second crystal (analyzer) of a double crystal monochromator. A monochromatic plane wave as well as a polychromatic spherical wave approach is described. The theoretical predictions of both methods are compared with experimental data measured in Bragg geometry and critically discussed
Quantum phase space theory for the calculation of v·j vector correlations
International Nuclear Information System (INIS)
Hall, G.E.
1995-01-01
The quantum state-counting phase space theory commonly used to describe barrierless dissociation is recast in a helicity basis to calculate photofragment v·j correlations. Counting pairs of fragment states with specific angular momentum projection numbers on the relative velocity provides a simple connection between angular momentum conservation and the v·j correlation, which is not so evident in the conventional basis for phase space state counts. The upper bound on the orbital angular momentum, l, imposed by the centrifugal barrier cannot be included simply in the helicity basis, where l is not a good quantum number. Two approaches for a quantum calculation of the v·j correlation are described to address this point. An application to the photodissociation of NCCN is consistent with recent classical phase space calculations of Cline and Klippenstein. The observed vector correlation exceeds the phase space theory prediction. The authors take this as evidence of incomplete mixing of the K states of the linear parent molecule at the transition state, corresponding to an evolution of the body-fixed projection number K into the total helicity of the fragment pair state. The average over a thermal distribution of parent angular momentum in the special case of a linear molecule does not significantly reduce the v·j correlation below that computed for total J = 0
Bykov, Dmitry A; Doskolovich, Leonid L; Soifer, Victor A
2017-01-23
We study resonances of guided-mode resonant gratings in conical mounting. By developing 2D time-dependent coupled-mode theory we obtain simple approximations of the transmission and reflection coefficients. Being functions of the incident light's frequency and in-plane wave vector components, the obtained approximations can be considered as multi-variable generalizations of the Fano line shape. We show that the approximations are in good agreement with the rigorously calculated transmission and reflection spectra. We use the developed theory to investigate angular tolerances of the considered structures and to obtain mode excitation conditions. In particular, we obtain the cross-polarization mode excitation conditions in the case of conical mounting.
International Nuclear Information System (INIS)
Streek, Jacco van de; Neumann, Marcus A.
2014-01-01
The accuracy of 215 experimental organic crystal structures from powder diffraction data is validated against a dispersion-corrected density functional theory method. In 2010 we energy-minimized 225 high-quality single-crystal (SX) structures with dispersion-corrected density functional theory (DFT-D) to establish a quantitative benchmark. For the current paper, 215 organic crystal structures determined from X-ray powder diffraction (XRPD) data and published in an IUCr journal were energy-minimized with DFT-D and compared to the SX benchmark. The on average slightly less accurate atomic coordinates of XRPD structures do lead to systematically higher root mean square Cartesian displacement (RMSCD) values upon energy minimization than for SX structures, but the RMSCD value is still a good indicator for the detection of structures that deserve a closer look. The upper RMSCD limit for a correct structure must be increased from 0.25 Å for SX structures to 0.35 Å for XRPD structures; the grey area must be extended from 0.30 to 0.40 Å. Based on the energy minimizations, three structures are re-refined to give more precise atomic coordinates. For six structures our calculations provide the missing positions for the H atoms, for five structures they provide corrected positions for some H atoms. Seven crystal structures showed a minor error for a non-H atom. For five structures the energy minimizations suggest a higher space-group symmetry. For the 225 SX structures, the only deviations observed upon energy minimization were three minor H-atom related issues. Preferred orientation is the most important cause of problems. A preferred-orientation correction is the only correction where the experimental data are modified to fit the model. We conclude that molecular crystal structures determined from powder diffraction data that are published in IUCr journals are of high quality, with less than 4% containing an error in a non-H atom
The use of diffraction efficiency theory in the design of soft x-ray monochromators
International Nuclear Information System (INIS)
Padmore, H.A.; Martynov, V.; Hollis, K.; Mount Vernon Hospital, Northwood
1993-01-01
In general, the diffraction efficiency of gratings is limited by the constraints imposed by the type of geometry used to scan the photon energy. In the simplest example, the spherical grating monochromator (SGM), the deviation angle, the grating groove width and depth and the groove density are all constrained by considerations of the maximum photon energy and the tuning range for individual gratings. We have examined the case in which these parameters are unconstrained, resulting in predictions of the ultimate performance of lamellar type gratings for groove densities from 300 to 2400 1/mm for gold and nickel coatings. The differential method of Neviere et al was used for modeling the behavior of the gratings and justification is presented for this by rigorous comparison with measurements. The implications of these results for future monochromators based on a variable included angle geometry are discussed
International Nuclear Information System (INIS)
Berger, C.
1995-11-01
Recent experiments on total hadronic cross sections are reviewed together with results on photo- and electroproduction of vector mesons. New data on diffractive deep inelastic scattering shed light on the nature of the pomeron. (orig.)
Lyapunov vectors and assimilation in the unstable subspace: theory and applications
International Nuclear Information System (INIS)
Palatella, Luigi; Carrassi, Alberto; Trevisan, Anna
2013-01-01
Based on a limited number of noisy observations, estimation algorithms provide a complete description of the state of a system at current time. Estimation algorithms that go under the name of assimilation in the unstable subspace (AUS) exploit the nonlinear stability properties of the forecasting model in their formulation. Errors that grow due to sensitivity to initial conditions are efficiently removed by confining the analysis solution in the unstable and neutral subspace of the system, the subspace spanned by Lyapunov vectors with positive and zero exponents, while the observational noise does not disturb the system along the stable directions. The formulation of the AUS approach in the context of four-dimensional variational assimilation (4DVar-AUS) and the extended Kalman filter (EKF-AUS) and its application to chaotic models is reviewed. In both instances, the AUS algorithms are at least as efficient but simpler to implement and computationally less demanding than their original counterparts. As predicted by the theory when error dynamics is linear, the optimal subspace dimension for 4DVar-AUS is given by the number of positive and null Lyapunov exponents, while the EKF-AUS algorithm, using the same unstable and neutral subspace, recovers the solution of the full EKF algorithm, but dealing with error covariance matrices of a much smaller dimension and significantly reducing the computational burden. Examples of the application to a simplified model of the atmospheric circulation and to the optimal velocity model for traffic dynamics are given. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (paper)
Energy Technology Data Exchange (ETDEWEB)
Kubo, R; Yokoyama, K
1974-11-01
The purpose of this work is to study the structure of c-number gauge transformation in connection with renormalization problem. In the wide theory of neutral vector fields, there is the gauge structure described essentially by free Lagrangian density. The c-number gauge transformation makes the Lagrangian invariant correspondingly to the usual case of quantum electrodynamics. The c-number transformation can be used to derive relationships among all relevant renormalization constants in the case of interacting fields. In the presence of interaction, total Lagrangian density L is written as L=L/sub 0/+L/sub 1/+L/sub 2/, where L/sub 1/ is given from matter-field Lagrangian density, and L/sub 2/ denotes necessary additional counter terms. In order to conserve the gauge structure, the form of L is invariant under the gauge transformation. Since L matter is self-adjoining, L/sub 1/ remains invariant by itself under the transformation. The form of L/sub 2/ is finally given from the observation that L/sub 3/ cannot contain wave-function renormalization constants. Since L/sub 2/ is invariant under q-number gauge transformation, this transformation in unrenormalized form makes the present L form-invariant. Therefore, together with the above results, auxiliary fields produce the q-number gauge transformation for renormalized fields.
Directory of Open Access Journals (Sweden)
Matthew D Sacchet
2015-02-01
Full Text Available Recently there has been considerable interest in understanding brain networks in Major Depressive Disorder (MDD. Neural pathways can be tracked in the living brain using diffusion weighted imaging (DWI; graph theory can then be used to study properties of the resulting fiber networks. To date, global abnormalities have not been reported in tractography-based graph metrics in MDD, so we used a machine learning approach based on ‘support vector machines’ to differentiate depressed from healthy individuals based on multiple brain network properties. We also assessed how important specific graph metrics were for this differentiation. Finally, we conducted a local graph analysis to identify abnormal connectivity at specific nodes of the network. We were able to classify depression using whole-brain graph metrics. Small-worldness was the most useful graph metric for classification. The right pars orbitalis, right inferior parietal cortex, and left rostral anterior cingulate all showed abnormal network connectivity in MDD. This is the first use of structural global graph metrics to classify depressed individuals. These findings highlight the importance of future research to understand network properties in depression across imaging modalities, improve classification results, and relate network alterations to psychiatric symptoms, medication, and co-morbidities.
Sacchet, Matthew D; Prasad, Gautam; Foland-Ross, Lara C; Thompson, Paul M; Gotlib, Ian H
2015-01-01
Recently, there has been considerable interest in understanding brain networks in major depressive disorder (MDD). Neural pathways can be tracked in the living brain using diffusion-weighted imaging (DWI); graph theory can then be used to study properties of the resulting fiber networks. To date, global abnormalities have not been reported in tractography-based graph metrics in MDD, so we used a machine learning approach based on "support vector machines" to differentiate depressed from healthy individuals based on multiple brain network properties. We also assessed how important specific graph metrics were for this differentiation. Finally, we conducted a local graph analysis to identify abnormal connectivity at specific nodes of the network. We were able to classify depression using whole-brain graph metrics. Small-worldness was the most useful graph metric for classification. The right pars orbitalis, right inferior parietal cortex, and left rostral anterior cingulate all showed abnormal network connectivity in MDD. This is the first use of structural global graph metrics to classify depressed individuals. These findings highlight the importance of future research to understand network properties in depression across imaging modalities, improve classification results, and relate network alterations to psychiatric symptoms, medication, and comorbidities.
Wolstenholme, E Œ
1978-01-01
Elementary Vectors, Third Edition serves as an introductory course in vector analysis and is intended to present the theoretical and application aspects of vectors. The book covers topics that rigorously explain and provide definitions, principles, equations, and methods in vector analysis. Applications of vector methods to simple kinematical and dynamical problems; central forces and orbits; and solutions to geometrical problems are discussed as well. This edition of the text also provides an appendix, intended for students, which the author hopes to bridge the gap between theory and appl
Hu, Lingfei; Chang, Guangcai; Liu, Peng; Zhou, Liang
2015-07-01
The multilayer Laue lens (MLL) is essentially a linear zone plate with large aspect ratio, which can theoretically focus hard X-rays to well below 1 nm with high efficiency when ideal structures are used. However, the focusing performance of a MLL depends heavily on the quality of the layers, especially the layer placement error which always exists in real MLLs. Here, a dynamical modeling approach, based on the coupled wave theory, is proposed to study the focusing performance of a MLL with layer placement error. The result of simulation shows that this method can be applied to various forms of layer placement error.
Directory of Open Access Journals (Sweden)
María Jesús Algar
2013-01-01
Full Text Available An efficient approach for the analysis of surface conformed reflector antennas fed arbitrarily is presented. The near field in a large number of sampling points in the aperture of the reflector is obtained applying the Geometrical Theory of Diffraction (GTD. A new technique named Master Points has been developed to reduce the complexity of the ray-tracing computations. The combination of both GTD and Master Points reduces the time requirements of this kind of analysis. To validate the new approach, several reflectors and the effects on the radiation pattern caused by shifting the feed and introducing different obstacles have been considered concerning both simple and complex geometries. The results of these analyses have been compared with the Method of Moments (MoM results.
On the treatment of primary extinction in diffraction theories based on intensity coupling
International Nuclear Information System (INIS)
Schneider, J.R.; Goncalves, O.D.; Graf, H.A.
1988-01-01
Czochralski-grown silicon crystals of approximately 10 cm diameter and 1 cm thickness have been annealed at 1470 K in order to create a homogeneous defect structure, which is a basic condition for all statistical treatment of extinction. Absolute values of the integrated reflecting power of the 220, 440 and 660 reflections have been measured with 0.0392 A γ-radiation in symmetrical Laue geometry for sample thicknesses between 1 and 3 cm. The amount of extinction in the experimental data varies between γ≅0.95 and γ≅0.05. Darwin's extinction theory has been used to describe the thickness dependence of the data sets. Despite some shortcomings of the model, it is shown that the assumption of a physically unrealistic Lorentzian mosaic distribution models the effect of primary extinction in an extinction theory based on the energy-transfer model. The sharp central part of the Lorentzian distribution produces a reduction of the effective sample thickness due to primary extinction, whereas the wings of the distribution dominate the correction for secondary extinction in the remaining part of the sample. A more flexible mosaic distribution function is proposed, which should be useful in cases of severe extinction. (orig.)
International Nuclear Information System (INIS)
Den Besten, J.L.; Jamieson, D.N.; Allen, L.J.
1998-01-01
The Lindhard theory on ion channeling in crystals has been widely accepted throughout ion beam analysis for use in simulating such experiments. The simulations use a Monte Carlo method developed by Barret, which utilises the classical 'billiard ball' theory of ions 'bouncing' between planes or tubes of atoms in the crystal. This theory is not valid for 'thin' crystals where the planes or strings of atoms can no longer be assumed to be of infinite proportions. We propose that a theory similar to that used for high energy electron diffraction can be applied to MeV ions, especially protons, in thin crystals to simulate the intensities of transmission channeling and of RBS spectra. The diffraction theory is based on a Bloch wave solution of the Schroedinger equation for an ion passing through the periodic crystal potential. The widely used universal potential for proton-nucleus scattering is used to construct the crystal potential. Absorption due to thermal diffuse scattering is included. Experimental parameters such as convergence angle, beam tilt and scanning directions are considered in our calculations. Comparison between theory and experiment is encouraging and suggests that further work is justified. (authors)
Observables of QCD diffraction
Mieskolainen, Mikael; Orava, Risto
2017-03-01
A new combinatorial vector space measurement model is introduced for soft QCD diffraction. The model independent mathematical construction resolves experimental complications; the theoretical framework of the approach includes the Good-Walker view of diffraction, Regge phenomenology together with AGK cutting rules and random fluctuations.
Holographic analysis of diffraction structure factors
International Nuclear Information System (INIS)
Marchesini, S.; Bucher, J.J.; Shuh, D.K.; Fabris, L.; Press, M.J.; West, M.W.; Hussain, Z.; Mannella, N.; Fadley, C.S.; Van Hove, M.A.; Stolte, W.C.
2002-01-01
We combine the theory of inside-source/inside-detector x-ray fluorescence holography and Kossel lines/ x ray standing waves in kinematic approximation to directly obtain the phases of the diffraction structure factors. The influence of Kossel lines and standing waves on holography is also discussed. We obtain partial phase determination from experimental data obtaining the sign of the real part of the structure factor for several reciprocal lattice vectors of a vanadium crystal
An application of vector coherent state theory to the SO95) proton-neutron quasi-spin algebra
International Nuclear Information System (INIS)
Berej, W.
2002-01-01
Vector coherent state theory (VCS), developed for computing Lie group and Lie algebra representations and coupling coefficients, has been used for many groups of interest an actual physics applications. It is shown that VCS construction of a rotor type can be performed for the SO(5) ∼ Sp(4) quasi-spin group where the relevant physical subgroup SU(2) x U(1) is generalized by the isospin operators and the number of particle operators [ru
Unified Theory for Decoding the Signals from X-Ray Florescence and X-Ray Diffraction of Mixtures.
Chung, Frank H
2017-05-01
For research and development or for solving technical problems, we often need to know the chemical composition of an unknown mixture, which is coded and stored in the signals of its X-ray fluorescence (XRF) and X-ray diffraction (XRD). X-ray fluorescence gives chemical elements, whereas XRD gives chemical compounds. The major problem in XRF and XRD analyses is the complex matrix effect. The conventional technique to deal with the matrix effect is to construct empirical calibration lines with standards for each element or compound sought, which is tedious and time-consuming. A unified theory of quantitative XRF analysis is presented here. The idea is to cancel the matrix effect mathematically. It turns out that the decoding equation for quantitative XRF analysis is identical to that for quantitative XRD analysis although the physics of XRD and XRF are fundamentally different. The XRD work has been published and practiced worldwide. The unified theory derives a new intensity-concentration equation of XRF, which is free from the matrix effect and valid for a wide range of concentrations. The linear decoding equation establishes a constant slope for each element sought, hence eliminating the work on calibration lines. The simple linear decoding equation has been verified by 18 experiments.
Shreeman, Paul K.
The statistical dynamical diffraction theory, which has been initially developed by late Kato remained in obscurity for many years due to intense and difficult mathematical treatment that proved to be quite challenging to implement and apply. With assistance of many authors in past (including Bushuev, Pavlov, Pungeov, and among the others), it became possible to implement this unique x-ray diffraction theory that combines the kinematical (ideally imperfect) and dynamical (the characteristically perfect diffraction) into a single system of equations controlled by two factors determined by long range order and correlation function within the structure. The first stage is completed by the publication (Shreeman and Matyi, J. Appl. Cryst., 43, 550 (2010)) demonstrating the functionality of this theory with new modifications hence called modified statistical dynamical diffraction theory (mSDDT). The foundation of the theory is also incorporated into this dissertation, and the next stage of testing the model against several ion-implanted SiGe materials has been published: (Shreeman and Matyi, physica status solidi (a)208(11), 2533-2538, 2011). The dissertation with all the previous results summarized, dives into comprehensive analysis of HRXRD analyses complete with several different types of reflections (symmetrical, asymmetrical and skewed geometry). The dynamical results (with almost no defects) are compared with well-known commercial software. The defective materials, to which commercially available modeling software falls short, is then characterized and discussed in depth. The results will exemplify the power of the novel approach in the modified statistical dynamical diffraction theory: Ability to detect and measure defective structures qualitatively and quantitatively. The analysis will be compared alongside with TEM data analysis for verification and confirmation. The application of this theory will accelerate the ability to quickly characterize the relaxed
van de Streek, Jacco; Neumann, Marcus A
2014-12-01
In 2010 we energy-minimized 225 high-quality single-crystal (SX) structures with dispersion-corrected density functional theory (DFT-D) to establish a quantitative benchmark. For the current paper, 215 organic crystal structures determined from X-ray powder diffraction (XRPD) data and published in an IUCr journal were energy-minimized with DFT-D and compared to the SX benchmark. The on average slightly less accurate atomic coordinates of XRPD structures do lead to systematically higher root mean square Cartesian displacement (RMSCD) values upon energy minimization than for SX structures, but the RMSCD value is still a good indicator for the detection of structures that deserve a closer look. The upper RMSCD limit for a correct structure must be increased from 0.25 Å for SX structures to 0.35 Å for XRPD structures; the grey area must be extended from 0.30 to 0.40 Å. Based on the energy minimizations, three structures are re-refined to give more precise atomic coordinates. For six structures our calculations provide the missing positions for the H atoms, for five structures they provide corrected positions for some H atoms. Seven crystal structures showed a minor error for a non-H atom. For five structures the energy minimizations suggest a higher space-group symmetry. For the 225 SX structures, the only deviations observed upon energy minimization were three minor H-atom related issues. Preferred orientation is the most important cause of problems. A preferred-orientation correction is the only correction where the experimental data are modified to fit the model. We conclude that molecular crystal structures determined from powder diffraction data that are published in IUCr journals are of high quality, with less than 4% containing an error in a non-H atom.
Three-vector, statistical theory of errors and the Planck constant
International Nuclear Information System (INIS)
Demers, P.
1981-01-01
The paper confirms an assertion of Pappas: T3 is not an Euclidean vector, it behaves like delta 3, a statistical error made of 3 component errors. T3 and delta 3 are 3-vectors, obeying Poincare's group for rotation, not for translation. The idea of T3 adds to the affinities between time, entropy, probability and Planck's constant, besides offering a proof of the non-existence of tachyons. (author)
van Haver, S.; Janssen, A. J. E. M.
2013-07-01
The computational methods for the diffraction integrals that occur in the Extended Nijboer-Zernike (ENZ-) approach to circular, aberrated, defocused optical systems are reviewed and updated. In the ENZ-approach, the Debye approximation of Rayleigh's integral for the through-focus, complex, point-spread function is evaluated in semi-analytic form. To this end, the generalized pupil function, comprising phase aberrations as well as amplitude non-uniformities, is assumed to be expanded into a series of Zernike circle polynomials, and the contribution of each of these Zernike terms to the diffraction integral is expressed in the form of a rapidly converging series (containing power functions and/or Bessel functions of various kinds). The procedure of expressing the through-focus point-spread function in terms of Zernike expansion coefficients of the pupil function can be reversed and has led to the ENZ-method of retrieval of pupil functions from measured through-focus (inte! nsity) point-spread functions. The review and update concern the computation for systems ranging from as basic as having low NA and small defocus parameter to high-NA systems, with vector fields and polarization, meant for imaging of extended objects into a multi-layered focal region. In the period 2002-2010, the evolution of the form of the diffraction integral (DI) was dictated by the agenda of the ENZ-team in which a next instance of the DI was handled by amending the computation scheme of the previous one. This has resulted into a variety of ad hoc measures, lack of transparency of the schemes, and sometimes prohibitively slow computer codes. It is the aim of the present paper to reconstruct the whole building of computation methods, using consistently more advanced mathematical tools. These tools are -explicit Zernike expansion of the focal factor in the DI, -Clebsch-Gordan coefficients for the omnipresent problem of linearizing products ofZernike circle polynomials, -recursions for Bessel
Tsang, Leung; Chan, Chi Hou; Kong, Jin AU; Joseph, James
1992-01-01
Complete polarimetric signatures of a canopy of dielectric cylinders overlying a homogeneous half space are studied with the first and second order solutions of the vector radiative transfer theory. The vector radiative transfer equations contain a general nondiagonal extinction matrix and a phase matrix. The energy conservation issue is addressed by calculating the elements of the extinction matrix and the elements of the phase matrix in a manner that is consistent with energy conservation. Two methods are used. In the first method, the surface fields and the internal fields of the dielectric cylinder are calculated by using the fields of an infinite cylinder. The phase matrix is calculated and the extinction matrix is calculated by summing the absorption and scattering to ensure energy conservation. In the second method, the method of moments is used to calculate the elements of the extinction and phase matrices. The Mueller matrix based on the first order and second order multiple scattering solutions of the vector radiative transfer equation are calculated. Results from the two methods are compared. The vector radiative transfer equations, combined with the solution based on method of moments, obey both energy conservation and reciprocity. The polarimetric signatures, copolarized and depolarized return, degree of polarization, and phase differences are studied as a function of the orientation, sizes, and dielectric properties of the cylinders. It is shown that second order scattering is generally important for vegetation canopy at C band and can be important at L band for some cases.
Wheeler, J; Mariani, E; Piazolo, S; Prior, D J; Trimby, P; Drury, M R
2009-03-01
The Weighted Burgers Vector (WBV) is defined here as the sum, over all types of dislocations, of [(density of intersections of dislocation lines with a map) x (Burgers vector)]. Here we show that it can be calculated, for any crystal system, solely from orientation gradients in a map view, unlike the full dislocation density tensor, which requires gradients in the third dimension. No assumption is made about gradients in the third dimension and they may be non-zero. The only assumption involved is that elastic strains are small so the lattice distortion is entirely due to dislocations. Orientation gradients can be estimated from gridded orientation measurements obtained by EBSD mapping, so the WBV can be calculated as a vector field on an EBSD map. The magnitude of the WBV gives a lower bound on the magnitude of the dislocation density tensor when that magnitude is defined in a coordinate invariant way. The direction of the WBV can constrain the types of Burgers vectors of geometrically necessary dislocations present in the microstructure, most clearly when it is broken down in terms of lattice vectors. The WBV has three advantages over other measures of local lattice distortion: it is a vector and hence carries more information than a scalar quantity, it has an explicit mathematical link to the individual Burgers vectors of dislocations and, since it is derived via tensor calculus, it is not dependent on the map coordinate system. If a sub-grain wall is included in the WBV calculation, the magnitude of the WBV becomes dependent on the step size but its direction still carries information on the Burgers vectors in the wall. The net Burgers vector content of dislocations intersecting an area of a map can be simply calculated by an integration round the edge of that area, a method which is fast and complements point-by-point WBV calculations.
A lifting-surface theory solution for the diffraction of internal sound sources by an engine nacelle
Martinez, R.
1986-07-01
Lifting-surface theory is used to solve the problem of diffraction by a rigid open-ended pipe of zero thickness and finite length, with application to the prediction of acoustic insertion-loss performance for the encasing structure of a ducted propeller or turbofan. An axisymmetric situation is assumed, and the incident field due to a force applied directly to the fluid in the cylinder axial direction is used. A virtual-source distribution of unsteady dipoles is found whose integrated component of radial velocity is set to cancel that of the incident field over the surface. The calculated virtual load is verified by whether its effect on the near-field input power at the actual source is consistent with the far-field power radiated by the system, a balance which is possible if the no-flow-through boundary condition has been satisfied over the rigid pipe surface such that the velocity component of the acoustic intensity is zero.
Grimbach, A; Knechtli, F; Palombi, Filippo
2008-01-01
We calculate analytically the improvement coefficients of the static axial and vector currents in O(a) improved lattice QCD at one-loop order of perturbation theory. The static quark is described by the hypercubic action, previously introduced in the literature in order to improve the signal-to-noise ratio of static observables. Within a Schroedinger Functional setup, we derive the Feynman rules of the hypercubic link in time-momentum representation. The improvement coefficients are obtained from on-shell correlators of the static axial and vector currents. As a by-product, we localise the minimum of the static self-energy as a function of the smearing parameters of the action at one-loop order and show that the perturbative minimum is close to its non-perturbative counterpart.
A representation theory for a class of vector autoregressive models for fractional processes
DEFF Research Database (Denmark)
Johansen, Søren
2008-01-01
Based on an idea of Granger (1986), we analyze a new vector autoregressive model defined from the fractional lag operator 1-(1-L)^{d}. We first derive conditions in terms of the coefficients for the model to generate processes which are fractional of order zero. We then show that if there is a un...... root, the model generates a fractional process X(t) of order d, d>0, for which there are vectors ß so that ß'X(t) is fractional of order d-b, 0...
Dynamical diffraction in periodic multilayers
Sears, V F
1997-01-01
Exact reflectivity curves are calculated numerically for various periodic multilayers using the optical matrix method in order to test the dynamical theory of diffraction. The theory is generally valid for values of the bilayer thickness d up to about 100 A. For somewhat larger values of d, where the theory begins to break down, the initial discrepancy is in the phase of the oscillations in the wings of the peaks. For very large values of d, where the first-order Bragg peak approaches the edge of the mirror reflection, two general types of multilayers can be distinguished. In the first (typified in the present work by Ni/Ti), there is a large (30% or more) reduction in the actual value of the critical wave vector for total reflection while, in the second (typified here by Fe/Ge), there is very little reduction (3 % or so). The origin of these two very different types of behavior is explained. It is also shown that, within the dynamical theory of diffraction, the change in the position of the center of the Dar...
International Nuclear Information System (INIS)
Shabbir, Ghulam; Khan, Suhail; Ali, Amjad
2011-01-01
In this paper we classify spatially homogeneous rotating space-times according to their teleparallel Killing vector fields using direct integration technique. It turns out that the dimension of the teleparallel Killing vector fields is 5 or 10. In the case of 10 teleparallel Killing vector fields the space-time becomes Minkowski and all the torsion components are zero. Teleparallel Killing vector fields in this case are exactly the same as in general relativity. In the cases of 5 teleparallel Killing vector fields we get two more conservation laws in the teleparallel theory of gravitation. Here we also discuss some well-known examples of spatially homogeneous rotating space-times according to their teleparallel Killing vector fields. (general)
Energy Technology Data Exchange (ETDEWEB)
Hauke, Philipp [ICFO-Institut de Ciencies Fotoniques, Meditarranean Technology Park, E-08860 Castelldefels, Barcelona (Spain); Roscilde, Tommaso [Laboratoire de Physique, Ecole Normale Superieure de Lyon, 46 Allee d' Italie, F-69007 Lyon (France); Murg, Valentin; Ignacio Cirac, J; Schmied, Roman, E-mail: Philipp.Hauke@icfo.e [Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching (Germany)
2010-05-15
We investigate a system of frustrated hardcore bosons, modeled by an XY antiferromagnet on the spatially anisotropic triangular lattice, using Takahashi's modified spin-wave (MSW) theory. In particular, we implement ordering vector optimization on the ordered reference state of MSW theory, which leads to significant improvement of the theory and accounts for quantum corrections to the classically ordered state. The MSW results at zero temperature compare favorably to exact diagonalization (ED) and projected entangled-pair state (PEPS) calculations. The resulting zero-temperature phase diagram includes a one-dimensional (1D) quasi-ordered phase, a 2D Neel ordered phase and a 2D spiraling ordered phase. Strong indications coming from the ED and PEPS calculations, as well as from the breakdown of MSW theory, suggest that the various ordered or quasi-ordered phases are separated by spin-liquid phases with short-range correlations, in analogy to what has been predicted for the Heisenberg model on the same lattice. Within MSW theory, we also explore the finite-temperature phase diagram. In agreement with the Berezinskii-Kosterlitz-Thouless (BKT) theory, we find that zero-temperature long-range-ordered phases turn into quasi-ordered phases (up to a BKT transition temperature), while zero-temperature quasi-ordered phases become short-range correlated at finite temperature. These results show that, despite its simplicity, MSW theory is very well suited to describing ordered and quasi-ordered phases of frustrated XY spins (or, equivalently, of frustrated lattice bosons) both at zero and finite temperatures. While MSW theory, just as other theoretical methods, cannot describe spin-liquid phases, its breakdown provides a fast and reliable method for singling out Hamiltonians that may feature these intriguing quantum phases. We thus suggest a tool for guiding our search for interesting systems whose properties are necessarily studied with a physical quantum simulator
Representation theory of 2-groups on finite dimensional 2-vector spaces
Elgueta, Josep
2004-01-01
In this paper, the 2-category $\\mathfrak{Rep}_{{\\bf 2Mat}_{\\mathbb{C}}}(\\mathbb{G})$ of (weak) representations of an arbitrary (weak) 2-group $\\mathbb{G}$ on (some version of) Kapranov and Voevodsky's 2-category of (complex) 2-vector spaces is studied. In particular, the set of equivalence classes of representations is computed in terms of the invariants $\\pi_0(\\mathbb{G})$, $\\pi_1(\\mathbb{G})$ and $[\\alpha]\\in H^3(\\pi_0(\\mathbb{G}),\\pi_1(\\mathbb{G}))$ classifying $\\mathbb{G}$. Also the categ...
Kriegner, D.; Assali, S.; Belabbes, A.; Etzelstorfer, T.; Holy, V.; Schülli, T.U.; Bechstedt, F.; Bakkers, E.P.A.M.; Bauer, G.; Stangl, J.
2013-01-01
We present structural characterization of the wurtzite crystal structure of GaP nanowires, which were recently shown to have a direct electronic band gap. The structural parameters of the wurtzite phase do consist of two lattice parameters and one internal degree of freedom, determining the Ga-P bond length along the c direction. Using density functional theory calculations, we study the influence of the internal degree of freedom on the band structure. By synchrotron x-ray diffraction studie...
The self-mass of vector bosons in gravity-modified quantum field theories
International Nuclear Information System (INIS)
Poelt, P.
1985-01-01
The self-mass of the W-boson is calculated using a gravitational modified Weinberg-Salam theory with an anomalous magnetic moment assumed to be variable. The self-mass is shown to be finite with Gsub(N)sup(-1/2) (Gsub(N) Newton's gravitational constant) as the cutoff parameter. But only certain values of the anomalous magnetic moment yield a correct order of magnitude. Lowest order of perturbation theory gives complex solutions for these magnetic moments. Nevertheless, additional terms of higher perturbation theory will modify the equation for the magnetic moment and possibly lead to the definite magnetic moment of the W-boson of the non-modified Weinberg-Salam theory. (Auth.)
Kawai, Kotaro; Kuzuwata, Mitsuru; Sasaki, Tomoyuki; Noda, Kohei; Kawatsuki, Nobuhiro; Ono, Hiroshi
2014-12-01
Blazed vector grating liquid crystal (LC) cells, in which the directors of low-molar-mass LCs are antisymmetrically distributed, were fabricated by one-step exposure of an empty glass cell inner-coated with a photocrosslinkable polymer LC (PCLC) to UV light. By adopting a LC cell structure, twisted nematic (TN) and homogeneous (HOMO) alignments were obtained in the blazed vector grating LC cells. Moreover, the diffraction efficiency of the blazed vector grating LC cells was greatly improved by increasing the thickness of the device in comparison with that of a blazed vector grating with a thin film structure obtained in our previous study. In addition, the diffraction efficiency and polarization states of ±1st-order diffracted beams from the resultant blazed vector grating LC cells were controlled by designing a blazed pattern in the alignment films, and these diffraction properties were well explained on the basis of Jones calculus and the elastic continuum theory of nematic LCs.
International Nuclear Information System (INIS)
Suzuki, Yoshifumi; Chikaura, Yoshinori; Ando, Masami
2011-01-01
Recently, dark-field imaging (DFI) and bright-field imaging (BFI) have been proposed and applied to visualize X-ray refraction effects yielded in biomedical objects. In order to clarify the spatial resolution due to a crystal analyzer in Laue geometry, a program based on the Takagi-Taupin equation was modified to be used for carrying out simulations to evaluate the spatial resolution of images coming into a Laue angular analyzer (LAA). The calculation was done with a perfect plane wave for diffraction wave-fields, which corresponded to BFI, under the conditions of 35 keV and a diffraction index 440 for a 2100 μm thick LAA. As a result, the spatial resolution along the g-vector direction showed approximately 37.5 μm. 126 μm-thick LAA showed a spatial resolution better than 3.1 μm under the conditions of 13.7 keV and a diffraction index 220.
Energy Technology Data Exchange (ETDEWEB)
Kabashima, Y [Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, Yokohama 226-8502 (Japan)], E-mail: kaba@dis.titech.ac.jp
2008-01-15
A framework to analyze inference performance in densely connected single-layer feed-forward networks is developed for situations where a given data set is composed of correlated patterns. The framework is based on the assumption that the left and right singular value bases of the given pattern matrix are generated independently and uniformly from Haar measures. This assumption makes it possible to characterize the objective system by a single function of two variables which is determined by the eigenvalue spectrum of the cross-correlation matrix of the pattern matrix. Links to existing methods for analysis of perceptron learning and Gaussian linear vector channels and an application to a simple but nontrivial problem are also shown.
International Nuclear Information System (INIS)
Kabashima, Y
2008-01-01
A framework to analyze inference performance in densely connected single-layer feed-forward networks is developed for situations where a given data set is composed of correlated patterns. The framework is based on the assumption that the left and right singular value bases of the given pattern matrix are generated independently and uniformly from Haar measures. This assumption makes it possible to characterize the objective system by a single function of two variables which is determined by the eigenvalue spectrum of the cross-correlation matrix of the pattern matrix. Links to existing methods for analysis of perceptron learning and Gaussian linear vector channels and an application to a simple but nontrivial problem are also shown
Kabashima, Y.
2008-01-01
A framework to analyze inference performance in densely connected single-layer feed-forward networks is developed for situations where a given data set is composed of correlated patterns. The framework is based on the assumption that the left and right singular value bases of the given pattern matrix are generated independently and uniformly from Haar measures. This assumption makes it possible to characterize the objective system by a single function of two variables which is determined by the eigenvalue spectrum of the cross-correlation matrix of the pattern matrix. Links to existing methods for analysis of perceptron learning and Gaussian linear vector channels and an application to a simple but nontrivial problem are also shown.
Energy Technology Data Exchange (ETDEWEB)
Rao Weifeng [Department of Materials Science and Engineering, Rutgers University, 607 Taylor Road, Piscataway, NJ 08854 (United States); Khachaturyan, Armen G., E-mail: khach@jove.rutgers.edu [Department of Materials Science and Engineering, Rutgers University, 607 Taylor Road, Piscataway, NJ 08854 (United States)
2011-06-15
A phase field theory of proper displacive transformations is developed to address the microstructure evolution and its response to applied fields in decomposing and martensitic systems. The theory is based on the explicit equation for the non-equilibrium free energy function of the transformation strain obtained by a consistent separation of the total strain into transformation and elastic strains. The transformation strain is considered to be a relaxing long-range order parameter evolving in accordance with the system energetics rather than as a fixed material constant used in the conventional Eshelby theory of coherent inclusions. The elastic strain is defined as a coherency strain recovering the crystal lattice compatibility. The obtained free energy function of the transformation strain leads to the concepts of structural anisotropy and directional flexibility of low symmetry phases. The formulated vector model of displacive transformation makes apparent a similarity between proper displacive transformation and ferromagnetic/ferroelectric transformation and, in particular, a similarity between the structural anisotropy and magnetic/polar anisotropy of ferromagnetic/ferroelectric materials. It even predicts the feasibility of a glass-like structural state with unlimited directional flexibility of the transformation strain that is conceptually similar to a ferromagnetic glass. The thermodynamics of the equilibrium between low symmetry phases and the thermodynamic conditions leading to the formation of adaptive states are formulated.
Gato-Rivera, B.
1993-01-01
We use the Kontsevich-Miwa transform to relate the different pictures describing matter coupled to topological gravity in two dimensions: topological theories, Virasoro constraints on integrable hierarchies, and a DDK-type formalism. With the help of the Kontsevich-Miwa transform, we solve the Virasoro constraints on the KP hierarchy in terms of minimal models dressed with a (free) Liouville-like scalar. The dressing prescription originates in a topological (twisted N=2) theory. The Virasoro constraints are thus related to essentially the N=2 null state decoupling equations. The N=2 generators are constructed out of matter, the `Liouville' scalar, and $c=-2$ ghosts. By a `dual' construction involving the reparametrization $c=-26$ ghosts, the DDK dressing prescription is reproduced from the N=2 symmetry. As a by-product we thus observe that there are two ways to dress arbitrary $d\\leq1$ or $d\\geq25$ matter theory, that allow its embedding into a topological theory. By th e Kontsevich-Miwa transform, which intr...
International Nuclear Information System (INIS)
Hollands, S.
2001-01-01
We consider a self-interacting, perturbative Klein-Gordon quantum field in a curved spacetime admitting a Killing vector field. We show that the action of this spacetime symmetry on interacting field operators can be implemented by a Noether charge which arises, in a certain sense, as a surface integral over the time-component of some interacting Noether current-density associated with the Killing field. The proof of this involves the demonstration of a corresponding set of Ward identities. Our work is based on the perturbative construction by Brunetti and Fredenhagen (Commun. Math. Phys. 208 (2000) 623-661) of self-interacting quantum field theories in general globally hyperbolic spacetimes. (orig.)
International Nuclear Information System (INIS)
Rabie, A.; El-Gazzar, M.A.; Abul-Magd, A.Y.
1980-11-01
Using an assumption concerning the spin-orbit potential, it was possible to reduce the five amplitudes of scattering of spin-1 projectiles to two amplitudes. The summations over the partial waves were evaluated by the Regge pole technique. The resulting simple expressions were used to analyze the data of the Heidelberg group for polarized 6 Li ions scattered on 12 C, 16 O, 28 Si and 58 Ni to give a reasonable fitting both for the differential cross-section and vector polarization. (author)
Czech Academy of Sciences Publication Activity Database
Schäfer, R.; Hamann, C.; McCord, J.; Schultz, L.; Kamberský, Vladimír
2010-01-01
Roč. 12, č. 5 (2010), 053006/1-053006/10 ISSN 1367-2630 Institutional research plan: CEZ:AV0Z10100521 Keywords : magnetooptics * magnetic domains * light diffraction Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 3.849, year: 2010
Multitrace Deformations of Vector and Adjoint Theories and their Holographic Duals
Elitzur, S; Porrati, M; Rabinovici, Eliezer
2006-01-01
We present general methods to study the effect of multitrace deformations in conformal theories admitting holographic duals in Anti de Sitter space. In particular, we analyse the case that these deformations introduce an instability both in the bulk AdS space and in the boundary CFT. We also argue that multitrace deformations of the O(N) linear sigma model in three dimensions correspond to nontrivial time-dependent backgrounds in certain theories of infinitely many interacting massless fields on AdS_4, proposed years ago by Fradkin and Vasiliev. We point out that the phase diagram of a truly marginal large-N deformation has an infrared limit in which only an O(N) singlet field survives. We draw from this case lessons on the full string-theoretical interpretation of instabilities of the dual boundary theory and exhibit a toy model that resolves the instability of the O(N) model, generated by a marginal multitrace deformation. The resolution suggests that the instability may not survive in an appropriate UV com...
Colmont, Marie; Palatinus, Lukas; Huvé, Marielle; Kabbour, Houria; Saitzek, Sébastien; Djelal, Nora; Roussel, Pascal
2016-03-07
A new lanthanum oxide, KLa5O5(VO4)2, was synthesized using a flux growth technique that involved solid-state reaction under an air atmosphere at 900 °C. The crystal structure was solved and refined using an innovative approach recently established and based on three-dimensional (3D) electron diffraction data, using precession of the electron beam and then validated against Rietveld refinement and denisty functional theory (DFT) calculations. It crystallizes in a monoclinic unit cell with space group C2/m and has unit cell parameters of a = 20.2282(14) Å, b = 5.8639(4) Å, c = 12.6060(9) Å, and β = 117.64(1)°. Its structure is built on Cresnel-like two-dimensional (2D) units (La5O5) of 4*3 (OLa4) tetrahedra, which run parallel to (001) plane, being surrounded by isolated VO4 tetrahedra. Four isolated vanadate groups create channels that host K(+) ions. Substitution of K(+) cations by another alkali metal is possible, going from lithium to rubidium. Li substitution led to a similar phase with a primitive monoclinic unit cell. A complementary selected area electron diffraction (SAED) study highlighted diffuse streaks associated with stacking faults observed on high-resolution electron microscopy (HREM) images of the lithium compound. Finally, preliminary catalytic tests for ethanol oxidation are reported, as well as luminescence evidence. This paper also describes how solid-state chemists can take advantages of recent progresses in electron crystallography, assisted by DFT calculations and powder X-ray diffraction (PXRD) refinements, to propose new structural types with potential applications to the physicist community.
Strong lensing probability in TeVeS (tensor-vector-scalar) theory
Chen, Da-Ming
2008-01-01
We recalculate the strong lensing probability as a function of the image separation in TeVeS (tensor-vector-scalar) cosmology, which is a relativistic version of MOND (MOdified Newtonian Dynamics). The lens is modeled by the Hernquist profile. We assume an open cosmology with Ωb = 0.04 and ΩΛ = 0.5 and three different kinds of interpolating functions. Two different galaxy stellar mass functions (GSMF) are adopted: PHJ (Panter, Heavens and Jimenez 2004 Mon. Not. R. Astron. Soc. 355 764) determined from SDSS data release 1 and Fontana (Fontana et al 2006 Astron. Astrophys. 459 745) from GOODS-MUSIC catalog. We compare our results with both the predicted probabilities for lenses from singular isothermal sphere galaxy halos in LCDM (Lambda cold dark matter) with a Schechter-fit velocity function, and the observational results for the well defined combined sample of the Cosmic Lens All-Sky Survey (CLASS) and Jodrell Bank/Very Large Array Astrometric Survey (JVAS). It turns out that the interpolating function μ(x) = x/(1+x) combined with Fontana GSMF matches the results from CLASS/JVAS quite well.
International Nuclear Information System (INIS)
Borovikov, V.A.; Kinber, B.E.
1988-01-01
The heuristic criteria (HC) of validity of geometric optics (GO) and of the geometric theory of diffraction (GTD), suggested in [2-7, 13, 14] and based on identifying the physical volume occupied by the ray with the Fresnel volume (FV) introduced in these papers (i.e., the envelope of the first Fresnel zone), are analyzed. Numerous examples of HC invalidity are given, as well as the reasons. In particular, HC provide an incorrect answer for all GO problems with caustics, since in these problems there always exists a ray, whose FV is nonlocal and covers the FV of other rays. The HC are shown to be unsuitable for multiple ray GTD problems, as well as for the simplest problems of diffraction of a cylindrical wave by a half-plane and of a plane wave by a curved half-plane
Thomas, E. G. F.
2012-01-01
This paper deals with the theory of integration of scalar functions with respect to a measure with values in a, not necessarily locally convex, topological vector space. It focuses on the extension of such integrals from bounded measurable functions to the class of integrable functions, proving
Scattering of massless vector, tensor, and other particles in string theory at high energy
International Nuclear Information System (INIS)
Antonov, E.N.
1990-01-01
The 2 → 2 and 2 → 3 processes are studied in the multi-Regge kinematics for gluons and gravitons, the first excited states of the open and closed strings. The factorization of the corresponding amplitudes is demonstrated. Explicit relations generalizing the Low-Gribov expressions are obtained in the kinematics where one of the external particles is produced with small transverse momentum. The expressions in the limit α' → 0 coincide with the results of Yang-Mills theory and gravitation at high energies
Constantinides, E. D.; Marhefka, R. J.
1994-01-01
A uniform geometrical optics (UGO) and an extended uniform geometrical theory of diffraction (EUTD) are developed for evaluating high frequency electromagnetic (EM) fields within transition regions associated with a two and three dimensional smooth caustic of reflected rays and a composite shadow boundary formed by the caustic termination or the confluence of the caustic with the reflection shadow boundary (RSB). The UGO is a uniform version of the classic geometrical optics (GO). It retains the simple ray optical expressions of classic GO and employs a new set of uniform reflection coefficients. The UGO also includes a uniform version of the complex GO ray field that exists on the dark side of the smooth caustic. The EUTD is an extension of the classic uniform geometrical theory of diffraction (UTD) and accounts for the non-ray optical behavior of the UGO reflected field near caustics by using a two-variable transition function in the expressions for the edge diffraction coefficients. It also uniformly recovers the classic UTD behavior of the edge diffracted field outside the composite shadow boundary transition region. The approach employed for constructing the UGO/EUTD solution is based on a spatial domain physical optics (PO) radiation integral representation for the fields which is then reduced using uniform asymptotic procedures. The UGO/EUTD analysis is also employed to investigate the far-zone RCS problem of plane wave scattering from two and three dimensional polynomial defined surfaces, and uniform reflection, zero-curvature, and edge diffraction coefficients are derived. Numerical results for the scattering and diffraction from cubic and fourth order polynomial strips are also shown and the UGO/EUTD solution is validated by comparison to an independent moment method (MM) solution. The UGO/EUTD solution is also compared with the classic GO/UTD solution. The failure of the classic techniques near caustics and composite shadow boundaries is clearly
International Nuclear Information System (INIS)
Del Duca, V.; Marage, P.
1996-08-01
The general framework of diffractive deep inelastic scattering is introduced and reports given in the session on diffractive interactions at the international workshop on deep-inelastic scattering and related phenomena, Rome, April 1996, are presented. (orig.)
To the theory of X-ray and electron dynamic scattering in defect-containing crystals
International Nuclear Information System (INIS)
Chukhovskij, F.N.
1982-01-01
The novel approach to the X-ray and electron dynamic scattering theory based on the dynamic equations ''in the dispersion surface representation'' is formulated. The formally exact solution of two-wave diffraction scattering problem is obtained using the scattering matrix, the obvious expression for which is found. The general formulae describing the plane wave diffraction scattering in absorbing crystals in the weak distortion range has been obtained. The formulae allows one to determine the total change sign of the displacement function Δα(x,y)=2πg vectorx(R vector (r vector) 1 -R vector(r vector) 2 ) on the base of the known sign of the mean deflection magnitude in a crystal as a whole from the exact Bragg position (g vector - the inverse lattice vector, R vector - the displacement field vector, t - the crystal thickness, R vector(r vector) 1 =R vector (r) ar z=t, R vector(r vector) 2 =R(r) at z=0). In the quasiclassical approximation the formation of the diffraction image of a dislocation positioned in such a way that the dislocation axis is parallel to the diffraction reflection vector is considered for the incident plane and spherical waves
International Nuclear Information System (INIS)
Fuhrer, Andreas; Manohar, Aneesh V.; Waalewijn, Wouter J.
2011-01-01
Soft-collinear effective theory (SCET) is applied to compute electroweak radiative corrections to Higgs production via gauge boson fusion, qq→qqH. There are several novel features which make this process an interesting application of SCET: The amplitude is proportional to the Higgs vacuum expectation value, and so is not a gauge singlet amplitude. Standard resummation methods require a gauge singlet operator and do not apply here. The SCET analysis requires operators with both collinear and soft external fields, with the Higgs vacuum expectation value being described by an external soft φ field. There is a scalar soft-collinear transition operator in the SCET Lagrangian which contributes to the scattering amplitude, and is derived here.
Rakkapao, Suttida; Prasitpong, Singha; Arayathanitkul, Kwan
2016-01-01
This study investigated the multiple-choice test of understanding of vectors (TUV), by applying item response theory (IRT). The difficulty, discriminatory, and guessing parameters of the TUV items were fit with the three-parameter logistic model of IRT, using the parscale program. The TUV ability is an ability parameter, here estimated assuming…
International Nuclear Information System (INIS)
Kraus, H.G.
1991-01-01
This paper discusses methods for calculating Fraunhofer intensity fields resulting from diffraction through one- and two-dimensional apertures are presented. These methods are based on the geometric concept of finite elements and on Fourier and Abbe transforms. The geometry of the two-dimensional diffracting aperture(s) is based on biquadratic isoparametric elements, which are used to define aperture(s) of complex geometry. These elements are also used to build complex amplitude and phase functions across the aperture(s) which may be of continuous or discontinuous form. The transform integrals are accurately and efficiently integrated numerically using Gaussian quadrature. The power of these methods is most evident in two dimensions, where several examples are presented which include secondary obstructions, straight and curved secondary spider supports, multiple-mirror arrays, synthetic aperture arrays, segmented mirrors, apertures covered by screens, apodization, and phase plates. Typically, the finite element Abbe transform method results in significant gains in computational efficiency over the finite element Fourier transform method, but is also subject to some loss in generality
Diffractive DIS: Where are we?
International Nuclear Information System (INIS)
Nikolaev, N.N.
2001-01-01
A brief review of the modern QCD theory of diffractive DIS is given. The recent progress has been remarkably rapid, all the principal predictions from the color dipole approach to diffraction - the (Q 2 + m V 2 ) scaling, the pattern of SCHNC, shrinkage of the diffraction cone in hard diffractive DIS, the strong impact of longitudinal gluons in inclusive J/Ψ production at Tevatron - have been confirmed experimentally
Feil, D.; Feil, Dirk
1992-01-01
Quantum chemistry and the concepts used daily in chemistry are increasingly growing apart. Among the concepts that are able to bridge the gap between theory and experimental practice, electron density distribution has an important place. The study of this distribution has led to new developments in
Dorofeyev, Illarion
2008-08-01
The classical Kirchhoff theory of diffraction is extended to the case of real optical properties of a screen and its finite thickness. A spectral power density of diffracted electromagnetic fields by a hole in a thin film with real optical properties was calculated. The problem was solved by use of the vector Green theorems and related Green function of the boundary value problem. A spectral and spatial selectivity of the considered system was demonstrated. Diffracted patterns were calculated for the coherent and incoherent incident fields in case of holes array in a screen of perfect conductivity.
International Nuclear Information System (INIS)
Dorofeyev, Illarion
2008-01-01
The classical Kirchhoff theory of diffraction is extended to the case of real optical properties of a screen and its finite thickness. A spectral power density of diffracted electromagnetic fields by a hole in a thin film with real optical properties was calculated. The problem was solved by use of the vector Green theorems and related Green function of the boundary value problem. A spectral and spatial selectivity of the considered system was demonstrated. Diffracted patterns were calculated for the coherent and incoherent incident fields in case of holes array in a screen of perfect conductivity
Hernandez-Figueroa, Hugo E; Recami, Erasmo
2013-01-01
This continuation and extension of the successful book ""Localized Waves"" by the same editors brings together leading researchers in non-diffractive waves to cover the most important results in their field and as such is the first to present the current state.The well-balanced presentation of theory and experiments guides readers through the background of different types of non-diffractive waves, their generation, propagation, and possible applications. The authors include a historical account of the development of the field, and cover different types of non-diffractive waves, including Airy
International Nuclear Information System (INIS)
Shabbir, Ghulam; Khan, Suhail
2010-01-01
In this paper we classify cylindrically symmetric static space-times according to their teleparallel homothetic vector fields using direct integration technique. It turns out that the dimensions of the teleparallel homothetic vector fields are 4, 5, 7 or 11, which are the same in numbers as in general relativity. In case of 4, 5 or 7 proper teleparallel homothetic vector fields exist for the special choice to the space-times. In the case of 11 teleparallel homothetic vector fields the space-time becomes Minkowski with all the zero torsion components. Teleparallel homothetic vector fields in this case are exactly the same as in general relativity. It is important to note that this classification also covers the plane symmetric static space-times. (general)
Hempler, Daniela; Schmidt, Martin U; van de Streek, Jacco
2017-08-01
More than 600 molecular crystal structures with correct, incorrect and uncertain space-group symmetry were energy-minimized with dispersion-corrected density functional theory (DFT-D, PBE-D3). For the purpose of determining the correct space-group symmetry the required tolerance on the atomic coordinates of all non-H atoms is established to be 0.2 Å. For 98.5% of 200 molecular crystal structures published with missed symmetry, the correct space group is identified; there are no false positives. Very small, very symmetrical molecules can end up in artificially high space groups upon energy minimization, although this is easily detected through visual inspection. If the space group of a crystal structure determined from powder diffraction data is ambiguous, energy minimization with DFT-D provides a fast and reliable method to select the correct space group.
Prévot, Geoffroy; Hogan, Conor; Leoni, Thomas; Bernard, Romain; Moyen, Eric; Masson, Laurence
2016-12-30
We report a combined grazing incidence x-ray diffraction (GIXD), scanning tunneling microscopy (STM), and density-functional theory (DFT) study which clearly elucidates the atomic structure of the Si nanoribbons grown on the missing-row reconstructed Ag(110) surface. Our study allows us to discriminate between the theoretical models published in the literature, including the most stable atomic configurations and those based on a missing-row reconstructed Ag(110) surface. GIXD measurements unambiguously validate the pentamer model grown on the reconstructed surface, obtained from DFT. This pentamer atomistic model accurately matches the high-resolution STM images of the Si nanoribbons adsorbed on Ag(110). Our study closes the long-debated atomic structure of the Si nanoribbons grown on Ag(110) and definitively excludes a honeycomb structure similar to that of freestanding silicene.
DEFF Research Database (Denmark)
Kumpf, C.; Müller, A.; Weigand, W.
2003-01-01
The atomic structure and lattice dynamics of epitaxial BeTe(001) thin films are derived from surface x-ray diffraction and Raman spectroscopy. On the Te-rich BeTe(001) surface [1 (1) over bar0]-oriented Te dimers are identified. They cause a (2 X 1) superstructure and induce a pronounced buckling...... in the underlying Te layer. The Be-rich surface exhibits a (4 X 1) periodicity with alternating Te dimers and Te-Be-Te trimers. A vibration eigenfrequency of 165 cm(-1) is observed for the Te-rich surface, while eigenmodes at 157 and 188 cm(-1) are found for the Be-rich surface. The experimentally derived atomic...... geometry and the vibration modes are in very good agreement with the results of density functional theory calculations....
Diffraction by disordered polycrystalline fibers
International Nuclear Information System (INIS)
Stroud, W.J.; Millane, R.P.
1995-01-01
X-ray diffraction patterns from some polycrystalline fibers show that the constituent microcrystallites are disordered. The relationship between the crystal structure and the diffracted intensities is then quite complicated and depends on the precise kind and degree of disorder present. The effects of disorder on diffracted intensities must be included in structure determinations using diffraction data from such specimens. Theory and algorithms are developed here that allow the full diffraction pattern to be calculated for a disordered polycrystalline fiber made up of helical molecules. The model accommodates various kinds of disorder and includes the effects of finite crystallite size and cylindrical averaging of the diffracted intensities from a fiber. Simulations using these methods show how different kinds, or components, of disorder produce particular diffraction effects. General properties of disordered arrays of helical molecules and their effects on diffraction patterns are described. Implications for structure determination are discussed. (orig.)
International Nuclear Information System (INIS)
Goodman, F.O.; Scribani, L.
1981-01-01
The CCGM theory of elastic atom--surface scattering, proposed by Cabrera, Celli, Goodman, and Manson [Surf. Sci. 19, 67 (1970)], is applied to the now-popular corrugated wall model of the scattering. Instead of the original ''hard'' wall, a ''softer'' wall, with finite potential step height, is used. The CCGM soft-wall results are compared with corresponding exact hard-wall results, for corrugations of the sinusoidal type and of other types, for example those with nondifferentiable corrugation functions. It is concluded that the CCGM soft-wall results agree well with the exact hard-wall results provided that neither the dimensionless corrugation amplitude nor the dimensionless atom wave number is too large, although no explanation of the reason for this agreement is given. The results are important because a typical exact calculation may be far more time consuming than is a typical CCGM calculation, particularly for the ''nastier'' corrugation functions
Hahne, G. E.
1991-01-01
A formal theory of the scattering of time-harmonic acoustic scalar waves from impenetrable, immobile obstacles is established. The time-independent formal scattering theory of nonrelativistic quantum mechanics, in particular the theory of the complete Green's function and the transition (T) operator, provides the model. The quantum-mechanical approach is modified to allow the treatment of acoustic-wave scattering with imposed boundary conditions of impedance type on the surface (delta-Omega) of an impenetrable obstacle. With k0 as the free-space wavenumber of the signal, a simplified expression is obtained for the k0-dependent T operator for a general case of homogeneous impedance boundary conditions for the acoustic wave on delta-Omega. All the nonelementary operators entering the expression for the T operator are formally simple rational algebraic functions of a certain invertible linear radiation impedance operator which maps any sufficiently well-behaved complex-valued function on delta-Omega into another such function on delta-Omega. In the subsequent study, the short-wavelength and the long-wavelength behavior of the radiation impedance operator and its inverse (the 'radiation admittance' operator) as two-point kernels on a smooth delta-Omega are studied for pairs of points that are close together.
Saka, Takashi
2016-05-01
The dynamical theory for perfect crystals in the Laue case was reformulated using the Riemann surface, as used in complex analysis. In the two-beam approximation, each branch of the dispersion surface is specified by one sheet of the Riemann surface. The characteristic features of the dispersion surface are analytically revealed using four parameters, which are the real and imaginary parts of two quantities specifying the degree of departure from the exact Bragg condition and the reflection strength. By representing these parameters on complex planes, these characteristics can be graphically depicted on the Riemann surface. In the conventional case, the absorption is small and the real part of the reflection strength is large, so the formulation is the same as the traditional analysis. However, when the real part of the reflection strength is small or zero, the two branches of the dispersion surface cross, and the dispersion relationship becomes similar to that of the Bragg case. This is because the geometrical relationships among the parameters are similar in both cases. The present analytical method is generally applicable, irrespective of the magnitudes of the parameters. Furthermore, the present method analytically revealed many characteristic features of the dispersion surface and will be quite instructive for further numerical calculations of rocking curves.
Borehole radar diffraction tomography
Energy Technology Data Exchange (ETDEWEB)
Cho, Seong Jun; Kim, Jung Ho; Yi, Myeong Jong; Chung, Seung Hwan; Lee, Hee Il [Korea Institute of Geology Mining and Materials, Taejon (Korea, Republic of)
1997-12-01
Tomography is widely used as imaging method for determining subsurface structure. Among the reconstruction algorithms for tomographic imaging, travel time tomography is almost applied to imaging subsurface. But isolated small body comparable with the wavelength could not be well recognized by travel time tomography. Other tomographic method are need to improve the imaging process. In the study of this year, diffraction tomography was investigated. The theory for diffraction tomography is based on the 1st-order Born approximation. Multisource holography, which is similar to Kirchihoff migration, is compared with diffraction tomography. To improve 1st-order Born diffraction tomography, two kinds of filter designed from multisource holography and 2-D green function, respectively, applied on the reconstructed image. The algorithm was tested for the numerical modeling data of which algorithm consists of the analytic computation of radar signal in transmitter and receiver regions and 2-D FDM scheme for the propagation of electromagnetic waves in media. The air-filled cavity model to show a typical diffraction pattern was applied to diffraction tomography imaging, and the result shows accurate location and area of cavity. But the calculated object function is not well matched the real object function, because the air-filled cavity model is not satisfied week scattered inhomogeneity for 1st born approximation, and the error term is included in estimating source wavelet from received signals. In spite of the object function error, the diffraction tomography assist for interpretation of subsurface as if conducted with travel time tomography. And the fracture model was tested, 1st born diffraction tomographic image is poor because of limited view angle coverage and violation of week scatter assumption, but the filtered image resolve the fracture somewhat better. The tested diffraction tomography image confirms effectiveness of filter for enhancing resolution. (author). 14
International Nuclear Information System (INIS)
Abarbanel, H.
1972-01-01
An attempt is made to analyse the present theoretical situation in the field of diffraction scattering. Two not yet fully answered questions related with a typical diffraction process AB→CD, namely: what is the structure of the transition matrix elements, and what is the structure of the exchange mechanism responsible for the scattering, are formulated and various proposals for answers are reviewed. Interesting general statement that the products (-1)sup(J)P, where J and P are respectively spin and parity, is conserved at each vertex has been discussed. The exchange mechanism in diffractive scattering has been considered using the language of the complex J-plane as the most appropriate. The known facts about the exchange mechanism are recalled and several routs to way out are proposed. The idea to consider the moving pole and associated branch points as like a particle and the associated two and many particle unitarity cuts is described in more details. (S.B.)
International Nuclear Information System (INIS)
Anon.
1986-01-01
Elastic scattering – when colliding particles 'bounce' off each other like billiard balls – has always had a special interest for high energy physicists. While its simplicity makes for deep analogies with classical ideas like diffraction, its jbtle details also test our understanding of the intricate inner mechanisms which drive particle interactions. With a new stock of elastic scattering data now available thanks to experiments at the CERN proton-antiproton Collider, and with studies at higher energies imminent or planned, some seventy physicists gathered in the magnificent chateau at Blois, France, for a 'Workshop on Elastic and Diffractive Scattering at the Collider and Beyond'
De Wolf, E.A.
2002-01-01
We discuss basic concepts and properties of diffractive phenomena in soft hadron collisions and in deep-inelastic scattering at low Bjorken-x. The paper is not a review of the rapidly developing field but presents an attempt to show in simple terms the close inter-relationship between the dynamics of high-energy hadronic and deep-inelastic diffraction. Using the saturation model of Golec-Biernat and Wusthoff as an example, a simple explanation of geometrical scaling is presented. The relation between the QCD anomalous multiplicity dimension and the Pomeron intercept is discussed.
International Nuclear Information System (INIS)
Wolf, E.A. de
2002-01-01
We discuss basic concepts and properties of diffractive phenomena in soft hadron collisions and in deep-inelastic scattering at low Bjorken - x. The paper is not a review of the rapidly developing field but presents an attempt to show in simple terms the close inter-relationship between the dynamics of high-energy hadronic and deep-inelastic diffraction. Using the saturation model of Golec-Biernat and Wuesthoff as an example, a simple explanation of geometrical scaling is presented. The relation between the QCD anomalous multiplicity dimension and the Pomeron intercept is discussed. (author)
Energy Technology Data Exchange (ETDEWEB)
Anon.
1986-03-15
Elastic scattering – when colliding particles 'bounce' off each other like billiard balls – has always had a special interest for high energy physicists. While its simplicity makes for deep analogies with classical ideas like diffraction, its jbtle details also test our understanding of the intricate inner mechanisms which drive particle interactions. With a new stock of elastic scattering data now available thanks to experiments at the CERN proton-antiproton Collider, and with studies at higher energies imminent or planned, some seventy physicists gathered in the magnificent chateau at Blois, France, for a 'Workshop on Elastic and Diffractive Scattering at the Collider and Beyond'.
Diffraction at a Straight Edge
Indian Academy of Sciences (India)
IAS Admin
teaching and understanding physics. ... and mathematical footing, using electromagnetic theory and the proper ... this article, we will use the word diffraction to cover all experiments ..... PES Institute of Technology. Campus ... communication!)
The energy transport in a vegetated (corn) surface layer is examined by solving the vector radiative transfer equation using a numerical iterative approach. This approach allows a higher order that includes the multiple scattering effects. Multiple scattering effects are important when the optical t...
International Nuclear Information System (INIS)
Walter, S; Blobner, F; Krause, M; Mueller, S; Heinz, K; Starke, U
2003-01-01
We present a combined experimental and theoretical investigation of the interface between a B2-type FeSi film and Si(111). Using an ultra-thin B2-FeSi film grown on Si(111), the interface is still reached by electrons, so quantitative low-energy electron diffraction (LEED) could be applied to determine the bonding geometry experimentally. As a result, the local configuration at the shallow buried interface is characterized by near-substrate Fe atoms being 8-fold coordinated to Si atoms and by the silicide unit cell being rotated by 180 deg. with respect to the Si unit cell (B8 configuration). The interface energetics were explored by total-energy calculations using density functional theory (DFT). The B8-type interface proves to be the most stable one, consistent with the experimental findings. The atomic geometries obtained experimentally (LEED) and theoretically (DFT) agree within the limits of errors. Additionally, the calculations explain the stabilization of the B2 phase, which is unstable as bulk material: the analysis of the elastic behaviour reveals a reversed energy hierarchy of B2 and the bulk stable B20 phase when epitaxial growth on Si(111) is enforced
Directory of Open Access Journals (Sweden)
A. Becker
2007-06-01
Full Text Available In this paper a hybrid method combining the Time-Domain Method of Moments (TD-MoM, the Time-Domain Uniform Theory of Diffraction (TD-UTD and the Finite-Difference Time-Domain Method (FDTD is presented. When applying this new hybrid method, thin-wire antennas are modeled with the TD-MoM, inhomogeneous bodies are modelled with the FDTD and large perfectly conducting plates are modelled with the TD-UTD. All inhomogeneous bodies are enclosed in a so-called FDTD-volume and the thin-wire antennas can be embedded into this volume or can lie outside. The latter avoids the simulation of white space between antennas and inhomogeneous bodies. If the antennas are positioned into the FDTD-volume, their discretization does not need to agree with the grid of the FDTD. By using the TD-UTD large perfectly conducting plates can be considered efficiently in the solution-procedure. Thus this hybrid method allows time-domain simulations of problems including very different classes of objects, applying the respective most appropriate numerical techniques to every object.
Radlow, Madlen; Czjzek, Mirjam; Jeudy, Alexandra; Dabin, Jerome; Delage, Ludovic; Leblanc, Catherine; Hartung, Jens
2018-05-18
X-ray diffraction of native bromoperoxidase II (EC 1.11.1.18) from the brown alga Ascophyllum nodosum reveals at a resolution of 2.26 Å details of orthovanadate binding and homohexameric protein organization. Three dimers interwoven in contact regions and tightened by hydrogen-bond-clamped guanidinium stacks along with regularly aligned water molecules form the basic structure of the enyzme. Intra- and intermolecular disulfide bridges further stabilize the enzyme preventing altogether the protein from denaturing up to a temperature of 90 °C, as evident from dynamic light scattering and the on-gel ortho-dianisidine assay. Every monomer binds one equivalent of orthovanadate in a cavity formed from side chains of three histidines, two arginines, one lysine, serine, and tryptophan. Protein binding occurs primarily through hydrogen bridges and superimposed by Coulomb attraction according to thermochemical model on density functional level of theory (B3LYP/6-311++G**). The strongest attractor is the arginine side chain mimic N-methylguanidinium, enhancing in positive cooperative manner hydrogen bridges toward weaker acceptors, such as residues from lysine and serine. Activating hydrogen peroxide occurs in the thermochemical model by side-on binding in orthovanadium peroxoic acid, oxidizing bromide with virtually no activation energy to hydrogen bonded hypobromous acid.
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.
Sesquilinear uniform vector integral
Indian Academy of Sciences (India)
theory, together with his integral, dominate contemporary mathematics. ... directions belonging to Bartle and Dinculeanu (see [1], [6], [7] and [2]). ... in this manner, namely he integrated vector functions with respect to measures of bounded.
Energy Technology Data Exchange (ETDEWEB)
Hart, M.
1995-12-31
the importance of x-ray powder diffraction as an analytical tool for phase identification of materials was first pointed out by Debye and Scherrer in Germany and, quite independently, by Hull in the US. Three distinct periods of evolution lead to ubiquitous application in many fields of science and technology. In the first period, until the mid-1940`s, applications were and developed covering broad categories of materials including inorganic materials, minerals, ceramics, metals, alloys, organic materials and polymers. During this formative period, the concept of quantitative phase analysis was demonstrated. In the second period there followed the blossoming of technology and commercial instruments became widely used. The history is well summarized by Parrish and by Langford and Loueer. By 1980 there were probably 10,000 powder diffractometers in routine use, making it the most widely used of all x-ray crystallographic instruments. In the third, present, period data bases became firmly established and sophisticated pattern fitting and recognition software made many aspects of powder diffraction analysis routine. High resolution, tunable powder diffractometers were developed at sources of synchrotron radiation. The tunability of the spectrum made it possible to exploit all the subtleties of x-ray spectroscopy in diffraction experiments.
International Nuclear Information System (INIS)
Hart, M.
1995-01-01
The importance of x-ray powder diffraction as an analytical tool for phase identification of materials was first pointed out by Debye and Scherrer in Germany and, quite independently, by Hull in the US. Three distinct periods of evolution lead to ubiquitous application in many fields of science and technology. In the first period, until the mid-1940's, applications were and developed covering broad categories of materials including inorganic materials, minerals, ceramics, metals, alloys, organic materials and polymers. During this formative period, the concept of quantitative phase analysis was demonstrated. In the second period there followed the blossoming of technology and commercial instruments became widely used. The history is well summarized by Parrish and by Langford and Loueer. By 1980 there were probably 10,000 powder diffractometers in routine use, making it the most widely used of all x-ray crystallographic instruments. In the third, present, period data bases became firmly established and sophisticated pattern fitting and recognition software made many aspects of powder diffraction analysis routine. High resolution, tunable powder diffractometers were developed at sources of synchrotron radiation. The tunability of the spectrum made it possible to exploit all the subtleties of x-ray spectroscopy in diffraction experiments
Focusing properties of cylindrical vector vortex beams
Xiaoqiang, Zhang; Ruishan, Chen; Anting, Wang
2018-05-01
In this paper, following Richards and Wolf vectorial diffraction theory, the focusing properties of cylindrical vector vortex beams (CVVB) are investigated, and a diffractive optical element (DOE) is designed to spatially modulate the amplitude of the CVVB. Simulated results show that the CVVB focused by an objective also carry orbital angular momentum (OAM), and the optical fields near the focal region can be modulated by changing the topological charge of the CVVB. We numerically simulate the focus properties of radially and azimuthally polarized beams with topological charge equal to 0, 1, 2 and 10 respectively. As a result, a dark channel with a length about 20 λ can be obtained. These new properties have the potential applications such as particle acceleration, optical trapping and material processing.
Diffraction radiation from relativistic particles
Potylitsyn, Alexander Petrovich; Strikhanov, Mikhail Nikolaevich; Tishchenko, Alexey Alexandrovich
2010-01-01
This book deals with diffraction radiation, which implies the boundary problems of electromagnetic radiation theory. Diffraction radiation is generated when a charged particle moves in a vacuum near a target edge. Diffraction radiation of non-relativistic particles is widely used to design intense emitters in the cm wavelength range. Diffraction radiation from relativistic charged particles is important for noninvasive beam diagnostics and design of free electron lasers based on Smith-Purcell radiation which is diffraction radiation from periodic structures. Different analytical models of diffraction radiation and results of recent experimental studies are presented in this book. The book may also serve as guide to classical electrodynamics applications in beam physics and electrodynamics. It can be of great use for young researchers to develop skills and for experienced scientists to obtain new results.
Diffraction radiation from relativistic particles
International Nuclear Information System (INIS)
Potylitsyn, Alexander Petrovich; Ryazanov, Mikhail Ivanovich; Strikhanov, Mikhail Nikolaevich; Tishchenko, Alexey Alexandrovich
2010-01-01
This book deals with diffraction radiation, which implies the boundary problems of electromagnetic radiation theory. Diffraction radiation is generated when a charged particle moves in a vacuum near a target edge. Diffraction radiation of non-relativistic particles is widely used to design intense emitters in the cm wavelength range. Diffraction radiation from relativistic charged particles is important for noninvasive beam diagnostics and design of free electron lasers based on Smith-Purcell radiation which is diffraction radiation from periodic structures. Different analytical models of diffraction radiation and results of recent experimental studies are presented in this book. The book may also serve as guide to classical electrodynamics applications in beam physics and electrodynamics. It can be of great use for young researchers to develop skills and for experienced scientists to obtain new results. (orig.)
International Nuclear Information System (INIS)
Keitel, Jan; Bartosch, Lorenz
2012-01-01
We consider the zero-dimensional O(N) vector model as a simple example to calculate n-point correlation functions using perturbation theory, the large-N expansion and the functional renormalization group (FRG). Comparing our findings with exact results, we show that perturbation theory breaks down for moderate interactions for all N, as one should expect. While the interaction-induced shift of the free energy and the self-energy are well described by the large-N expansion even for small N, this is not the case for higher order correlation functions. However, using the FRG in its one-particle irreducible formalism, we see that very few running couplings suffice to get accurate results for arbitrary N in the strong coupling regime, outperforming the large-N expansion for small N. We further remark on how the derivative expansion, a well-known approximation strategy for the FRG, reduces to an exact method for the zero-dimensional O(N) vector model. (paper)
Complex Polynomial Vector Fields
DEFF Research Database (Denmark)
The two branches of dynamical systems, continuous and discrete, correspond to the study of differential equations (vector fields) and iteration of mappings respectively. In holomorphic dynamics, the systems studied are restricted to those described by holomorphic (complex analytic) functions...... or meromorphic (allowing poles as singularities) functions. There already exists a well-developed theory for iterative holomorphic dynamical systems, and successful relations found between iteration theory and flows of vector fields have been one of the main motivations for the recent interest in holomorphic...... vector fields. Since the class of complex polynomial vector fields in the plane is natural to consider, it is remarkable that its study has only begun very recently. There are numerous fundamental questions that are still open, both in the general classification of these vector fields, the decomposition...
Vogt, Natalja; Marochkin, Ilya I; Rykov, Anatolii N
2018-04-18
The accurate molecular structure of picolinic acid has been determined from experimental data and computed at the coupled cluster level of theory. Only one conformer with the O[double bond, length as m-dash]C-C-N and H-O-C[double bond, length as m-dash]O fragments in antiperiplanar (ap) positions, ap-ap, has been detected under conditions of the gas-phase electron diffraction (GED) experiment (Tnozzle = 375(3) K). The semiexperimental equilibrium structure, rsee, of this conformer has been derived from the GED data taking into account the anharmonic vibrational effects estimated from the ab initio force field. The equilibrium structures of the two lowest-energy conformers, ap-ap and ap-sp (with the synperiplanar H-O-C[double bond, length as m-dash]O fragment), have been fully optimized at the CCSD(T)_ae level of theory in conjunction with the triple-ζ basis set (cc-pwCVTZ). The quality of the optimized structures has been improved due to extrapolation to the quadruple-ζ basis set. The high accuracy of both GED determination and CCSD(T) computations has been disclosed by a correct comparison of structures having the same physical meaning. The ap-ap conformer has been found to be stabilized by the relatively strong NH-O hydrogen bond of 1.973(27) Å (GED) and predicted to be lower in energy by 16 kJ mol-1 with respect to the ap-sp conformer without a hydrogen bond. The influence of this bond on the structure of picolinic acid has been analyzed within the Natural Bond Orbital model. The possibility of the decarboxylation of picolinic acid has been considered in the GED analysis, but no significant amounts of pyridine and carbon dioxide could be detected. To reveal the structural changes reflecting the mesomeric and inductive effects due to the carboxylic substituent, the accurate structure of pyridine has been also computed at the CCSD(T)_ae level with basis sets from triple- to 5-ζ quality. The comprehensive structure computations for pyridine as well as for
International Nuclear Information System (INIS)
Wilkens, P.H.
1978-01-01
This system of gauging is now being designed to fit on an Excello NC lathe to measure the form, accuracy, and size of external contoured surfaces as they approach the finish machined size. A template profile of the finished workpiece, but 0.003 in. bigger on radius, will be aligned with the workpiece using a reference diameter and face on the machining fixture to leave a gap between the profile of the template and workpiece. A helium--neon laser beam will be projected through this gap using a rotating retroreflector and a fixed laser. The resulting diffraction pattern produced by the laser beam passing through the template to workpiece gap will be reflected and focused on a fixed diode array via a second retroreflector which moves and remains in optical alignment with the first. These retroreflectors will be rotated about a center that will enable the laser beam, which is shaped in a long slit, to scan the template workpiece gap from the pole to the equator of the workpiece. The characteristic diffraction pattern will be detected by the fixed diode array, and the signal levels from this array will be processed in a mini-computer programmed to produce a best fit through the two minima of the diode signals. The separation of the two minima will yield the size of the workpiece to template gap and this information will be presented to the machine tool operator
Hard scattering and a diffractive trigger
International Nuclear Information System (INIS)
Berger, E.L.; Collins, J.C.; Soper, D.E.; Sterman, G.
1986-02-01
Conclusions concerning the properties of hard scattering in diffractively produced systems are summarized. One motivation for studying diffractive hard scattering is to investigate the interface between Regge theory and perturbative QCD. Another is to see whether diffractive triggering can result in an improvement in the signal-to-background ratio of measurements of production of very heavy quarks. 5 refs
International Nuclear Information System (INIS)
Nashed, Gamal G. L.
2010-01-01
The energy–momentum tensor, which is coordinate-independent, is used to calculate energy, momentum and angular momentum of two different tetrad fields. Although, the two tetrad fields reproduce the same space-time their energies are different. Therefore, a regularized expression of the gravitational energy–momentum tensor of the teleparallel equivalent of general relativity (TEGR), is used to make the energies of the two tetrad fields equal. The definition of the gravitational energy–momentum is used to investigate the energy within the external event horizon. The components of angular momentum associated with these space–times are calculated. In spite of using a static space–time, we get a non-zero component of angular momentum! Therefore, we derive the Killing vectors associated with these space–times using the definition of the Lie derivative of a second rank tensor in the framework of the TEGR to make the picture more clear. (general)
González-López, Jorge; Cockcroft, Jeremy K; Fernández-González, Ángeles; Jimenez, Amalia; Grau-Crespo, Ricardo
2017-10-01
The cobalt carbonate hydroxide Co 2 CO 3 (OH) 2 is a technologically important solid which is used as a precursor for the synthesis of cobalt oxides in a wide range of applications. It also has relevance as a potential immobilizer of the toxic element cobalt in the natural environment, but its detailed crystal structure is so far unknown. The structure of Co 2 CO 3 (OH) 2 has now been investigated using density functional theory (DFT) simulations and powder X-ray diffraction (PXRD) measurements on samples synthesized via deposition from aqueous solution. Two possible monoclinic phases are considered, with closely related but symmetrically different crystal structures, based on those of the minerals malachite [Cu 2 CO 3 (OH) 2 ] and rosasite [Cu 1.5 Zn 0.5 CO 3 (OH) 2 ], as well as an orthorhombic phase that can be seen as a common parent structure for the two monoclinic phases, and a triclinic phase with the structure of the mineral kolwezite [Cu 1.34 Co 0.66 CO 3 (OH) 2 ]. The DFT simulations predict that the rosasite-like and malachite-like phases are two different local minima of the potential energy landscape for Co 2 CO 3 (OH) 2 and are practically degenerate in energy, while the orthorhombic and triclinic structures are unstable and experience barrierless transformations to the malachite phase upon relaxation. The best fit to the PXRD data is obtained using a rosasite model [monoclinic with space group P112 1 /n and cell parameters a = 3.1408 (4) Å, b = 12.2914 (17) Å, c = 9.3311 (16) Å and γ = 82.299 (16)°]. However, some features of the PXRD pattern are still not well accounted for by this refinement and the residual parameters are relatively poor. The relationship between the rosasite and malachite phases of Co 2 CO 3 (OH) 2 is discussed and it is shown that they can be seen as polytypes. Based on the similar calculated stabilities of these two polytypes, it is speculated that some level of stacking disorder could account for the poor
Newell, Homer E
2006-01-01
When employed with skill and understanding, vector analysis can be a practical and powerful tool. This text develops the algebra and calculus of vectors in a manner useful to physicists and engineers. Numerous exercises (with answers) not only provide practice in manipulation but also help establish students' physical and geometric intuition in regard to vectors and vector concepts.Part I, the basic portion of the text, consists of a thorough treatment of vector algebra and the vector calculus. Part II presents the illustrative matter, demonstrating applications to kinematics, mechanics, and e
Hoffmann, Banesh
1975-01-01
From his unusual beginning in ""Defining a vector"" to his final comments on ""What then is a vector?"" author Banesh Hoffmann has written a book that is provocative and unconventional. In his emphasis on the unresolved issue of defining a vector, Hoffmann mixes pure and applied mathematics without using calculus. The result is a treatment that can serve as a supplement and corrective to textbooks, as well as collateral reading in all courses that deal with vectors. Major topics include vectors and the parallelogram law; algebraic notation and basic ideas; vector algebra; scalars and scalar p
Grazing incidence diffraction : A review
Energy Technology Data Exchange (ETDEWEB)
Gilles, B [LTPCM, ENSEEG. St. Martin d` Heres. (France)
1996-09-01
Different Grazing Incidence Diffraction (GID) methods for the analysis of thin films and multilayer structures are reviewed in three sections: the reflectivity is developed in the first one, which includes the non-specular diffuse scattering. The second one is devoted to the extremely asymmetric Bragg diffraction and the third one to the in-plane Bragg diffraction. Analytical formulations of the scattered intensities are developed for each geometry, in the framework of the kinetical analysis as well as the dynamical theory. Experimental examples are given to illustrate the quantitative possibility of the GID techniques.
Reciprocity in electron diffraction
International Nuclear Information System (INIS)
Gunning, J.; Goodman, P.
1991-01-01
The symmetry of reciprocity is reviewed in the context of relativistic quantum mechanics with the specific aim of relating to P-C-T invariances. From this investigation global time reversal is found to be sufficient condition for reciprocity to hold in scattering from a vector potential. Elastic scattering is assumed. The paper also deals exclusively with the scattering of a charged particle by an electromagnetic field. The present proof is free from assumptions of small angle scattering and from restrictions on z-dependent terms in the scattering equation, and by avoiding S-matrix theory is thought to be accessible to undergraduate teaching. 9 refs., 1 tab., 1 fig
Reciprocity in electron diffraction
International Nuclear Information System (INIS)
Gunning, J.; Goodman, P.
1992-01-01
The symmetry of reciprocity is reviewed in the context of relativistic quantum mechanics with the specific aim of relating to C, P and T invariances. From this investigation global time reversal is found to be a sufficient condition for reciprocity to hold in scattering from a vector potential. The present proof is free from assumptions of small-angle scattering and from restrictions on z-dependent terms in the scattering equation, and by avoiding S-matrix theory is thought to be accessible to undergraduate teaching. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Fillaux, François, E-mail: francois.fillaux@upmc.fr [Sorbonne Universités, UPMC Univ Paris 06, UMR 8233, MONARIS, F-7505 Paris (France); Cousson, Alain, E-mail: alain-f.cousson@cea.fr [Laboratoire Léon Brillouin (CEA-CNRS), C.E. Saclay, 91191 Gif-sur-Yvette cedex (France)
2016-11-10
Highlights: • Proton transfer and tautomerism are revisited from quantum viewpoint. • Neutron-diffraction gives evidence for long-range correlations for protons. • We introduce a decoherence-free macroscopic-scale crystal-state. • All observations accord with the principle of complementarity. • Computational-chemistry models are inappropriate. - Abstract: Measurements via different techniques of the crystal of benzoic acid have led to conflicting conceptions of tautomerism: statistical disorder for diffraction; semiclassical jumps for relaxometry; quantum states for vibrational spectroscopy. We argue that these conflicts follow from the prejudice that nuclear positions and eigenstates are pre-existing to measurements, what is at variance with the principle of complementarity. We propose a self-contained quantum theory. First of all, new single-crystal neutron-diffraction data accord with long-range correlation for proton-site occupancies. Then we introduce a macroscopic-scale quantum-state emerging from phonon condensation, for which nuclear positions and eigenstates are indefinite. As to quantum-measurements, an incoming wave (neutron or photon) entangled with the condensate realizes a transitory state, either in the space of static nuclear-coordinates (diffraction), or in that of the symmetry coordinates (spectroscopy and relaxometry). We derive temperature-laws for proton-site occupancies and for the relaxation rate, which compare favorably with measurements.
Selection vector filter framework
Lukac, Rastislav; Plataniotis, Konstantinos N.; Smolka, Bogdan; Venetsanopoulos, Anastasios N.
2003-10-01
We provide a unified framework of nonlinear vector techniques outputting the lowest ranked vector. The proposed framework constitutes a generalized filter class for multichannel signal processing. A new class of nonlinear selection filters are based on the robust order-statistic theory and the minimization of the weighted distance function to other input samples. The proposed method can be designed to perform a variety of filtering operations including previously developed filtering techniques such as vector median, basic vector directional filter, directional distance filter, weighted vector median filters and weighted directional filters. A wide range of filtering operations is guaranteed by the filter structure with two independent weight vectors for angular and distance domains of the vector space. In order to adapt the filter parameters to varying signal and noise statistics, we provide also the generalized optimization algorithms taking the advantage of the weighted median filters and the relationship between standard median filter and vector median filter. Thus, we can deal with both statistical and deterministic aspects of the filter design process. It will be shown that the proposed method holds the required properties such as the capability of modelling the underlying system in the application at hand, the robustness with respect to errors in the model of underlying system, the availability of the training procedure and finally, the simplicity of filter representation, analysis, design and implementation. Simulation studies also indicate that the new filters are computationally attractive and have excellent performance in environments corrupted by bit errors and impulsive noise.
Vector correlations in rotationally inelastic molecular collisions
International Nuclear Information System (INIS)
Lemeshko, Mikhail
2011-01-01
The thesis presents an analytic model that describes scalar and vector properties of molecular collisions, both field-free and in fields. The model is based on the sudden approximation and treats molecular scattering as the Fraunhofer diffraction of matter waves from the hard-core part of the interaction potential. The theory has no fitting parameters and is inherently quantum, rendering fully state- and energy-resolved scattering amplitudes and all the quantities that unfold from them in analytic form. This allows to obtain complex polarization moments inherent to quantum stereodynamics, and to account for interference and other non-classical effects. The simplicity and analyticity of the model paves a way to understanding the origin of the features observed in experiment and exact computations, such as the angular oscillations in the state-to-state differential cross sections and the polarization moments, the rotational-state dependent variation of the integral cross sections, and change of these quantities as a function of the applied field. The theory was applied to study the k - k ' vector correlation (differential cross section) for the following collision systems: Ar-NO(X 2 Π) and Ne-OCS(X 1 Σ) in an electrostatic field, Na + -N 2 (X 1 Σ) in a laser field, and He-CaH( 2 Σ), He-O 2 (X 3 Σ), and He-OH(X 2 Π) in a magnetic field. The model was able to reproduce the behavior of the differential cross sections and their variation with field strength. Combining the Fraunhofer model with the quantum theory of vector correlations made it possible to study three- and four-vector properties. The model results for the k-k ' -j ' vector correlation in Ar-NO(X 2 Π) and He-NO(X 2 Π) scattering were found to be in good agreement with experiment and exact computations. This allowed to demonstrate that the stereodynamics of such collisions is contained solely in the diffractive part of the scattering amplitude which is governed by a single Legendre moment
Vector correlations in rotationally inelastic molecular collisions
Energy Technology Data Exchange (ETDEWEB)
Lemeshko, Mikhail
2011-04-13
The thesis presents an analytic model that describes scalar and vector properties of molecular collisions, both field-free and in fields. The model is based on the sudden approximation and treats molecular scattering as the Fraunhofer diffraction of matter waves from the hard-core part of the interaction potential. The theory has no fitting parameters and is inherently quantum, rendering fully state- and energy-resolved scattering amplitudes and all the quantities that unfold from them in analytic form. This allows to obtain complex polarization moments inherent to quantum stereodynamics, and to account for interference and other non-classical effects. The simplicity and analyticity of the model paves a way to understanding the origin of the features observed in experiment and exact computations, such as the angular oscillations in the state-to-state differential cross sections and the polarization moments, the rotational-state dependent variation of the integral cross sections, and change of these quantities as a function of the applied field. The theory was applied to study the k - k{sup '} vector correlation (differential cross section) for the following collision systems: Ar-NO(X{sup 2}{pi}) and Ne-OCS(X{sup 1}{sigma}) in an electrostatic field, Na{sup +}-N{sub 2}(X{sup 1}{sigma}) in a laser field, and He-CaH({sup 2}{sigma}), He-O{sub 2}(X{sup 3}{sigma}), and He-OH(X{sup 2}{pi}) in a magnetic field. The model was able to reproduce the behavior of the differential cross sections and their variation with field strength. Combining the Fraunhofer model with the quantum theory of vector correlations made it possible to study three- and four-vector properties. The model results for the k-k{sup '}-j{sup '} vector correlation in Ar-NO(X{sup 2}{pi}) and He-NO(X{sup 2}{pi}) scattering were found to be in good agreement with experiment and exact computations. This allowed to demonstrate that the stereodynamics of such collisions is contained solely in the
International Nuclear Information System (INIS)
Horvat, R.; Kekez, D.; Krecak, Z.; Ljubicic, A.
2008-01-01
In this experiment we aim to detect Kaluza-Klein (KK) excitations of the bulk gauge field, emitted in a bremsstrahlung process on solar plasma constituents, by looking at a process analogous to the photoelectric effect inside the HPGe detector. Using a generic feature of the underlying effective theory that the unknown four-dimensional gauge coupling is independent of the number of extra large dimensions δ, we show that the expected number of events in the detector is insensitive to the true scale of quantum gravity for δ=2. With the entire data collection time of 202 days in the energy interval 1.7-3.8 keV, the number of events detected was as low as 1.1x10 6 , compared to 2.7x10 6 from the expected high multiplicity of the solar KK excitations for δ=2. Hence, our bound from the presumed existence of new forces associated with additional gauge bosons actually conforms with very stringent bounds set from various astrophysical considerations. Baring any modifications of the infrared part of the KK spectrum, this bound would therefore rule out the possibility of observing any signal at the LHC for δ=2. Although a dependence on the fundamental scale referring to (4+δ)-dimensional gravity turns on again for δ=3, the experimental sensitivity of the present setup proves insufficient to draw any constraint for δ>2.
High-energy particle diffraction
International Nuclear Information System (INIS)
Barone, V.; Predazzi, E.
2002-01-01
This monograph gives a comprehensive and up-to-date overview of soft and hard diffraction processes in strong interaction physics. The first part covers the general formalism (the optical analogy, the eikonal picture, high-energy kinematics, S-matrix theory) and soft hadron-hadron scattering (including the Regge theory) in a complete and mature presentation. It can be used as a textbook in particle physics classes. The remainder of the book is devoted to the 'new diffraction': the pomeron in QCD, low-x physics, diffractive deep inelastic scattering and related processes, jet production etc. It presents recent results and experimental findings and their phenomenological interpretations. This part addresses graduate students as well as researchers. (orig.)
When fast atom diffraction turns 3D
International Nuclear Information System (INIS)
Zugarramurdi, Asier; Borisov, Andrei G.
2013-01-01
Fast atom diffraction at surfaces (FAD) in grazing incidence geometry is characterized by the slow motion in the direction perpendicular to the surface and fast motion parallel to the surface plane along a low index direction. It is established experimentally that for the typical surfaces the FAD reveals the 2D diffraction patterns associated with exchange of the reciprocal lattice vector perpendicular to the direction of fast motion. The reciprocal lattice vector exchange along the direction of fast motion is negligible. The usual approximation made in the description of the experimental data is then to assume that the effective potential leading to the diffraction results from the averaging of the 3D surface potential along the atomic strings forming the axial channel. In this work we use full quantum wave packet propagation calculations to study theoretically the possibility to observe the 3D diffraction in FAD experiments. We show that for the surfaces with large unit cell, such as can be the case for reconstructed or vicinal surfaces, the 3D diffraction can be observed. The reciprocal lattice vector exchange along the direction of fast motion leads to several Laue circles in the diffraction pattern
LEED (Low Energy Electron Diffraction)
International Nuclear Information System (INIS)
Aberdam, M.
1973-01-01
The various types of systems studied by LEED, and for which the geometry of diffraction patterns is exploited, are reviewed, intensity profiles being another source of information. Two representative approaches of the scattering phenomenon are examined; the band structure theory and the T matrix approach [fr
Brand, Louis
2006-01-01
The use of vectors not only simplifies treatments of differential geometry, mechanics, hydrodynamics, and electrodynamics, but also makes mathematical and physical concepts more tangible and easy to grasp. This text for undergraduates was designed as a short introductory course to give students the tools of vector algebra and calculus, as well as a brief glimpse into these subjects' manifold applications. The applications are developed to the extent that the uses of the potential function, both scalar and vector, are fully illustrated. Moreover, the basic postulates of vector analysis are brou
Directory of Open Access Journals (Sweden)
Suttida Rakkapao
2016-10-01
Full Text Available This study investigated the multiple-choice test of understanding of vectors (TUV, by applying item response theory (IRT. The difficulty, discriminatory, and guessing parameters of the TUV items were fit with the three-parameter logistic model of IRT, using the parscale program. The TUV ability is an ability parameter, here estimated assuming unidimensionality and local independence. Moreover, all distractors of the TUV were analyzed from item response curves (IRC that represent simplified IRT. Data were gathered on 2392 science and engineering freshmen, from three universities in Thailand. The results revealed IRT analysis to be useful in assessing the test since its item parameters are independent of the ability parameters. The IRT framework reveals item-level information, and indicates appropriate ability ranges for the test. Moreover, the IRC analysis can be used to assess the effectiveness of the test’s distractors. Both IRT and IRC approaches reveal test characteristics beyond those revealed by the classical analysis methods of tests. Test developers can apply these methods to diagnose and evaluate the features of items at various ability levels of test takers.
Directory of Open Access Journals (Sweden)
VIAN RISKA AYUNING TYAS
2014-01-01
Full Text Available The Arbitrage Pricing Theory (APT is an alternative model to estimate the price of securities based of arbitrage concept. In APT, the returns of securities are affected by several factors. This research is aimed to estimate the expected returns of securities using APT model and Vector Autoregressive model. There are ten stocks incorporated in Kompas100 index and four macroeconomic variables, these are inflation, exchange rates, the amountof circulate money (JUB, and theinterest rateof Bank Indonesia(SBI are applied in this research. The first step in using VAR is to test the stationary of the data using colerogram and the results indicate that all data are stationary. The second step is to select the optimal lag based on the smallest value of AIC. The Granger causality test shows that the LPKR stock is affected by the inflation and the exchange rate while the nine other stocks do not show the existence of the expected causality. The results of causality test are then estimated by the VAR models in order to obtain expected returnof macroeconomic factors. The expected return of macroeconomic factors obtained is used in the APT model, then the expected return stock LPKR is calculated. It shows that the expected return of LPKR is 3,340%
Directory of Open Access Journals (Sweden)
VIAN RISKA AYUNING TYAS
2014-08-01
Full Text Available The Arbitrage Pricing Theory (APT is an alternative model to estimate the price of securities based of arbitrage concept. In APT, the returns of securities are affected by several factors. This research is aimed to estimate the expected returns of securities using APT model and Vector Autoregressive model. There are ten stocks incorporated in Kompas100 index and four macroeconomic variables, these are inflation, exchange rates, the amountof circulate money (JUB, and theinterest rateof Bank Indonesia(SBI are applied in this research. The first step in using VAR is to test the stationary of the data using colerogram and the results indicate that all data are stationary. The second step is to select the optimal lag based on the smallest value of AIC. The Granger causality test shows that the LPKR stock is affected by the inflation and the exchange rate while the nine other stocks do not show the existence of the expected causality. The results of causality test are then estimated by the VAR models in order to obtain expected returnof macroeconomic factors. The expected return of macroeconomic factors obtained is used in the APT model, then the expected return stock LPKR is calculated. It shows that the expected return of LPKR is 3,340%
Rakkapao, Suttida; Prasitpong, Singha; Arayathanitkul, Kwan
2016-12-01
This study investigated the multiple-choice test of understanding of vectors (TUV), by applying item response theory (IRT). The difficulty, discriminatory, and guessing parameters of the TUV items were fit with the three-parameter logistic model of IRT, using the parscale program. The TUV ability is an ability parameter, here estimated assuming unidimensionality and local independence. Moreover, all distractors of the TUV were analyzed from item response curves (IRC) that represent simplified IRT. Data were gathered on 2392 science and engineering freshmen, from three universities in Thailand. The results revealed IRT analysis to be useful in assessing the test since its item parameters are independent of the ability parameters. The IRT framework reveals item-level information, and indicates appropriate ability ranges for the test. Moreover, the IRC analysis can be used to assess the effectiveness of the test's distractors. Both IRT and IRC approaches reveal test characteristics beyond those revealed by the classical analysis methods of tests. Test developers can apply these methods to diagnose and evaluate the features of items at various ability levels of test takers.
Champenois, Gilles
2007-01-01
The mnesor theory is the adaptation of vectors to artificial intelligence. The scalar field is replaced by a lattice. Addition becomes idempotent and multiplication is interpreted as a selection operation. We also show that mnesors can be the foundation for a linear calculus.
Diffraction efficiency calculations of polarization diffraction gratings with surface relief
Nazarova, D.; Sharlandjiev, P.; Berberova, N.; Blagoeva, B.; Stoykova, E.; Nedelchev, L.
2018-03-01
In this paper, we evaluate the optical response of a stack of two diffraction gratings of equal one-dimensional periodicity. The first one is a surface-relief grating structure; the second, a volume polarization grating. This model is based on our experimental results from polarization holographic recordings in azopolymer films. We used films of commercially available azopolymer (poly[1-[4-(3-carboxy-4-hydroxyphenylazo) benzenesulfonamido]-1,2-ethanediyl, sodium salt]), shortly denoted as PAZO. During the recording process, a polarization grating in the volume of the material and a relief grating on the film surface are formed simultaneously. In order to evaluate numerically the optical response of this “hybrid” diffraction structure, we used the rigorous coupled-wave approach (RCWA). It yields stable numerical solutions of Maxwell’s vector equations using the algebraic eigenvalue method.
International Nuclear Information System (INIS)
Kohn, V. G.
2008-01-01
The effect of total reflection (switching) of a spherical X-ray wave in the case of Laue diffraction in a crystal with bending deformation is analyzed by the trajectory method. Qualitative analytical description and computation of the spatial structure of the reflected beam for large and small distances between the spherical-wave source and the crystal are performed. The mechanism of much more efficient reflection of an X-ray beam by a deformed crystal in comparison with a perfect crystal is clearly demonstrated. It is also shown that the trajectory method is very convenient for description of the total reflection phenomenon.
International Nuclear Information System (INIS)
Kohn, V. G.
2008-01-01
The effect of total reflection (switching) of a spherical X-ray wave in the case of Laue diffraction in a crystal with bending deformation is analyzed by the trajectory method. Qualitative analytical description and computation of the spatial structure of the reflected beam for large and small distances between the spherical-wave source and the crystal are performed. The mechanism of much more efficient reflection of an X-ray beam by a deformed crystal in comparison with a perfect crystal is clearly demonstrated. It is also shown that the trajectory method is very convenient for description of the total reflection phenomenon
DEFF Research Database (Denmark)
2012-01-01
The present invention relates to a compact, reliable and low-cost vector velocimeter for example for determining velocities of particles suspended in a gas or fluid flow, or for determining velocity, displacement, rotation, or vibration of a solid surface, the vector velocimeter comprising a laser...
DEFF Research Database (Denmark)
Hempler, Daniela; Schmidt, Martin U.; Van De Streek, Jacco
2017-01-01
More than 600 molecular crystal structures with correct, incorrect and uncertain space-group symmetry were energy-minimized with dispersion-corrected density functional theory (DFT-D, PBE-D3). For the purpose of determining the correct space-group symmetry the required tolerance on the atomic...... with missed symmetry were investigated by dispersion-corrected density functional theory. In 98.5% of the cases the correct space group is found....
International Nuclear Information System (INIS)
Shabbir, Ghulam; Khan, Suhail
2010-01-01
In this paper we classify Kantowski-Sachs and Bianchi type III space-times according to their teleparallel Killing vector fields using direct integration technique. It turns out that the dimension of the teleparallel Killing vector fields are 4 or 6, which are the same in numbers as in general relativity. In case of 4 the teleparallel Killing vector fields are multiple of the corresponding Killing vector fields in general relativity by some function of t. In the case of 6 Killing vector fields the metric functions become constants and the Killing vector fields in this case are exactly the same as in general relativity. Here we also discuss the Lie algebra in each case. (general)
Diffraction limit of refractive compound lens
International Nuclear Information System (INIS)
Kolchevsky, N.N.; Petrov, P.V.
2015-01-01
A compound X-ray and neutron lenses is an array of lenses with a common axis. The resolution limited by aberration and by diffraction. Diffraction limit comes from theory based on absorption aperture of the compound refractive lenses. Beam passing through transparent lenses form Airy pattern. Results of calculation of diffraction resolution limit for non-transparent X-ray and neutron lenses are discussed. (authors)
High-energy electron diffraction and microscopy
Peng, L M; Whelan, M J
2011-01-01
This book provides a comprehensive introduction to high energy electron diffraction and elastic and inelastic scattering of high energy electrons, with particular emphasis on applications to modern electron microscopy. Starting from a survey of fundamental phenomena, the authors introduce the most important concepts underlying modern understanding of high energy electron diffraction. Dynamical diffraction in transmission (THEED) and reflection (RHEED) geometries is treated using ageneral matrix theory, where computer programs and worked examples are provided to illustrate the concepts and to f
Rakhmatullin, Aydar; Polovov, Ilya B; Maltsev, Dmitry; Allix, Mathieu; Volkovich, Vladimir; Chukin, Andrey V; Boča, Miroslav; Bessada, Catherine
2018-02-05
The structures of several fluoroscandate compounds are presented here using a characterization approach combining powder X-ray diffraction and solid-state NMR. The structure of K 5 Sc 3 F 14 was fully determined from Rietveld refinement performed on powder X-ray diffraction data. Moreover, the local structures of NaScF 4 , Li 3 ScF 6 , KSc 2 F 7 , and Na 3 ScF 6 compounds were studied in detail from solid-state 19 F and 45 Sc NMR experiments. The 45 Sc chemical shift ranges for six- and seven-coordinated scandium environments were defined. The 19 F chemical shift ranges for bridging and terminal fluorine atoms were also determined. First-principles calculations of the 19 F and 45 Sc NMR parameters were carried out using plane-wave basis sets and periodic boundary conditions (CASTEP), and the results were compared with the experimental data. A good agreement between the calculated shielding constants and experimental chemical shifts was obtained. This demonstrates the good potential of computational methods in spectroscopic assignments of solid-state 45 Sc NMR spectroscopy.
X-ray topography and multiple diffraction
International Nuclear Information System (INIS)
Chang, S.-L.
1983-01-01
A short summary on X-ray topography, which is based on the dynamical theory of X-ray diffraction, is made. The applications and properties related to the use of the multiple diffraction technique are analized and discussed. (L.C.) [pt
Geometrical optics and the diffraction phenomenon
International Nuclear Information System (INIS)
Timofeev, Aleksandr V
2005-01-01
This note outlines the principles of the geometrical optics of inhomogeneous waves whose description necessitates the use of complex values of the wave vector. Generalizing geometrical optics to inhomogeneous waves permits including in its scope the analysis of the diffraction phenomenon. (methodological notes)
Diffractive dissociation and new quarks
International Nuclear Information System (INIS)
White, A.R.
1983-04-01
We argue that the chiral limit of QCD can be identified with the strong (diffractive dissociation) coupling limit of reggeon field theory. Critical Pomeron scaling at high energy must then be directly related to an infra-red fixed-point of massless QCD and so requires a large number of flavors. This gives a direct argument that the emergence of diffraction-peak scaling, KNO scaling etc. at anti p-p colliders are evidence of a substantial quark structure still to be discovered
Guilfoyle, Richard A.; Smith, Lloyd M.
1994-01-01
A vector comprising a filamentous phage sequence containing a first copy of filamentous phage gene X and other sequences necessary for the phage to propagate is disclosed. The vector also contains a second copy of filamentous phage gene X downstream from a promoter capable of promoting transcription in a bacterial host. In a preferred form of the present invention, the filamentous phage is M13 and the vector additionally includes a restriction endonuclease site located in such a manner as to substantially inactivate the second gene X when a DNA sequence is inserted into the restriction site.
Guilfoyle, R.A.; Smith, L.M.
1994-12-27
A vector comprising a filamentous phage sequence containing a first copy of filamentous phage gene X and other sequences necessary for the phage to propagate is disclosed. The vector also contains a second copy of filamentous phage gene X downstream from a promoter capable of promoting transcription in a bacterial host. In a preferred form of the present invention, the filamentous phage is M13 and the vector additionally includes a restriction endonuclease site located in such a manner as to substantially inactivate the second gene X when a DNA sequence is inserted into the restriction site. 2 figures.
Energy Technology Data Exchange (ETDEWEB)
Rejon-Barrera, Fernando [Institute for Theoretical Physics, University of Amsterdam,Science Park 904, Postbus 94485, 1090 GL, Amsterdam (Netherlands); Robbins, Daniel [Department of Physics, Texas A& M University,TAMU 4242, College Station, TX 77843 (United States)
2016-01-22
We work out all of the details required for implementation of the conformal bootstrap program applied to the four-point function of two scalars and two vectors in an abstract conformal field theory in arbitrary dimension. This includes a review of which tensor structures make appearances, a construction of the projectors onto the required mixed symmetry representations, and a computation of the conformal blocks for all possible operators which can be exchanged. These blocks are presented as differential operators acting upon the previously known scalar conformal blocks. Finally, we set up the bootstrap equations which implement crossing symmetry. Special attention is given to the case of conserved vectors, where several simplifications occur.
Diffraction of high energy electrons
International Nuclear Information System (INIS)
Bourret, A.
1981-10-01
The diffraction of electrons by a crystal is examined to study its structure. As the electron-substance interaction is strong, it must be treated in a dynamic manner. Using the N waves theory and physical optics the base equations giving the wave at the outlet are deduced for a perfect crystal and their equivalence is shown. The more complex case of an imperfect crystal is then envisaged in these two approaches. In both cases, only the diffraction of high energy electrons ( > 50 KeV) are considered since in the diffraction of slow electrons back scattering cannot be ignored. Taking into account an increasingly greater number of beams, through fast calculations computer techniques, enables images to be simulated in very varied conditions. The general use of the Fast Fourier Transform has given a clear cut practical advantage to the multi-layer method [fr
Levine, Robert
2004-01-01
The cross-product is a mathematical operation that is performed between two 3-dimensional vectors. The result is a vector that is orthogonal or perpendicular to both of them. Learning about this for the first time while taking Calculus-III, the class was taught that if AxB = AxC, it does not necessarily follow that B = C. This seemed baffling. The…
Search for intermediate vector bosons
International Nuclear Information System (INIS)
Cline, D.B.; Rubbia, C.; van der Meer, S.
1982-01-01
Over the past 15 years a new class of unified theories has been developed to describe the forces acting between elementary particles. The most successful of the new theories establishes a link between electromagnetism and the weak force. A crucial prediction of this unified electroweak theory is the existence of three massive particles called intermediate vector bosons. If these intermediate vector bosons exist and if they have properties attributed to them by electroweak theory, they should soon be detected, as the world's first particle accelerator with enough energy to create such particles has recently been completed at the European Organization for Nuclear Research (CERN) in Geneva. The accelerator has been converted to a colliding beam machine in which protons and antiprotons collide head on. According to electroweak theory, intermediate vector bosons can be created in proton-antiproton collisions. (SC)
General projective relativity and the vector-tensor gravitational field
International Nuclear Information System (INIS)
Arcidiacono, G.
1986-01-01
In the general projective relativity, the induced 4-dimensional metric is symmetric in three cases, and we obtain the vector-tensor, the scalar-tensor, and the scalar-vector-tensor theories of gravitation. In this work we examine the vector-tensor theory, similar to the Veblen's theory, but with a different physical interpretation
Diffraction coherence in optics
Françon, M; Green, L L
2013-01-01
Diffraction: Coherence in Optics presents a detailed account of the course on Fraunhofer diffraction phenomena, studied at the Faculty of Science in Paris. The publication first elaborates on Huygens' principle and diffraction phenomena for a monochromatic point source and diffraction by an aperture of simple form. Discussions focus on diffraction at infinity and at a finite distance, simplified expressions for the field, calculation of the path difference, diffraction by a rectangular aperture, narrow slit, and circular aperture, and distribution of luminous flux in the airy spot. The book th
Diffraction of polarized light on periodic structures
International Nuclear Information System (INIS)
Bukanina, V; Divakov, D; Tyutyunnik, A; Hohlov, A
2012-01-01
Periodic structures as photonic crystals are widely used in modern laser devices, communication technologies and for creating various beam splitters and filters. Diffraction gratings are applied for creating 3D television sets, DVD and Blu-ray drives and reflective structures (Berkley mirror). It is important to simulate diffraction on such structures to design optical systems with predetermined properties based on photonic crystals and diffraction gratings. Methods of simulating diffraction on periodic structures uses theory of Floquet-Bloch and rigorous coupled-wave analysis (RCWA). Current work is dedicated to analysis of photonic band gaps and simulating diffraction on one-dimensional binary diffraction grating using RCWA. The Maxwell's equations for isotropic media and constitutive relations based on the cgs system were used as a model.
Directory of Open Access Journals (Sweden)
Qiang Shang
2016-08-01
Full Text Available Short-term traffic flow prediction is an important part of intelligent transportation systems research and applications. For further improving the accuracy of short-time traffic flow prediction, a novel hybrid prediction model (multivariate phase space reconstruction–combined kernel function-least squares support vector machine based on multivariate phase space reconstruction and combined kernel function-least squares support vector machine is proposed. The C-C method is used to determine the optimal time delay and the optimal embedding dimension of traffic variables’ (flow, speed, and occupancy time series for phase space reconstruction. The G-P method is selected to calculate the correlation dimension of attractor which is an important index for judging chaotic characteristics of the traffic variables’ series. The optimal input form of combined kernel function-least squares support vector machine model is determined by multivariate phase space reconstruction, and the model’s parameters are optimized by particle swarm optimization algorithm. Finally, case validation is carried out using the measured data of an expressway in Xiamen, China. The experimental results suggest that the new proposed model yields better predictions compared with similar models (combined kernel function-least squares support vector machine, multivariate phase space reconstruction–generalized kernel function-least squares support vector machine, and phase space reconstruction–combined kernel function-least squares support vector machine, which indicates that the new proposed model exhibits stronger prediction ability and robustness.
Jets and diffraction results from HERA
International Nuclear Information System (INIS)
Buniatyan, A.
2014-01-01
The latest results on precision measurements of jet and diffractive cross sections obtained by the H1 and ZEUS experiments at HERA are reported. The inclusive jet and multi-jet cross-sections are used in QCD calculations at next-to-leading order (NLO) to determine the strong coupling α s . The cross-section measurements for diffractive inclusive DIS processes with a leading proton in the final state are combined for the H1 and ZEUS experiments in order to improve the precision and extend the kinematic range. The di-jet cross sections are measured in diffractive DIS with a leading proton and compared with QCD predictions based on diffractive parton densities in the proton. The cross sections for exclusive heavy vector meson photoproduction are studied in terms of the momentum transfer at the proton vertex and of the photon-proton centre-of-mass energy. (author)
International Nuclear Information System (INIS)
Checon, A.
1983-01-01
Theoretical formulation of a straight edge diffraction shows a phase difference of π/2 between the incoming and diffracted waves. Experiments using two straight edges do not confirm the π/2 difference but suggest that the incoming wave is in phase with the wave diffracted into the shadowed region of the edge and out of phase by a factor of π with the wave diffracted into the illuminated region. (Author) [pt
Electroproduction and photoproduction of vector mesons and generalized vector meson dominance
International Nuclear Information System (INIS)
Fraas, H.; Kuroda, M.
1977-05-01
Using generalized vector meson dominance, electro- and photoproduction of vector mesons is studied. The unnatural parity exchange part of ω(1.2) production is estimated to be about one fourth of that of ω-production. The off diagonal transition model suggests the suppression of diffractive rho(1.2) and ω(1.2) production. (orig.) [de
Robinson, Gilbert de B
2011-01-01
This brief undergraduate-level text by a prominent Cambridge-educated mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement for Gilbert de B. Robinson's text, which is the result of several years of teaching and learning the most effective methods from discussions with students. Topics include lines and planes, determinants and linear equations, matrices, groups and linear transformations, and vectors and vector spaces. Additional subjects range from conics and quadrics to homogeneous coordinates and projective geom
Vector model for polarized second-harmonic generation microscopy under high numerical aperture
International Nuclear Information System (INIS)
Wang, Xiang-Hui; Chang, Sheng-Jiang; Lin, Lie; Wang, Lin-Rui; Huo, Bing-Zhong; Hao, Shu-Jian
2010-01-01
Based on the vector diffraction theory and the generalized Jones matrix formalism, a vector model for polarized second-harmonic generation (SHG) microscopy is developed, which includes the roles of the axial component P z , the weight factor and the cross-effect between the lateral components. The numerical results show that as the relative magnitude of P z increases, the polarization response of the second-harmonic signal will vary from linear polarization to elliptical polarization and the polarization orientation of the second-harmonic signal is different from that under the paraxial approximation. In addition, it is interesting that the polarization response of the detected second-harmonic signal can change with the value of the collimator lens NA. Therefore, it is more advantageous to adopt the vector model to investigate the property of polarized SHG microscopy for a variety of cases
Spider diffraction: a comparison of curved and straight legs
International Nuclear Information System (INIS)
Richter, J.L.
1984-01-01
It has been known for some time that, if curved legs rather than the usual straight ones are used in the spider that supports the secondary optics in certain telescopes, the visible diffraction effect is reduced. Fraunhofer theory is used to calculate the diffraction effects due to the curved leg spider. Calculated and photographic diffraction patterns are compared for straight and curved leg spiders
Integrated intensities and flipping ratios in neutron diffraction by perfect magnetic crystals
International Nuclear Information System (INIS)
Guigay, J.P.; Schlenker, M.
1979-01-01
A theoretical study of neutron diffraction by perfect magnetic crystals is presented which shows that when the magnetization is perpendicular to the diffraction vector (β- π/2), the dispersion surface is made up of two hyperbolic surfaces corresponding to simple polarization states and the results of the two-beam dynamical theory for non-magnetic crystals can be directly applied. The asymptotic properties of the dispersion surface are of the dispersion surface are also discussed in the more general case (β is not equal to π/2) and an analytical treatment of the kinematical limit is presented. Integrated intensities and flipping ratios outside this limit can only be calculated numerically. It is shown that the wave fields defined by the different points of the dispersion surface are polarized in the (g, B 0 ) plane; this is a generalization of the fact that they are (+-) states with respect to B 0 in the simple case (β=π/2). (UK)
International Nuclear Information System (INIS)
Ishida, Hidenobu
2015-01-01
The dynamical diffraction theory of X-rays for a distorted crystal with the Green's function method is applied to the Bragg case. The transmitted and diffracted crystal waves are represented as the solutions of the integral equations using the Green's function. For a perfect crystal, the most exact form of the solution of the equations is given by the Green's function and its derivatives, and the waves are analytically expressed by using them. The results can be applied in a general case where the amplitude modulation of the incident wave is not negligibly small compared with the wave vector. If the amplitude modulation is small, those results are reduced essentially to the same as those given by Takagi's theory. (author)
An introduction to vectors, vector operators and vector analysis
Joag, Pramod S
2016-01-01
Ideal for undergraduate and graduate students of science and engineering, this book covers fundamental concepts of vectors and their applications in a single volume. The first unit deals with basic formulation, both conceptual and theoretical. It discusses applications of algebraic operations, Levi-Civita notation, and curvilinear coordinate systems like spherical polar and parabolic systems and structures, and analytical geometry of curves and surfaces. The second unit delves into the algebra of operators and their types and also explains the equivalence between the algebra of vector operators and the algebra of matrices. Formulation of eigen vectors and eigen values of a linear vector operator are elaborated using vector algebra. The third unit deals with vector analysis, discussing vector valued functions of a scalar variable and functions of vector argument (both scalar valued and vector valued), thus covering both the scalar vector fields and vector integration.
DEFF Research Database (Denmark)
Davis, Christopher James; Kedlaya, Kiran
2014-01-01
We study the kernel and cokernel of the Frobenius map on the p-typical Witt vectors of a commutative ring, not necessarily of characteristic p. We give many equivalent conditions to surjectivity of the Frobenius map on both finite and infinite length Witt vectors. In particular, surjectivity...... on finite Witt vectors turns out to be stable under certain integral extensions; this provides a clean formulation of a strong generalization of Faltings’s almost purity theorem from p-adic Hodge theory, incorporating recent improvements by Kedlaya–Liu and by Scholze....
Giani, S; Niewiadomski, H; Antchev, G; Aspell, P; Avati, V; Bagliesi, M G; Berardi, V; Berretti, M; Besta, M; Bozzo, M; Brücken, E; Buzzo, A; Cafagna, F; Calicchio, M; Catanesi, M G
2010-01-01
The primary objective of the TOTEM experiment at the LHC is the measurement of the total proton-proton cross section with the luminosity-independent method and the study of elastic proton-proton cross-section over a wide |t|-range. In addition TOTEM also performs a comprehensive study of diffraction, spanning from cross-section measurements of individual diffractive processes to the analysis of their event topologies. Hard diffraction will be studied in collaboration with CMS taking advantage...
Antchev, G.; Aspell, P.; Avati, V.; Bagliesi, M.G.; Berardi, V.; Berretti, M.; Bottigli, U.; Bozzo, M.; Brucken, E.; Buzzo, A.; Cafagna, F.; Calicchio, M.; Catanesi, M.G.; Catastini, P.L.; Cecchi, R.
2008-01-01
The TOTEM experiment at the LHC measures the total proton-proton cross section with the luminosity-independent method and the elastic proton-proton cross-section over a wide |t|-range. It also performs a comprehensive study of diffraction, spanning from cross-section measurements of individual diffractive processes to the analysis of their event topologies. Hard diffraction will be studied in collaboration with CMS taking advantage of the large common rapidity coverage for charged and neutral...
QCD and hard diffraction at the LHC
International Nuclear Information System (INIS)
Albrow, Michael G.; Fermilab
2005-01-01
As an introduction to QCD at the LHC I given an overview of QCD at the Tevatron, emphasizing the high Q 2 frontier which will be taken over by the LHC. After describing briefly the LHC detectors I discuss high mass diffraction, in particular central exclusive production of Higgs and vector boson pairs. I introduce the FP420 project to measure the scattered protons 420 m downstream of ATLAS and CMS
Vector manifestation and violation of vector dominance in hot matter
International Nuclear Information System (INIS)
Harada, Masayasu; Sasaki, Chihiro
2004-01-01
We show the details of the calculation of the hadronic thermal corrections to the two-point functions in the effective field theory of QCD for pions and vector mesons based on the hidden local symmetry (HLS) in hot matter using the background field gauge. We study the temperature dependence of the pion velocity in the low-temperature region determined from the hadronic thermal corrections, and show that, due to the presence of the dynamical vector meson, the pion velocity is smaller than the speed of the light already at one-loop level, in contrast to the result obtained in the ordinary chiral perturbation theory including only the pion at one-loop. Including the intrinsic temperature dependences of the parameters of the HLS Lagrangian determined from the underlying QCD through the Wilsonian matching, we show how the vector manifestation (VM), in which the massless vector meson becomes the chiral partner of pion, is realized at the critical temperature. We present a new prediction of the VM on the direct photon-π-π coupling which measures the validity of the vector dominance (VD) of the electromagnetic form factor of the pion: we find that the VD is largely violated at the critical temperature, which indicates that the assumption of the VD made in several analyses on the dilepton spectra in hot matter may need to be weakened for consistently including the effect of the dropping mass of the vector meson
An experiment in diffractive physics
International Nuclear Information System (INIS)
Santoro, Alberto
2001-01-01
The purpose of this talk is to show one of the next future experiment in diffractive Physics which will be installed at the DO experiment at Tevatron/Fermilab for run II, and the importance for Quantum Chromodynamics (QCD) as the theory of the strong interactions. The apparatus that we have developed is the Forward Proton Detector (FPD) to be introduced on the beam line of the Tevatron at both sides of the DO detector. The FPD is composed by a set of Roman Pots as we will see in the text below
Grzelak, Adam; Gawraczyński, Jakub; Jaroń, Tomasz; Somayazulu, Maddury; Derzsi, Mariana; Struzhkin, Viktor; Grochala, Wojciech
2017-05-15
The X-ray diffraction data collected up to ca. 56 GPa and the Raman spectra measured up to 74.8 GPa for AgO, or Ag I Ag III O 2 , which is a prototypical mixed valence (disproportionated) oxide, indicate that two consecutive phase transitions occur: the first-order phase transition occurs between 16.1 GPa and 19.7 GPa, and a second-order phase transition occurs at ca. 40 GPa. All polymorphic forms host the square planar [Ag III O 4 ] units typical of low-spin Ag III . The disproportionated Imma form persists at least up to 74.8 GPa, as indicated by Raman spectra. Theoretical hybrid density functional theory (DFT) calculations show that the first-order transition is phonon-driven. AgO stubbornly remains disproportionated up to at least 100 GPa-in striking contrast to its copper analogue-and the fundamental band gap of AgO is ∼0.3 eV at this pressure and is weakly pressure-dependent. Metallization of AgO is yet to be achieved.
Diffractive sub-picosecond manipulation of x-rays
International Nuclear Information System (INIS)
Adams, B.
2004-01-01
A class of X-ray optical elements for the sub-picosecond manipulation of X-rays is proposed. The design of these elements is based upon a time-dependent dynamical diffraction theory that synthesizes the eikonal theory with the Takagi-Taupin theory. A brief outline of the theory is given
Extinction correction in white X-ray and neutron diffraction
International Nuclear Information System (INIS)
Tomiyoshi, S.; Yamada, M.; Watanabe, H.
1980-01-01
Extinction effects in white-beam X-ray and neutron diffraction are considered. In white-beam diffraction, a small deviation of the wavelength from the Bragg condition Δlambda is a variable which represents the line profile of the diffraction peaks, so that by using the new parameter Δlambda the theory is converted to one in white-beam diffraction. It is shown that for a convex crystal, primary extinction agrees with the results calculated already for monochromatic diffraction. The same relation is shown to hold in secondary extinction. It is concluded that extinction theory derived for monochromatic diffraction is applicable without any modification in white-beam diffraction. (Auth.)
Diffraction Theory and Almost Periodic Distributions
Strungaru, Nicolae; Terauds, Venta
2016-09-01
We introduce and study the notions of translation bounded tempered distributions, and autocorrelation for a tempered distribution. We further introduce the spaces of weakly, strongly and null weakly almost periodic tempered distributions and show that for weakly almost periodic tempered distributions the Eberlein decomposition holds. For translation bounded measures all these notions coincide with the classical ones. We show that tempered distributions with measure Fourier transform are weakly almost periodic and that for this class, the Eberlein decomposition is exactly the Fourier dual of the Lebesgue decomposition, with the Fourier-Bohr coefficients specifying the pure point part of the Fourier transform. We complete the project by looking at few interesting examples.
International Nuclear Information System (INIS)
Rodríguez, Yeinzon; Navarro, Andrés A.
2017-01-01
An alternative for the construction of fundamental theories is the introduction of Galileons. These are fields whose action leads to non higher than second-order equations of motion. As this is a necessary but not sufficient condition to make the Hamiltonian bounded from below, as long as the action is not degenerate, the Galileon construction is a way to avoid pathologies both at the classical and quantum levels. Galileon actions are, therefore, of great interest in many branches of physics, specially in high energy physics and cosmology. This proceedings contribution presents the generalities of the construction of both scalar and vector Galileons following two different but complimentary routes. (paper)
Diffraction. Powder, amorphous, liquid
International Nuclear Information System (INIS)
Sosnowska, I.M.
1999-01-01
Neutron powder diffraction is a unique tool to observe all possible diffraction effects appearing in crystal. High-resolution neutron diffractometers have to be used in this study. Analysis of the magnetic structure of polycrystalline materials requires the use of high-resolution neutron diffraction in the range of large interplanar distances. As distinguished from the double axis diffractometers (DAS), which show high resolution only at small interplanar distances, TOF (time-of-flight) diffractometry offers the best resolution at large interplanar distances. (K.A.)
The dynamics of diffracted rays in foams
Energy Technology Data Exchange (ETDEWEB)
Tufaile, A., E-mail: tufaile@usp.br; Tufaile, A.P.B.
2015-12-18
We have studied some aspects of the optics of the light scattering in foams. This paper describes the difference between rays and diffracted rays from the point of view of geometrical theory of diffraction. We have represented some bifurcations of light rays using dynamical systems. Based on our observations of foams, we created a solid optical device. The interference patterns of light scattering in foams forming Airy fringes were explored observing the pattern named as the eye of Horus. In the cases we examine, these Airy fringes are associated with light scattering in curved surfaces, while the halo formation is related to the law of edge diffraction. We are proposing a Pohl interferometer using a three-sided bubble/Plateau border system. - Highlights: • We obtained halos scattering light in foams. • We model the light scattering in foams using the geometrical theory of diffraction. • We examine the difference between rays and the diffracted rays. • We developed optical devices for diffracted rays.
A study of biorthogonal multiple vector-valued wavelets
International Nuclear Information System (INIS)
Han Jincang; Cheng Zhengxing; Chen Qingjiang
2009-01-01
The notion of vector-valued multiresolution analysis is introduced and the concept of biorthogonal multiple vector-valued wavelets which are wavelets for vector fields, is introduced. It is proved that, like in the scalar and multiwavelet case, the existence of a pair of biorthogonal multiple vector-valued scaling functions guarantees the existence of a pair of biorthogonal multiple vector-valued wavelet functions. An algorithm for constructing a class of compactly supported biorthogonal multiple vector-valued wavelets is presented. Their properties are investigated by means of operator theory and algebra theory and time-frequency analysis method. Several biorthogonality formulas regarding these wavelet packets are obtained.
Dynamical neutron diffraction by curved crystals in the Laue geometry
International Nuclear Information System (INIS)
Albertini, G.; Melone, S.; Lagomarsino, S.; Mazkedian, S.; Puliti, P.; Rustichelli, F.
1977-01-01
The Taupin dynamical theory of X-ray diffraction by deformed crystals which was previously extended to the neutron diffraction by curved crystals in the Bragg geometry, is applied to calculate neutron diffraction patterns in the Laue geometry. The theoretical results are compared with experimental data on curved silicon crystals. The agreement is quite satisfactory. In the second part a simple model recently presented to describe neutron diffraction properties in the Bragg case is extended to the Laue case. The predictions of such a model are in satisfactory agreement with the rigorous theory and the experimental results. (author)
Antchev, G.; Avati, V.; Bagliesi, M.G.; Berardi, V.; Berretti, M.; Bottigli, U.; Bozzo, M.; Brucken, E.; Buzzo, A.; Cafagna, F.; Calicchio, M.; Catanesi, M.G.; Catastini, P.L.; Cecchi, R.; Ciocci, M.A.; Deile, M.; Dimovasili, E.; Eggert, K.; Eremin, V.; Ferro, F.; Garcia, F.; Giani, S.; Greco, V.; Heino, J.; Hilden, T.; Kaspar, J.; Kopal, J.; Kundrat, V.; Kurvinen, K.; Lami, S.; Latino, G.; Lauhakangas, R.; Lippmaa, E.; Lokajicek, M.; Lo Vetere, M.; Lucas Rodriguez, F.; Macri, M.; Magazzu, G.; Meucci, M.; Minutoli, S.; Niewiadomski, H.; Noschis, E.; Notarnicola, G.; Oliveri, E.; Oljemark, F.; Orava, R.; Oriunno, M.; Osterberg, K.; Palazzi, P.; Pedreschi, E.; Petajajarvi, J.; Quinto, M.; Radermacher, E.; Radicioni, E.; Ravotti, F.; Rella, G.; Robutti, E.; Ropelewski, L.; Ruggiero, G.; Rummel, A.; Saarikko, H.; Sanguinetti, G.; Santroni, A.; Scribano, A.; Sette, G.; Snoeys, W.; Spinella, F.; Squillacioti, P.; Ster, A.; Taylor, C.; Trummal, A.; Turini, N.; Whitmore, J.; Wu, J.
2009-01-01
The TOTEM experiment at the LHC measures the total proton-proton cross section with the luminosity-independent method and the elastic proton-proton cross-section over a wide |t|-range. It also performs a comprehensive study of diffraction, spanning from cross-section measurements of individual diffractive processes to the analysis of their event topologies. Hard diffraction will be studied in collaboration with CMS taking advantage of the large common rapidity coverage for charged and neutral particle detection and the large variety of trigger possibilities even at large luminosities. TOTEM will take data under all LHC beam conditions including standard high luminosity runs to maximize its physics reach. This contribution describes the main features of the TOTEM physics programme including measurements to be made in the early LHC runs. In addition, a novel scheme to extend the diffractive proton acceptance for high luminosity runs by installing proton detectors at IP3 is described.
Giani, S; Antchev, G; Aspell, P; Avati, V; Bagliesi, M G; Berardi, V; Berretti, M; Besta, M; Bozzo, M; Brücken, E; Buzzo, A; Cafagna, F; Calicchio, M; Catanesi, M G; Cecchi, R; Ciocci, M A; Dadel, P; Deile, M; Dimovasili, E; Eggert, K; Eremin, V; Ferro, F; Fiergolski, A; García, F; Greco, V; Grzanka, L; Heino, J; Hildén, T; Kaspar, J; Kopal, J; Kundrát, V; Kurvinen, K; Lami, S; Latino, G; Lauhakangas, R; Leszko, R; Lippmaa, E; Lokajícek, M; Lo Vetere, M; Lucas Rodriguez, F; Macrí, M; Magazzù, G; Meucci, M; Minutoli, S; Notarnicola, G; Oliveri, E; Oljemark, F; Orava, R; Oriunno, M; Österberg, K; Pedreschi, E; Petäjäjärvi, J; Prochazka, J; Quinto, M; Radermacher, E; Radicioni, E; Ravotti, F; Rella, G; Robutti, E; Ropelewski, L; Rostkowski, M; Ruggiero, G; Rummel, A; Saarikko, H; Sanguinetti, G; Santroni, A; Scribano, A; Sette, G; Snoeys, W; Spinella, F; Ster, A; Taylor, C; Trummal, A; Turini, N; Whitmore, J; Wu, J; Zalewski, M
2010-01-01
The primary objective of the TOTEM experiment at the LHC is the measurement of the total proton-proton cross section with the luminosity-independent method and the study of elastic proton-proton cross-section over a wide |t|-range. In addition TOTEM also performs a comprehensive study of diffraction, spanning from cross-section measurements of individual diffractive processes to the analysis of their event topologies. Hard diffraction will be studied in collaboration with CMS taking advantage of the large common rapidity coverage for charged and neutral particle detection and the large variety of trigger possibilities even at large luminosities. TOTEM will take data under all LHC beam conditions including standard high luminosity runs to maximise its physics reach. This contribution describes the main features of the TOTEM diffractive physics programme including measurements to be made in the early LHC runs.
Duality in diffraction dissociations
International Nuclear Information System (INIS)
Santoro, Alberto.
1977-01-01
Diffractive dissociations (aN→a*πN) are naturally explained and a model that accounts for the three-variable correlation (mass-transfer-Jackson angle correlation) is presented. This model takes into account the three possible exchanges: t (pion), u(a*) and s(a) channel exchanger. The physical consequences of the model are: a strong mass-slope correlation due to the zeros of the amplitude, a factorization of diffractive dissociations (factorization of the Pomeron), the possibility of extending this model to double diffractive dissociation and diffraction by nuclei. This model was applied to the NN→NπN reaction. Using the usual parameters of the Deck model, a comparison is made with experiments for all available distributions. the strong slope of the peak at 1400 MeV is naturally explained [fr
DIFFRACTION SYNCHRONIZATION OF LASERS,
semiconductor lasers while suppressing parasitic generation in the plane of the mirror. The diffraction coupling coefficient of open resonators is calculated, and the stability conditions of the synchronized system is determined.
The logarithmic slope in diffractive DIS
International Nuclear Information System (INIS)
Gay Ducati, M.B.; Goncalves, V.P.; Machado, M.V.T.
2002-01-01
The logarithmic slope of diffractive structure function is a potential observable to separate the hard and soft contributions in diffraction, allowing to disentangle the QCD dynamics at small-x region. In this paper we extend our previous analyzes and calculate the diffractive logarithmic slope for three current approaches in the literature: (i) the Bartels-Wusthoff model, based on perturbative QCD, (ii) the CKMT model, based on Regge theory and (iii) the Golec-Biernat-Wusthoff model which assumes that the saturation phenomena is present in the HERA kinematic region. We analyze the transition region of small to large momentum transfer and verify that future experimental results on the diffractive logarithmic slope could discriminate between these approaches
X-ray diffraction 2 - diffraction principles
International Nuclear Information System (INIS)
O'Connor, B.
1999-01-01
Full text: The computation of powder diffraction intensities is based on the principle that the powder pattern comprises the summation of the intensity contributions from each of the crystallites (or single crystals) in the material. Therefore, it is of value for powder diffractionists to appreciate the form of the expression for calculating single crystal diffraction pattern intensities. This knowledge is especially important for Rietveld analysis practitioners in terms of the (i) mathematics of the method and (ii) retrieving single crystal structure data from the literature. We consider the integrated intensity from a small single crystal being rotated at velocity ω through the Bragg angle θ for reflection (hkl).... I(hkl) = [l o /ω]. [e 4 /m 2 c 4 ]. [λ 3 δV F(hkl) 2 /υ 2 ].[(1+cos 2 2θ)/2sin2θ] where e, m and c are the usual fundamental constants; λ is the x-ray wavelength, δV is the crystallite volume; F(hkl) is the structure factor; υ is the unit cell volume; and (1+cos 2 θ)/2sin2θ] is the Lorentz-polarisation factor for an unpolarised incident beam. The expression does not include a contribution for extinction. The influence of factors λ, δV, F(hkl) and υ on the intensities should be appreciated by powder diffractionists, especially the structure factor, F(hkl), which is responsible for the fingerprint nature of diffraction patterns, such as the rise and fall of intensity from peak to peak. The structure factor expression represents the summation of the scattered waves from each of the j scattering centres (i e atoms) in the unit cell: F(hkl) Σ f j exp[2πi (h.x j +k.y i +l. z i )] T j . Symbol f is the scattering factor (representing the atom-type scattering efficiency); (x, y, z) are the fractional position coordinates of atom j within the unit cell; and T is the thermal vibration factor for the atom given by: T j = 8π 2 2 > sin 2 θ/λ 2 with 2 > being the mean-square vibration amplitude of the atom (assumed to be isotropic). The
International Nuclear Information System (INIS)
Ginelli, Francesco; Politi, Antonio; Chaté, Hugues; Livi, Roberto
2013-01-01
Recent years have witnessed a growing interest in covariant Lyapunov vectors (CLVs) which span local intrinsic directions in the phase space of chaotic systems. Here, we review the basic results of ergodic theory, with a specific reference to the implications of Oseledets’ theorem for the properties of the CLVs. We then present a detailed description of a ‘dynamical’ algorithm to compute the CLVs and show that it generically converges exponentially in time. We also discuss its numerical performance and compare it with other algorithms presented in the literature. We finally illustrate how CLVs can be used to quantify deviations from hyperbolicity with reference to a dissipative system (a chain of Hénon maps) and a Hamiltonian model (a Fermi–Pasta–Ulam chain). This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (paper)
Optical cage generated by azimuthal- and radial-variant vector beams.
Man, Zhongsheng; Bai, Zhidong; Li, Jinjian; Zhang, Shuoshuo; Li, Xiaoyu; Zhang, Yuquan; Ge, Xiaolu; Fu, Shenggui
2018-05-01
We propose a method to generate an optical cage using azimuthal- and radial-variant vector beams in a high numerical aperture optical system. A new kind of vector beam that has azimuthal- and radial-variant polarization states is proposed and demonstrated theoretically. Then, an integrated analytical model to calculate the electromagnetic field and Poynting vector distributions of the input azimuthal- and radial-variant vector beams is derived and built based on the vector diffraction theory of Richards and Wolf. From calculations, a full polarization-controlled optical cage is obtained by simply tailoring the radial index of the polarization, the uniformity U of which is up to 0.7748, and the cleanness C is zero. Additionally, a perfect optical cage can be achieved with U=1, and C=0 by introducing an amplitude modulation; its magnetic field and energy flow are also demonstrated in detail. Such optical cages may be helpful in applications such as optical trapping and high-resolution imaging.
Energy Technology Data Exchange (ETDEWEB)
Mangir Murshed, M., E-mail: murshed@uni-bremen.de [Chemische Kristallographie fester Stoffe, Institut für Anorganische Chemie, Universität Bremens, Leobener Straße, D-28359 Bremen (Germany); Mendive, Cecilia B.; Curti, Mariano [Departamento de Química, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Dean Funes 3350, B7600AYL Mar del Plata (Argentina); Šehović, Malik [Chemische Kristallographie fester Stoffe, Institut für Anorganische Chemie, Universität Bremens, Leobener Straße, D-28359 Bremen (Germany); Friedrich, Alexandra [Institut für Geowissenschaften, Abteilung Kristallographie, Goethe-Universität Frankfurt, Altenhöferallee 1, D-60438 Frankfurt am Main (Germany); Fischer, Michael [Kristallographie, FB Geowissenschaften, Universität Bremen, Klagenfurter Straße, D-28359 Bremen (Germany); Gesing, Thorsten M. [Chemische Kristallographie fester Stoffe, Institut für Anorganische Chemie, Universität Bremens, Leobener Straße, D-28359 Bremen (Germany)
2015-09-15
Polycrystalline Bi{sub 2}Al{sub 4}O{sub 9} powder samples were synthesized using the glycerine method. Single crystals were produced from the powder product in a Bi{sub 2}O{sub 3} melt. The lattice thermal expansion of the mullite-type compound was studied using X-ray diffraction, Raman spectroscopy and density functional theory (DFT). The metric parameters were modeled using Grüneisen approximation for the zero pressure equation of state, where the temperature-dependent vibrational internal energy was calculated from the Debye characteristic frequency. Both the first-order and second-order Grüneisen approximations were applied for modeling the volumetric expansion, and the second-order approach provided physically meaningful axial parameters. The phonon density of states as well as phonon dispersion guided to set the characteristic frequency for simulation. The experimental infrared and Raman phonon bands were compared with those calculate from the DFT calculations. Selective Raman modes were analyzed for the thermal anharmonic behaviors using simplified Klemens model. The respective mode Grüneisen parameters were calculated from the pressure-dependent Raman spectra. - Graphical abstract: Crystal structure of mullite-type Bi{sub 2}Al{sub 4}O{sub 9} showing the edge-sharing AlO{sub 6} octahedra running parallel to the c-axis. - Highlights: • Thermal expansion of Bi{sub 2}Al{sub 4}O{sub 9} was studied using XRD, FTIR, Raman and DFT. • Metric parameters were modeled using Grüneisen approximation. • Phonon DOS and phonon dispersion helped to set the Debye frequency. • Mode Grüneisen parameters were calculated from the pressure-dependent Raman spectra. • Anharmonicity was analyzed for some selective Raman modes.
Taddei, Marco; Tiana, Davide; Casati, Nicola; van Bokhoven, Jeroen A; Smit, Berend; Ranocchiari, Marco
2017-01-04
The use of mixed-linker metal-organic frameworks (MIXMOFs) is one of the most effective strategies to modulate the physical-chemical properties of MOFs without affecting the overall crystal structure. In many instances, MIXMOFs have been recognized as solid solutions, with random distribution of ligands, in agreement with the empirical rule known as Vegard's law. In this work, we have undertaken a study combining high-resolution powder X-ray diffraction (HR-PXRD) and density functional theory (DFT) calculations with the aim of understanding the reasons why UiO-66-based amino- and bromo-functionalized MIXMOFs (MIXUiO-66) undergo cell expansion obeying Vegard's law and how this behaviour is related to their physical-chemical properties. DFT calculations predict that the unit cell in amino-functionalized UiO-66 experiences only minor expansion as a result of steric effects, whereas major modification to the electronic features of the framework leads to weaker metal-linker interaction and consequently to the loss of stability at higher degrees of functionalization. For bromo-functionalized UiO-66, steric repulsion due to the size of bromine yields a large cell expansion, but the electronic features remain very similar to pristine UiO-66, preserving the stability of the framework upon functionalization. MIXUiO-66 obtained by either direct synthesis or by post-synthetic exchange shows Vegard-like behaviour, suggesting that both preparation methods yield solid solutions, but the thermal stability and the textural properties of the post-synthetic exchanged materials do not display a clear dependence on the chemical composition, as observed for the MOFs obtained by direct synthesis.
1987-05-01
plvdl ’ , systems, Applied Optics, 16( 12), 1181 - iAQ. Champion, 7. ’., G . H . Meeten and ". enir, ’ " . , ’ particles in the colloidal state, ourna: ,f...he her, 4a London, Faraday Transactions * - Champion, J. V. , G . H . Meeten , 1. 4. U 0 1n and -arp. Optical extinction of randomly ,oriented in, T...distance into the (poly) dispersion. We can find T -from f du fdy fda G (u,y,$) Qi(u,y,S) n(u) g (y) h (B) (15) where u is some parameter specifying
Diffraction. Single crystal, magnetic
International Nuclear Information System (INIS)
Heger, G.
1999-01-01
The analysis of crystal structure and magnetic ordering is usually based on diffraction phenomena caused by the interaction of matter with X-rays, neutrons, or electrons. Complementary information is achieved due to the different character of X-rays, neutrons and electrons, and hence their different interactions with matter and further practical aspects. X-ray diffraction using conventional laboratory equipment and/or synchrotron installations is the most important method for structure analyses. The purpose of this paper is to discuss special cases, for which, in addition to this indispensable part, neutrons are required to solve structural problems. Even though the huge intensity of modern synchrotron sources allows in principle the study of magnetic X-ray scattering the investigation of magnetic structures is still one of the most important applications of neutron diffraction. (K.A.)
Topological vector spaces and distributions
Horvath, John
2012-01-01
""The most readable introduction to the theory of vector spaces available in English and possibly any other language.""-J. L. B. Cooper, MathSciNet ReviewMathematically rigorous but user-friendly, this classic treatise discusses major modern contributions to the field of topological vector spaces. The self-contained treatment includes complete proofs for all necessary results from algebra and topology. Suitable for undergraduate mathematics majors with a background in advanced calculus, this volume will also assist professional mathematicians, physicists, and engineers.The precise exposition o
Factorization and non-factorization in diffractive hard scattering
International Nuclear Information System (INIS)
Berera, Arjun
1997-01-01
Factorization, in the sense defined for inclusive hard scattering, is discussed for diffractive hard scattering. A factorization theorem similar to its inclusive counterpart is presented for diffractive DIS. For hadron-hadron diffractive hard scattering, in contrast to its inclusive counterpart, the expected breakdown of factorization is discussed. Cross section estimates are given from a simple field theory model for non-factorizing double-pomeron-exchange (DPE) dijet production with and without account for Sudakov suppression
Diffraction in nuclear scattering
International Nuclear Information System (INIS)
Wojciechowski, H.
1986-01-01
The elastic scattering amplitudes for charged and neutral particles have been decomposed into diffractive and refractive parts by splitting the nuclear elastic scattering matrix elements into components responsible for these effects. It has been shown that the pure geometrical diffractive effect which carries no information about the nuclear interaction is always predominant at forward angle of elastic angular distributions. This fact suggests that for strongly absorbed particles only elastic cross section at backward angles, i.e. the refractive cross section, can give us basic information about the central nuclear potential. 12 refs., 4 figs., 1 tab. (author)
International Nuclear Information System (INIS)
Goodwin, Andrew L.; Tucker, Matthew G.; Cope, Elizabeth R.; Dove, Martin T.; Keen, David A.
2006-01-01
We explore the possibility that detailed dynamical information might be extracted from powder diffraction data. Our focus is a recently reported technique that employs statistical analysis of atomistic configurations to calculate dynamical properties from neutron total scattering data. We show that it is possible to access the phonon dispersion of low-frequency modes using such an approach, without constraining the results in terms of some pre-defined dynamical model. The high-frequency regions of the phonon spectrum are found to be less well preserved in the diffraction data
Towards automated diffraction tomography. Part II-Cell parameter determination
International Nuclear Information System (INIS)
Kolb, U.; Gorelik, T.; Otten, M.T.
2008-01-01
Automated diffraction tomography (ADT) allows the collection of three-dimensional (3d) diffraction data sets from crystals down to a size of only few nanometres. Imaging is done in STEM mode, and diffraction data are collected with quasi-parallel beam nanoelectron diffraction (NED). Here, we present a set of developed processing steps necessary for automatic unit-cell parameter determination from the collected 3d diffraction data. Cell parameter determination is done via extraction of peak positions from a recorded data set (called the data reduction path) followed by subsequent cluster analysis of difference vectors. The procedure of lattice parameter determination is presented in detail for a beam-sensitive organic material. Independently, we demonstrate a potential (called the full integration path) based on 3d reconstruction of the reciprocal space visualising special structural features of materials such as partial disorder. Furthermore, we describe new features implemented into the acquisition part
Periodically distributed objects with quasicrystalline diffraction pattern
Energy Technology Data Exchange (ETDEWEB)
Wolny, Janusz, E-mail: wolny@fis.agh.edu.pl; Strzalka, Radoslaw [Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow (Poland); Kuczera, Pawel [Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow (Poland); Laboratory of Crystallography, ETH Zurich, Wolfgang-Pauli-Strasse 10, CH-8093 Zurich (Switzerland)
2015-03-30
It is possible to construct fully periodically distributed objects with a diffraction pattern identical to the one obtained for quasicrystals. These objects are probability distributions of distances obtained in the statistical approach to aperiodic structures distributed periodically. The diffraction patterns have been derived by using a two-mode Fourier transform—a very powerful method not used in classical crystallography. It is shown that if scaling is present in the structure, this two-mode Fourier transform can be reduced to a regular Fourier transform with appropriately rescaled scattering vectors and added phases. Detailed case studies for model sets 1D Fibonacci chain and 2D Penrose tiling are discussed. Finally, it is shown that crystalline, quasicrystalline, and approximant structures can be treated in the same way.
Diffraction at collider energies
International Nuclear Information System (INIS)
Frankfurt, L.L.
1992-01-01
Lessons with ''soft'' hadron physics to explain (a) feasibility to observe and to investigate color transparency, color opacity effects at colliders; (b) significant probability and specific features of hard diffractive processes; (c) feasibility to investigate components of parton wave functions of hadrons with minimal number of constituents. This new physics would be more important with increase of collision energy
Diffraction through partial identity
International Nuclear Information System (INIS)
Blum, W.
1981-06-01
A model of diffraction dissociation is proposed in which the quantum-mechanical interference between the incoming and the outgoing wave determines the cross-section. This interference occurs due to the finite life-time of the excited state. (orig.)
Diffractive optics for industrial and commercial applications
Energy Technology Data Exchange (ETDEWEB)
Turunen, J. [Joensuu Univ. (Finland); Wyrowski, F. [eds.] [Jena Univ. (Germany)
1997-12-31
The following topics were dealt with: diffractive optics, diffraction gratings, optical system design with diffractive optics, continuous-relief diffractive lenses and microlens arrays, diffractive bifocal intraocular lenses, diffractive laser resonators, diffractive optics for semiconductor lasers, diffractive elements for optical image processing, photorefractive crystals in optical measurement systems, subwavelenth-structured elements, security applications, diffractive optics for solar cells, holographic microlithography. 999 refs.
Axial channeling in electron diffraction
International Nuclear Information System (INIS)
Ichimiya, A.; Lehmpfuhl, G.
1978-01-01
Kossel patterns from Silicon and Niobium were obtained with a convergent electron beam. An intensity maximum in the direction of the zone axes [001] and [111] of Nb was interpreted as axial channeling. The intensity distribution in Kossel patterns was calculated by means of the Bloch wave picture of the dynamical theory of electron diffraction. Particularly zone axis patterns were calculated for different substance-energy combinations and they were compared with experimental observations. The intensity distribution in the calculated Kossel patterns was very sensitive to the model of absorption and it was found that a treatment of the absorption close to the model of Humphreys and Hirsch [Phil. Mag. 18, 115 (1968)] gave the best agreement with the experimental observations. Furthermore it is shown which Bloch waves are important for the intensity distribution in the Kossel patterns, how they are absorbed and how they change with energy. (orig.) [de
1993-08-27
been invested in the 1 1FIa I of aerindw as researchers Lam to Pieram a new doss of thre- iterative kfteueny-domai splad lmdudn dimn al meshes spedik v...159’ 4. w tji Omm -zcrO -m IfCa Mwe of modeling composite media in meshes is one of fundemental electromagnetic theory rather than Goa for...anisotropic coau"n.siate. * ~A24 1 Re- investing dsclroesapitics 161 Again consider the FD-TD/LM nion-lacar optim- front verte of the J-targt. with the
Weidemaier, P.
2005-06-01
The trace problem on the hypersurface y_n=0 is investigated for a function u=u(y,t) \\in L_q(0,T;W_{\\underline p}^{\\underline m}(\\mathbb R_+^n)) with \\partial_t u \\in L_q(0,T; L_{\\underline p}(\\mathbb R_+^n)), that is, Sobolev spaces with mixed Lebesgue norm L_{\\underline p,q}(\\mathbb R^n_+\\times(0,T))=L_q(0,T;L_{\\underline p}(\\mathbb R_+^n)) are considered; here \\underline p=(p_1,\\dots,p_n) is a vector and \\mathbb R^n_+=\\mathbb R^{n-1} \\times (0,\\infty). Such function spaces are useful in the context of parabolic equations. They allow, in particular, different exponents of summability in space and time. It is shown that the sharp regularity of the trace in the time variable is characterized by the Lizorkin-Triebel space F_{q,p_n}^{1-1/(p_nm_n)}(0,T;L_{\\widetilde{\\underline p}}(\\mathbb R^{n-1})), \\underline p=(\\widetilde{\\underline p},p_n). A similar result is established for first order spatial derivatives of u. These results allow one to determine the exact spaces for the data in the inhomogeneous Dirichlet and Neumann problems for parabolic equations of the second order if the solution is in the space L_q(0,T; W_p^2(\\Omega)) \\cap W_q^1(0,T;L_p(\\Omega)) with p \\le q.
Search for intermediate vector bosons
International Nuclear Information System (INIS)
Klajn, D.B.; Rubbia, K.; Meer, S.
1983-01-01
Problem of registration and search for intermediate vector bosons is discussed. According to weak-current theory there are three intermediate vector bosons with +1(W + )-1(W - ) and zero (Z 0 ) electric charges. It was suggested to conduct the investigation into particles in 1976 by cline, Rubbia and Makintair using proton-antiproton beams. Major difficulties of the experiment are related to the necessity of formation of sufficient amount of antiparticles and the method of antiproton beam ''cooling'' for the purpose of reduction of its random movements. The stochastic method was suggested by van der Meer in 1968 as one of possible cooling methods. Several large detectors were designed for searching intermediate vector bosons
3D reconstruction of tensors and vectors
International Nuclear Information System (INIS)
Defrise, Michel; Gullberg, Grant T.
2005-01-01
Here we have developed formulations for the reconstruction of 3D tensor fields from planar (Radon) and line-integral (X-ray) projections of 3D vector and tensor fields. Much of the motivation for this work is the potential application of MRI to perform diffusion tensor tomography. The goal is to develop a theory for the reconstruction of both Radon planar and X-ray or line-integral projections because of the flexibility of MRI to obtain both of these type of projections in 3D. The development presented here for the linear tensor tomography problem provides insight into the structure of the nonlinear MRI diffusion tensor inverse problem. A particular application of tensor imaging in MRI is the potential application of cardiac diffusion tensor tomography for determining in vivo cardiac fiber structure. One difficulty in the cardiac application is the motion of the heart. This presents a need for developing future theory for tensor tomography in a motion field. This means developing a better understanding of the MRI signal for diffusion processes in a deforming media. The techniques developed may allow the application of MRI tensor tomography for the study of structure of fiber tracts in the brain, atherosclerotic plaque, and spine in addition to fiber structure in the heart. However, the relations presented are also applicable to other fields in medical imaging such as diffraction tomography using ultrasound. The mathematics presented can also be extended to exponential Radon transform of tensor fields and to other geometric acquisitions such as cone beam tomography of tensor fields
Diffraction studies applicable to 60-foot microwave research facilities
Schmidt, R. F.
1973-01-01
The principal features of this document are the analysis of a large dual-reflector antenna system by vector Kirchhoff theory, the evaluation of subreflector aperture-blocking, determination of the diffraction and blockage effects of a subreflector mounting structure, and an estimate of strut-blockage effects. Most of the computations are for a frequency of 15.3 GHz, and were carried out using the IBM 360/91 and 360/95 systems at Goddard Space Flight Center. The FORTRAN 4 computer program used to perform the computations is of a general and modular type so that various system parameters such as frequency, eccentricity, diameter, focal-length, etc. can be varied at will. The parameters of the 60-foot NRL Ku-band installation at Waldorf, Maryland, were entered into the program for purposes of this report. Similar calculations could be performed for the NELC installation at La Posta, California, the NASA Wallops Station facility in Virginia, and other antenna systems, by a simple change in IBM control cards. A comparison is made between secondary radiation patterns of the NRL antenna measured by DOD Satellite and those obtained by analytical/numerical methods at a frequency of 7.3 GHz.
The Massive Yang-Mills Model and Diffractive Scattering
Forshaw, J R; Parrinello, C
1999-01-01
We argue that the massive Yang-Mills model of Kunimasa and Goto, Slavnov, and Cornwall, in which massive gauge vector bosons are introduced in a gauge-invariant way without resorting to the Higgs mechanism, may be useful for studying diffractive scattering of strongly interacting particles. With this motivation, we perform in this model explicit calculations of S-matrix elements between quark states, at tree level, one loop, and two loops, and discuss issues of renormalisability and unitarity. In particular, it is shown that the S-matrix element for quark scattering is renormalisable at one-loop order and is only logarithmically non-renormalisable at two loops. The discrepancies in the ultraviolet regime between the one-loop predictions of this model and those of massless QCD are discussed in detail. In addition, some of the similarities and differences between the massive Yang-Mills model and theories with a Higgs mechanism are analysed at the level of the S-matrix. As an elementary application of the model ...
Raster images vectorization system
Genytė, Jurgita
2006-01-01
The problem of raster images vectorization was analyzed and researched in this work. Existing vectorization systems are quite expensive, the results are inaccurate, and the manual vectorization of a large number of drafts is impossible. That‘s why our goal was to design and develop a new raster images vectorization system using our suggested automatic vectorization algorithm and the way to record results in a new universal vectorial file format. The work consists of these main parts: analysis...
Zeno dynamics in wave-packet diffraction spreading
Energy Technology Data Exchange (ETDEWEB)
Porras, Miguel A. [Departamento de Fisica Aplicada, Universidad Politecnica de Madrid, Rios Rosas 21, ES-28003 Madrid (Spain); Luis, Alfredo; Gonzalo, Isabel [Departamento de Optica, Facultad de Ciencias Fisicas, Universidad Complutense, ES-28040 Madrid (Spain); Sanz, Angel S. [Instituto de Fisica Fundamental-CSIC, Serrano 123, ES-28006 Madrid (Spain)
2011-11-15
We analyze a simple and feasible practical scheme displaying Zeno, anti-Zeno, and inverse-Zeno effects in the observation of wave-packet spreading caused by free evolution. The scheme is valid both in spatial diffraction of classical optical waves and in time diffraction of a quantum wave packet. In the optical realization, diffraction spreading is observed by placing slits between a light source and a light-power detector. We show that the occurrence of Zeno or anti-Zeno effects depends just on the frequency of observations between the source and detector. These effects are seen to be related to the diffraction mode theory in Fabry-Perot resonators.
An amplitude and phase hybrid modulation Fresnel diffractive optical element
Li, Fei; Cheng, Jiangao; Wang, Mengyu; Jin, Xueying; Wang, Keyi
2018-04-01
An Amplitude and Phase Hybrid Modulation Fresnel Diffractive Optical Element (APHMFDOE) is proposed here. We have studied the theory of APHMFDOE and simulated the focusing properties of it along the optical axis, which show that the focus can be blazed to other positions with changing the quadratic phase factor. Moreover, we design a Composite Fresnel Diffraction Optical Element (CFDOE) based on the characteristics of APHMFDOE. It greatly increases the outermost zone width without changing the F-number, which brings a lot of benefits to the design and processing of diffraction device. More importantly, the diffraction efficiency of the CFDOE is almost unchanged compared with AFZP at the same focus.
Czech Academy of Sciences Publication Activity Database
Colmont, M.; Palatinus, Lukáš; Huvé, M.; Kabbour, H.; Saitzek, S.; Dielal, N.; Roussel, P.
2016-01-01
Roč. 55, č. 5 (2016), s. 2252-2260 ISSN 0020-1669 Institutional support: RVO:68378271 Keywords : electron difraction tomography * oxychloride * luminiscence * dynamical diffraction Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 4.857, year: 2016
International Nuclear Information System (INIS)
Einstein, J.R.; Wei, C.H.
1982-01-01
We have been interested in structural elucidation by x-ray diffraction of compounds of biological interest. Understanding exactly how atoms are arranged in three-dimensional arrays as molecules can help explain the relationship between structure and functions. The species investigated may vary in size and shape; our recent studies included such diverse substances as antischistosomal drugs, a complex of cadmium with nucleic acid base, nitrate salts of adenine, and proteins
International Nuclear Information System (INIS)
Pavicic, Mladen; Merlet, Jean-Pierre; McKay, Brendan; Megill, Norman D
2005-01-01
We give a constructive and exhaustive definition of Kochen-Specker (KS) vectors in a Hilbert space of any dimension as well as of all the remaining vectors of the space. KS vectors are elements of any set of orthonormal states, i.e., vectors in an n-dimensional Hilbert space, H n , n≥3, to which it is impossible to assign 1s and 0s in such a way that no two mutually orthogonal vectors from the set are both assigned 1 and that not all mutually orthogonal vectors are assigned 0. Our constructive definition of such KS vectors is based on algorithms that generate MMP diagrams corresponding to blocks of orthogonal vectors in R n , on algorithms that single out those diagrams on which algebraic (0)-(1) states cannot be defined, and on algorithms that solve nonlinear equations describing the orthogonalities of the vectors by means of statistically polynomially complex interval analysis and self-teaching programs. The algorithms are limited neither by the number of dimensions nor by the number of vectors. To demonstrate the power of the algorithms, all four-dimensional KS vector systems containing up to 24 vectors were generated and described, all three-dimensional vector systems containing up to 30 vectors were scanned, and several general properties of KS vectors were found
Renormalizable Electrodynamics of Scalar and Vector Mesons. Part II
Salam, Abdus; Delbourgo, Robert
1964-01-01
The "gauge" technique" for solving theories introduced in an earlier paper is applied to scalar and vector electrodynamics. It is shown that for scalar electrodynamics, there is no {lambda}φ*2φ2 infinity in the theory, while with conventional subtractions vector electrodynamics is completely finite. The essential ideas of the gauge technique are explained in section 3, and a preliminary set of rules for finite computation in vector electrodynamics is set out in Eqs. (7.28) - (7.34).
Directory of Open Access Journals (Sweden)
Mok Tik
2014-06-01
Full Text Available This study formulates regression of vector data that will enable statistical analysis of various geodetic phenomena such as, polar motion, ocean currents, typhoon/hurricane tracking, crustal deformations, and precursory earthquake signals. The observed vector variable of an event (dependent vector variable is expressed as a function of a number of hypothesized phenomena realized also as vector variables (independent vector variables and/or scalar variables that are likely to impact the dependent vector variable. The proposed representation has the unique property of solving the coefficients of independent vector variables (explanatory variables also as vectors, hence it supersedes multivariate multiple regression models, in which the unknown coefficients are scalar quantities. For the solution, complex numbers are used to rep- resent vector information, and the method of least squares is deployed to estimate the vector model parameters after transforming the complex vector regression model into a real vector regression model through isomorphism. Various operational statistics for testing the predictive significance of the estimated vector parameter coefficients are also derived. A simple numerical example demonstrates the use of the proposed vector regression analysis in modeling typhoon paths.
Experimental method for testing diffraction properties of reflection waveguide holograms.
Xie, Yi; Kang, Ming-Wu; Wang, Bao-Ping
2014-07-01
Waveguide holograms' diffraction properties include peak wavelength and diffraction efficiency, which play an important role in determining their display performance. Based on the record and reconstruction theory of reflection waveguide holograms, a novel experimental method for testing diffraction properties is introduced and analyzed in this paper, which uses a plano-convex lens optically contacted to the surface of the substrate plate of the waveguide hologram, so that the diffracted light beam can be easily detected. Then an experiment is implemented. The designed reconstruction wavelength of the test sample is 530 nm, and its diffraction efficiency is 100%. The experimental results are a peak wavelength of 527.7 nm and a diffraction efficiency of 94.1%. It is shown that the tested value corresponds well with the designed value.
International Nuclear Information System (INIS)
Vries, J.L. de.
1976-01-01
The seventh edition of Philips' Review of literature on X-ray diffraction begins with a list of conference proceedings on the subject, organised by the Philips' organisation at regular intervals in various European countries. This is followed by a list of bulletins. The bibliography is divided according to the equipment (cameras, diffractometers, monochromators) and its applications. The applications are subdivided into sections for high/low temperature and pressure, effects due to the equipment, small angle scattering and a part for stress, texture and phase analyses of metals and quantitative analysis of minerals
Developments in diffraction databases
International Nuclear Information System (INIS)
Jenkins, R.
1999-01-01
Full text: There are a number of databases available to the diffraction community. Two of the more important of these are the Powder Diffraction File (PDF) maintained by the International Centre for Diffraction Data (ICDD), and the Inorganic Crystal Structure Database (ICSD) maintained by Fachsinformationzentrum (FIZ, Karlsruhe). In application, the PDF has been used as an indispensable tool in phase identification and identification of unknowns. The ICSD database has extensive and explicit reference to the structures of compounds: atomic coordinates, space group and even thermal vibration parameters. A similar database, but for organic compounds, is maintained by the Cambridge Crystallographic Data Centre. These databases are often used as independent sources of information. However, little thought has been given on how to exploit the combined properties of structural database tools. A recently completed agreement between ICDD and FIZ, plus ICDD and Cambridge, provides a first step in complementary use of the PDF and the ICSD databases. The focus of this paper (as indicated below) is to examine ways of exploiting the combined properties of both databases. In 1996, there were approximately 76,000 entries in the PDF and approximately 43,000 entries in the ICSD database. The ICSD database has now been used to calculate entries in the PDF. Thus, to derive d-spacing and peak intensity data requires the synthesis of full diffraction patterns, i.e., we use the structural data in the ICSD database and then add instrumental resolution information. The combined data from PDF and ICSD can be effectively used in many ways. For example, we can calculate PDF data for an ideally random crystal distribution and also in the absence of preferred orientation. Again, we can use systematic studies of intermediate members in solid solutions series to help produce reliable quantitative phase analyses. In some cases, we can study how solid solution properties vary with composition and
Meromorphic Vector Fields and Circle Packings
DEFF Research Database (Denmark)
Dias, Kealey
The objective of the Ph.D. project is to initiate a classification of bifurcations of meromorphic vector fields and to clarify their relation to circle packings. Technological applications are to image analysis and to effective grid generation using discrete conformal mappings. The two branches...... of dynamical systems, continuous and discrete, correspond to the study of differential equations (vector fields) and iteration of mappings respectively. In holomorphic dynamics, the systems studied are restricted to those described by holomorphic (complex analytic) functions or meromorphic (allowing poles...... as singularities) functions. There already exists a well-developed theory for iterative holomorphic dynamical systems, and successful relations found between iteration theory and flows of vector fields have been one of the main motivations for the recent interest in holomorphic vector fields. Restricting...
General solution of linear vector supersymmetry
International Nuclear Information System (INIS)
Blasi, Alberto; Maggiore, Nicola
2007-01-01
We give the general solution of the Ward identity for the linear vector supersymmetry which characterizes all topological models. Such a solution, whose expression is quite compact and simple, greatly simplifies the study of theories displaying a supersymmetric algebraic structure, reducing to a few lines the proof of their possible finiteness. In particular, the cohomology technology, usually involved for the quantum extension of these theories, is completely bypassed. The case of Chern-Simons theory is taken as an example
Varnes, Erich; The ATLAS collaboration
2017-01-01
Vector like quarks appear in many theories beyond the Standard Model as a way to cancel the mass divergence for the Higgs boson. The current status of the ATLAS searches for the production of vector like quarks will be reviewed for proton-proton collisions at 13 TeV. This presentation will address the analysis techniques, in particular the selection criteria, the background modeling and the related experimental uncertainties. The phenomenological implications of the obtained results will also be discussed.
Euclidean fields: vector mesons and photons
International Nuclear Information System (INIS)
Loffelholz, J.
1979-01-01
Free transverse vector fields of mass >= 0 are studied. The model is related to the usual free vector meson and electromagnetic quantum field theories by extension of the field operators from transverse to arbitrary test functions. The one-particle states in transverse gauge and their localization are described. Reflexion positivity is proved and derived are free Feynman-Kac-Nelson formulas. An Euclidean approach to a photon field in a spherical world using dilatation covariance and inversions is given
U.S. Department of Health & Human Services — VectorBase is a Bioinformatics Resource Center for invertebrate vectors. It is one of four Bioinformatics Resource Centers funded by NIAID to provide web-based...
Generalization of concurrence vectors
International Nuclear Information System (INIS)
Yu Changshui; Song Heshan
2004-01-01
In this Letter, based on the generalization of concurrence vectors for bipartite pure state with respect to employing tensor product of generators of the corresponding rotation groups, we generalize concurrence vectors to the case of mixed states; a new criterion of separability of multipartite pure states is given out, for which we define a concurrence vector; we generalize the vector to the case of multipartite mixed state and give out a good measure of free entanglement
Ebrahimi, Javad; Fragouli, Christina
2010-01-01
We develop new algebraic algorithms for scalar and vector network coding. In vector network coding, the source multicasts information by transmitting vectors of length L, while intermediate nodes process and combine their incoming packets by multiplying them with L X L coding matrices that play a similar role as coding coefficients in scalar coding. Our algorithms for scalar network jointly optimize the employed field size while selecting the coding coefficients. Similarly, for vector co...
Vector Network Coding Algorithms
Ebrahimi, Javad; Fragouli, Christina
2010-01-01
We develop new algebraic algorithms for scalar and vector network coding. In vector network coding, the source multicasts information by transmitting vectors of length L, while intermediate nodes process and combine their incoming packets by multiplying them with L x L coding matrices that play a similar role as coding c in scalar coding. Our algorithms for scalar network jointly optimize the employed field size while selecting the coding coefficients. Similarly, for vector coding, our algori...
Diffractive ''semioptical'' model for nucleus-nucleus collisions
International Nuclear Information System (INIS)
Barashenkov, V.S.; Musulmanbekov, Zh.Zh.
1979-01-01
Diffraction Glauber theory for nucleus-nucleus collisions is considered in approximation when the initial nucleus interacts as a whole with nucleons of the target nucleus. Such an approach, being intermediate between precise Glauber theory and its optical limit, essentially simplifies numerical calculations and gives a good agreement with experiments as well. (author)
Convexity and Marginal Vectors
van Velzen, S.; Hamers, H.J.M.; Norde, H.W.
2002-01-01
In this paper we construct sets of marginal vectors of a TU game with the property that if the marginal vectors from these sets are core elements, then the game is convex.This approach leads to new upperbounds on the number of marginal vectors needed to characterize convexity.An other result is that
DEFF Research Database (Denmark)
Becciolini, Diego; Franzosi, Diogo Buarque; Foadi, Roshan
2015-01-01
We analyze the Large Hadron Collider (LHC) phenomenology of heavy vector resonances with a $SU(2)_L\\times SU(2)_R$ spectral global symmetry. This symmetry partially protects the electroweak S-parameter from large contributions of the vector resonances. The resulting custodial vector model spectrum...
The influence of texture on the strain measured by diffraction
International Nuclear Information System (INIS)
Penning, P.; Brakman, C.M.
1988-01-01
Strain, as determined by diffraction techniques, is calculated from its constituents. First, the fraction of the crystals that have the proper orientation for diffraction. One degree of freedom is present: the angle of rotation φ 2 '' about the scattering vector that the diffracting crystals have in common. The proper orientations, expressed in Euler angles, lie on a line ('trace') in orientation space. The density along the trace is asserted to be known as a Fourier series in φ 2 ''. Second, the strain in the diffracting crystals. The simplest possible models are discussed: the Voigt and Reuss approximations. The symmetries of the crystal (m3 or m3m) and of the orientation distribution function (o.d.f.) are taken into account. The dilatation in spacing of the reflecting planes is found as a Fourier series in φ 2 '' also. Only the zeroth, first and second harmonic (including phase angles: five parameters) play a part. The diffraction strain is the average over the angle φ 2 '' of the dilatation, weighted with the product of the orientation density and the square of the structure factor. For each contributing trace, the corresponding Fourier coefficients have to be multiplied and added to obtain the diffraction strain. The symmetry of the diffraction pole figure is derived. (orig.)
Exclusive diffractive processes at HERA within the dipole picture
International Nuclear Information System (INIS)
Kowalski, H.; Motkyka, L.; Uniwersytet Jagiellonski, Krakow; Watt, G.; Univ. College London
2006-08-01
We present a simultaneous analysis, within an impact parameter dependent saturated dipole model, of exclusive diffractive vector meson (J/ψ, φ and ρ) production, deeply virtual Compton scattering and the total γ * p cross section data measured at HERA. Various cross sections measured as a function of the kinematic variables Q 2 , W and t are well described, with little sensitivity to the details of the vector meson wave functions. We determine the properties of the gluon density in the proton in both longitudinal and transverse dimensions, including the impact parameter dependent saturation scale. The overall success of the description indicates universality of the emerging gluon distribution and proton shape. (orig.)
Birefringent coherent diffraction imaging
Karpov, Dmitry; dos Santos Rolo, Tomy; Rich, Hannah; Kryuchkov, Yuriy; Kiefer, Boris; Fohtung, E.
2016-10-01
Directional dependence of the index of refraction contains a wealth of information about anisotropic optical properties in semiconducting and insulating materials. Here we present a novel high-resolution lens-less technique that uses birefringence as a contrast mechanism to map the index of refraction and dielectric permittivity in optically anisotropic materials. We applied this approach successfully to a liquid crystal polymer film using polarized light from helium neon laser. This approach is scalable to imaging with diffraction-limited resolution, a prospect rapidly becoming a reality in view of emergent brilliant X-ray sources. Applications of this novel imaging technique are in disruptive technologies, including novel electronic devices, in which both charge and spin carry information as in multiferroic materials and photonic materials such as light modulators and optical storage.
Dremin, I. M.
I begin with a tribute to V.N. Gribov and then come to a particular problem which would be of interest for him. His first paper on reggeology was devoted to elastic scatterings of hadrons. Here, using the unitarity relation in combination with experimental data about the elastic scattering in the diffraction cone, I show how the shape and the darkness of the interaction region of colliding protons change with the increase of their energies. In particular, the collisions become fully absorptive at small impact parameters at LHC energies that results in some special features of inelastic processes as well. The possible evolution with increasing energy of the shape from the dark core at the LHC to the fully transparent one at higher energies is discussed. It implies that the terminology of the black disk would be replaced by the black torus.
International Nuclear Information System (INIS)
Anon.
1995-01-01
In the United States, phrases such as ''small-x evolution'', ''the BFKL Pomeron'', ''deep-inelastic rapiditygap events'' and ''hard-diffraction'' do not generate the same intensity of discussion amongst high-energy physicists that they do in Europe. However, for three days in the fall such discussion filled the air at Fermilab. The ''2nd Workshop on Small-x and Diffractive Physics at the Tevatron'' was a review of the rapid theoretical and experimental progress taking place in this field. Although Quantum Chromo-dynamics (QCD) has been established as the theory of strong interactions for twenty years, as yet neither perturbative high-energy calculations nor low-energy non-perturbative techniques have been successfully extended to the mixture of high energy and low transverse momenta which characterize traditional ''soft'' diffractive processes. The simplest soft diffractive process is elastic scattering. In this case it is easiest to accept that there is an exchanged ''pomeron'', which can be pictured as a virtual entity with no electric charge or strong charge (colour), perhaps like an excitation of the vacuum. The same pomeron is expected to appear in all diffractive processes. Understanding the pomeron in QCD is a fundamental theoretical and experimental challenge. In the last two or three years the ''frontier'' in this challenging area of QCD has been pushed back significantly in both theory and experiment. Progress has been achieved by studying the evolution of hard collisions to relatively smaller constituent momenta (small x) and by studying ''hard'' diffractive collisions containing simultaneous signatures of diffraction and hard perturbative processes. The hard processes have included high transverse momentum jet production, deep inelastic lepton scattering, and (most recently) W
Unitary unified field theories
International Nuclear Information System (INIS)
Sudarshan, E.C.G.
1976-01-01
This is an informal exposition of some recent developments. Starting with an examination of the universality of electromagnetic and weak interactions, the attempts at their unification are outlined. The theory of unitary renormalizable self-coupled vector mesons with dynamical sources is formulated for a general group. With masses introduced as variable parameters it is shown that the theory so defined is indeed unitary. Diagrammatic rules are developed in terms of a chosen set of fictitious particles. A number of special examples are outlined including a theory with strongly interacting vector and axial vector mesons and weak mesons. Applications to weak interactions of strange particles is briefly outlined. (Auth.)
Boundary diffraction wave integrals for diffraction modeling of external occulters
Cady, E.
2012-01-01
An occulter is a large diffracting screen which may be flown in conjunction with a telescope to image extrasolar planets. The edge is shaped to minimize the diffracted light in a region beyond the occulter, and a telescope may be placed in this dark shadow to view an extrasolar system with the starlight removed. Errors in position, orientation, and shape of the occulter will diffract additional light into this region, and a challenge of modeling an occulter system is to accurately and quickly...
Rotations with Rodrigues' vector
International Nuclear Information System (INIS)
Pina, E
2011-01-01
The rotational dynamics was studied from the point of view of Rodrigues' vector. This vector is defined here by its connection with other forms of parametrization of the rotation matrix. The rotation matrix was expressed in terms of this vector. The angular velocity was computed using the components of Rodrigues' vector as coordinates. It appears to be a fundamental matrix that is used to express the components of the angular velocity, the rotation matrix and the angular momentum vector. The Hamiltonian formalism of rotational dynamics in terms of this vector uses the same matrix. The quantization of the rotational dynamics is performed with simple rules if one uses Rodrigues' vector and similar formal expressions for the quantum operators that mimic the Hamiltonian classical dynamics.
Polynomial Vector Fields in One Complex Variable
DEFF Research Database (Denmark)
Branner, Bodil
In recent years Adrien Douady was interested in polynomial vector fields, both in relation to iteration theory and as a topic on their own. This talk is based on his work with Pierrette Sentenac, work of Xavier Buff and Tan Lei, and my own joint work with Kealey Dias.......In recent years Adrien Douady was interested in polynomial vector fields, both in relation to iteration theory and as a topic on their own. This talk is based on his work with Pierrette Sentenac, work of Xavier Buff and Tan Lei, and my own joint work with Kealey Dias....
Applied electromagnetic scattering theory
Osipov, Andrey A
2017-01-01
Besides classical applications (radar and stealth, antennas, microwave engineering), scattering and diffraction are enabling phenomena for some emerging research fields (artificial electromagnetic materials or metamaterials, terahertz technologies, electromagnetic aspects of nano-science). This book is a tutorial for advanced students who need to study diffraction theory. The textbook gives fundamental knowledge about scattering and diffraction of electromagnetic waves and provides some working examples of solutions for practical high-frequency scattering and diffraction problems. The book focuses on the most important diffraction effects and mechanisms influencing the scattering process and describes efficient and physically justified simulation methods - physical optics (PO) and the physical theory of diffraction (PTD) - applicable in typical remote sensing scenarios. The material is presented in a comprehensible and logical form, which relates the presented results to the basic principles of electromag...
Vectors, a tool in statistical regression theory
Corsten, L.C.A.
1958-01-01
Using linear algebra this thesis developed linear regression analysis including analysis of variance, covariance analysis, special experimental designs, linear and fertility adjustments, analysis of experiments at different places and times. The determination of the orthogonal projection, yielding
Electron microscopy and diffraction
International Nuclear Information System (INIS)
Gjoennes, J.; Olsen, A.
1986-01-01
This report is a description of research activities and plans at the electron microscopy laboratorium, Physics Department, University of Oslo. Since the first electron microscope was installed in 1968, the research has covered inorganic structures, physical metallurgy, as well as theory of electron scattering and the development of methods in this field. The current plans involve efforts in the development of crystallographic and spectroscopic methods
CMS results on hard diffraction
INSPIRE-00107098
2013-01-01
In these proceedings we present CMS results on hard diffraction. Diffractive dijet production in pp collisions at $\\sqrt{s}$=7 TeV is discussed. The cross section for dijet production is presented as a function of $\\tilde{\\xi}$, representing the fractional momentum loss of the scattered proton in single-diffractive events. The observation of W and Z boson production in events with a large pseudo-rapidity gap is also presented.
X-ray diffraction patterns in high-energy proton implanted silicon
International Nuclear Information System (INIS)
Wieteska, K.; Dluzewska, K.D.; Wierzchowski, W.; Graeff, W.
1998-01-01
Silicon crystals implanted with 1 and 1.6 MeV protons were studied by means of conventional source double-crystal and synchrotron multi-crystal arrangements. Both the rocking curves and series of topographs were recorded in different parallel settings employing different reflections and wavelengths of radiation. A comparison of rocking curves in different regions of implanted areas was performed in synchrotron multi-crystal arrangement with a beam of a very small diameter. The rocking curves exhibited subsidiary interference maxima with increasing periodicity on the low angle side. The plane wave topographs taken at different angular setting revealed characteristic fringes whose number decreased with increasing distance from the main maximum. The fringe pattern did not depend on the direction of the diffraction vector. The number of fringes for equivalent angular distance from the maximum was larger for higher order of reflection. The shape of the rocking curve and other diffraction patterns were reasonably explained assuming the lattice parameter change depth distribution proportional to the profile obtained from the Biersack-Ziegler theory and lateral non-uniformity of ion dose. A good approximation of the experimental results was obtained using numerical integration of the Takagi-Taupin equations. (orig.)
International Nuclear Information System (INIS)
Prasad, R.
1975-01-01
Results of researches into Unified Field Theory over the past seven years are presented. The subject is dealt with in chapters entitled: the choice of affine connection, algebraic properties of the vector fields, field laws obtained from the affine connection based on the path integral method, application to quantum theory and cosmology, interpretation of physical theory in terms of geometry. (U.K.)
Optical diffraction from fractals with a structural transition
International Nuclear Information System (INIS)
Perez Rodriguez, F.; Canessa, E.
1994-04-01
A macroscopic characterization of fractals showing up a structural transition from dense to multibranched growth is made using optical diffraction theory. Such fractals are generated via the numerical solution of the 2D Poisson and biharmonic equations and are compared to more 'regular' irreversible clusters such as diffusion limited and Laplacian aggregates. The optical diffraction method enables to identify a decrease of the fractal dimension above the structural point. (author). 19 refs, 6 figs
Polarisation resonance in X-ray diffraction
International Nuclear Information System (INIS)
Goodman, P.; Paterson, D.; Matheson, S.
1994-01-01
The study of crystal structures by means of dynamic X-ray diffraction has placed a challenge to theoreticians to revise the X-ray diffraction theory based on Maxwell's equation. In this paper the feasibility of using 'polarisation resonance' as a tool in the determination of absolute configuration for asymmetric structures is investigated. Two (left- and right-handed), σ + and σ- , circular polarization states for 3-beam conditions are considered. Moreover, extending interaction into the 3 rd. dimension (normal to the beam) opens the possibility of absolute configuration determination of asymmetric structures in 3 dimensions. The computational scheme used is shown in terms of scattering diagrams. 7 refs., 1 tab., 6 figs
International Nuclear Information System (INIS)
Crawford, G.N.
1981-01-01
The analysis is directed at a causal description of photon diffraction, which is explained in terms of a wave exerting real forces and providing actual guidance to each quantum of energy. An undulatory PSI wave is associated with each photon, and this wave is assumed to imply more than an informative probability function, so that it actually carries real energy, in much the same way as does an electro-magnetic wave. Whether or not it may be in some way related to the electromagnetic wave is left as a matter of on-going concern. A novel application of the concept of a minimum energy configuration is utilized; that is, a system of energy quanta seeks out relative positions and orientations of least mutual energy, much as an electron seeks its Bohr radius as a position of least mutual energy. Thus the concept implies more a guiding interaction of the PSI waves than an interfering cancellation of these waves. Similar concepts have been suggested by L. de Broglie and D. Bohm
Study of optical Laue diffraction
International Nuclear Information System (INIS)
Chakravarthy, Giridhar; Allam, Srinivasa Rao; Satyanarayana, S. V. M.; Sharan, Alok
2014-01-01
We present the study of the optical diffraction pattern of one and two-dimensional gratings with defects, designed using desktop pc and printed on OHP sheet using laser printer. Gratings so prepared, using novel low cost technique provides good visual aid in teaching. Diffraction pattern of the monochromatic light (632.8nm) from the grating so designed is similar to that of x-ray diffraction pattern of crystal lattice with point defects in one and two-dimensions. Here both optical and x-ray diffractions are Fraunhofer. The information about the crystalline lattice structure and the defect size can be known
Gluon radiation in diffractive electroproduction
International Nuclear Information System (INIS)
Buchmueller, W.; McDermott, M.F.; Hebecker, A.
1996-07-01
Order α s -correlations to the diffractive structure functions F L D and F 2 D at large Q 2 and small x are evaluated in the semiclassical approach, where the initial proton is treated as a classical colour field. The diffractive final state contains a fast gluon in addition to a quark-antiquark pair. Two of these partons may have large transverse momentum. Our calculations lead to an intuitive picture of deep-inelastic diffractive processes which is very similar to Bjorken's aligned-jet model. Both diffractive structure functions contain leading twist contributions from high-p perpendicular to jets. (orig.)
Study of optical Laue diffraction
Energy Technology Data Exchange (ETDEWEB)
Chakravarthy, Giridhar, E-mail: cgiridhar84@gmail.com, E-mail: aloksharan@email.com; Allam, Srinivasa Rao, E-mail: cgiridhar84@gmail.com, E-mail: aloksharan@email.com; Satyanarayana, S. V. M., E-mail: cgiridhar84@gmail.com, E-mail: aloksharan@email.com; Sharan, Alok, E-mail: cgiridhar84@gmail.com, E-mail: aloksharan@email.com [Department of Physics, Pondicherry University, Puducherry-605014 (India)
2014-10-15
We present the study of the optical diffraction pattern of one and two-dimensional gratings with defects, designed using desktop pc and printed on OHP sheet using laser printer. Gratings so prepared, using novel low cost technique provides good visual aid in teaching. Diffraction pattern of the monochromatic light (632.8nm) from the grating so designed is similar to that of x-ray diffraction pattern of crystal lattice with point defects in one and two-dimensions. Here both optical and x-ray diffractions are Fraunhofer. The information about the crystalline lattice structure and the defect size can be known.
Diffractive optics and nanophotonics resolution below the diffraction limit
Minin, Igor
2016-01-01
In this book the authors present several examples of techniques used to overcome the Abby diffraction limit using flat and 3D diffractive optical elements, photonic crystal lenses, photonic jets, and surface plasmon diffractive optics. The structures discussed can be used in the microwave and THz range and also as scaled models for optical frequencies. Such nano-optical microlenses can be integrated, for example, into existing semiconductor heterostructure platforms for next-generation optoelectronic applications. Chapter 1 considers flat diffractive lenses and innovative 3D radiating structures including a conical millimeter-wave Fresnel zone plate (FZP) lens proposed for subwavelength focusing. In chapter 2 the subwavelength focusing properties of diffractive photonic crystal lenses are considered and it is shown that at least three different types of photonic crystal lens are possible. With the aim of achieving subwavelength focusing, in chapter 3 an alternative mechanism to produce photonic jets at Tera...
Supergravity inspired vector curvaton
International Nuclear Information System (INIS)
Dimopoulos, Konstantinos
2007-01-01
It is investigated whether a massive Abelian vector field, whose gauge kinetic function is growing during inflation, can be responsible for the generation of the curvature perturbation in the Universe. Particle production is studied and it is shown that the vector field can obtain a scale-invariant superhorizon spectrum of perturbations with a reasonable choice of kinetic function. After inflation the vector field begins coherent oscillations, during which it corresponds to pressureless isotropic matter. When the vector field dominates the Universe, its perturbations give rise to the observed curvature perturbation following the curvaton scenario. It is found that this is possible if, after the end of inflation, the mass of the vector field increases at a phase transition at temperature of order 1 TeV or lower. Inhomogeneous reheating, whereby the vector field modulates the decay rate of the inflaton, is also studied
Becciolini, Diego; Franzosi, Diogo Buarque; Foadi, Roshan; Frandsen, Mads T.; Hapola, Tuomas; Sannino, Francesco
2015-07-01
We analyze the Large Hadron Collider (LHC) phenomenology of heavy vector resonances with a S U (2 )L×S U (2 )R spectral global symmetry. This symmetry partially protects the electroweak S parameter from large contributions of the vector resonances. The resulting custodial vector model spectrum and interactions with the standard model fields lead to distinct signatures at the LHC in the diboson, dilepton, and associated Higgs channels.
HITZER, Eckhard MS
2002-01-01
This paper treats the fundamentals of the vector differential calculus part of universal geometric calculus. Geometric calculus simplifies and unifies the structure and notation of mathematics for all of science and engineering, and for technological applications. In order to make the treatment self-contained, I first compile all important geometric algebra relationships,which are necesssary for vector differential calculus. Then differentiation by vectors is introduced and a host of major ve...
Directory of Open Access Journals (Sweden)
Jean-François Degbomont
2010-10-01
Full Text Available This paper addresses the symbolic representation of non-convex real polyhedra, i.e., sets of real vectors satisfying arbitrary Boolean combinations of linear constraints. We develop an original data structure for representing such sets, based on an implicit and concise encoding of a known structure, the Real Vector Automaton. The resulting formalism provides a canonical representation of polyhedra, is closed under Boolean operators, and admits an efficient decision procedure for testing the membership of a vector.
International Nuclear Information System (INIS)
Brown, F.B.
1981-01-01
Examination of the global algorithms and local kernels of conventional general-purpose Monte Carlo codes shows that multigroup Monte Carlo methods have sufficient structure to permit efficient vectorization. A structured multigroup Monte Carlo algorithm for vector computers is developed in which many particle events are treated at once on a cell-by-cell basis. Vectorization of kernels for tracking and variance reduction is described, and a new method for discrete sampling is developed to facilitate the vectorization of collision analysis. To demonstrate the potential of the new method, a vectorized Monte Carlo code for multigroup radiation transport analysis was developed. This code incorporates many features of conventional general-purpose production codes, including general geometry, splitting and Russian roulette, survival biasing, variance estimation via batching, a number of cutoffs, and generalized tallies of collision, tracklength, and surface crossing estimators with response functions. Predictions of vectorized performance characteristics for the CYBER-205 were made using emulated coding and a dynamic model of vector instruction timing. Computation rates were examined for a variety of test problems to determine sensitivities to batch size and vector lengths. Significant speedups are predicted for even a few hundred particles per batch, and asymptotic speedups by about 40 over equivalent Amdahl 470V/8 scalar codes arepredicted for a few thousand particles per batch. The principal conclusion is that vectorization of a general-purpose multigroup Monte Carlo code is well worth the significant effort required for stylized coding and major algorithmic changes
Vectors and their applications
Pettofrezzo, Anthony J
2005-01-01
Geared toward undergraduate students, this text illustrates the use of vectors as a mathematical tool in plane synthetic geometry, plane and spherical trigonometry, and analytic geometry of two- and three-dimensional space. Its rigorous development includes a complete treatment of the algebra of vectors in the first two chapters.Among the text's outstanding features are numbered definitions and theorems in the development of vector algebra, which appear in italics for easy reference. Most of the theorems include proofs, and coordinate position vectors receive an in-depth treatment. Key concept
Symbolic computer vector analysis
Stoutemyer, D. R.
1977-01-01
A MACSYMA program is described which performs symbolic vector algebra and vector calculus. The program can combine and simplify symbolic expressions including dot products and cross products, together with the gradient, divergence, curl, and Laplacian operators. The distribution of these operators over sums or products is under user control, as are various other expansions, including expansion into components in any specific orthogonal coordinate system. There is also a capability for deriving the scalar or vector potential of a vector field. Examples include derivation of the partial differential equations describing fluid flow and magnetohydrodynamics, for 12 different classic orthogonal curvilinear coordinate systems.
Shan, Mao
2016-10-01
In this dissertation, the mathematical model of effect of manufacturing errors including microstructure relative height error and relative width error on diffraction efficiency for the harmonic diffractive optical elements (HDEs) is set up. According to the expression of the phase delay and diffraction efficiency of the HDEs, the expression of diffraction efficiency of refraction and diffractive optical element with the microstructure height and periodic width errors in fabrication process is presented in this paper. Furthermore, the effect of manufacturing errors on diffraction efficiency for the harmonic diffractive optical elements is studied, and diffraction efficiency change is analyzed as the relative microstructure height-error in the same and in the opposite sign as well as relative width-error in the same and in the opposite sign. Example including infrared wavelength with materials GE has been discussed in this paper. Two kinds of manufacturing errors applied in 3.7 4.3um middle infrared and 8.7-11.5um far infrared optical system which results in diffraction efficiency and PIDE of HDEs are studied. The analysis results can be used for manufacturing error control in micro-structure height and periodic width. Results can be used for HDEs processing.
A unified development of several techniques for the representation of random vectors and data sets
Bundick, W. T.
1973-01-01
Linear vector space theory is used to develop a general representation of a set of data vectors or random vectors by linear combinations of orthonormal vectors such that the mean squared error of the representation is minimized. The orthonormal vectors are shown to be the eigenvectors of an operator. The general representation is applied to several specific problems involving the use of the Karhunen-Loeve expansion, principal component analysis, and empirical orthogonal functions; and the common properties of these representations are developed.
Diamond-anvil cell for radial x-ray diffraction
International Nuclear Information System (INIS)
Chesnut, G N; Schiferl, D; Streetman, B D; Anderson, W W
2006-01-01
We have designed a new diamond-anvil cell capable of radial x-ray diffraction to pressures of a few hundred GPa. The diffraction geometry allows access to multiple angles of Ψ, which is the angle between each reciprocal lattice vector g(hkl) and the compression axis of the cell. At the 'magic angle', Ψ∼54.7 0 , the effects of deviatoric stresses on the interplanar spacings, d(hkl), are significantly reduced. Because the systematic errors, which are different for each d(hkl), are significantly reduced, the crystal structures and the derived equations of state can be determined reliably. At other values of Ψ, the effects of deviatoric stresses on the diffraction pattern could eventually be used to determine elastic constants
A vector space approach to geometry
Hausner, Melvin
2010-01-01
The effects of geometry and linear algebra on each other receive close attention in this examination of geometry's correlation with other branches of math and science. In-depth discussions include a review of systematic geometric motivations in vector space theory and matrix theory; the use of the center of mass in geometry, with an introduction to barycentric coordinates; axiomatic development of determinants in a chapter dealing with area and volume; and a careful consideration of the particle problem. 1965 edition.
Construction and decomposition of biorthogonal vector-valued wavelets with compact support
International Nuclear Information System (INIS)
Chen Qingjiang; Cao Huaixin; Shi Zhi
2009-01-01
In this article, we introduce vector-valued multiresolution analysis and the biorthogonal vector-valued wavelets with four-scale. The existence of a class of biorthogonal vector-valued wavelets with compact support associated with a pair of biorthogonal vector-valued scaling functions with compact support is discussed. A method for designing a class of biorthogonal compactly supported vector-valued wavelets with four-scale is proposed by virtue of multiresolution analysis and matrix theory. The biorthogonality properties concerning vector-valued wavelet packets are characterized with the aid of time-frequency analysis method and operator theory. Three biorthogonality formulas regarding them are presented.
Isometric Reflection Vectors and Characterizations of Hilbert Spaces
Directory of Open Access Journals (Sweden)
Donghai Ji
2014-01-01
Full Text Available A known characterization of Hilbert spaces via isometric reflection vectors is based on the following implication: if the set of isometric reflection vectors in the unit sphere SX of a Banach space X has nonempty interior in SX, then X is a Hilbert space. Applying a recent result based on well-known theorem of Kronecker from number theory, we improve this by substantial reduction of the set of isometric reflection vectors needed in the hypothesis.
Non-coaxial superposition of vector vortex beams.
Aadhi, A; Vaity, Pravin; Chithrabhanu, P; Reddy, Salla Gangi; Prabakar, Shashi; Singh, R P
2016-02-10
Vector vortex beams are classified into four types depending upon spatial variation in their polarization vector. We have generated all four of these types of vector vortex beams by using a modified polarization Sagnac interferometer with a vortex lens. Further, we have studied the non-coaxial superposition of two vector vortex beams. It is observed that the superposition of two vector vortex beams with same polarization singularity leads to a beam with another kind of polarization singularity in their interaction region. The results may be of importance in ultrahigh security of the polarization-encrypted data that utilizes vector vortex beams and multiple optical trapping with non-coaxial superposition of vector vortex beams. We verified our experimental results with theory.
Vector and parallel processors in computational science
International Nuclear Information System (INIS)
Duff, I.S.; Reid, J.K.
1985-01-01
This book presents the papers given at a conference which reviewed the new developments in parallel and vector processing. Topics considered at the conference included hardware (array processors, supercomputers), programming languages, software aids, numerical methods (e.g., Monte Carlo algorithms, iterative methods, finite elements, optimization), and applications (e.g., neutron transport theory, meteorology, image processing)
Time-dependent Bragg diffraction by multilayer gratings
International Nuclear Information System (INIS)
André, Jean-Michel; Jonnard, Philippe
2016-01-01
Time-dependent Bragg diffraction by multilayer gratings working by reflection or by transmission is investigated. The study is performed by generalizing the time-dependent coupled-wave theory previously developed for one-dimensional photonic crystals (André J-M and Jonnard P 2015 J. Opt. 17 085609) and also by extending the Takagi–Taupin approach of the dynamical theory of diffraction. The indicial response is calculated. It presents a time delay with a transient time that is a function of the extinction length for reflection geometry and of the extinction length combined with the thickness of the grating for transmission geometry. (paper)
Vector-Vector Scattering on the Lattice
Romero-López, Fernando; Urbach, Carsten; Rusetsky, Akaki
2018-03-01
In this work we present an extension of the LüScher formalism to include the interaction of particles with spin, focusing on the scattering of two vector particles. The derived formalism will be applied to Scalar QED in the Higgs Phase, where the U(1) gauge boson acquires mass.
International Nuclear Information System (INIS)
Clark, T.E.; Love, S.T.; Nitta, Muneto; Veldhuis, T. ter; Xiong, C.
2009-01-01
Local oscillations of the brane world are manifested as massive vector fields. Their coupling to the Standard Model can be obtained using the method of nonlinear realizations of the spontaneously broken higher-dimensional space-time symmetries, and to an extent, are model independent. Phenomenological limits on these vector field parameters are obtained using LEP collider data and dark matter constraints
Measurement of Charmless B to Vector-Vector decays at BaBar
International Nuclear Information System (INIS)
Olaiya, Emmanuel
2011-01-01
The authors present results of B → vector-vector (VV) and B → vector-axial vector (VA) decays B 0 → φX(X = φ,ρ + or ρ 0 ), B + → φK (*)+ , B 0 → K*K*, B 0 → ρ + b 1 - and B + → K* 0 α 1 + . The largest dataset used for these results is based on 465 x 10 6 Υ(4S) → B(bar B) decays, collected with the BABAR detector at the PEP-II B meson factory located at the Stanford Linear Accelerator Center (SLAC). Using larger datasets, the BABAR experiment has provided more precise B → VV measurements, further supporting the smaller than expected longitudinal polarization fraction of B → φK*. Additional B meson to vector-vector and vector-axial vector decays have also been studied with a view to shedding light on the polarization anomaly. Taking into account the available errors, we find no disagreement between theory and experiment for these additional decays.
Energy Technology Data Exchange (ETDEWEB)
Adachi, Masaaki; Ogasawara, Shinobu; Kume, Etsuo [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment; Ishizuki, Shigeru; Nemoto, Toshiyuki; Kawasaki, Nobuo; Kawai, Wataru [Fujitsu Ltd., Tokyo (Japan); Yatake, Yo-ichi [Hitachi Ltd., Tokyo (Japan)
2001-02-01
Several computer codes in the nuclear field have been vectorized, parallelized and trans-ported on the FUJITSU VPP500 system, the AP3000 system, the SX-4 system and the Paragon system at Center for Promotion of Computational Science and Engineering in Japan Atomic Energy Research Institute. We dealt with 18 codes in fiscal 1999. These results are reported in 3 parts, i.e., the vectorization and the parallelization part on vector processors, the parallelization part on scalar processors and the porting part. In this report, we describe the vectorization and parallelization on vector processors. In this vectorization and parallelization on vector processors part, the vectorization of Relativistic Molecular Orbital Calculation code RSCAT, a microscopic transport code for high energy nuclear collisions code JAM, three-dimensional non-steady thermal-fluid analysis code STREAM, Relativistic Density Functional Theory code RDFT and High Speed Three-Dimensional Nodal Diffusion code MOSRA-Light on the VPP500 system and the SX-4 system are described. (author)
Complex Polynomial Vector Fields
DEFF Research Database (Denmark)
Dias, Kealey
vector fields. Since the class of complex polynomial vector fields in the plane is natural to consider, it is remarkable that its study has only begun very recently. There are numerous fundamental questions that are still open, both in the general classification of these vector fields, the decomposition...... of parameter spaces into structurally stable domains, and a description of the bifurcations. For this reason, the talk will focus on these questions for complex polynomial vector fields.......The two branches of dynamical systems, continuous and discrete, correspond to the study of differential equations (vector fields) and iteration of mappings respectively. In holomorphic dynamics, the systems studied are restricted to those described by holomorphic (complex analytic) functions...
Non-existence of limit cycles for planar vector fields
Directory of Open Access Journals (Sweden)
Jaume Gine
2014-03-01
Full Text Available This article presents sufficient conditions for the non-existence of limit cycles for planar vector fields. Classical methods for the nonexistence of limit cycles are connected with the theory developed here.
Symposium on Singularities, Representation of Algebras, and Vector Bundles
Trautmann, Günther
1987-01-01
It is well known that there are close relations between classes of singularities and representation theory via the McKay correspondence and between representation theory and vector bundles on projective spaces via the Bernstein-Gelfand-Gelfand construction. These relations however cannot be considered to be either completely understood or fully exploited. These proceedings document recent developments in the area. The questions and methods of representation theory have applications to singularities and to vector bundles. Representation theory itself, which had primarily developed its methods for Artinian algebras, starts to investigate algebras of higher dimension partly because of these applications. Future research in representation theory may be spurred by the classification of singularities and the highly developed theory of moduli for vector bundles. The volume contains 3 survey articles on the 3 main topics mentioned, stressing their interrelationships, as well as original research papers.
International Nuclear Information System (INIS)
Malinowski, S.
1984-01-01
It is shown that the total field energy for general solutions of the sourceless Maxwell's equations with E-vector parallel to B-vector is infinite. Moreover the action and/or the ''pseudoscalar charge'' must be infinite too in this case. Therefore the expected similarity to the instanton or meron solutions of nonabelian gauge theories is illusory. 5 refs. (author)
Diffraction dissociation at the LHC
Energy Technology Data Exchange (ETDEWEB)
Jenkovszky, Laszlo [Bogolyubov Institute for Theoretical Physics (BITP), Ukrainian National Academy of Sciences 14-b, Metrolohichna str., Kiev, 03680, Ukraine and Wigner Research Centre for Physics, Hungarian Academy of Sciences 1525 Budapest, POB 49 (Hungary); Orava, Risto [Institute of Physics, Division of Elementary Particle Physics, P.O. Box 64 (Gustaf Haellstroeminkatu 2a), FI-00014 University of Helsinki, Finland and CERN, CH-1211 Geneva 23 (Switzerland); Salii, Andrii [Bogolyubov Institute for Theoretical Physics (BITP), Ukrainian National Academy of Sciences 14-b, Metrolohichna str., Kiev, 03680 (Ukraine)
2013-04-15
We report on recent calculations of low missing mass single (SD) and double (DD) diffractive dissociation at LHC energies. The calculations are based on a dual-Regge model, dominated by a single Pomeron exchange. The diffractively excited states lie on the nucleon trajectory N*, appended by the isolated Roper resonance. Detailed predictions for the squared momentum transfer and missing mass dependence of the differential and integrated single-and double diffraction dissociation in the kinematical range of present and future LHC measurements are given.
Diffraction dissociation at the LHC
International Nuclear Information System (INIS)
Jenkovszky, László; Orava, Risto; Salii, Andrii
2013-01-01
We report on recent calculations of low missing mass single (SD) and double (DD) diffractive dissociation at LHC energies. The calculations are based on a dual-Regge model, dominated by a single Pomeron exchange. The diffractively excited states lie on the nucleon trajectory N*, appended by the isolated Roper resonance. Detailed predictions for the squared momentum transfer and missing mass dependence of the differential and integrated single-and double diffraction dissociation in the kinematical range of present and future LHC measurements are given.
The diffractive achromat full spectrum computational imaging with diffractive optics
Peng, Yifan
2016-07-11
Diffractive optical elements (DOEs) have recently drawn great attention in computational imaging because they can drastically reduce the size and weight of imaging devices compared to their refractive counterparts. However, the inherent strong dispersion is a tremendous obstacle that limits the use of DOEs in full spectrum imaging, causing unacceptable loss of color fidelity in the images. In particular, metamerism introduces a data dependency in the image blur, which has been neglected in computational imaging methods so far. We introduce both a diffractive achromat based on computational optimization, as well as a corresponding algorithm for correction of residual aberrations. Using this approach, we demonstrate high fidelity color diffractive-only imaging over the full visible spectrum. In the optical design, the height profile of a diffractive lens is optimized to balance the focusing contributions of different wavelengths for a specific focal length. The spectral point spread functions (PSFs) become nearly identical to each other, creating approximately spectrally invariant blur kernels. This property guarantees good color preservation in the captured image and facilitates the correction of residual aberrations in our fast two-step deconvolution without additional color priors. We demonstrate our design of diffractive achromat on a 0.5mm ultrathin substrate by photolithography techniques. Experimental results show that our achromatic diffractive lens produces high color fidelity and better image quality in the full visible spectrum. © 2016 ACM.
Nuclear dynamical diffraction using synchrotron radiation
Energy Technology Data Exchange (ETDEWEB)
Brown, Dennis Eugene [Stanford Univ., CA (United States)
1993-05-01
The scattering of synchrotron radiation by nuclei is extensively explored in this thesis. From the multipole electric field expansion resulting from time-dependent nonrelativistic perturbation theory, a dynamical scattering theory is constructed. This theory is shown, in the many particle limit, to be equivalent to the semi-classical approach where a quantum mechanical scattering amplitude is used in the Maxwell inhomogeneous wave equation. The Moessbauer specimen whose low-lying energy levels were probed is a ferromagnetic lattice of ^{57}Fe embedded in a yttrium iron garnet (YIG) crystal matrix. The hyperfine fields in YIG thin films were studied at low and room temperature using time-resolved quantum beat spectroscopy. Nuclear hyperfine structure quantum beats were measured using a fast plastic scintillator coincidence photodetector and associated electronics having a time resolution of 2.5 nsec. The variation of the quantum beat patterns near the Bragg [0 0 2] diffraction peak gave a Lamb-Moessbauer factor of 8.2±0.4. Exploring characteristic dynamical features in the higher order YIG [0 0 10] reflection revealed that one of the YIG crystals had bifurcated into two different layers. The dynamics of nuclear superradiance was explored. This phenomenon includes the radiative speedup exhibited by a collective state of particles, and, in striking concurrence, resonance frequency shifts. A speedup of a factor of 4 in the total decay rate and a beat frequency shift of 11/2 natural resonance linewidths were observed. Nuclear resonance scattering was also found to be a useful way of performing angular interferometry experiments, and it was used to observe the phase shift of a rotated quantum state. On the whole, nuclear dynamical diffraction theory has superbly explained many of the fascinating features of resonant magnetic dipole radiation scattered by a lattice of nuclei.
Nuclear dynamical diffraction using synchrotron radiation
International Nuclear Information System (INIS)
Brown, D.E.
1993-05-01
The scattering of synchrotron radiation by nuclei is extensively explored in this thesis. From the multipole electric field expansion resulting from time-dependent nonrelativistic perturbation theory, a dynamical scattering theory is constructed. This theory is shown, in the many particle limit, to be equivalent to the semi-classical approach where a quantum mechanical scattering amplitude is used in the Maxwell inhomogeneous wave equation. The Moessbauer specimen whose low-lying energy levels were probed is a ferromagnetic lattice of 57 Fe embedded in a yttrium iron garnet (YIG) crystal matrix. The hyperfine fields in YIG thin films were studied at low and room temperature using time-resolved quantum beat spectroscopy. Nuclear hyperfine structure quantum beats were measured using a fast plastic scintillator coincidence photodetector and associated electronics having a time resolution of 2.5 nsec. The variation of the quantum beat patterns near the Bragg [0 0 2] diffraction peak gave a Lamb-Moessbauer factor of 8.2±0.4. Exploring characteristic dynamical features in the higher order YIG [0 0 10] reflection revealed that one of the YIG crystals had bifurcated into two different layers. The dynamics of nuclear superradiance was explored. This phenomenon includes the radiative speedup exhibited by a collective state of particles, and, in striking concurrence, resonance frequency shifts. A speedup of a factor of 4 in the total decay rate and a beat frequency shift of 1 1/2 natural resonance linewidths were observed. Nuclear resonance scattering was also found to be a useful way of performing angular interferometry experiments, and it was used to observe the phase shift of a rotated quantum state. On the whole, nuclear dynamical diffraction theory has superbly explained many of the fascinating features of resonant magnetic dipole radiation scattered by a lattice of nuclei
Neutron diffraction studies of glasses
International Nuclear Information System (INIS)
Wright, A.C.
1987-01-01
A survey is given of the application of neutron diffraction to structural studies of oxide and halide glasses. As with crystalline materials, neutron and X-ray diffraction are the major structural probes for glasses and other amorphous solids, particularly in respect of intermediate range order. The glasses discussed mostly have structures which are dominated by a network in which the bonding is predominantly covalent. The examples discussed demonstrate the power of the neutron diffraction technique in the investigation of the structures of inorganic glasses. The best modern diffraction experiments are capable of providing accurate data with high real space resolution, which if used correctly, are an extremely fine filter for the various structural models proposed in the literature. 42 refs
Diffraction at a Straight Edge
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 20; Issue 5. Diffraction at a Straight Edge: A Gem from Sommerfeld's Work in Classical Physics. Rajaram Nityananda. General Article Volume 20 Issue 5 May 2015 pp 389-400 ...
Neutron Powder Diffraction in Sweden
International Nuclear Information System (INIS)
Tellgren, R.
1986-01-01
Neutron powder diffraction in Sweden has developed around the research reactor R2 in Studsvik. The article describes this facility and presents a historical review of research results obtained. It also gives some ideas of plans for future development
Tomography with energy dispersive diffraction
Stock, S. R.; Okasinski, J. S.; Woods, R.; Baldwin, J.; Madden, T.; Quaranta, O.; Rumaiz, A.; Kuczewski, T.; Mead, J.; Krings, T.; Siddons, P.; Miceli, A.; Almer, J. D.
2017-09-01
X-ray diffraction can be used as the signal for tomographic reconstruction and provides a cross-sectional map of the crystallographic phases and related quantities. Diffraction tomography has been developed over the last decade using monochromatic x-radiation and an area detector. This paper reports tomographic reconstruction with polychromatic radiation and an energy sensitive detector array. The energy dispersive diffraction (EDD) geometry, the instrumentation and the reconstruction process are described and related to the expected resolution. Results of EDD tomography are presented for two samples containing hydroxyapatite (hAp). The first is a 3D-printed sample with an elliptical crosssection and contains synthetic hAp. The second is a human second metacarpal bone from the Roman-era cemetery at Ancaster, UK and contains bio-hAp which may have been altered by diagenesis. Reconstructions with different diffraction peaks are compared. Prospects for future EDD tomography are also discussed.
Experimental studies of diffractive phenomena
International Nuclear Information System (INIS)
Cool, R.L.
1984-01-01
The coherent inelastic scattering process, usually called inclusive diffraction dissociation, is discussed. Topics include: t and M/sub x/ dependence, factorization, finite mass sum rule and charged particle multiplicities. 6 references, 14 figures
Topological vector spaces and their applications
Bogachev, V I
2017-01-01
This book gives a compact exposition of the fundamentals of the theory of locally convex topological vector spaces. Furthermore it contains a survey of the most important results of a more subtle nature, which cannot be regarded as basic, but knowledge which is useful for understanding applications. Finally, the book explores some of such applications connected with differential calculus and measure theory in infinite-dimensional spaces. These applications are a central aspect of the book, which is why it is different from the wide range of existing texts on topological vector spaces. In addition, this book develops differential and integral calculus on infinite-dimensional locally convex spaces by using methods and techniques of the theory of locally convex spaces. The target readership includes mathematicians and physicists whose research is related to infinite-dimensional analysis.
ATLAS - analysis of time-of-flight diffraction data from liquid and amorphous samples
International Nuclear Information System (INIS)
Soper, A.K.; Howells, W.S.; Hannon, A.C.
1989-05-01
The purpose of this manual is to describe a package of data analysis routines which have been developed at the Rutherford Appleton Laboratory for the analysis of time-of-flight diffraction data from liquids, gases, and amorphous materials. There is no fundamental barrier to diffraction data being accurately analysed to structure factor or even pair correlation function within a very short time of the completion of the experiment. Section 1 describes the time-of-flight neutron diffraction experiment and looks at diffraction theory. Section 2 indicates the steps in data analysis of time-of-flight diffraction data and Section 3 gives details of how to run the procedures. (author)
Optical diffraction by ordered 2D arrays of silica microspheres
International Nuclear Information System (INIS)
Shcherbakov, A.A.; Shavdina, O.; Tishchenko, A.V.; Veillas, C.; Verrier, I.; Dellea, O.; Jourlin, Y.
2017-01-01
The article presents experimental and theoretical studies of angular dependent diffraction properties of 2D monolayer arrays of silica microspheres. High-quality large area defect-free monolayers of 1 μm diameter silica microspheres were deposited by the Langmuir-Blodgett technique under an accurate optical control. Measured angular dependencies of zeroth and one of the first order diffraction efficiencies produced by deposited samples were simulated by the rigorous Generalized Source Method taking into account particle size dispersion and lattice nonideality. - Highlights: • High quality silica microsphere monolayer was fabricated. • Accurate measurements of diffraction efficiency angular dependencies. • Rigorous diffraction simulation of both ideal hexagonal and realistic microsphere arrangements. • Qualitative rationalization of the obtained results and the observed differences between the experiment and the theory.
Diffractive production and hadron structure
International Nuclear Information System (INIS)
Nussinov, S.; Szwed, J.
1979-01-01
Analysis of diffractive production on nuclei implied cross sections of the diffractively produced system on nucleons which are smaller than the corresponding projectile nucleon cross sections. A natural explanation for this feature is provided in the Good-Walker coherent production formalism. A specific realization of the Good-Walker formalism stated in terms of quarks and connecting electric flux tubes and some ensuing consequences are also discussed briefly. (Auth.)
CONFERENCE: Elastic and diffractive scattering
Energy Technology Data Exchange (ETDEWEB)
White, Alan
1989-09-15
Elastic scattering, when particles appear to 'bounce' off each other, and the related phenomena of diffractive scattering are currently less fashionable than the study of hard scattering processes. However this could change rapidly if unexpected results from the UA4 experiment at the CERN Collider are confirmed and their implications tested. These questions were highlighted at the third 'Blois Workshop' on Elastic and Diffractive Scattering, held early in May on the Evanston campus of Northwestern University, near Chicago.
Theoretical review of diffractive phenomena
International Nuclear Information System (INIS)
Golec-Biernat, K.
2005-01-01
We review QCD based descriptions of diffractive deep inelastic scattering emphasising the role of models with parton saturation. These models provide natural explanation of such experimentally observed facts as the constant ratio of σ diff /σ tot as a function of the Bjorken variable x, and Regge factorization of diffractive parton distributions. The Ingelman-Schlein model and the soft color interaction model are also presented
The Diffraction Response Interpolation Method
DEFF Research Database (Denmark)
Jespersen, Søren Kragh; Wilhjelm, Jens Erik; Pedersen, Peder C.
1998-01-01
Computer modeling of the output voltage in a pulse-echo system is computationally very demanding, particularly whenconsidering reflector surfaces of arbitrary geometry. A new, efficient computational tool, the diffraction response interpolationmethod (DRIM), for modeling of reflectors in a fluid...... medium, is presented. The DRIM is based on the velocity potential impulseresponse method, adapted to pulse-echo applications by the use of acoustical reciprocity. Specifically, the DRIM operates bydividing the reflector surface into planar elements, finding the diffraction response at the corners...
Fractal vector optical fields.
Pan, Yue; Gao, Xu-Zhen; Cai, Meng-Qiang; Zhang, Guan-Lin; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian
2016-07-15
We introduce the concept of a fractal, which provides an alternative approach for flexibly engineering the optical fields and their focal fields. We propose, design, and create a new family of optical fields-fractal vector optical fields, which build a bridge between the fractal and vector optical fields. The fractal vector optical fields have polarization states exhibiting fractal geometry, and may also involve the phase and/or amplitude simultaneously. The results reveal that the focal fields exhibit self-similarity, and the hierarchy of the fractal has the "weeding" role. The fractal can be used to engineer the focal field.
Loss of coherence in double-slit diffraction experiments
Sanz, A.S.; Borondo, F.; Bastiaans, M.J.
2005-01-01
By using optical models based on the theory of partially coherent light, and the quantum decoherence model proposed by Joos and Zeh [Z. Phys. B 59, 223 (1985)], we explore incoherence and decoherence in interference phenomena. The problem chosen to study is that of the double-slit diffraction
Noncausal Bayesian Vector Autoregression
DEFF Research Database (Denmark)
Lanne, Markku; Luoto, Jani
We propose a Bayesian inferential procedure for the noncausal vector autoregressive (VAR) model that is capable of capturing nonlinearities and incorporating effects of missing variables. In particular, we devise a fast and reliable posterior simulator that yields the predictive distribution...
Curjel, C. R.
1990-01-01
Presented are activities that help students understand the idea of a vector field. Included are definitions, flow lines, tangential and normal components along curves, flux and work, field conservation, and differential equations. (KR)
Minnesota Department of Natural Resources — This vector dataset is a detailed (1-acre minimum), hierarchically organized vegetation cover map produced by computer classification of combined two-season pairs of...
Kansas Data Access and Support Center — The Kansas Tagged Vector Contour (TVC) dataset consists of digitized contours from the 7.5 minute topographic quadrangle maps. Coverage for the state is incomplete....
Czech Academy of Sciences Publication Activity Database
Krejčí, Pavel
1991-01-01
Roč. 2, - (1991), s. 281-292 ISSN 0956-7925 Keywords : vector hysteresis operator * hysteresis potential * differential inequality Subject RIV: BA - General Mathematics http://www.math.cas.cz/~krejci/b15p.pdf
Support vector machines applications
Guo, Guodong
2014-01-01
Support vector machines (SVM) have both a solid mathematical background and good performance in practical applications. This book focuses on the recent advances and applications of the SVM in different areas, such as image processing, medical practice, computer vision, pattern recognition, machine learning, applied statistics, business intelligence, and artificial intelligence. The aim of this book is to create a comprehensive source on support vector machine applications, especially some recent advances.
International Nuclear Information System (INIS)
Akama, K.; Hattori, T.; Yasue, M.
1991-01-01
An exotic composite vector boson V is introduced in two dynamical models of composite quarks, leptons, W, and Z. One is based on four-Fermi interactions, in which composite vector bosons are regarded as fermion-antifermion bound states and the other is based on the confining SU(2) L gauge model, in which they are given by scalar-antiscalar bound states. Both approaches describe the same effective interactions for the sector of composite quarks, leptons, W, Z, γ, and V
Melillo Fenech, Tanya
2010-01-01
A vector-borne disease is one in which the pathogenic microorganism is transmitted from an infected individual to another individual by an arthropod or other agent. The transmission depends upon the attributes and requirements of at least three different Iiving organisms : the pathologic agent which is either a virus, protozoa, bacteria or helminth (worm); the vector, which is commonly an arthropod such as ticks or mosquitoes; and the human host.
International Nuclear Information System (INIS)
Yan, Zhenya
2011-01-01
The coupled nonlinear volatility and option pricing model presented recently by Ivancevic is investigated, which generates a leverage effect, i.e., stock volatility is (negatively) correlated to stock returns, and can be regarded as a coupled nonlinear wave alternative of the Black–Scholes option pricing model. In this Letter, we analytically propose vector financial rogue waves of the coupled nonlinear volatility and option pricing model without an embedded w-learning. Moreover, we exhibit their dynamical behaviors for chosen different parameters. The vector financial rogue wave (rogon) solutions may be used to describe the possible physical mechanisms for the rogue wave phenomena and to further excite the possibility of relative researches and potential applications of vector rogue waves in the financial markets and other related fields. -- Highlights: ► We investigate the coupled nonlinear volatility and option pricing model. ► We analytically present vector financial rogue waves. ► The vector financial rogue waves may be used to describe the extreme events in financial markets. ► This results may excite the relative researches and potential applications of vector rogue waves.
Vector pulsing soliton of self-induced transparency in waveguide
International Nuclear Information System (INIS)
Adamashvili, G.T.
2015-01-01
A theory of an optical resonance vector pulsing soliton in waveguide is developed. A thin transition layer containing semiconductor quantum dots forms the boundary between the waveguide and one of the connected media. Analytical and numerical solutions for the optical vector pulsing soliton in waveguide are obtained. The vector pulsing soliton in the presence of excitonic and bi-excitonic excitations is compared with the soliton for waveguide TM-modes with parameters that can be used in modern optical experiments. It is shown that these nonlinear waves have significantly different parameters and shapes. - Highlights: • An optical vector pulsing soliton in a planar waveguide is presented. • Explicit form of the optical vector pulsing soliton are obtained. • The vector pulsing soliton and the soliton have different parameters and profiles
Introductory photoemission theory
International Nuclear Information System (INIS)
Arai, Hiroko; Fujikawa, Takashi
2010-01-01
An introductory review is presented on the basis of many-body scattering theory. Some fundamental aspects of photoemission theory are discussed in detail. A few applications are also discussed; photoelectron diffraction, depth distribution function and multi-atom resonant photoemission are also discussed briefly. (author)
Neutron diffraction and oxide research
International Nuclear Information System (INIS)
Hunter, B.; Howard, C.J.; Kennedy, B.J.
1999-01-01
Oxide compounds form a large class of interesting materials that have a diverse range of mechanical and electronic properties. This diversity and its commercial implications has had a significant impact on physics research. This is particularly evident in the fields of superconductivity magnetoresistivity and ferroelectricity, where discoveries in the last 15 years have given rise to significant shifts in research activities. Historically, oxides have been studied for many years, but it is only recently that significant effort has been diverted to the study of oxide materials for their application to mechanical and electronic devices. An important property of such materials is the atomic structure, for the determination of which diffraction techniques are ideally suited. Recent examples of structure determinations using neutron diffraction in oxide based systems are high temperature superconductors, where oxygen defects are a key factor. Here, neutron diffraction played a major role in determining the effect of oxygen on the superconducting properties. Similarly, neutron diffraction has enjoyed much success in the determination of the structures of the manganate based colossal magnetoresistive (CMR) materials. In both these cases the structure plays a pivotal role in determining theoretical models of the electronic properties. The neutron scattering group at ANSTO has investigated several oxide systems using neutron powder diffraction. Two such systems are presented in this paper; the zirconia-based materials that are used as engineering materials, and the perovskite-based oxides that include the well known cuprate superconductors and the manganate CMR materials
Photon diffractive dissociation in deep inelastic scattering
International Nuclear Information System (INIS)
Wuesthoff, M.
1995-09-01
The cross section of the Photon Diffractive Dissociation in Deep Inelastic Scattering is calculated in the frame work of perturbative QCD. In the triple Regge region the BFKL-approximation is used to evaluate the leading contributions of the corresponding Feynman diagrams with a subsequent resummation in terms of integral equations. These equations are partly solved leading to an effective two to four gluons transition vertex. This exhibits remarkable properties like the total symmetry under the interchange of gluons, the conformal invariance and a simple colour structure. The presence of four interacting gluons in the t-channel does not support the simple triple Pomeron picture with solely a local vertex. A dimensional conservation law is found for zero momentum transfer with the consequence that a direct coupling of the three BFKL-singularities is absent. Another consequence is the dominance of small transverse momenta at the triple Pomeron vertex. Beyond the triple Regge limit a slightly different approach is used in which the diagrams are calculated with leading log(Q 2 ) accuracy. Higher twist contributions are neglected except for the longitudinal part of the cross section which dominates at small invariant masses M in accordance with QCD-predictions and measurements for the exclusive production of vector mesons. For the comparison with the recently measured Photon Diffractive Dissociation-data from H1 and ZEUS a model for the Pomeron is introduced based on the F 2 -data. In the spirit of the k t -factorization theorem this model is inserted in place of the BFKL-Pomeron. Considering the fact that this approach does not contain free parameters the agreement between the theoretical prediction and the data is found to be good. (orig.)
2D vector-cyclic deformable templates
DEFF Research Database (Denmark)
Schultz, Nette; Conradsen, Knut
1998-01-01
In this paper the theory of deformable templates is a vector cycle in 2D is described. The deformable template model originated in (Grenander, 1983) and was further investigated in (Grenander et al., 1991). A template vector distribution is induced by parameter distribution from transformation...... matrices applied to the vector cycle. An approximation in the parameter distribution is introduced. The main advantage by using the deformable template model is the ability to simulate a wide range of objects trained by e.g. their biological variations, and thereby improve restoration, segmentation...... and probabillity measurement. The case study concerns estimation of meat percent in pork carcasses. Given two cross-sectional images - one at the front and one near the ham of the carcass - the areas of lean and fat and a muscle in the lean area are measured automatically by the deformable templates....
Application of Vector Triggering Random Decrement
DEFF Research Database (Denmark)
Asmussen, J. C.; Ibrahim, S. R.; Brincker, Rune
result is a Random Decrement function from each measurement. In traditional Random Decrement estimation the triggering condition is a scalar condition, which should only be fulfilled in a single measurement. In vector triggering Random Decrement the triggering condition is a vector condition......This paper deals with applications of the vector triggering Random Decrement technique. This technique is new and developed with the aim of minimizing estimation time and identification errors. The theory behind the technique is discussed in an accompanying paper. The results presented...... in this paper should be regarded as a further documentation of the technique. The key point in Random Decrement estimation is the formulation of a triggering condition. If the triggering condition is fulfilled a time segment from each measurement is picked out and averaged with previous time segments. The final...
Application of Vector Triggering Random Decrement
DEFF Research Database (Denmark)
Asmussen, J. C.; Ibrahim, S. R.; Brincker, Rune
1997-01-01
result is a Random Decrement function from each measurement. In traditional Random Decrement estimation the triggering condition is a scalar condition, which should only be fulfilled in a single measurement. In vector triggering Random Decrement the triggering condition is a vector condition......This paper deals with applications of the vector triggering Random Decrement technique. This technique is new and developed with the aim of minimizing estimation time and identification errors. The theory behind the technique is discussed in an accompanying paper. The results presented...... in this paper should be regarded as a further documentation of the technique. The key point in Random Decrement estimation is the formulation of a triggering condition. If the triggering condition is fulfilled a time segment from each measurement is picked out and averaged with previous time segments. The final...
Hard diffraction and rapidity gaps
International Nuclear Information System (INIS)
Brandt, A.
1995-09-01
The field of hard diffraction, which studies events with a rapidity gap and a hard scattering, has expanded dramatically recently. A review of new results from CDF, D OE, H1 and ZEUS will be given. These results include diffractive jet production, deep-inelastic scattering in large rapidity gap events, rapidity gaps between high transverse energy jets, and a search for diffractive W-boson production. The combination of these results gives new insight into the exchanged object, believed to be the pomeron. The results axe consistent with factorization and with a hard pomeron that contains both quarks and gluons. There is also evidence for the exchange of a strongly interacting color singlet in high momentum transfer (36 2 ) events
Light diffraction through a feather
Directory of Open Access Journals (Sweden)
Pérez García, Hugo;
2012-01-01
Full Text Available We have used a feather to study light diffraction, in a qualitative as well as in a quantitative manner. Experimental measurement of the separation between the bright spots obtained with a laser pointer allowed the determination of the space between feather's barbs and barbules. The results we have obtained agree satisfactorily with those corresponding to a typical feather. Due to the kind of materials, the related concepts and the experimental results, this activity becomes an excellent didactic resource suitable for studying diffraction, both in introductory undergraduate as well as in secondary school physics courses.
CONFERENCE: Elastic and diffractive scattering
International Nuclear Information System (INIS)
White, Alan
1989-01-01
Elastic scattering, when particles appear to 'bounce' off each other, and the related phenomena of diffractive scattering are currently less fashionable than the study of hard scattering processes. However this could change rapidly if unexpected results from the UA4 experiment at the CERN Collider are confirmed and their implications tested. These questions were highlighted at the third 'Blois Workshop' on Elastic and Diffractive Scattering, held early in May on the Evanston campus of Northwestern University, near Chicago
CERN vector boson hunt successful
International Nuclear Information System (INIS)
Robinson, A.L.
1983-01-01
UA-1 and UA-2 are code names for two groups of physicists at the European Laboratory for Particle Physics (CERN), together comprising almost 200 researchers. From data collected in two 3-month-long runs last fall and spring, the groups have collected 100 intermediate vector bosons (90 W's and 10 Z 0 's) whose properties so far fit the predictions of the unified quantum field theory of the electromagnetic and weak forces. Although the number of events is short of staggering, the discovery is immensely important. Physicists have been looking for the W for about 50 years. The Z 0 is crucial to the success of the method by which the two forces were melded into one - the electro-weak force
High-energy X-ray diffraction studies of disordered materials
International Nuclear Information System (INIS)
Kohara, Shinji; Suzuya, Kentaro
2003-01-01
With the arrival of the latest generation of synchrotron sources and the introduction of advanced insertion devices (wigglers and undulators), the high-energy (E≥50 keV) X-ray diffraction technique has become feasible, leading to new approaches in the quantitative study of the structure of disordered materials. High-energy X-ray diffraction has several advantages: higher resolution in real space due to a wide range of scattering vector Q, smaller correction terms (especially the absorption correction), reduction of truncation errors, the feasibility of running under extreme environments, including high-temperatures and high-pressures, and the ability to make direct comparisons between X-ray and neutron diffraction data. Recently, high-energy X-ray diffraction data have been combined with neutron diffraction data from a pulsed source to provide more detailed and reliable structural information than that hitherto available
Vectorization in quantum chemistry
International Nuclear Information System (INIS)
Saunders, V.R.
1987-01-01
It is argued that the optimal vectorization algorithm for many steps (and sub-steps) in a typical ab initio calculation of molecular electronic structure is quite strongly dependent on the target vector machine. Details such as the availability (or lack) of a given vector construct in the hardware, vector startup times and asymptotic rates must all be considered when selecting the optimal algorithm. Illustrations are drawn from: gaussian integral evaluation, fock matrix construction, 4-index transformation of molecular integrals, direct-CI methods, the matrix multiply operation. A cross comparison of practical implementations on the CDC Cyber 205, the Cray-IS and Cray-XMP machines is presented. To achieve portability while remaining optimal on a wide range of machines it is necessary to code all available algorithms in a machine independent manner, and to select the appropriate algorithm using a procedure which is based on machine dependent parameters. Most such parameters concern the timing of certain vector loop kernals, which can usually be derived from a 'bench-marking' routine executed prior to the calculation proper
Studies of diffraction with the ATLAS detector
International Nuclear Information System (INIS)
Trzebinski, Maciej
2013-01-01
The thesis is devoted to the study of diffractive physics with the ATLAS detector at the LHC. After a short introduction to diffractive physics including soft and hard diffraction, we discuss Jet-Gap-Jet production at the LHC which is particularly interesting for testing the Balitski Fadin Kuraev Lipatov QCD evolution equation. Using the signal selection requirements and a gap definition based on tracks reconstructed in the ATLAS Inner Detector, we observe a clear signal of Jet-Gap-Jet events in the data. Starting from the half-gap size of 0.8 the data cannot be properly described using only the Jet Monte Carlo sample without gaps. Furthermore, we demonstrated that DPE JGJ production, with both protons tagged in the AFP stations, should provide a significant test of the BFKL theory, once the 300 pb -1 of integrated luminosity is collected. In the last part of the thesis, we discussed the processes of Central Exclusive Jet and Exclusive π + π - production. After the data selection, the signal to background ratio is found to be of about 5/9 (1/13) for μ= 23 (46). For a collected integrated luminosity of 40(300) fb -1 (for pile-up of 23(46)) this measurement will deliver ten times better constraints on the theoretical models than the most recent ones. The additional measurement of exclusive pion production, relying on the use of the ALFA stations, allows to constrain further the exclusive models. We demonstrated that a data sample collected by the ALFA detectors should be sufficient to measure the cross section and to study various distributions, especially the invariant mass of the pion-pion system. (author) [fr
Structure of amorphous selenium studied by neutron diffraction
DEFF Research Database (Denmark)
Hansen, Flemming Yssing; Knudsen, Torben Steen; Carneiro, K.
1975-01-01
Neutron diffraction measurements on amorphous selenium have been performed at 293 and 80 K. Careful analyses of the instrumental corrections were made to avoid systematic errors in the measured structure factor S (kappa) in the wave vector region 0 ? kappa ? 12 Å−1. As a result of the data...... treatment, the neutron scattering cross sections of selenium are determined to be sigmacoh = 8.4±0.1 b and sigmainc = 0.1±0.1 b. Using the fact that S (kappa) for large kappa's is determined by the short distances in the sample, a new method for extrapolation of the experimental S (kappa) until convergence....... Finally, we give a brief discussion of the different models for the structure of amorphous selenium, taking both diffraction measurements and thermodynamic considerations into account. The Journal of Chemical Physics is copyrighted by The American Institute of Physics....
Vector Fields on Product Manifolds
Kurz, Stefan
2011-01-01
This short report establishes some basic properties of smooth vector fields on product manifolds. The main results are: (i) On a product manifold there always exists a direct sum decomposition into horizontal and vertical vector fields. (ii) Horizontal and vertical vector fields are naturally isomorphic to smooth families of vector fields defined on the factors. Vector fields are regarded as derivations of the algebra of smooth functions.
Microarcsecond relative astrometry from the ground with a diffractive pupil
Energy Technology Data Exchange (ETDEWEB)
Ammons, S M; Bendek, E; Guyon, O
2011-09-08
The practical use of astrometry to detect exoplanets via the reflex motion of the parent star depends critically on the elimination of systematic floors in imaging systems. In the diffractive pupil technique proposed for space-based detection of exo-earths, extended diffraction spikes generated by a dotted primary mirror are referenced against a wide-field grid of background stars to calibrate changing optical distortion and achieve microarcsecond astrometric precision on bright targets (Guyon et al. 2010). We describe applications of this concept to ground-based uncrowded astrometry using a diffractive, monopupil telescope and a wide-field camera to image as many as {approx}4000 background reference stars. Final relative astrometric precision is limited by differential tip/tilt jitter caused by high altitude layers of turbulence. A diffractive 3-meter telescope is capable of reaching {approx}35 {micro}as relative astrometric error per coordinate perpendicular to the zenith vector in three hours on a bright target star (I < 10) in fields of moderate stellar density ({approx}40 stars arcmin{sup -2} with I < 23). Smaller diffractive apertures (D < 1 m) can achieve 100-200 {micro}as performance with the same stellar density and exposure time and a large telescope (6.5-10 m) could achieve as low as 10 {micro}as, nearly an order of magnitude better than current space-based facilities. The diffractive pupil enables the use of larger fields of view through calibration of changing optical distortion as well as brighter target stars (V < 6) by preventing star saturation. Permitting the sky to naturally roll to average signals over many thousands of pixels can mitigate the effects of detector imperfections.
Vector-Quantization using Information Theoretic Concepts
DEFF Research Database (Denmark)
Lehn-Schiøler, Tue; Hegde, Anant; Erdogmus, Deniz
2005-01-01
interpretation and relies on minimization of a well defined cost-function. It is also shown how the potential field approach can be linked to information theory by use of the Parzen density estimator. In the light of information theory it becomes clear that minimizing the free energy of the system is in fact......The process of representing a large data set with a smaller number of vectors in the best possible way, also known as vector quantization, has been intensively studied in the recent years. Very efficient algorithms like the Kohonen Self Organizing Map (SOM) and the Linde Buzo Gray (LBG) algorithm...... have been devised. In this paper a physical approach to the problem is taken, and it is shown that by considering the processing elements as points moving in a potential field an algorithm equally efficient as the before mentioned can be derived. Unlike SOM and LBG this algorithm has a clear physical...
X-ray diffraction at Bragg angles around π/2
International Nuclear Information System (INIS)
Mayolo, C.M.G. de.
1991-01-01
X-ray diffraction at Bragg angles around π/2 is studied from the theoretical and experimental points of view. The proposed corrections to the dynamical theory in the θ β ≅ π/2 cases, has been reviewed showing the equivalence between two formalisms leading to a corrected expression for the dependence of the angular parameter y with the angle of incidence. An expression for y valid in the conventional and θ β ≅ π/2 cases has been obtained. A general expression for Bragg law and for energy resolution after a Bragg diffraction was also deduced. (author)
Dorofeyev, Illarion
2009-03-01
Characteristics of a quasi-spherical wave front of an electromagnetic field diffracted by a subwavelength hole in a thin film with real optical properties are studied. Related diffraction problem is solved in general by use of the scalar and vector Green's theorems and related Green's function of a boundary-value problem. Local phase deviations of a diffracted wave front from an ideal spherical front are calculated. Diffracted patterns are calculated for the coherent incident fields in case of holes array in a screen of perfect conductivity.
2013-09-01
justifier l’élaboration d’une nouvelle analyse des pics de DRX dans les installations de RDDC Atlantique. Résultats : Plusieurs auteurs se sont penchés...2 3 X-Ray Diffraction Theory ...3 X-Ray Diffraction Theory The manifestation of desirable physical and chemical material properties may be readily discerned through investigation
CMS results on soft diffraction
INSPIRE-00086121
2013-01-01
We present measurements of soft single- and double-diffractive cross sections, as well as of forward rapidity gap cross sections at 7 TeV at the LHC, and compare the results to other measurements and to theoretical predictions implemented in various Monte Carlo simulations.
A QCD analysis of ZEUS diffractive data
Energy Technology Data Exchange (ETDEWEB)
Chekanov, S.; Derrick, M.; Magill, S. [Argonne National Laboratory, Argonne, IL (US)] (and others)
2009-11-15
ZEUS inclusive diffractive cross-section measurements have been used in a DGLAP next-to-leading-order QCD analysis to extract the diffractive parton distribution functions. Data on diffractive dijet production in deep inelastic scattering have also been included to constrain the gluon density. Predictions based on the extracted parton densities are compared to diffractive charm and dijet photoproduction data. (orig.)
A QCD analysis of ZEUS diffractive data
International Nuclear Information System (INIS)
Chekanov, S.; Derrick, M.; Magill, S.
2009-11-01
ZEUS inclusive diffractive cross-section measurements have been used in a DGLAP next-to-leading-order QCD analysis to extract the diffractive parton distribution functions. Data on diffractive dijet production in deep inelastic scattering have also been included to constrain the gluon density. Predictions based on the extracted parton densities are compared to diffractive charm and dijet photoproduction data. (orig.)
Electro-optic diffraction grating tuned laser
International Nuclear Information System (INIS)
Hughes, R.S.
1975-01-01
An electro-optic diffraction grating tuned laser comprising a laser medium, output mirror, retro-reflective grating and an electro-optic diffraction grating beam deflector positioned between the laser medium and the reflective diffraction grating is described. An optional angle multiplier may be used between the electro-optic diffraction grating and the reflective grating. (auth)
Diffraction dissociation: thirty five years after
International Nuclear Information System (INIS)
Zotov, N.P.; Tsarev, V.A.
1988-01-01
Review of the basic results and stages of studying one of the most interesting phenomena in high energy physics-diffraction dissociation (DD) of hadrons is presented. The review contains complete information concerning the basic experimental results and the most ''set'' DD theoretical models. Though the discussion focuses primarily on considering a single nucleon DD, this still allows one to fully describe the basic features of the phenomenon under investigation. The last part of the review is devoted to the most notable results obtained during DD experimental investigation in the last five years, which have not been reflected in the earlier published reviews. Signs of excited system parton structure and pomeron are clearly found in the new experimental data. It is underlined that DD mechanism understanding is closely connected with the solution of the confinement problem in the strong interaction theory and requires further experimental and theoretical investigations
Bunyavirus-Vector Interactions
Directory of Open Access Journals (Sweden)
Kate McElroy Horne
2014-11-01
Full Text Available The Bunyaviridae family is comprised of more than 350 viruses, of which many within the Hantavirus, Orthobunyavirus, Nairovirus, Tospovirus, and Phlebovirus genera are significant human or agricultural pathogens. The viruses within the Orthobunyavirus, Nairovirus, and Phlebovirus genera are transmitted by hematophagous arthropods, such as mosquitoes, midges, flies, and ticks, and their associated arthropods not only serve as vectors but also as virus reservoirs in many cases. This review presents an overview of several important emerging or re-emerging bunyaviruses and describes what is known about bunyavirus-vector interactions based on epidemiological, ultrastructural, and genetic studies of members of this virus family.
Yurinsky, Vadim Vladimirovich
1995-01-01
Surveys the methods currently applied to study sums of infinite-dimensional independent random vectors in situations where their distributions resemble Gaussian laws. Covers probabilities of large deviations, Chebyshev-type inequalities for seminorms of sums, a method of constructing Edgeworth-type expansions, estimates of characteristic functions for random vectors obtained by smooth mappings of infinite-dimensional sums to Euclidean spaces. A self-contained exposition of the modern research apparatus around CLT, the book is accessible to new graduate students, and can be a useful reference for researchers and teachers of the subject.
Duality in vector optimization
Bot, Radu Ioan
2009-01-01
This book presents fundamentals and comprehensive results regarding duality for scalar, vector and set-valued optimization problems in a general setting. After a preliminary chapter dedicated to convex analysis and minimality notions of sets with respect to partial orderings induced by convex cones a chapter on scalar conjugate duality follows. Then investigations on vector duality based on scalar conjugacy are made. Weak, strong and converse duality statements are delivered and connections to classical results from the literature are emphasized. One chapter is exclusively consecrated to the s
Multithreading in vector processors
Evangelinos, Constantinos; Kim, Changhoan; Nair, Ravi
2018-01-16
In one embodiment, a system includes a processor having a vector processing mode and a multithreading mode. The processor is configured to operate on one thread per cycle in the multithreading mode. The processor includes a program counter register having a plurality of program counters, and the program counter register is vectorized. Each program counter in the program counter register represents a distinct corresponding thread of a plurality of threads. The processor is configured to execute the plurality of threads by activating the plurality of program counters in a round robin cycle.
Eisenman, Richard L
2005-01-01
This outstanding text and reference applies matrix ideas to vector methods, using physical ideas to illustrate and motivate mathematical concepts but employing a mathematical continuity of development rather than a physical approach. The author, who taught at the U.S. Air Force Academy, dispenses with the artificial barrier between vectors and matrices--and more generally, between pure and applied mathematics.Motivated examples introduce each idea, with interpretations of physical, algebraic, and geometric contexts, in addition to generalizations to theorems that reflect the essential structur
Free topological vector spaces
Gabriyelyan, Saak S.; Morris, Sidney A.
2016-01-01
We define and study the free topological vector space $\\mathbb{V}(X)$ over a Tychonoff space $X$. We prove that $\\mathbb{V}(X)$ is a $k_\\omega$-space if and only if $X$ is a $k_\\omega$-space. If $X$ is infinite, then $\\mathbb{V}(X)$ contains a closed vector subspace which is topologically isomorphic to $\\mathbb{V}(\\mathbb{N})$. It is proved that if $X$ is a $k$-space, then $\\mathbb{V}(X)$ is locally convex if and only if $X$ is discrete and countable. If $X$ is a metrizable space it is shown ...
Spanning forests and the vector bundle Laplacian
Kenyon, Richard
2011-01-01
The classical matrix-tree theorem relates the determinant of the combinatorial Laplacian on a graph to the number of spanning trees. We generalize this result to Laplacians on one- and two-dimensional vector bundles, giving a combinatorial interpretation of their determinants in terms of so-called cycle rooted spanning forests (CRSFs). We construct natural measures on CRSFs for which the edges form a determinantal process. ¶ This theory gives a natural generalization of the spanning tre...
Comparison of infrared laser beam shaping by diffractive and refractive methods
CSIR Research Space (South Africa)
Forbes, A
2005-08-01
Full Text Available Infra-red laser beam shaping has the inherent difficulty that simple ray tracing methods often yield anomalous results, due primarily to the propagation effects at longer wavelengths. Techniques based on diffraction theory have been developed...
Diffraction of an inhomogeneous plane wave by an impedance wedge in a lossy medium
CSIR Research Space (South Africa)
Manara, G
1998-11-01
Full Text Available The diffraction of an inhomogeneous plane wave by an impedance wedge embedded in a lossy medium is analyzed. The rigorous integral representation for the field is asymptotically evaluated in the context of the uniform geometrical theory...
Cobordism Obstructions to Vector Fields and a Generalization of Lin's Theorem
DEFF Research Database (Denmark)
Svane, Anne Marie
Atiyah and Dupont have studied the existence of linearly independent vector fields on manifolds by means of K-theory. They obtained the complete conditions for up to three independent vector fields. In the thesis, we try to copy their approach using certain spectra related to cobordism theory. We...
Digital diffractive optics: Have diffractive optics entered mainstream industry yet?
Kress, Bernard; Hejmadi, Vic
2010-05-01
When a new technology is integrated into industry commodity products and consumer electronic devices, and sold worldwide in retail stores, it is usually understood that this technology has then entered the realm of mainstream technology and therefore mainstream industry. Such a leap however does not come cheap, as it has a double edge sword effect: first it becomes democratized and thus massively developed by numerous companies for various applications, but also it becomes a commodity, and thus gets under tremendous pressure to cut down its production and integration costs while not sacrificing to performance. We will show, based on numerous examples extracted from recent industry history, that the field of Diffractive Optics is about to undergo such a major transformation. Such a move has many impacts on all facets of digital diffractive optics technology, from the optical design houses to the micro-optics foundries (for both mastering and volume replication), to the final product integrators or contract manufacturers. The main causes of such a transformation are, as they have been for many other technologies in industry, successive technological bubbles which have carried and lifted up diffractive optics technology within the last decades. These various technological bubbles have been triggered either by real industry needs or by virtual investment hype. Both of these causes will be discussed in the paper. The adjective ""digital"" in "digital diffractive optics" does not refer only, as it is done in digital electronics, to the digital functionality of the element (digital signal processing), but rather to the digital way they are designed (by a digital computer) and fabricated (as wafer level optics using digital masking techniques). However, we can still trace a very strong similarity between the emergence of micro-electronics from analog electronics half a century ago, and the emergence of digital optics from conventional optics today.
DEFF Research Database (Denmark)
2000-01-01
Using a pulsed ultrasound field, the two-dimensional velocity vector can be determined with the invention. The method uses a transversally modulated ultrasound field for probing the moving medium under investigation. A modified autocorrelation approach is used in the velocity estimation. The new...
Production of lentiviral vectors
Directory of Open Access Journals (Sweden)
Otto-Wilhelm Merten
2016-01-01
Full Text Available Lentiviral vectors (LV have seen considerably increase in use as gene therapy vectors for the treatment of acquired and inherited diseases. This review presents the state of the art of the production of these vectors with particular emphasis on their large-scale production for clinical purposes. In contrast to oncoretroviral vectors, which are produced using stable producer cell lines, clinical-grade LV are in most of the cases produced by transient transfection of 293 or 293T cells grown in cell factories. However, more recent developments, also, tend to use hollow fiber reactor, suspension culture processes, and the implementation of stable producer cell lines. As is customary for the biotech industry, rather sophisticated downstream processing protocols have been established to remove any undesirable process-derived contaminant, such as plasmid or host cell DNA or host cell proteins. This review compares published large-scale production and purification processes of LV and presents their process performances. Furthermore, developments in the domain of stable cell lines and their way to the use of production vehicles of clinical material will be presented.
Indian Academy of Sciences (India)
The Gram-Schmidt process is one of the first things one learns in a course ... We might want to stay as close to the experimental data as possible when converting these vectors to orthonormal ones demanded by the model. The process of finding the closest or- thonormal .... is obtained by writing the matrix A = [aI, an], then.
Treiman, Jay S
2014-01-01
Calculus with Vectors grew out of a strong need for a beginning calculus textbook for undergraduates who intend to pursue careers in STEM. fields. The approach introduces vector-valued functions from the start, emphasizing the connections between one-variable and multi-variable calculus. The text includes early vectors and early transcendentals and includes a rigorous but informal approach to vectors. Examples and focused applications are well presented along with an abundance of motivating exercises. All three-dimensional graphs have rotatable versions included as extra source materials and may be freely downloaded and manipulated with Maple Player; a free Maple Player App is available for the iPad on iTunes. The approaches taken to topics such as the derivation of the derivatives of sine and cosine, the approach to limits, and the use of "tables" of integration have been modified from the standards seen in other textbooks in order to maximize the ease with which students may comprehend the material. Additio...
Indian Academy of Sciences (India)
[G] Giannessi F, Theorems of alternative, quadratic programs and complementarity problems, in: Variational Inequalities and Complementarity Problems (eds) R W Cottle, F Giannessi and J L Lions (New York: Wiley) (1980) pp. 151±186. [K1] Kazmi K R, Existence of solutions for vector optimization, Appl. Math. Lett. 9 (1996).
Centers for Disease Control (CDC) Podcasts
2011-04-18
This podcast discusses emerging vector-borne pathogens, their role as prominent contributors to emerging infectious diseases, how they're spread, and the ineffectiveness of mosquito control methods. Created: 4/18/2011 by National Center for Emerging Zoonotic and Infectious Diseases (NCEZID). Date Released: 4/27/2011.
Nuclear surface diffuseness revealed in nucleon-nucleus diffraction
Hatakeyama, S.; Horiuchi, W.; Kohama, A.
2018-05-01
The nuclear surface provides useful information on nuclear radius, nuclear structure, as well as properties of nuclear matter. We discuss the relationship between the nuclear surface diffuseness and elastic scattering differential cross section at the first diffraction peak of high-energy nucleon-nucleus scattering as an efficient tool in order to extract the nuclear surface information from limited experimental data involving short-lived unstable nuclei. The high-energy reaction is described by a reliable microscopic reaction theory, the Glauber model. Extending the idea of the black sphere model, we find one-to-one correspondence between the nuclear bulk structure information and proton-nucleus elastic scattering diffraction peak. This implies that we can extract both the nuclear radius and diffuseness simultaneously, using the position of the first diffraction peak and its magnitude of the elastic scattering differential cross section. We confirm the reliability of this approach by using realistic density distributions obtained by a mean-field model.
Phase modulation due to crystal diffraction by ptychographic imaging
Civita, M.; Diaz, A.; Bean, R. J.; Shabalin, A. G.; Gorobtsov, O. Yu.; Vartanyants, I. A.; Robinson, I. K.
2018-03-01
Solving the phase problem in x-ray crystallography has occupied a considerable scientific effort in the 20th century and led to great advances in structural science. Here we use x-ray ptychography to demonstrate an interference method which measures the phase of the beam transmitted through a crystal, relative to the incoming beam, when diffraction takes place. The observed phase change of the direct beam through a small gold crystal is found to agree with both a quasikinematical model and full dynamical theories of diffraction. Our discovery of a diffraction contrast mechanism will enhance the interpretation of data obtained from crystalline samples using the ptychography method, which provides some of the most accurate x-ray phase-contrast images.
Multiple x-ray diffraction simulation and applications
International Nuclear Information System (INIS)
Costa, C.A.B.S. da.
1989-09-01
A computer program (MULTX) was implemented for simulation X-ray multiple diffraction diagrams in Renninger geometries. The program uses the X-ray multiple diffraction theory for imperfect crystals. The iterative calculation of the intensities is based on the Taylor series general term, and the primary beam power expansion is given as function of the beam x penetration in the crystal surface. This development allows to consider the simultaneous interaction of the beams involved in the multiple diffraction phenomenon. The simulated diagrams are calculated point-to-point and the tests for the Si and GaAs presented good reproduction of the experimental diagrams for different primary reflections. (L.C.J.A.)
Neutron diffraction on pulsed sources
International Nuclear Information System (INIS)
Aksenov, V.L.; Balagurov, A.M.
2016-01-01
The possibilities currently offered and major scientific problems solved by time-of-flight neutron diffraction are reviewed. The reasons for the rapid development of the method over the last two decades has been mainly the emergence of third generation pulsed sources with a MW time-averaged power and advances in neutron-optical devices and detector systems. The paper discusses some historical aspects of time-of-flight neutron diffraction and examines the contribution to this method by F.L.Shapiro whose 100th birth anniversary was celebrated in 2015. The state of the art with respect to neutron sources for studies on output beams is reviewed in a special section. [ru
Statistical anisotropy from vector curvaton in D-brane inflation
International Nuclear Information System (INIS)
Dimopoulos, Konstantinos; Wills, Danielle; Zavala, Ivonne
2013-01-01
We investigate the possibility of embedding the vector curvaton paradigm in D-brane models of inflation in type IIB string theory in a simple toy model. The vector curvaton is identified with the U(1) gauge field that lives on the world volume of a D3-brane, which may be stationary or undergoing general motion in the internal space. The dilaton is considered as a spectator field which modulates the evolution of the vector field. In this set-up, the vector curvaton is able to generate measurable statistical anisotropy in the spectrum and bispectrum of the curvature perturbation assuming that the dilaton evolves as e −φ ∝a 2 where a(t) is the scale factor. Our work constitutes a first step towards exploring how such distinctive features may arise from the presence of several light fields that naturally appear in string theory models of cosmology.
Industrial applications of neutron diffraction
International Nuclear Information System (INIS)
Felcher, G.P.
1989-01-01
Neutron diffraction (or, to be more general, neutron scattering) is a most versatile and universal tool, which has been widely employed to probe the structure, the dynamics and the magnetism of condensed matter. Traditionally used for fundamental research in solid state physics, this technique more recently has been applied to problems of immediate industrial interest, as illustrated in examples covering the main fields of endeavour. 14 refs., 14 figs
Neutron diffraction and Vitamin E
Energy Technology Data Exchange (ETDEWEB)
Harroun, T A; Marquardt, D; Katsaras, J; Atkinson, J, E-mail: tharroun@brocku.ca
2010-11-01
It is generally accepted that neutron diffraction from model membrane systems is an effective biophysical technique for determining membrane structure. Here we describe an example of how deuterium labelling can elucidate the location of specific membrane soluble molecules, including a brief discussion of the technique itself. We show that deuterium labelled {alpha}-tocopherol sits upright in the bilayer, as might be expected, but at very different locations within the bilayer, depending on the degree of lipid chain unsaturation.
Diffraction dissociation and elastic scattering
International Nuclear Information System (INIS)
Verebryusov, V.S.; Ponomarev, L.A.; Smorodinskaya, N.Ya.
1987-01-01
In the framework of Regge scheme with supercritical pomeron a model is suggested for the NN-scattering amplitude which takes into account the contribution introduced to the intermediate state by diffraction dissociation (DD) processes. The DD amplitude is written in terms of the Deck model which has been previously applied to describing the main DD features. The calculated NN cross sections are compared with those obtained experimentally. Theoretical predictions for higher energy are presented
A new mass relation among the hadron vector resonances
Chizhov, M.V.
2001-01-01
We show that the hadron vector resonances are described by fields transforming according to different inequivalent representations of the Lorentz group: (1/2,1/2) and (1,0)+(0,1). The vector representation (1/2,1/2) is well studied and corresponds to the gauge fields. On the other hand, the chiral representations (1,0) and (0,1) are described by the second rank antisymmetric tensor fields, for which interaction theory has not yet been constructed. In the framework of the phenomenological Nambu - Jona-Lasinio approach we have introduced and used all these fields for a description of the vector resonances. A new mass relation between low-lying hadron vector and axial-vector resonances is obtained. This relation is in agreement with the present experimental data.
2015-01-01
A one-sentence definition of operator theory could be: The study of (linear) continuous operations between topological vector spaces, these being in general (but not exclusively) Fréchet, Banach, or Hilbert spaces (or their duals). Operator theory is thus a very wide field, with numerous facets, both applied and theoretical. There are deep connections with complex analysis, functional analysis, mathematical physics, and electrical engineering, to name a few. Fascinating new applications and directions regularly appear, such as operator spaces, free probability, and applications to Clifford analysis. In our choice of the sections, we tried to reflect this diversity. This is a dynamic ongoing project, and more sections are planned, to complete the picture. We hope you enjoy the reading, and profit from this endeavor.
Hashiguchi, Koichi
2014-01-01
This book was written to serve as the standard textbook of elastoplasticity for students, engineers and researchers in the field of applied mechanics. The present second edition is improved thoroughly from the first edition by selecting the standard theories from various formulations and models, which are required to study the essentials of elastoplasticity steadily and effectively and will remain universally in the history of elastoplasticity. It opens with an explanation of vector-tensor analysis and continuum mechanics as a foundation to study elastoplasticity theory, extending over various strain and stress tensors and their rates. Subsequently, constitutive equations of elastoplastic and viscoplastic deformations for monotonic, cyclic and non-proportional loading behavior in a general rate and their applications to metals and soils are described in detail, and constitutive equations of friction behavior between solids and its application to the prediction of stick-slip phenomena are delineated. In additi...
International Nuclear Information System (INIS)
MacDowell, Alastair; Celestre, Richard; Tamura, Nobumichi; Spolenak, Ralph; Valek, Bryan; Brown, Walter; Bravman, John; Padmore, Howard; Batterman, Boris; Patel, Jamshed
2000-01-01
At the Advanced Light Source in Berkeley the authors have instrumented a beam line that is devoted exclusively to x-ray micro diffraction problems. By micro diffraction they mean those classes of problems in Physics and Materials Science that require x-ray beam sizes in the sub-micron range. The instrument is for instance, capable of probing a sub-micron size volume inside micron sized aluminum metal grains buried under a silicon dioxide insulating layer. The resulting Laue pattern is collected on a large area CCD detector and automatically indexed to yield the grain orientation and deviatoric (distortional) strain tensor of this sub-micron volume. A four-crystal monochromator is then inserted into the beam, which allows monochromatic light to illuminate the same part of the sample. Measurement of diffracted photon energy allows for the determination of d spacings. The combination of white and monochromatic beam measurements allow for the determination of the total strain/stress tensor (6 components) inside each sub-micron sized illuminated volume of the sample
Diffraction Techniques in Structural Biology
Egli, Martin
2016-01-01
A detailed understanding of chemical and biological function and the mechanisms underlying the molecular activities ultimately requires atomic-resolution structural data. Diffraction-based techniques such as single-crystal X-ray crystallography, electron microscopy, and neutron diffraction are well established and they have paved the road to the stunning successes of modern-day structural biology. The major advances achieved in the last 20 years in all aspects of structural research, including sample preparation, crystallization, the construction of synchrotron and spallation sources, phasing approaches, and high-speed computing and visualization, now provide specialists and nonspecialists alike with a steady flow of molecular images of unprecedented detail. The present unit combines a general overview of diffraction methods with a detailed description of the process of a single-crystal X-ray structure determination experiment, from chemical synthesis or expression to phasing and refinement, analysis, and quality control. For novices it may serve as a stepping-stone to more in-depth treatises of the individual topics. Readers relying on structural information for interpreting functional data may find it a useful consumer guide. PMID:27248784
Neutron diffraction and lattice defects
International Nuclear Information System (INIS)
Hamaguchi, Yoshikazu
1974-01-01
Study on lattice defects by neutron diffraction technique is described. Wave length of neutron wave is longer than that of X-ray, and absorption cross-section is small. Number of defects observed by ESR is up to several defects, and the number studied with electron microscopes is more than 100. Information obtained by neutron diffraction concerns the number of defects between these two ranges. For practical analysis, several probable models are selected from the data of ESR or electron microscopes, and most probable one is determined by calculation. Then, defect concentration is obtained from scattering cross section. It is possible to measure elastic scattering exclusively by neutron diffraction. Minimum detectable concentration estimated is about 0.5% and 10 20 - 10 21 defects per unit volume. A chopper and a time of flight system are used as a measuring system. Cold neutrons are obtained from the neutron sources inserted into reactors. Examples of measurements by using similar equipments to PTNS-I system of Japan Atomic Energy Research Institute are presented. Interstitial concentration in the graphite irradiated by fast neutrons is shown. Defects in irradiated MgO were also investigated by measuring scattering cross section. Study of defects in Ge was made by measuring total cross section, and model analysis was performed in comparison with various models. (Kato, T.)
Probability theory and mathematical statistics for engineers
Pugachev, V S
1984-01-01
Probability Theory and Mathematical Statistics for Engineers focuses on the concepts of probability theory and mathematical statistics for finite-dimensional random variables.The publication first underscores the probabilities of events, random variables, and numerical characteristics of random variables. Discussions focus on canonical expansions of random vectors, second-order moments of random vectors, generalization of the density concept, entropy of a distribution, direct evaluation of probabilities, and conditional probabilities. The text then examines projections of random vector
Invariant hyperplanes and Darboux integrability of polynomial vector fields
International Nuclear Information System (INIS)
Zhang Xiang
2002-01-01
This paper is composed of two parts. In the first part, we provide an upper bound for the number of invariant hyperplanes of the polynomial vector fields in n variables. This result generalizes those given in Artes et al (1998 Pac. J. Math. 184 207-30) and Llibre and Rodriguez (2000 Bull. Sci. Math. 124 599-619). The second part gives an extension of the Darboux theory of integrability to polynomial vector fields on algebraic varieties
Search for vector-like quarks at ATLAS
Ellinghaus, Frank; The ATLAS collaboration
2017-01-01
Vector like quarks appear in many theories beyond the Standard Model as a way to cancel the mass divergence for the Higgs boson. The current status of the ATLAS searches for the production of vector-like quarks will be reviewed for proton-proton collisions at 13 TeV. This presentation will address the analysis techniques, in particular, the selection criteria, the background modelling and the related experimental uncertainties. The phenomenological implications of the obtained results will also be discussed.
Photoelectron diffraction and holography: Present status and future prospects
Energy Technology Data Exchange (ETDEWEB)
Fadley, C.S. [California Univ., Davis, CA (United States). Dept. of Physics]|[Lawrence Berkeley Lab., CA (United States); Thevuthasan, S. [California Univ., Davis, CA (United States). Dept. of Physics; Kaduwela, A.P. [Lawrence Berkeley Lab., CA (United States)] [and others
1993-07-01
Photoelectron diffraction and photoelectron holography, a newly developed variant of it, can provide a rich range of information concerning surface structure. These methods are sensitive to atomic type, chemical state, and spin state. The theoretical prediction of diffraction patterns is also well developed at both the single scattering and multiple scattering levels, and quantitative fits of experiment to theory can lead to structures with accuracies in the {plus_minus}0.03 {Angstrom} range. Direct structural information can also be derived from forward scattering in scanned-angle measurements at higher energies, path length differences contained in scanned-energy data at lower energies, and holographic inversions of data sets spanning some region in angle and energy space. Diffraction can also affect average photoelectron emission depths. Circular dichroism in core-level emission can be fruitfully interpreted in terms of photoelectron diffraction theory, as can measurements with spin-resolved core-spectra, and studies of surface magnetic structures and phase transitions should be possible with these methods. Synchrotron radiation is a key element of fully utilizing these techniques.
Vector grammars and PN machines
Institute of Scientific and Technical Information of China (English)
蒋昌俊
1996-01-01
The concept of vector grammars under the string semantic is introduced.The dass of vector grammars is given,which is similar to the dass of Chomsky grammars.The regular vector grammar is divided further.The strong and weak relation between the vector grammar and scalar grammar is discussed,so the spectrum system graph of scalar and vector grammars is made.The equivalent relation between the regular vector grammar and Petri nets (also called PN machine) is pointed.The hybrid PN machine is introduced,and its language is proved equivalent to the language of the context-free vector grammar.So the perfect relation structure between vector grammars and PN machines is formed.
Vector condensate and AdS soliton instability induced by a magnetic field
International Nuclear Information System (INIS)
Cai, Rong-Gen; Li, Li; Li, Li-Fang; Wu, You
2014-01-01
We continue to study the holographic p-wave superconductor model in the Einstein-Maxwell-complex vector field theory with a non-minimal coupling between the complex vector field and the Maxwell field. In this paper we work in the AdS soliton background which describes a conformal field theory in the confined phase and focus on the probe approximation. We find that an applied magnetic field can lead to the condensate of the vector field and the AdS soliton instability. As a result, a vortex lattice structure forms in the spatial directions perpendicular to the applied magnetic field. As a comparison, we also discuss the vector condensate in the Einstein-SU(2) Yang-Mills theory and find that in the setup of the present paper, the Einstein-Maxwell-complex vector field model is a generalization of the SU(2) model in the sense that the vector field has a general mass and gyromagnetic ratio
Limited-diffraction solutions to Maxwell and Schroedinger equations
International Nuclear Information System (INIS)
Lu, Jian-yu; Greenleaf, J.F.
1996-10-01
The authors have developed a new family of limited diffraction electromagnetic X-shaped waves based on the scalar X-shaped waves discovered previously. These waves are diffraction-free in theory and particle-like (wave packets), in that they maintain their shape as they propagate to an infinite distance. The 'X waves' possess (theoretically) infinitely extended 'arms' and - at least, the ones studied in this paper - have an infinite total energy: therefore, they are not physically realizable. However, they can be truncated in both space and time and 'approximated' by means of a finite aperture radiator so to get a large enough depth of interest (depth of field). In addition to the Maxwell equations, X wave solutions to the free Schroedinger equation are also obtained. Possible applications of these new waves are discussed. Finally, the authors discuss the appearance of the X-shaped solutions from the purely geometric point of view of the special relativity theory
2015-09-28
buoyant underwater vehicle with an interior space in which a length of said underwater vehicle is equal to one tenth of the acoustic wavelength...underwater vehicle with an interior space in which a length of said underwater vehicle is equal to one tenth of the acoustic wavelength; an...unmanned underwater vehicle that can function as an acoustic vector sensor. (2) Description of the Prior Art [0004] It is known that a propagating
Reciprocity in Vector Acoustics
2017-03-01
Green’s Theorem to the left hand side of Equation (3.2) converts it to a surface integral that vanishes for the impedance boundary conditions one...There are situations where this assumption does not hold, such as at boundaries between layers or in an inhomogeneous layer , because the density gradient...instead of requiring one model run for each source location. Application of the vector-scalar reciprocity principle is demonstrated with analytic
Tensor Calculus: Unlearning Vector Calculus
Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita
2018-01-01
Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can…