WorldWideScience

Sample records for two-scale scattering approximation

  1. On Born approximation in black hole scattering

    Science.gov (United States)

    Batic, D.; Kelkar, N. G.; Nowakowski, M.

    2011-12-01

    A massless field propagating on spherically symmetric black hole metrics such as the Schwarzschild, Reissner-Nordström and Reissner-Nordström-de Sitter backgrounds is considered. In particular, explicit formulae in terms of transcendental functions for the scattering of massless scalar particles off black holes are derived within a Born approximation. It is shown that the conditions on the existence of the Born integral forbid a straightforward extraction of the quasi normal modes using the Born approximation for the scattering amplitude. Such a method has been used in literature. We suggest a novel, well defined method, to extract the large imaginary part of quasinormal modes via the Coulomb-like phase shift. Furthermore, we compare the numerically evaluated exact scattering amplitude with the Born one to find that the approximation is not very useful for the scattering of massless scalar, electromagnetic as well as gravitational waves from black holes.

  2. Uniform semiclassical approximation for absorptive scattering systems

    International Nuclear Information System (INIS)

    Hussein, M.S.; Pato, M.P.

    1987-07-01

    The uniform semiclassical approximation of the elastic scattering amplitude is generalized to absorptive systems. An integral equation is derived which connects the absorption modified amplitude to the absorption free one. Division of the amplitude into a diffractive and refractive components is then made possible. (Author) [pt

  3. Coated sphere scattering by geometric optics approximation.

    Science.gov (United States)

    Mengran, Zhai; Qieni, Lü; Hongxia, Zhang; Yinxin, Zhang

    2014-10-01

    A new geometric optics model has been developed for the calculation of light scattering by a coated sphere, and the analytic expression for scattering is presented according to whether rays hit the core or not. The ray of various geometric optics approximation (GOA) terms is parameterized by the number of reflections in the coating/core interface, the coating/medium interface, and the number of chords in the core, with the degeneracy path and repeated path terms considered for the rays striking the core, which simplifies the calculation. For the ray missing the core, the various GOA terms are dealt with by a homogeneous sphere. The scattering intensity of coated particles are calculated and then compared with those of Debye series and Aden-Kerker theory. The consistency of the results proves the validity of the method proposed in this work.

  4. The adiabatic approximation in multichannel scattering

    International Nuclear Information System (INIS)

    Schulte, A.M.

    1978-01-01

    Using two-dimensional models, an attempt has been made to get an impression of the conditions of validity of the adiabatic approximation. For a nucleon bound to a rotating nucleus the Coriolis coupling is neglected and the relation between this nuclear Coriolis coupling and the classical Coriolis force has been examined. The approximation for particle scattering from an axially symmetric rotating nucleus based on a short duration of the collision, has been combined with an approximation based on the limitation of angular momentum transfer between particle and nucleus. Numerical calculations demonstrate the validity of the new combined method. The concept of time duration for quantum mechanical collisions has also been studied, as has the collective description of permanently deformed nuclei. (C.F.)

  5. Multiple Scattering Model for Optical Coherence Tomography with Rytov Approximation

    KAUST Repository

    Li, Muxingzi

    2017-01-01

    of speckles due to multiple scatterers within the coherence length, and other random noise. Motivated by the above two challenges, a multiple scattering model based on Rytov approximation and Gaussian beam optics is proposed for the OCT setup. Some previous

  6. Fermion-boson scattering in ladder approximation

    International Nuclear Information System (INIS)

    Jafarov, R.G.; Hadjiev, S.A.

    1992-10-01

    A method of calculation of forward scattering amplitude for fermions and scalar bosons with exchanging of scalar particle is suggested. The Bethe-Salpeter ladder equation for the imaginary part of the amplitude is constructed and a solution in Regge asymptotical form is found and the corrections to the amplitude due to the exit from mass shell are calculated. (author). 8 refs

  7. On quasiclassical approximation in the inverse scattering method

    International Nuclear Information System (INIS)

    Geogdzhaev, V.V.

    1985-01-01

    Using as an example quasiclassical limits of the Korteweg-de Vries equation and nonlinear Schroedinger equation, the quasiclassical limiting variant of the inverse scattering problem method is presented. In quasiclassical approximation the inverse scattering problem for the Schroedinger equation is reduced to the classical inverse scattering problem

  8. A surprise in the first Born approximation for electron scattering

    International Nuclear Information System (INIS)

    Treacy, M.M.J.; Van Dyck, D.

    2012-01-01

    A standard textbook derivation for the scattering of electrons by a weak potential under the first Born approximation suggests that the far-field scattered wave should be in phase with the incident wave. However, it is well known that waves scattered from a weak phase object should be phase-shifted by π/2 relative to the incident wave. A disturbing consequence of this missing phase is that, according to the Optical Theorem, the total scattering cross section would be zero in the first Born approximation. We resolve this mystery pedagogically by showing that the first Born approximation fails to conserve electrons even to first order. Modifying the derivation to conserve electrons introduces the correct phase without changing the scattering amplitude. We also show that the far-field expansion for the scattered waves used in many texts is inappropriate for computing an exit wave from a sample, and that the near-field expansion also give the appropriately phase-shifted result. -- Highlights: ► The first Born approximation is usually invoked as the theoretical physical basis for kinematical electron scattering theory. ► Although it predicts the correct scattering amplitude, it predicts the wrong phase; the scattered wave is missing a prefactor of i. ► We show that this arises because the standard textbook version of the first Born approximation does not conserve electrons. ► We show how this can be fixed.

  9. Variational, projection methods and Pade approximants in scattering theory

    International Nuclear Information System (INIS)

    Turchetti, G.

    1980-12-01

    Several aspects on the scattering theory are discussed in a perturbative scheme. The Pade approximant method plays an important role in such a scheme. Solitons solutions are also discussed in this same scheme. (L.C.) [pt

  10. Scattering theory and effective medium approximations to heterogeneous materials

    International Nuclear Information System (INIS)

    Gubernatis, J.E.

    1977-01-01

    The formal analogy existing between problems studied in the microscopic theory of disordered alloys and problems concerned with the effective (macroscopic) behavior of heterogeneous materials is discussed. Attention is focused on (1) analogous approximations (effective medium approximations) developed for the microscopic problems by scattering theory concepts and techniques, but for the macroscopic problems principally by intuitive means, (2) the link, provided by scattering theory, of the intuitively developed approximations to a well-defined perturbative analysis, (3) the possible presence of conditionally convergent integrals in effective medium approximations

  11. Geometrical-optics approximation of forward scattering by coated particles.

    Science.gov (United States)

    Xu, Feng; Cai, Xiaoshu; Ren, Kuanfang

    2004-03-20

    By means of geometrical optics we present an approximation algorithm with which to accelerate the computation of scattering intensity distribution within a forward angular range (0 degrees-60 degrees) for coated particles illuminated by a collimated incident beam. Phases of emerging rays are exactly calculated to improve the approximation precision. This method proves effective for transparent and tiny absorbent particles with size parameters larger than 75 but fails to give good approximation results at scattering angles at which refractive rays are absent. When the absorption coefficient of a particle is greater than 0.01, the geometrical optics approximation is effective only for forward small angles, typically less than 10 degrees or so.

  12. Jacob's ladder of approximations to paraxial dynamic electron scattering

    OpenAIRE

    Lubk, A.; Rusz, Jan

    2015-01-01

    Dynamical scattering theory describes the dominant scattering process of beam electrons at targets in the transmission electron microscope (TEM). Hence, practically every quantitative TEM study has to consider its ramifications, typically by some approximate modeling. Here, we elaborate on a hierarchy within the various approximations focusing on the two principal approaches used in practice, Bloch wave and multislice. We reveal characteristic differences in the capability of these methods to...

  13. Effects of scattering anisotropy approximation in multigroup radiation shielding calculations

    International Nuclear Information System (INIS)

    Altiparmakov, D.

    1983-01-01

    Expansion of the scattering cross sections into Legendre series is the usual way of solving neutron transport problems. Because of the large space gradients of the neutron flux, the effects of that approximation become especially remarkable in the radiation shielding calculations. In this paper, a method taking into account the scattering anisotropy is presented. From the point od view of the accuracy and computing rate, the optimal approximation of the scattering anisotropy is established for the basic protective materials on the basis of simple problem calculations. (author)

  14. No surprise in the first Born approximation for electron scattering

    International Nuclear Information System (INIS)

    Lentzen, M.

    2014-01-01

    In a recent article it is argued that the far-field expansion of electron scattering, a pillar of electron diffraction theory, is wrong (Treacy and Van Dyck, 2012 [1]). It is further argued that in the first Born approximation of electron scattering the intensity of the electron wave is not conserved to first order in the scattering potential. Thus a “mystery of the missing phase” is investigated, and the supposed flaw in scattering theory is seeked to be resolved by postulating a standing spherical electron wave (Treacy and Van Dyck, 2012 [1]). In this work we show, however, that these theses are wrong. A review of the essential parts of scattering theory with careful checks of the underlying assumptions and limitations for high-energy electron scattering yields: (1) the traditional form of the far-field expansion, comprising a propagating spherical wave, is correct; (2) there is no room for a missing phase; (3) in the first Born approximation the intensity of the scattered wave is conserved to first order in the scattering potential. The various features of high-energy electron scattering are illustrated by wave-mechanical calculations for an explicit target model, a Gaussian phase object, and for a Si atom, considering the geometric conditions in high-resolution transmission electron microscopy. - Highlights: Treacy and Van Dyck (2012) argue that the far-field expansion of electron scattering is wrong. The chief theses of that former work are wrong. There is no room for the missing phase proposed by Treacy and Van Dyck. There is no violation of the intensity conservation to first order in the scattering potential. Calculations for a phase object and an atomic target confirm traditional scattering theory

  15. Approximate Coulomb effects in the three-body scattering problem

    International Nuclear Information System (INIS)

    Haftel, M.I.; Zankel, H.

    1981-01-01

    From the momentum space Faddeev equations we derive approximate expressions which describe the Coulomb-nuclear interference in the three-body elastic scattering, rearrangement, and breakup problems and apply the formalism to p-d elastic scattering. The approximations treat the Coulomb interference as mainly a two-body effect, but we allow for the charge distribution of the deuteron in the p-d calculations. Real and imaginary parts of the Coulomb correction to the elastic scattering phase shifts are described in terms of on-shell quantities only. In the case of pure Coulomb breakup we recover the distorted-wave Born approximation result. Comparing the derived approximation with the full Faddeev p-d elastic scattering calculation, which includes the Coulomb force, we obtain good qualitative agreement in S and P waves, but disagreement in repulsive higher partial waves. The on-shell approximation investigated is found to be superior to other current approximations. The calculated differential cross sections at 10 MeV raise the question of whether there is a significant Coulomb-nuclear interference at backward angles

  16. Light scattering by cubical particle in the WKB approximation

    Directory of Open Access Journals (Sweden)

    redouane lamsoudi

    2017-11-01

    Full Text Available In this work, we determined the analytical expressions of the form factor of a cubical particle in the WKB approximation. We adapted some variables (size parameter, refractive index, the scattering angle and found the form factor in the approximation of Rayleigh-Gans-Debye (RGD, Anomalous Diffraction (AD, and determined the efficiency factor of the extinction. Finally, to illustrate our formalism, we analyzed some numerical examples

  17. Approximate solutions of some problems of scattering of surface ...

    Indian Academy of Sciences (India)

    A Choudhary

    Abstract. A class of mixed boundary value problems (bvps), occurring in the study of scattering of surface water waves by thin vertical rigid barriers placed in water of finite depth, is examined for their approximate solutions. Two different placings of vertical barriers are analyzed, namely, (i) a partially immersed barrier and.

  18. Quantum scattering beyond the plane-wave approximation

    Science.gov (United States)

    Karlovets, Dmitry

    2017-12-01

    While a plane-wave approximation in high-energy physics works well in a majority of practical cases, it becomes inapplicable for scattering of the vortex particles carrying orbital angular momentum, of Airy beams, of the so-called Schrödinger cat states, and their generalizations. Such quantum states of photons, electrons and neutrons have been generated experimentally in recent years, opening up new perspectives in quantum optics, electron microscopy, particle physics, and so forth. Here we discuss the non-plane-wave effects in scattering brought about by the novel quantum numbers of these wave packets. For the well-focused electrons of intermediate energies, already available at electron microscopes, the corresponding contribution can surpass that of the radiative corrections. Moreover, collisions of the cat-like superpositions of such focused beams with atoms allow one to probe effects of the quantum interference, which have never played any role in particle scattering.

  19. Multiple Scattering Model for Optical Coherence Tomography with Rytov Approximation

    KAUST Repository

    Li, Muxingzi

    2017-04-24

    Optical Coherence Tomography (OCT) is a coherence-gated, micrometer-resolution imaging technique that focuses a broadband near-infrared laser beam to penetrate into optical scattering media, e.g. biological tissues. The OCT resolution is split into two parts, with the axial resolution defined by half the coherence length, and the depth-dependent lateral resolution determined by the beam geometry, which is well described by a Gaussian beam model. The depth dependence of lateral resolution directly results in the defocusing effect outside the confocal region and restricts current OCT probes to small numerical aperture (NA) at the expense of lateral resolution near the focus. Another limitation on OCT development is the presence of a mixture of speckles due to multiple scatterers within the coherence length, and other random noise. Motivated by the above two challenges, a multiple scattering model based on Rytov approximation and Gaussian beam optics is proposed for the OCT setup. Some previous papers have adopted the first Born approximation with the assumption of small perturbation of the incident field in inhomogeneous media. The Rytov method of the same order with smooth phase perturbation assumption benefits from a wider spatial range of validity. A deconvolution method for solving the inverse problem associated with the first Rytov approximation is developed, significantly reducing the defocusing effect through depth and therefore extending the feasible range of NA.

  20. Analytical approximations to seawater optical phase functions of scattering

    Science.gov (United States)

    Haltrin, Vladimir I.

    2004-11-01

    This paper proposes a number of analytical approximations to the classic and recently measured seawater light scattering phase functions. The three types of analytical phase functions are derived: individual representations for 15 Petzold, 41 Mankovsky, and 91 Gulf of Mexico phase functions; collective fits to Petzold phase functions; and analytical representations that take into account dependencies between inherent optical properties of seawater. The proposed phase functions may be used for problems of radiative transfer, remote sensing, visibility and image propagation in natural waters of various turbidity.

  1. Departures from the impulse approximation in deep inelastic neutron scattering

    International Nuclear Information System (INIS)

    Mayers, J.

    1989-01-01

    A new formulation of the impulse approximation (IA) in deep inelastic neutron scattering is developed. It is shown that observed departures from the IA at intermediate momentum transfers are caused by the quantum nature of the initial state rather than final state effects, as has previously been assumed and that these effects become small at high temperatures. It is also argued that final state broadening is significant for He liquids in all feasible experiments, but that in other systems the IA is approached at high momentum transfers. (author)

  2. Vibrationally inelastic electron scattering in a two-channel approximation

    Czech Academy of Sciences Publication Activity Database

    Čársky, Petr; Čurík, Roman

    2008-01-01

    Roč. 41, č. 5 (2008), , , 055203-1-6 ISSN 0953-4075 R&D Projects: GA AV ČR IAA100400501; GA AV ČR 1ET400400413; GA AV ČR KJB400400803; GA ČR GA202/08/0631; GA MŠk ME 857 Institutional research plan: CEZ:AV0Z40400503 Keywords : inelastic electron scattering * two-channel approximation Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 2.089, year: 2008

  3. An analytic distorted wave approximation for intermediate energy proton scattering

    International Nuclear Information System (INIS)

    Di Marzio, F.; Amos, K.

    1982-01-01

    An analytic Distorted Wave approximation has been developed for use in analyses of intermediate energy proton inelastic scattering from nuclei. Applications are made to analyse 402 and 800 MeV data from the isoscalar and isovector 1 + and 2 + states in 12 C and to the 800 MeV data from the excitation of the 2 - (8.88MeV) state in 16 O. Comparisons of predictions made using different model two-nucleon t-matrices and different models of nuclear structure are given

  4. Coupled states approximation for scattering of two diatoms

    International Nuclear Information System (INIS)

    Heil, T.G.; Green, S.; Kouri, D.J.

    1978-01-01

    The coupled states (CS) approximation is developed in detail for the general case of two colliding diatomic molecules. The high energy limit of the exact Lippmann-Schwinger equation is used to obtain the CS equations so that the sufficiency conditions of Kouri, Heil, and Shimoni apply. In addition, care is taken to ensure correct treatment of parity in the CS, as well as correct labeling of the CS by an effective orbital angular momentum. The analysis follows that given by Shimoni and Kouri for atom-diatom collisions where the coupled rotor angular momentum j 12 and projection lambda 12 replace the single diatom angular momentum j and projection lambda. The result is an expression for the differential scattering amplitude which is a generalization of the highly successful McGuire-Kouri differential scattering amplitude for atom-diatom collisions. Also, the opacity function is found to be a generalization of the Clebsch-Gordon weight atom-diatom expression of Shimoni and Kouri. The diatom-diatom CS body frame T matrix T/sup J/(j 1 'j 2 'j 12 'lambda 12 'vertical-bar j 1 j 2 j 12 lambda 12 ) is also found to be nondiagonal in lambda' 12 ,lambda 12 , just as in the atom-diatom case. The parity and identical molecule interchange symmetries are also considered in detail in both the exact close coupling and CS approximations. Symmetrized expressions for all relevant quantities are obtained, along with the symmetrized coupled equations one must solve. The properly labeled and symmetrized CS equations have not been derived before this present work. The present correctly labeled CS theory is tested computationally by applications to three different diatom-diatom potentials. First we carry out calculations for para-para, ortho-ortho, and ortho-para H 2 -H 2 collisions using the experimental potential of Farrar and Lee

  5. Induced Compton scattering effects in radiation transport approximations

    International Nuclear Information System (INIS)

    Gibson, D.R. Jr.

    1982-01-01

    In this thesis the method of characteristics is used to solve radiation transport problems with induced Compton scattering effects included. The methods used to date have only addressed problems in which either induced Compton scattering is ignored, or problems in which linear scattering is ignored. Also, problems which include both induced Compton scattering and spatial effects have not been considered previously. The introduction of induced scattering into the radiation transport equation results in a quadratic nonlinearity. Methods are developed to solve problems in which both linear and nonlinear Compton scattering are important. Solutions to scattering problems are found for a variety of initial photon energy distributions

  6. Induced Compton-scattering effects in radiation-transport approximations

    International Nuclear Information System (INIS)

    Gibson, D.R. Jr.

    1982-02-01

    The method of characteristics is used to solve radiation transport problems with induced Compton scattering effects included. The methods used to date have only addressed problems in which either induced Compton scattering is ignored, or problems in which linear scattering is ignored. Also, problems which include both induced Compton scattering and spatial effects have not been considered previously. The introduction of induced scattering into the radiation transport equation results in a quadratic nonlinearity. Methods are developed to solve problems in which both linear and nonlinear Compton scattering are important. Solutions to scattering problems are found for a variety of initial photon energy distributions

  7. A scatter-corrected list-mode reconstruction and a practical scatter/random approximation technique for dynamic PET imaging

    International Nuclear Information System (INIS)

    Cheng, J-C; Rahmim, Arman; Blinder, Stephan; Camborde, Marie-Laure; Raywood, Kelvin; Sossi, Vesna

    2007-01-01

    We describe an ordinary Poisson list-mode expectation maximization (OP-LMEM) algorithm with a sinogram-based scatter correction method based on the single scatter simulation (SSS) technique and a random correction method based on the variance-reduced delayed-coincidence technique. We also describe a practical approximate scatter and random-estimation approach for dynamic PET studies based on a time-averaged scatter and random estimate followed by scaling according to the global numbers of true coincidences and randoms for each temporal frame. The quantitative accuracy achieved using OP-LMEM was compared to that obtained using the histogram-mode 3D ordinary Poisson ordered subset expectation maximization (3D-OP) algorithm with similar scatter and random correction methods, and they showed excellent agreement. The accuracy of the approximated scatter and random estimates was tested by comparing time activity curves (TACs) as well as the spatial scatter distribution from dynamic non-human primate studies obtained from the conventional (frame-based) approach and those obtained from the approximate approach. An excellent agreement was found, and the time required for the calculation of scatter and random estimates in the dynamic studies became much less dependent on the number of frames (we achieved a nearly four times faster performance on the scatter and random estimates by applying the proposed method). The precision of the scatter fraction was also demonstrated for the conventional and the approximate approach using phantom studies

  8. Approximate scattering wave functions for few-particle continua

    International Nuclear Information System (INIS)

    Briggs, J.S.

    1990-01-01

    An operator identity which allows the wave operator for N particles interacting pairwise to be expanded as products of operators in which fewer than N particles interact is given. This identity is used to derive appproximate scattering wave functions for N-particle continua that avoid certain difficulties associated with Faddeev-type expansions. For example, a derivation is given of a scattering wave function used successfully recently to describe the three-particle continuum occurring in the electron impact ionization of the hydrogen atom

  9. Closure approximation to the absorptive potential in heavy ion scattering

    International Nuclear Information System (INIS)

    Vinh Mau, N.

    1986-02-01

    We propose a simple model which is based on the Feshbach's theory of optical potential. The use of closure relation in both nuclei implies that we implicitly include all possible channels, in particular inelastic scattering and one nucleon transfer processes. The local absorptive potential is calculated at large distances and its energy dependence is studied. The results are compared to other theoretical works and to phenomenological potentials

  10. Obe approximation of NN scattering in bag-model QCD

    International Nuclear Information System (INIS)

    Bakker, B.L.G.; Maslow, J.N.; Weber, H.J.

    1981-01-01

    A partial-wave helicity-state analysis of nucleon-nucleon scattering is carried out in momentum space. Its basis is a one-boson and two-pion exchange amplitude from bag-model quantum chromodynamics. The resulting phase shifts and bound-state parameters of the deuteron are compared with data up to laboratory energies of approx. equal to 350 MeV. (orig.)

  11. Anisotropic scattering in three dimensional differential approximation of radiation heat transfer

    International Nuclear Information System (INIS)

    Condiff, D.W.

    1987-01-01

    The differential approximation is extended to account for anisotropic scattering in invariant three dimensional form. A moment method using polyadic Legendre functions establishes that pressure cross sections should take precedence over extinction cross sections for treating radiation heat transfer in an absorbing, emitting, and scattering medium, and that use of these cross sections accounts for the extent of preferred forward or backwards scattering. The procedure and principle is extended to polyadic P-N approximations

  12. Approximate solution to neutron transport equation with linear anisotropic scattering

    International Nuclear Information System (INIS)

    Coppa, G.; Ravetto, P.; Sumini, M.

    1983-01-01

    A method to obtain an approximate solution to the transport equation, when both sources and collisions show a linearly anisotropic behavior, is outlined and the possible implications for numerical calculations in applied neutronics as well as shielding evaluations are investigated. The form of the differential system of equations taken by the method is quite handy and looks simpler and more manageable than any other today available technique. To go deeper into the efficiency of the method, some typical calculations concerning critical dimension of multiplying systems are then performed and the results are compared with the ones coming from the classical Ssub(N) approximations. The outcome of such calculations leads us to think of interesting developments of the method which could be quite useful in alternative to other today widespread approximate procedures, for any geometry, but especially for curved ones. (author)

  13. Multiple Scattering in Random Mechanical Systems and Diffusion Approximation

    Science.gov (United States)

    Feres, Renato; Ng, Jasmine; Zhang, Hong-Kun

    2013-10-01

    This paper is concerned with stochastic processes that model multiple (or iterated) scattering in classical mechanical systems of billiard type, defined below. From a given (deterministic) system of billiard type, a random process with transition probabilities operator P is introduced by assuming that some of the dynamical variables are random with prescribed probability distributions. Of particular interest are systems with weak scattering, which are associated to parametric families of operators P h , depending on a geometric or mechanical parameter h, that approaches the identity as h goes to 0. It is shown that ( P h - I)/ h converges for small h to a second order elliptic differential operator on compactly supported functions and that the Markov chain process associated to P h converges to a diffusion with infinitesimal generator . Both P h and are self-adjoint (densely) defined on the space of square-integrable functions over the (lower) half-space in , where η is a stationary measure. This measure's density is either (post-collision) Maxwell-Boltzmann distribution or Knudsen cosine law, and the random processes with infinitesimal generator respectively correspond to what we call MB diffusion and (generalized) Legendre diffusion. Concrete examples of simple mechanical systems are given and illustrated by numerically simulating the random processes.

  14. Quantum Theory of (H,H{Sub 2}) Scattering: Approximate Treatments of Reactive Scattering

    Science.gov (United States)

    Tang, K. T.; Karplus, M.

    1970-10-01

    A quantum mechanical study is made of reactive scattering in the (H, H{sub 2}) system. The problem is formulated in terms of a form of the distorted-wave Born approximation (DWBA) suitable for collisions in which all particles have finite mass. For certain incident energies, differential and total cross sections, as well as other attributes of the reactive collisions, (e.g. reaction configuration), are determined. Two limiting models in the DWBA formulation are compared; in one, the molecule is unperturbed by the incoming atom and in the other, the molecule adiabatically follows the incoming atom. For thermal incident energies and semi-empirical interaction potential employed, the adiabatic model seems to be more appropriate. Since the DWBA method is too complicated for a general study of the (H, H{sub 2}) reaction, a much simpler approximation method, the “linear model” is developed. This model is very different in concept from treatments in which the three atoms are constrained to move on a line throughout the collision. The present model includes the full three-dimensional aspect of the collision and it is only the evaluation of the transition matrix element itself that is simplified. It is found that the linear model, when appropriately normalized, gives results in good agreement with that of the DWBA method. By application of this model, the energy dependence, rotational state of dependence and other properties of the total and differential reactions cross sections are determined. These results of the quantum mechanical treatment are compared with the classical calculation for the same potential surface. The most important result is that, in agreement with the classical treatment, the differential cross sections are strongly backward peaked at low energies and shifts in the forward direction as the energy increases. Finally, the implications of the present calculations for a theory of chemical kinetics are discussed.

  15. Study on the Light Scattering from Random Rough Surfaces by Kirrhoff Approximation

    Directory of Open Access Journals (Sweden)

    Keding Yan

    2014-07-01

    Full Text Available In order to study the space distribution characteristics of light scattering from random rough surfaces, the linear filtering method is used to generate a series of Gaussian randomly rough surfaces, and the Kirchhoff Approximation is used to calculate the scattered light intensity distribution from random metal and dielectric rough surfaces. The three characteristics of the scattered light intensity distribution peak, the intensity distribution width and the position of peak are reviewed. Numerical calculation results show that significant differences between scattering characteristics of metal surfaces and the dielectric surfaces exist. The light scattering characteristics are jointly influenced by the slope distribution and reflectance of surface element. The scattered light intensity distribution is affected by common influence of surface local slope distribution and surface local reflectivity. The results can provide a basis theory for the research to lidar target surface scattering characteristics.

  16. Effects of the scattering anisotropy approximation in multigroup radiation shielding calculations

    International Nuclear Information System (INIS)

    Altiparmarkov, D.

    1983-01-01

    Expansion of the scattering cross-sections into Legendre series is the usual way of solving the neutron transport problem. Because of the large space gradients of the neutron flux, the effects of that approximations become especially remarkable in the radiation shielding calculations. In this paper, a method taking into account scattering anisotropy is presented. From the point of view of the accuracy and computing speed, the optimal approximation of the scattering anisotropy is established for the basic protective materials on the basis of simple problem calculations (author) [sr

  17. Distorted-wave Born approximation in the case of an optical scattering potential

    International Nuclear Information System (INIS)

    Mytnichenko, Sergey V.

    2005-01-01

    Application of the distorted-wave Born approximation in the conventional form developed for the case of a real scattering potential is shown to cause significant errors in calculating X-ray diffuse scattering from non-ideal crystals, superlattices, multilayers and other objects if energy dissipation (photoabsorption, inelastic scattering, and so on) is not negligible, or in other words, in the case of an optical (complex) scattering potential. We show how a correct expression for the X-ray diffuse-scattering cross-section can be obtained in this case. Generally, the diffuse-scattering cross-section from an optical potential is not T-invariant, i.e. the reciprocity principle is violated. Violations of T-invariance are more evident when the dynamical nature of the diffraction is more critical

  18. Quantum theory of atom-surface scattering: exact solutions and evaluation of approximations

    International Nuclear Information System (INIS)

    Chiroli, C.; Levi, A.C.

    1976-01-01

    In a recent article a hard corrugated surface was proposed as a simple model for atom-surface scattering. The problem was not solved exactly, however, but several alternative approximations were considered. Since these three similar, but inequivalent, approximations were proposed, the problem arose to evaluate these approximations in order to choose between them. In the present letter some exact calculations are presented which make this choice rationally possible. (Auth.)

  19. Continuum orbital approximations in weak-coupling theories for inelastic electron scattering

    International Nuclear Information System (INIS)

    Peek, J.M.; Mann, J.B.

    1977-01-01

    Two approximations, motivated by heavy-particle scattering theory, are tested for weak-coupling electron-atom (ion) inelastic scattering theory. They consist of replacing the one-electron scattering orbitals by their Langer uniform approximations and the use of an average trajectory approximation which entirely avoids the necessity for generating continuum orbitals. Numerical tests for a dipole-allowed and a dipole-forbidden event, based on Coulomb-Born theory with exchange neglected, reveal the error trends. It is concluded that the uniform approximation gives a satisfactory prediction for traditional weak-coupling theories while the average approximation should be limited to collision energies exceeding at least twice the threshold energy. The accuracy for both approximations is higher for positive ions than for neutral targets. Partial-wave collision-strength data indicate that greater care should be exercised in using these approximations to predict quantities differential in the scattering angle. An application to the 2s 2 S-2p 2 P transition in Ne VIII is presented

  20. Rayleigh scatter in kilovoltage x-ray imaging: is the independent atom approximation good enough?

    OpenAIRE

    Poludniowski, G; Evans, PM; Webb, S

    2009-01-01

    Monte Carlo simulation is the gold standard method for modelling scattering processes in medical x-ray imaging. General-purpose Monte Carlo codes, however, typically use the independent atom approximation (IAA). This is known to be inaccurate for Rayleigh scattering, for many materials, in the forward direction. This work addresses whether the IAA is sufficient for the typical modelling tasks in medical kilovoltage x-ray imaging. As a means of comparison, we incorporate a more realistic 'inte...

  1. Finite-measuring approximation of operators of scattering theory in representation of wave packets

    International Nuclear Information System (INIS)

    Kukulin, V.I.; Rubtsova, O.A.

    2004-01-01

    Several types of the packet quantization of the continuos spectrum in the scattering theory quantum problems are considered. Such a quantization leads to the convenient finite-measuring (i.e. matrix) approximation of the integral operators in the scattering theory and it makes it possible to reduce the solution of the singular integral equations, complying with the scattering theory, to the convenient purely algebraic equations on the analytical basis, whereby all the singularities are separated in the obvious form. The main attention is paid to the problems of the method practical realization [ru

  2. Second Born approximation in elastic-electron scattering from nuclear static electro-magnetic multipoles

    International Nuclear Information System (INIS)

    Al-Khamiesi, I.M.; Kerimov, B.K.

    1988-01-01

    Second Born approximation corrections to electron scattering by nuclei with arbitrary spin are considered. Explicit integral expressions for the charge, magnetic dipole and interference differential cross sections are obtained. Magnetic and interference relative corrections are then investigated in the case of backward electron scattering using shell model form factors for nuclear targets 9 Be, 10 B, and 14 N. To understand exponential growth of these corrections with square of the electron energy K 0 2 , the case of electron scattering by 6 Li is considered using monopole model charge form factor with power-law asymptotics. 11 refs., 2 figs. (author)

  3. Limiting cases of the small-angle scattering approximation solutions for the propagation of laser beams in anisotropic scattering media

    Science.gov (United States)

    Box, M. A.; Deepak, A.

    1981-01-01

    The propagation of photons in a medium with strongly anisotropic scattering is a problem with a considerable history. Like the propagation of electrons in metal foils, it may be solved in the small-angle scattering approximation by the use of Fourier-transform techniques. In certain limiting cases, one may even obtain analytic expressions. This paper presents some of these results in a model-independent form and also illustrates them by the use of four different phase-function models. Sample calculations are provided for comparison purposes

  4. Rayleigh scatter in kilovoltage x-ray imaging: is the independent atom approximation good enough?

    Science.gov (United States)

    Poludniowski, G.; Evans, P. M.; Webb, S.

    2009-11-01

    Monte Carlo simulation is the gold standard method for modelling scattering processes in medical x-ray imaging. General-purpose Monte Carlo codes, however, typically use the independent atom approximation (IAA). This is known to be inaccurate for Rayleigh scattering, for many materials, in the forward direction. This work addresses whether the IAA is sufficient for the typical modelling tasks in medical kilovoltage x-ray imaging. As a means of comparison, we incorporate a more realistic 'interference function' model into a custom-written Monte Carlo code. First, we conduct simulations of scatter from isolated voxels of soft tissue, adipose, cortical bone and spongiosa. Then, we simulate scatter profiles from a cylinder of water and from phantoms of a patient's head, thorax and pelvis, constructed from diagnostic-quality CT data sets. Lastly, we reconstruct CT numbers from simulated sets of projection images and investigate the quantitative effects of the approximation. We show that the IAA can produce errors of several per cent of the total scatter, across a projection image, for typical x-ray beams and patients. The errors in reconstructed CT number, however, for the phantoms simulated, were small (typically < 10 HU). The IAA can therefore be considered sufficient for the modelling of scatter correction in CT imaging. Where accurate quantitative estimates of scatter in individual projection images are required, however, the appropriate interference functions should be included.

  5. Geometrical-optics approximation of forward scattering by gradient-index spheres.

    Science.gov (United States)

    Li, Xiangzhen; Han, Xiang'e; Li, Renxian; Jiang, Huifen

    2007-08-01

    By means of geometrical optics we present an approximation method for acceleration of the computation of the scattering intensity distribution within a forward angular range (0-60 degrees ) for gradient-index spheres illuminated by a plane wave. The incident angle of reflected light is determined by the scattering angle, thus improving the approximation accuracy. The scattering angle and the optical path length are numerically integrated by a general-purpose integrator. With some special index models, the scattering angle and the optical path length can be expressed by a unique function and the calculation is faster. This method is proved effective for transparent particles with size parameters greater than 50. It fails to give good approximation results at scattering angles whose refractive rays are in the backward direction. For different index models, the geometrical-optics approximation is effective only for forward angles, typically those less than 60 degrees or when the refractive-index difference of a particle is less than a certain value.

  6. Comparison of approximate methods for multiple scattering in high-energy collisions. II

    International Nuclear Information System (INIS)

    Nolan, A.M.; Tobocman, W.; Werby, M.F.

    1976-01-01

    The scattering in one dimension of a particle by a target of N like particles in a bound state has been studied. The exact result for the transmission probability has been compared with the predictions of the Glauber theory, the Watson optical potential model, and the adiabatic (or fixed scatterer) approximation. The approximate methods optical potential model is second best. The Watson method is found to work better when the kinematics suggested by Foldy and Walecka are used rather than that suggested by Watson, that is to say, when the two-body of the nucleon-nucleon reduced mass

  7. Impurity scattering in unconventional density waves: non-crossing approximation for arbitrary scattering rate

    International Nuclear Information System (INIS)

    Vanyolos, Andras; Dora, Balazs; Maki, Kazumi; Virosztek, Attila

    2007-01-01

    We present a detailed theoretical study on the thermodynamic properties of impure quasi-one-dimensional unconventional charge and spin density waves in the framework of mean-field theory. The impurities are of the ordinary non-magnetic type. Making use of the full self-energy that takes into account all ladder- and rainbow-type diagrams, we are able to calculate the relevant low temperature quantities for arbitrary scattering rates. These are the density of states, specific heat and the shift in the chemical potential. Our results therefore cover the whole parameter space: they include both the self-consistent Born and the resonant unitary limits, and most importantly give exact results in between

  8. Formal analysis of inelastic scattering in the coulomb-projected eikonal approximation

    CERN Document Server

    Qian, W J; Yan, S; Yang, Z S; Bo, D Y

    1998-01-01

    A formal procedure within the frame-work of the eikonal approximation for the inelastic scattering of many-electron atoms is formulated on the basis of the Racah algebra in the non-partial wave version, where an arbitrary complex wavefunction, including the contribution from all partial waves, can be used for the process calculations.

  9. Scattering of particles with inclusions. Modeling and inverse problem solution in the Rayleigh-Gans approximation

    International Nuclear Information System (INIS)

    Otero, F A; Frontini, G L; Elicabe, G E

    2011-01-01

    An analytic model for the scattering of a spherical particle with spherical inclusions has been proposed under the RG approximation. The model can be used without limitations to describe an X-ray scattering experiment. However, for light scattering several conditions must be fulfilled. Based on this model an inverse methodology is proposed to estimate the radii of host particle and inclusions, the number of inclusions and the Distance Distribution Functions (DDF's) of the distances between inclusions and the distances between inclusions and the origin of coordinates. The methodology is numerically tested in a light scattering example in which the host particle is eliminated by matching the refractive indices of host particle and medium. The results obtained for this cluster particle are very satisfactory.

  10. Amplitude of Light Scattering by a Truncated Pyramid and Cone in the Rayleigh-Gans-Debye Approximation

    Directory of Open Access Journals (Sweden)

    Konstantin A. Shapovalov

    2013-01-01

    Full Text Available The article considers general approach to structured particle and particle system form factor calculation in the Rayleigh-Gans-Debye (RGD approximation. Using this approach, amplitude of light scattering by a truncated pyramid and cone formulas in RGD approximation are obtained. Light scattering indicator by a truncated pyramid and cone in the RGD approximation are calculated.

  11. The analysis of the elastic scattering of 11Be and 6Li by adiabatic approximation

    International Nuclear Information System (INIS)

    Takagi, S.

    2000-01-01

    The unstable nuclei, particularly, the neutron halo nuclei which exist near by the neutron dripline, are recently one of the interesting topics in the nuclear physics. By the adiabatic approximation, R. C. Jhonson et al. have reproduced the experimental differential cross-section of the elastic scattering of the neutron halo nucleus 11 Be (+ l2 C) [1]. We have applied their method to the elastic scattering of another nucleus 6 Li which is not a halo nucleus but has the cluster structure as 11 Be. But it couldn't reproduce the experimental data, so that the method of Johnson et al. is poor in the case of 6 Li. (author)

  12. Scattering phases for particles with nonzero orbital momenta and resonance regimes in the Pais approximation

    International Nuclear Information System (INIS)

    Bruk, Yulii M; Voloshchuk, Aleksandr N

    2012-01-01

    The functional Pais equation for scattering phases with nonzero orbital momenta is solved in the case of low-energy particles. For short-range screened potentials, in particular, Yukawa or Thomas-Fermi potentials, the Pais equation is shown to reduce to transcendental equations. For the potentials varying ∼r - n , n > 0, simple algebraic equations are obtained for determining the phases δ l , l≠0. Possible applications of the Pais approximation to the problem of finding resonance regimes in the scattering of low-energy particles with nonzero orbital momenta are discussed. (methodological notes)

  13. Nucleon-nucleus inelastic scattering using a relativistic impulse approximation with exchange

    International Nuclear Information System (INIS)

    Rost, E.; Shepard, J.R.

    1987-01-01

    We formulate a microscopic relativistic treatment of nucleon-nucleus inelastic scattering in a distorted wave impulse approximation. The interaction is taken from a Lorentz invariant formulation with explicit direct and exchange terms constrained by fitting to experimental NN amplitudes. This procedure allows us to apply the theory in the lower range of intermediate energies (100--400 MeV) where exchange effects are likely to be important. Application to inelastic scattering uses this interaction for both the distorting potentials and the transition interaction. Effects of explicit exchange are studied and a preliminary analysis of /sup 12/C(p,p') data is presented

  14. Analysis of a finite PML approximation to the three dimensional elastic wave scattering problem

    KAUST Repository

    Bramble, James H.

    2010-01-01

    We consider the application of a perfectly matched layer (PML) technique to approximate solutions to the elastic wave scattering problem in the frequency domain. The PML is viewed as a complex coordinate shift in spherical coordinates which leads to a variable complex coefficient equation for the displacement vector posed on an infinite domain (the complement of the scatterer). The rapid decay of the PML solution suggests truncation to a bounded domain with a convenient outer boundary condition and subsequent finite element approximation (for the truncated problem). We prove existence and uniqueness of the solutions to the infinite domain and truncated domain PML equations (provided that the truncated domain is sufficiently large). We also show exponential convergence of the solution of the truncated PML problem to the solution of the original scattering problem in the region of interest. We then analyze a Galerkin numerical approximation to the truncated PML problem and prove that it is well posed provided that the PML damping parameter and mesh size are small enough. Finally, computational results illustrating the efficiency of the finite element PML approximation are presented. © 2010 American Mathematical Society.

  15. Physical explanation of the SLIPI technique by the large scatterer approximation of the RTE

    International Nuclear Information System (INIS)

    Kristensson, Elias; Kristensson, Gerhard

    2017-01-01

    Visualizing the interior of a turbid scattering media by means light-based methods is not a straightforward task because of multiple light scattering, which generates image blur. To overcome this issue, a technique called Structured Laser Illumination Planar Imaging (SLIPI) was developed within the field of spray imaging. The method is based on a ‘light coding’ strategy to distinguish between directly and multiply scattered light, allowing the intensity from the latter to be suppressed by means of data post-processing. Recently, the performance of the SLIPI technique was investigated, during which deviations from theoretical predictions were discovered. In this paper, we aim to explain the origin of these deviations, and to achieve this end, we have performed several SLIPI measurements under well-controlled conditions. Our experimental results are compared with a theoretical model that is based on the large scatterer approximation of the Radiative Transfer Equation but modified according to certain constraints. Specifically, our model is designed to (1) ignore all off-axis intensity contributions, (2) to treat unperturbed- and forward-scattered light equally and (3) to accept light to scatter within a narrow forward-cone as we believe these are the rules governing the SLIPI technique. The comparison conclusively shows that optical measurements based on scattering and/or attenuation in turbid media can be subject to significant errors if not all aspects of light-matter interactions are considered. Our results indicate, as were expected, that forward-scattering can lead to deviations between experiments and theoretical predictions, especially when probing relatively large particles. Yet, the model also suggests that the spatial frequency of the superimposed ‘light code’ as well as the spreading of the light-probe are important factors one also needs to consider. The observed deviations from theoretical predictions could, however, potentially be exploited to

  16. Three-body scattering problem in the fixed center approximation: The case of attraction

    Energy Technology Data Exchange (ETDEWEB)

    Kudryavtsev, Alexander E. [National Research Center Kurchatov Institute, Institute for Theoretical and Experimental Physics, Moscow (Russian Federation); Gani, Vakhid A. [National Research Center Kurchatov Institute, Institute for Theoretical and Experimental Physics, Moscow (Russian Federation); National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow (Russian Federation); Romanov, Alexander I. [National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow (Russian Federation)

    2016-12-15

    We study the scattering of a light particle on a bound pair of heavy particles (e.g., the deuteron) within the fixed center approximation in the case of light-heavy attraction, solving the integral equation for the three-body Green's function both in the coordinate and in the momentum space. The results for the three-body scattering amplitude appear to be ambiguous -they depend on a single real parameter. This parameter may be fixed by a three-body input, e.g., the three-body scattering length. We also solve the integral equation for the three-body Green function in the momentum space, introducing a finite cut-off. We show that all three approaches are equivalent. We also discuss how our approach to the problem matches with the introduction of three-body contact interaction as done by other authors. (orig.)

  17. Nucleus-Nucleus Scattering in the High-Energy Approximation and the Optical Folding Potential

    CERN Document Server

    Lukyanov, V K; Lukyanov, K V

    2004-01-01

    For the nucleus-nucleus scattering, the complex potential is obtained which corresponds to the eikonal phase of an optical limit of the Glauber-Sitenko high-energy approximation. The potential does not include free parameters, its real and imaginary parts depend on energy and are determined by the reported data on the nuclear density distributions and nucleon-nucleon scattering amplitude. Alternatively, for the real part, the folding potential can be utilized which includes the effective NN-forces and the exchange term, as well. As a result, the microscopic optical potential is constructed where contributions of the calculated real and imaginary parts are formed by fitting the two respective factors. An efficient of the approach is confirmed by agreements of calculations with the experimental data on elastic scattering cross-sections.

  18. Spectral analysis of the SN approximations in a slab with quadratically anisotropic scattering

    International Nuclear Information System (INIS)

    Ourique, L.E.; Pazos, R.P.; Vilhena, M.T.; Barros, R.C.

    2003-01-01

    The spectral analysis of the S N approximations to the one-dimensional transport equation began with 3 and 4, following the studies of 1 and 2 about the discrete eigenvalues of the transport equation. In previous work about the influence of a parameter in the solutions of S N approximations, it was considered the total macroscopic cross section as a control parameter and was analyzed how its variation changes the nature of the eigenvalues of the S N transport matrix, in problems with linearly anisotropic scattering. It was showed the existence of bifurcations points, i.e., there exist some values of control parameters for which the S N transport matrix has only real eigenvalues while for other values the S N relation between the eigenvalues of S N transport matrix and control parameter, supposing quadratically anisotropic scattering. Numerical results are reported. (author)

  19. Spectral analysis of the S{sub N} approximations in a slab with quadratically anisotropic scattering

    Energy Technology Data Exchange (ETDEWEB)

    Ourique, L.E.; Pazos, R.P. [Pontificia Univ. Catolica do Rio Grande do Sul, Porto Alegre, RS (Brazil)]. E-mail: ourique@pucrs.br; rpp@pucrs.br; Vilhena, M.T. [Rio Grande do Sul Univ., Porto Alegre, RS (Brazil). Escola de Engenharia); vilhena@cesup.ufrgs.br; Barros, R.C. [Universidade do Estado, Nova Friburgo, RJ (Brazil). Instituto Politecnico]. E-mail: dickbarros@uol.com.br

    2003-07-01

    The spectral analysis of the S{sub N} approximations to the one-dimensional transport equation began with 3 and 4, following the studies of 1 and 2 about the discrete eigenvalues of the transport equation. In previous work about the influence of a parameter in the solutions of S{sub N} approximations, it was considered the total macroscopic cross section as a control parameter and was analyzed how its variation changes the nature of the eigenvalues of the S{sub N} transport matrix, in problems with linearly anisotropic scattering. It was showed the existence of bifurcations points, i.e., there exist some values of control parameters for which the S{sub N} transport matrix has only real eigenvalues while for other values the S{sub N} relation between the eigenvalues of S{sub N} transport matrix and control parameter, supposing quadratically anisotropic scattering. Numerical results are reported. (author)

  20. Inverse scattering problem for a magnetic field in the Glauber approximation

    International Nuclear Information System (INIS)

    Bogdanov, I.V.

    1985-01-01

    New results in the general theory of scattering are obtained. An inverse problem at fixed energy for an axisymmetric magnetic field is formulated and solved within the frames of the quantum-mechanical Glauber approximation. The solution is found in quadratures in the form of an explicit inversion algorithm reproducing a vector potential by the angular dependence of the scattering amplitude. Extreme transitions from the eikonal inversion method to the classical and Born ones are investigated. Integral and differential equations are derived for the eikonal amplitude that ensure the real value of the vector potential and its energy independence. Magnetoelectric analogies the existence of equivalent axisymmetric electric and magnetic fields scattering charged particles in the same manner both in the Glauber and Born approximation are established. The mentioned analogies permit to simulate ion-potential scattering by potential one that is of interest from the practical viewpoint. Three-dimensional (excentral) eikonal inverse problems for the electric and magnetic fields are discussed. The results of the paper can be used in electron optics

  1. A S-matrix-like approximation in the charged particle scattering by the hydrogen atom

    International Nuclear Information System (INIS)

    Mignaco, J.A.; Tort, A.C.

    1979-01-01

    The Born approximation for charged particle scattering by the hydrogen atom is unfit at low energies. From a S-matrix-like consideration on the dominance of the neighbour singularities, the calculation of other contributions is suggested. The inclusion of bound states is made, following Eden's and his colaborators' ideas, which are described by their interest and likeness with procedures in the intermediate energy physics. (Author) [pt

  2. Collective coordinate approximation to the scattering of solitons in modified NLS and sine-Gordon models

    International Nuclear Information System (INIS)

    Baron, H.E.; Zakrzewski, W.J.

    2016-01-01

    We investigate the validity of collective coordinate approximations to the scattering of two solitons in several classes of (1+1) dimensional field theory models. We consider models which are deformations of the sine-Gordon (SG) or the nonlinear Schrödinger (NLS) model which posses soliton solutions (which are topological (SG) or non-topological (NLS)). Our deformations preserve their topology (SG), but change their integrability properties, either completely or partially (models become ‘quasi-integrable’). As the collective coordinate approximation does not allow for the radiation of energy out of a system we look, in some detail, at how the approximation fares in models which are ‘quasi-integrable’ and therefore have asymptotically conserved charges (i.e. charges Q(t) for which Q(t→−∞)=Q(t→∞)). We find that our collective coordinate approximation, based on geodesic motion etc, works amazingly well in all cases where it is expected to work. This is true for the physical properties of the solitons and even for their quasi-conserved (or not) charges. The only time the approximation is not very reliable (and even then the qualitative features are reasonable, but some details are not reproduced well) involves the processes when the solitons come very close together (within one width of each other) during their scattering.

  3. Analysis of a Cartesian PML approximation to acoustic scattering problems in and

    KAUST Repository

    Bramble, James H.

    2013-08-01

    We consider the application of a perfectly matched layer (PML) technique applied in Cartesian geometry to approximate solutions of the acoustic scattering problem in the frequency domain. The PML is viewed as a complex coordinate shift ("stretching") and leads to a variable complex coefficient equation for the acoustic wave posed on an infinite domain, the complement of the bounded scatterer. The use of Cartesian geometry leads to a PML operator with simple coefficients, although, still complex symmetric (non-Hermitian). The PML reformulation results in a problem whose solution coincides with the original solution inside the PML layer while decaying exponentially outside. The rapid decay of the PML solution suggests truncation to a bounded domain with a convenient outer boundary condition and subsequent finite element approximation (for the truncated problem). This paper provides new stability estimates for the Cartesian PML approximations both on the infinite and the truncated domain. We first investigate the stability of the infinite PML approximation as a function of the PML strength σ0. This is done for PML methods which involve continuous piecewise smooth stretching as well as piecewise constant stretching functions. We next introduce a truncation parameter M which determines the size of the PML layer. Our analysis shows that the truncated PML problem is stable provided that the product of Mσ0 is sufficiently large, in which case the solution of the problem on the truncated domain converges exponentially to that of the original problem in the domain of interest near the scatterer. This justifies the simple computational strategy of selecting a fixed PML layer and increasing σ0 to obtain the desired accuracy. The results of numerical experiments varying M and σ0 are given which illustrate the theoretically predicted behavior. © 2013 Elsevier B.V. All rights reserved.

  4. Analysis of the spectrum of a Cartesian Perfectly Matched Layer (PML) approximation to acoustic scattering problems

    KAUST Repository

    Kim, Seungil

    2010-01-01

    In this paper, we study the spectrum of the operator which results when the Perfectly Matched Layer (PML) is applied in Cartesian geometry to the Laplacian on an unbounded domain. This is often thought of as a complex change of variables or "complex stretching." The reason that such an operator is of interest is that it can be used to provide a very effective domain truncation approach for approximating acoustic scattering problems posed on unbounded domains. Stretching associated with polar or spherical geometry lead to constant coefficient operators outside of a bounded transition layer and so even though they are on unbounded domains, they (and their numerical approximations) can be analyzed by more standard compact perturbation arguments. In contrast, operators associated with Cartesian stretching are non-constant in unbounded regions and hence cannot be analyzed via a compact perturbation approach. Alternatively, to show that the scattering problem PML operator associated with Cartesian geometry is stable for real nonzero wave numbers, we show that the essential spectrum of the higher order part only intersects the real axis at the origin. This enables us to conclude stability of the PML scattering problem from a uniqueness result given in a subsequent publication. © 2009 Elsevier Inc. All rights reserved.

  5. Approximation of Schroedinger operators and scattering data using multi resolution analysis

    International Nuclear Information System (INIS)

    Holst, A.

    1994-04-01

    Let Η 0 =-Δ and Η = Η 0 +V, where V is multiplication by a real-valued Hoelder-continuous potential ν which satisfies the estimation |ν(χ)| less then or equal to C(χ) -ρ , for some ρ > 0. We use a multiresolution technique to construct a sequence of finite rank operators V κ so that the operators Η 0 +V κ are good approximations of Η for large κ. In particular, ||φ(Η) - φ (Η 0 φV κ )|| → 0 as κ ∞, when φ Ε C 0 . If ρ > 1 we also achieve that the scattering amplitudes for the systems Η 0 ,Η 0 +V κ converge to the scattering amplitude for the system Η 0 ,Η 0 +V uniformly on any compact subinterval of R + . We gives estimates for the rate of convergence in terms of the regularity and decay properties of υ. We discuss some properties of the approximate scattering amplitudes. For low energies their integral kernels are trigonometric polynomials and there is a simple matrix formula for their coefficients. 37 refs

  6. Elastic scattering of virtual photons via a quark loop in the double-logarithmic approximation

    Science.gov (United States)

    Ermolaev, B. I.; Ivanov, D. Yu.; Troyan, S. I.

    2018-04-01

    We calculate the amplitude of elastic photon-photon scattering via a single quark loop in the double-logarithmic approximation, presuming all external photons to be off-shell and unpolarized. At the same time we account for the running coupling effects. We consider this process in the forward kinematics at arbitrary relations between t and the external photon virtualities. We obtain explicit expressions for the photon-photon scattering amplitudes in all double-logarithmic kinematic regions. Then we calculate the small-x asymptotics of the obtained amplitudes and compare them with the parent amplitudes, thereby fixing the applicability regions of the asymptotics, i.e., fixing the applicability region for the nonvacuum Reggeons. We find that these Reggeons should be used at x <10-8 only.

  7. Kirchhoff approximation and closed-form expressions for atom-surface scattering

    International Nuclear Information System (INIS)

    Marvin, A.M.

    1980-01-01

    In this paper an approximate solution for atom-surface scattering is presented beyond the physical optics approximation. The potential is well represented by a hard corrugated surface but includes an attractive tail in front. The calculation is carried out analytically by two different methods, and the limit of validity of our formulas is well established in the text. In contrast with other workers, I find those expressions to be exact in both limits of small (Rayleigh region) and large momenta (classical region), with the correct behavior at the threshold. The result is attained through a particular use of the extinction theorem in writing the scattered amplitudes, hitherto not employed, and not for particular boundary values of the field. An explicit evaluation of the field on the surface shows in fact the present formulas to be simply related to the well known Kirchhoff approximation (KA) or more generally to an ''extended'' KA fit to the potential model above. A possible application of the theory to treat strong resonance-overlapping effects is suggested in the last part of the work

  8. Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. I. By a spherical particle.

    Science.gov (United States)

    Xu, Feng; Ren, Kuan Fang; Cai, Xiaoshu

    2006-07-10

    The geometrical-optics approximation of light scattering by a transparent or absorbing spherical particle is extended from plane wave to Gaussian beam incidence. The formulas for the calculation of the phase of each ray and the divergence factor are revised, and the interference of all the emerging rays is taken into account. The extended geometrical-optics approximation (EGOA) permits one to calculate the scattering diagram in all directions from 0 degrees to 180 degrees. The intensities of the scattered field calculated by the EGOA are compared with those calculated by the generalized Lorenz-Mie theory, and good agreement is found. The surface wave effect in Gaussian beam scattering is also qualitatively analyzed by introducing a flux ratio factor. The approach proposed is particularly important to the further extension of the geometrical-optics approximation to the scattering of large spheroidal particles.

  9. Comparison of the Born series and rational approximants in potential scattering. [Pade approximants, Yikawa and exponential potential

    Energy Technology Data Exchange (ETDEWEB)

    Garibotti, C R; Grinstein, F F [Rosario Univ. Nacional (Argentina). Facultad de Ciencias Exactas e Ingenieria

    1976-05-08

    It is discussed the real utility of Born series for the calculation of atomic collision processes in the Born approximation. It is suggested to make use of Pade approximants and it is shown that this approach provides very fast convergent sequences over all the energy range studied. Yukawa and exponential potential are explicitly considered and the results are compared with high-order Born approximation.

  10. Punctual Pade approximants as a regularization procedure for divergent and oscillatory partial wave expansions of the scattering amplitude

    International Nuclear Information System (INIS)

    Garibotti, C.R.; Grinstein, F.F.

    1978-01-01

    Previous theorems on the convergence of the [n,n+m] punctual Pade approximants to the scattering amplitude are extended. The new proofs include the cases of nonforward and backward scattering corresponding to potentials having 1/r and 1/r 2 long-range behaviors, for which the partial wave expansions are divergent and oscillatory, respectively. In this way, the ability of the approximation scheme as a summation method is established for all of the long-range potentials of interest in potential scattering

  11. Punctual Pade Approximants as a regularization procedure for divergent and oscillatory partial wave expansions of the scattering amplitude

    International Nuclear Information System (INIS)

    Garibotti, C.R.; Grinstein, F.F.

    1978-01-01

    Previous theorems on the convergence of the [n, n+m] Punctual Pade Approximants to the scattering amplitude are extended. The new proofs include the cases of non-forward and backward scattering corresponding to potentials having 1/r and 1/r 2 long range behaviours, for which the partial wave expansions are divergent and oscillatory, respectively. In this way, the ability of the approximation scheme as a summation method is established for all of the long range potentials of interest in potential scattering [pt

  12. Anomalous diffraction approximation for light scattering cross section: Case of random clusters of non-absorbent spheres

    Energy Technology Data Exchange (ETDEWEB)

    Jacquier, Sandra [Ecole Nationale Superieure des Mines de Saint-Etienne, 158 Cours Fauriel, 42023 F-St. Etienne (France); Gruy, Frederic [Ecole Nationale Superieure des Mines de Saint-Etienne, 158 Cours Fauriel, 42023 F-St. Etienne (France)], E-mail: fgruy@emse.fr

    2008-11-15

    We previously [Jacquier S, Gruy F. Approximation of the light scattering cross-section for aggregated spherical non-absorbent particles. JQSRT 2008;109:789-810] reformulated the anomalous diffraction (AD) approximation to calculate the light scattering cross section of aggregates by introducing their chord length distribution (CLD). It was applied to several ordered aggregates. This new method is entitled ADr, with the r for rapid because this one is at least 100 times faster than the standard AD method. In this article, we are searching for an approximated expression for CLD suitable all at once for ordered and disordered aggregates. The corresponding scattering cross-section values are compared to the ones coming from the standard AD approximation.

  13. Anomalous diffraction approximation for light scattering cross section: Case of random clusters of non-absorbent spheres

    International Nuclear Information System (INIS)

    Jacquier, Sandra; Gruy, Frederic

    2008-01-01

    We previously [Jacquier S, Gruy F. Approximation of the light scattering cross-section for aggregated spherical non-absorbent particles. JQSRT 2008;109:789-810] reformulated the anomalous diffraction (AD) approximation to calculate the light scattering cross section of aggregates by introducing their chord length distribution (CLD). It was applied to several ordered aggregates. This new method is entitled ADr, with the r for rapid because this one is at least 100 times faster than the standard AD method. In this article, we are searching for an approximated expression for CLD suitable all at once for ordered and disordered aggregates. The corresponding scattering cross-section values are compared to the ones coming from the standard AD approximation

  14. Scattering Light by а Cylindrical Capsule with Arbitrary End Caps in the Rayleigh-Gans-Debye Approximation

    Directory of Open Access Journals (Sweden)

    K. A. Shapovalov

    2015-01-01

    Full Text Available The paper concerns the light scattering problem of biological objects of complicated structure.It considers optically “soft” (having a refractive index close to that of a surrounding medium homogeneous cylindrical capsules, composed of three parts: central one that is cylindrical and two symmetrical rounding end caps. Such capsules can model more broad class of biological objects than the ordinary shapes of a spheroid or sphere. But, unfortunately, if a particle has other than a regular geometrical shape, then it is very difficult or impossible to solve the scattering problem analytically in its most general form that oblige us to use numerical and approximate analytical methods. The one of such approximate analytical method is the Rayleigh-Gans-Debye approximation (or the first Born approximation.So, the Rayleigh-Gans-Debye approximation is valid for different objects having size from nanometer to millimeter and depending on wave length and refractive index of an object under small phase shift of central ray.The formulas for light scattering amplitude of cylindrical capsule with arbitrary end caps in the Rayleigh-Gans-Debye approximation in scalar form are obtained. Then the light scattering phase function [or element of scattering matrix f11] for natural incident light (unpolarized or arbitrary polarized light is calculated.Numerical results for light scattering phase functions of cylindrical capsule with conical, spheroidal, paraboloidal ends in the Rayleigh-Gans-Debye approximation are compared. Also numerical results for light scattering phase function of cylindrical capsule with conical ends in the Rayleigh-Gans-Debye approximation and in the method of Purcell-Pennypacker (or Discrete Dipole method are compared. The good agreement within an application range of the RayleighGans-Debye approximation is obtained.Further continuation of the work, perhaps, is a consideration of multilayer cylindrical capsule in the Rayleigh

  15. Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions

    International Nuclear Information System (INIS)

    Tarvainen, Tanja; Vauhkonen, Marko; Kolehmainen, Ville; Arridge, Simon R; Kaipio, Jari P

    2005-01-01

    In this paper, a coupled radiative transfer equation and diffusion approximation model is extended for light propagation in turbid medium with low-scattering and non-scattering regions. The light propagation is modelled with the radiative transfer equation in sub-domains in which the assumptions of the diffusion approximation are not valid. The diffusion approximation is used elsewhere in the domain. The two equations are coupled through their boundary conditions and they are solved simultaneously using the finite element method. The streamline diffusion modification is used to avoid the ray-effect problem in the finite element solution of the radiative transfer equation. The proposed method is tested with simulations. The results of the coupled model are compared with the finite element solutions of the radiative transfer equation and the diffusion approximation and with results of Monte Carlo simulation. The results show that the coupled model can be used to describe photon migration in turbid medium with low-scattering and non-scattering regions more accurately than the conventional diffusion model

  16. Multiple-scattering formalism beyond the quasistatic approximation: Analyzing resonances in plasmonic chains

    DEFF Research Database (Denmark)

    de Lasson, Jakob Rosenkrantz; Kristensen, Philip Trøst; Mørk, Jesper

    2012-01-01

    We present a multiple-scattering formalism for simulating scattering of electromagnetic waves on spherical inhomogeneities in 3D. The formalism is based on the Lippmann-Schwinger equation and the electromagnetic Green's tensor and applies an expansion of the electric field on spherical...

  17. Off-shell properties of the second-order Born approximation for laser-assisted potential scattering

    International Nuclear Information System (INIS)

    Trombetta, F.

    1991-01-01

    A formal method is presented to evaluate the second-order Born approximation of the laser-assisted potential scattering. It is an implicit closure technique that includes intermediate virtual-state transitions and enables one to find the exact explicit expression of the transition amplitude. This is of interest from two standpoints: first, one can deal with ranges of parameters in which the first-order Born approximation is a poor one; second, one can set limits of on-shell approximations that are also widely used to analyze recent laser-assisted experiments. The off-shell character yields new terms in the exact amplitude, and in particular, it is shown to play a crucial role in forward scattering from a long-range potential

  18. Elastic and inelastic proton-nucleus scattering at 156MeV: experimental study and analysis in impulse approximation

    International Nuclear Information System (INIS)

    Comparat, Vincent.

    1975-01-01

    In this work a high spatial resolution hodoscope is described. Scattered particles are detected in the image plane of a magnetic spectrometer by a proportional chamber with 96 wires of 1mm spacing. This hodoscope has been used for elastic and inelastic scattering experiments, of 156MeV protons, on 11 targets ranging from 12 C to 209 Bi. A phenomenological optical model calculation has been carried out to analyse the experimental elastic cross sections data. The dependance of the parameters as a function of the number of mass or the incident energy has been studied. The inelastic scattering results have been interpreted within the framework of the D.W.I.A. As the final results are dependant of the nucleon model, the optical potential parameters as well as the finite range approximation, several trials have been performed. Nevertheless, the DWIA seems to give about twice the experimental values for collective excitations in light or medium nuclei. The first order optical potential derived from the impulse approximation was calculated and the results compared to the experimental elastic cross sections. Several approximations were tested as non locality, off energy shell effects and the motion of the target nucleon. The usual approximation on these quantities are justified if the momentum transfer is less than 3fm -1 . The nucleon-nucleus transition matrix is obtained by solving the Lippmann-Schwinger equation, using the moment method. The first order optical potential derived from these calculations is not realistic. The intensity of the nucleon-nucleon transition is too important, and that explained the disagreement at low momentum transfers. This study shows that the multiple scattering expansion of the Lippmann-Schwinger equation, is not a good method to obtain the exact solution. It is better to do some approximations (i.e. of shell approximation) directly on the integral equation [fr

  19. A variational approach to operator and matrix Pade approximation. Applications to potential scattering and field theory

    International Nuclear Information System (INIS)

    Mery, P.

    1977-01-01

    The operator and matrix Pade approximation are defined. The fact that these approximants can be derived from the Schwinger variational principle is emphasized. In potential theory, using this variational aspect it is shown that the matrix Pade approximation allow to reproduce the exact solution of the Lippman-Schwinger equation with any required accuracy taking only into account the knowledge of the first two coefficients in the Born expansion. The deep analytic structure of this variational matrix Pade approximation (hyper Pade approximation) is discussed

  20. Quantitative assessment of submicron scale anisotropy in tissue multifractality by scattering Mueller matrix in the framework of Born approximation

    Science.gov (United States)

    Das, Nandan Kumar; Dey, Rajib; Chakraborty, Semanti; Panigrahi, Prasanta K.; Meglinski, Igor; Ghosh, Nirmalya

    2018-04-01

    A number of tissue-like disordered media exhibit local anisotropy of scattering in the scaling behavior. Scaling behavior contains wealth of fractal or multifractal properties. We demonstrate that the spatial dielectric fluctuations in a sample of biological tissue exhibit multifractal anisotropy. Multifractal anisotropy encoded in the wavelength variation of the light scattering Mueller matrix and manifesting as an intriguing spectral diattenuation effect. We developed an inverse method for the quantitative assessment of the multifractal anisotropy. The method is based on the processing of relevant Mueller matrix elements in Fourier domain by using Born approximation, followed by the multifractal analysis. The approach promises for probing subtle micro-structural changes in biological tissues associated with the cancer and precancer, as well as for non-destructive characterization of a wide range of scattering materials.

  1. Scattering in particle-hole space: simple approximations to nuclear RPA calculations in the continuum

    International Nuclear Information System (INIS)

    Toledo Piza, A.F.R. de.

    1987-01-01

    The Random Phase Approximation (RPA) treatment of nuclear small amplitude vibrations including particle-hole continua is handled in terms of previously developed techniques to treat single-particle resonances in a reaction theoretical framework. A hierarchy of interpretable approximations is derived and a simple working approximation is proposed which involves a numerical effort no larger than that involved in standard, discrete RPA calculations. (Author) [pt

  2. Analysis of the spectrum of a Cartesian Perfectly Matched Layer (PML) approximation to acoustic scattering problems

    KAUST Repository

    Kim, Seungil; Pasciak, Joseph E.

    2010-01-01

    is stable for real nonzero wave numbers, we show that the essential spectrum of the higher order part only intersects the real axis at the origin. This enables us to conclude stability of the PML scattering problem from a uniqueness result given in a

  3. Analysis of a Cartesian PML approximation to acoustic scattering problems in and

    KAUST Repository

    Bramble, James H.; Pasciak, Joseph E.

    2013-01-01

    to that of the original problem in the domain of interest near the scatterer. This justifies the simple computational strategy of selecting a fixed PML layer and increasing σ0 to obtain the desired accuracy. The results of numerical experiments varying M and σ0 are given

  4. A Spectral Geometrical Model for Compton Scatter Tomography Based on the SSS Approximation

    DEFF Research Database (Denmark)

    Kazantsev, Ivan G.; Olsen, Ulrik Lund; Poulsen, Henning Friis

    2016-01-01

    The forward model of single scatter in the Positron Emission Tomography for a detector system possessing an excellent spectral resolution under idealized geometrical assumptions is investigated. This model has the form of integral equations describing a flux of photons emanating from the same ann...

  5. New approximations of the differential electron-atom elastic scattering cross-sections

    International Nuclear Information System (INIS)

    Niculescu, V.I.R.; Catana, D.

    1994-01-01

    In the present note concerning the electron-atom interaction a cubic Spline method was used to obtain approximations of the differential cross-sections. These approximations gave a 20 times reduction of the computing time preserving also the accuracy (2%). The example is for Al in the 1-256 keV electron energy range. (Author) 2 Tabs., 3 Refs

  6. Low-energy P-wave phaseshifts for positron-hydrogen elastic scattering using an adiabatic approximation

    International Nuclear Information System (INIS)

    Armour, E.A.G.; Beker, C.A.; Farina, J.E.G.

    1981-01-01

    P-wave phaseshifts for positron-hydrogen elastic scattering are calculated using a new adiabatic approximation in which the length of the radius vector from the proton to the positron is fixed but its direction is allowed to vary. This adiabatic approximation makes possible the full inclusion in the calculation of virtual states in which angular momentum is transferred to the target H atom. The results obtained agree qualitatively with the highly accurate results of Bhatia and co-workers (Phys. Rev.; A9:219 (1974)) and are much closer to them than the results obtained using the usual adiabatic approximation in which the radius vector from the proton to the positron is fixed. (author)

  7. Medium energy nucleon-nucleus scattering theory by semi-classical distorted wave approximation

    Energy Technology Data Exchange (ETDEWEB)

    Ogata, Kazuyuki [Kyushu Univ., Fukuoka (Japan)

    1998-07-01

    The semiclassical distorted wave model (SCDW) is one of the quantum mechanical models for nucleon inelastic and charge exchange scattering at intermediate energies. SCDW can reproduce the double differential inclusive cross sections for multi-step direct processes quite well in the angular and outgoing energy regions where the model is expected to work. But the model hitherto assumed on-the-energy-shell (on-shell) nucleon-nucleon scattering in the nucleus, neglecting the difference in the distorting potentials for the incoming and the outgoing particles and also the Q-value in the case of (p,n) reactions. There had also been a problem in the treatment of the exchange of colliding nucleons. Now we modify the model to overcome those problems and put SCDW on sounder theoretical foundations. The modification results in slight reduction (increase) of double differential cross sections at forward (backward) angles. We also examine the effect of the in-medium modification of N-N cross sections in SCDW and find it small. A remedy of the disagreement at very small and large angles in terms of the Wigner transform of the single particle density matrix is also discussed. This improvement gives very promising results. (author)

  8. Study of the performance of collision short time approximation for neutron scattering using discrete frequency distribution

    International Nuclear Information System (INIS)

    D'Oliveira, A.B.; Amorim, E.S. do; Galvao, O.B.

    1981-03-01

    Double differential cross sections for thermal neutrons, based on incoherent approximation, using continum distribution as discrete frequency set are theoretically estimated, regarding two models previously done. The FASTT computer program is used in order to obtain a numerical estimation. (L.C.) [pt

  9. The analysis of the elastic scattering of {sup 11}Be and {sup 6}Li by adiabatic approximation

    Energy Technology Data Exchange (ETDEWEB)

    Takagi, S. [Osaka City Univ. (Japan). Dept. of Physics

    2000-01-01

    The unstable nuclei, particularly, the neutron halo nuclei which exist near by the neutron dripline, are recently one of the interesting topics in the nuclear physics. By the adiabatic approximation, R. C. Jhonson et al. have reproduced the experimental differential cross-section of the elastic scattering of the neutron halo nucleus {sup 11}Be (+{sup l2}C) [1]. We have applied their method to the elastic scattering of another nucleus {sup 6}Li which is not a halo nucleus but has the cluster structure as {sup 11}Be. But it couldn't reproduce the experimental data, so that the method of Johnson et al. is poor in the case of {sup 6}Li. (author)

  10. SANS [small-angle neutron scattering] evaluation of the RPA [random phase approximation] theory for binary homopolymer mixtures

    International Nuclear Information System (INIS)

    Bates, F.S.; Koehler, W.C.; Wignall, G.D.; Fetters, L.J.

    1986-12-01

    A well characterized binary mixture of normal (protonated) and perdeuterated monodisperse 1,2 polybutenes has been studied by small-angle neutron scattering (SANS). For scattering wavevectors q greater than the inverse radius-of-gyration R/sub g/ -1 , the SANS intensity is quantitatively predicted by the random phase approximation (RPA) theory of deGennes over all measured values of the segment-segment interaction parameter Chi. In the region (Chi s-Chi)Chi s -1 > 0.5 the interaction parameter determined using the RPA theory for q > R/sub g/ -1 is greater than that calculated from the zero-angle intensity based on an Ornstein-Zernike plot, where Chi s represents the limit of single phase stability. These findings indicate a correlation between the critical fluctuation length ξ and R/sub g/ which is not accounted for by the RPA theory

  11. Validity of the independent-processes approximation for resonance structures in electron-ion scattering cross sections

    International Nuclear Information System (INIS)

    Badnell, N.R.; Pindzola, M.S.; Griffin, D.C.

    1991-01-01

    The total inelastic cross section for electron-ion scattering may be found in the independent-processes approximation by adding the resonant cross section to the nonresonant background cross section. We study the validity of this approximation for electron excitation of multiply charged ions. The resonant-excitation cross section is calculated independently using distorted waves for various Li-like and Na-like ions using (N+1)-electron atomic-structure methods previously developed for the calculation of dielectronic-recombination cross sections. To check the effects of interference between the two scattering processes, we also carry out detailed close-coupling calculations for the same atomic ions using the R-matrix method. For low ionization stages, interference effects manifest themselves sometimes as strong window features in the close-coupling cross section, which are not present in the independent-processes cross section. For higher ionization stages, however, the resonance features found in the independent-processes approximation are found to be in good agreement with the close-coupling results

  12. Extended low-frequency approximation for laser-modified electron scattering: Coulomb effects

    International Nuclear Information System (INIS)

    Mittleman, M.H.

    1988-01-01

    The Kroll-Watson [N.M. Kroll and K. M. Watson, Phys. Rev. A 8, 804 (1973)] theory for electron scattering in the field of a low-frequency laser has been extended by L. Rosenberg [Phys. Rev. A 23, 2283 (1981); 28, 2727 (1983)] to apply to higher intensities. That result is rederived in another way so as to make the correction second order. The correction terms are obtained and shown to be small in the high-intensity low-energy regime in which the original theory is weakest. The special case of a Coulomb potential is analyzed and shown to present special peculiarities in the extended theory just as in the original Kroll-Watson theory

  13. Space and time dependent boltzmann calculation in the forward backward scattering approximation

    International Nuclear Information System (INIS)

    Boeuf, J.P.; Marode, E.; Segur, P.

    1984-01-01

    The spatio-temporal evolution of an electron swarm under a uniform field has been simulated for a forward/backward scattering model, using a Mac Cormak numerical scheme. Using model cross-sections, the effect of attachment and ionization on the spatial variations of the swarm density and velocity distribution function and on the higher order transport coefficients has been analysed. It is shown that the non uniform spatial distribution of energy within the swarm can induce, for the electron number density, a large deviation from the Gaussian shape. This deviation is due mainly to the fact that ionization is more important in the front of the swarm while attachment prevails in the back of the swarm

  14. Sensitivity of relativistic impulse approximation proton-nucleus elastic scattering calculations on relativistic mean-field parameterizations

    International Nuclear Information System (INIS)

    Hojsik, M.; Gmuca, S.

    1998-01-01

    Relativistic microscopic calculations are presented for proton elastic scattering from 40 Ca at 500 MeV. The underlying target densities are calculated within the framework of the relativistic mean-field theory with several parameter sets commonly in use. The self consistency of the scalar and vector densities (and thus to relativistic mean-field parameters) is investigated. Recently, the relativistic impulse approximation (RIA) has been widely and repeatedly used for the calculations of proton-nucleus scattering at intermediate energies. These calculations have exhibited significant improvements over the nonrelativistic approaches. The relativistic impulse approximation calculations. in particular, provide a dramatically better description of the spin observables, namely the analyzing power, A y , and the spin-rotation function, Q, at least for energies higher than 400 MeV. In the relativistic impulse approximation, the Dirac optical potential is obtained by folding of the local Lorentz-invariant amplitudes with the corresponding nuclear densities. For the spin zero targets the scalar and vector terms give the dominant contributions. Thus the scalar and vector nuclear densities (both, proton and neutron ones) play the dominant role in the relativistic impulse approximation. While the proton vector densities can be obtained by unfolding from the empirically known charge densities, all other densities used rely to a great extent on theoretical models. The various recipes are used to construct the neutron vector densities and the scalar densities for both, neutrons and protons. In this paper we will study the sensitivity of the relativistic impulse approximation results on the various sets of relativistic mean-field parameters currently in use

  15. A fast, exact code for scattered thermal radiation compared with a two-stream approximation

    International Nuclear Information System (INIS)

    Cogley, A.C.; Pandey, D.K.

    1980-01-01

    A two-stream accuracy study for internally (thermal) driven problems is presented by comparison with a recently developed 'exact' adding/doubling method. The resulting errors in external (or boundary) radiative intensity and flux are usually larger than those for the externally driven problems and vary substantially with the radiative parameters. Error predictions for a specific problem are difficult. An unexpected result is that the exact method is computationally as fast as the two-stream approximation for nonisothermal media

  16. SAM revisited: absorptive uniform semiclassical approximation and application to heavy-ion elastic scattering

    International Nuclear Information System (INIS)

    Pato, M.P.; Hussein, M.S.

    1989-06-01

    The Uniform Semiclassical Approximation is modified to take into account absorption. Symbol calculus and pseudodifferential operators techniques are employed for the purpose. The resulting theory, very similar to the one developed by Frahn and Gross permits the decomposition of the near-side and far-side amplitudes into diffractive and refractive components. Application to several heavy-ion systems at intermediate energies is made. (author) [pt

  17. Accuracy of the ''decoupled l-dominant'' approximation for atom--molecule scattering

    International Nuclear Information System (INIS)

    Green, S.

    1976-01-01

    Cross sections for rotational excitation and spectral pressure broadening of HD, HCl, CO, and HCN due to collisions with low energy He atoms have been computed within the ''decoupled l-dominant'' (DLD) approximation recently suggested by DePristo and Alexander. These are compared with accurate close coupling results and also with two similar approximations, the effective potential of Rabitz and the coupled states of McGuire and Kouri. These collision systems are all dominated by short-range repulsive interactions although they have varying degrees of anisotropy and inelasticity. The coupled states method is expected to be valid for such systems, but they should be a severe test to the DLD approximation which is expected to be better for long-range interactions. Nonetheless, DLD predictions of state-to-state cross sections are rather good, being only slightly less accurate than coupled states results. DLD is far superior to either the coupled states or effective potential methods for pressure broadening calculations, although it may not be uniformly of the quantitative accuracy desirable for obtaining intermolecular potentials from experimental data

  18. Time-dependent radiation transfer with rayleigh scattering in finite plane-parallel media using pomraning-eddington approximation

    International Nuclear Information System (INIS)

    El-Wakil, S.A.; Sallah, M.; Degheidy, A.R.

    2005-01-01

    The time-dependent radiation transfer equation in plane geometry with Rayleigh scattering is studied. The traveling wave transformation is used to obtain the corresponding stationary-like equation. Pomraning-Eddington approximation is then used to calculate the radiation intensity in finite plane-parallel media. Numerical results and shielding calculations are shown for reflectivity and transmissivity at different times. The medium is assumed to have specular-reflecting boundaries. For the sake of comparison, two different weight functions are introduced and to force the boundary conditions to be fulfilled

  19. (Quasi)Elastic Electron-Muon Large-Angle Scattering to a Two-Loop Approximation: Vertex Contributions

    CERN Document Server

    Bytev, V V; Shaikhatdenov, B G

    2002-01-01

    We consider a process of quasielastic e\\mu large-angle scattering at high energies with radiative corrections up to a two-loop level. The lowest order radiative correction arising both from one-loop virtual photon emission and a real soft emission are presented to a power accuracy. Two-loop level corrections are supposed to be of three gauge-invariant classes. One of them, so-called vertex contribution, is given in logarithmic approximation. Relation with the renormalization group approach is discussed.

  20. (Quasi)Elastic Electron-Muon Large-Angle Scattering to a Two-Loop Approximation Vertex Contributions

    CERN Document Server

    Bytev, V V; Shaikhatdenov, B G

    2002-01-01

    We consider a process of quasielastic e\\mu large-angle scattering at high energies with radiative corrections up to a two-loop level. The lowest order radiative correction arising both from one-loop virtual photon emission and a real soft emission are presented to a power accuracy. Two-loop level corrections are supposed to be of three gauge-invariant classes. One of them, so-called vertex contribution, is given in logarithmic approximation. Relation with the renormalization group approach is discussed.

  1. Scattering of plane waves by rough surfaces in the sense of Born approximation

    OpenAIRE

    Arnold, Thomas

    2014-01-01

    Das Thema dieser Arbeit ist die Streuung elektromagnetischer ebener Wellen an rauen Oberflächen, also an ebenen Oberflächen mit glatten und beschränkten Störungen. Darüber hinaus wird ein kleiner Kontrast der Materialkonstanten zwischen dem Deckmaterial und dem Material unter der rauen Oberfläche angenommen. Unter diesen Voraussetzungen wird ein Fernfeld-Formel für das gestreute Feld mit Hilfe von Born-Approximation und Fourier-Techniken hergeleitet. Dieser Ansatz basiert auf einer Modifikati...

  2. Electron-deuteron scattering in the equal-time formalism: beyond the impulse approximation

    Energy Technology Data Exchange (ETDEWEB)

    D.R. Phillips; Stephen Wallace; N.K. Devine

    2004-11-01

    Using a three-dimensional formalism that includes relativistic kinematics, the effects of negative-energy states, approximate boosts of the two-body system, and current conservation, we calculate the electromagnetic form factors of the deuteron up to Q{sup 2} of 4 GeV{sup 2}. This is done using a dynamical boost for two-body systems with spin. We first compute form factors in impulse approximation, but then also add an isoscalar meson-exchange current of pion range that involves the gamma-pi contact operator associated with pseudovector pi-N coupling. We also consider effects of the rho-pi-gamma meson-exchange current. The experimentally measured quantities A, B, and t20 are calculated over the kinematic range probed in recent Jefferson Laboratory experiments. The rho-pi-gamma meson-exchange current provides significant strength in A at large Q{sup 2} and the gamma-pi contact-term exchange current shifts t20, providing good agreement with the JLab data. Relativistic effects and the gamma-pi meson-exchange current do not provide an explanation of the B observable, but the rho-pi-gamma current could help to provide agreement if a nonstandard value is used for the tensor rho-N coupling that enters this contribution.

  3. Thinning Approximation for Two-Dimensional Scattering Patterns from Coarse-Grained Polymer Melts under Shear Flow

    Science.gov (United States)

    Hagita, Katsumi; Murashima, Takahiro; Takano, Hiroshi; Kawakatsu, Toshihiro

    2017-12-01

    We proposed a thinning approximation (TA) for estimation of the two-dimensional (2D) wide-angle scattering patterns from Kremer-Grest polymer melts under shear. In the TA, extra particles are inserted at the middle of bonds for fine-graining of the coarse-grained polymers. For the case without the TA, spots corresponding to the orientation of bonds at a high shear rate are difficult to observe because the bond length of successive particles is comparable to the distance between neighboring particles. With the insertion of the extra particles, a ring pattern originating from the neighboring particles can be moved to a wide-angle region. Thus, we can observe the spots at high shear rates. We also examined the relationship between 2D scattering patterns and the Weissenberg number, which is defined as the product of the shear rate and the longest relaxation time. It is confirmed that the relationship for coarse-grained polymers with the TA is consistent with that of the all-atomistic model of polyethylene.

  4. Measurements of Atomic Rayleigh Scattering Cross-Sections: A New Approach Based on Solid Angle Approximation and Geometrical Efficiency

    Science.gov (United States)

    Rao, D. V.; Takeda, T.; Itai, Y.; Akatsuka, T.; Seltzer, S. M.; Hubbell, J. H.; Cesareo, R.; Brunetti, A.; Gigante, G. E.

    Atomic Rayleigh scattering cross-sections for low, medium and high Z atoms are measured in vacuum using X-ray tube with a secondary target as an excitation source instead of radioisotopes. Monoenergetic Kα radiation emitted from the secondary target and monoenergetic radiation produced using two secondary targets with filters coupled to an X-ray tube are compared. The Kα radiation from the second target of the system is used to excite the sample. The background has been reduced considerably and the monochromacy is improved. Elastic scattering of Kα X-ray line energies of the secondary target by the sample is recorded with Hp Ge and Si (Li) detectors. A new approach is developed to estimate the solid angle approximation and geometrical efficiency for a system with experimental arrangement using X-ray tube and secondary target. The variation of the solid angle is studied by changing the radius and length of the collimators towards and away from the source and sample. From these values the variation of the total solid angle and geometrical efficiency is deduced and the optimum value is used for the experimental work. The efficiency is larger because the X-ray fluorescent source acts as a converter. Experimental results based on this system are compared with theoretical estimates and good agreement is observed in between them.

  5. Study on the generalized WKB approximation for the inverse scattering problem at fixed energy for complex potentials

    International Nuclear Information System (INIS)

    Pozdnyakov, Yu.A.; Terenetskij, K.O.

    1981-01-01

    The approximate method for solution of the inverse scattering problem (ISP) at fixed energy for complex spherically symmetric potentials decreasing faster 1/r is considered. The method is based on using a generalized WKB approximation. For the designed potential V(r) a sufficiently ''close'' reference potential V(r) has been chosen. For both potentials S-matrix elements (ME) have been calculated and inversion procedure has been carried out. S-ME have been calculated for integral-valued and intermediate angular moment values. S-ME are presented in a graphical form for being restored reference, and restored potentials for proton scattering with Esub(p)=49.48 MeV energy on 12 C nuclei. The restoration is the better the ''closer'' the sought-for potential to the reference one. This allows to specify the potential by means of iterations: the restored potential can be used as a reference one, etc. The operation of a restored potential smoothing before the following iteration is introduced. Drawbacks and advantages of the ISP solution method under consideration are pointed out. The method application is strongly limited by the requirement that the energy should be higher than a certain ''critical'' one. The method is applicable in a wider region of particle energies (in the low-energies direction) than the ordinary WKB method. The method is more simple in realization conformably to complex potentials. The investigations carried out of the proposed ISP solution method at fixed energy for complex spherically-symmetric potentials allow to conclude that the method can be successFully applied to specify the central part of interaction of nucleons, α-particles and heavy ions of average and high energies with atomic nuclei [ru

  6. Modeling C-band single scattering properties of hydrometeors using discrete-dipole approximation and T-matrix method

    International Nuclear Information System (INIS)

    Tyynelae, Jani; Nousiainen, Timo; Goeke, Sabine; Muinonen, Karri

    2009-01-01

    We study the applicability of the discrete-dipole approximation by modeling centimeter (C-band) radar echoes for hydrometeors, and compare the results to exact theories. We use ice and water particles of various shapes with varying water-content to investigate how the backscattering, extinction, and absorption cross sections change as a function of particle radius. We also compute radar parameters, such as the differential reflectivity, the linear depolarization ratio, and the copolarized correlation coefficient. We find that using discrete-dipole approximation (DDA) to model pure ice and pure water particles at the C-band, is a lot more accurate than particles containing both ice and water. For coated particles, a large grid-size is recommended so that the coating is modeled adequately. We also find that the absorption cross section is significantly less accurate than the scattering and backscattering cross sections. The accuracy of DDA can be increased by increasing the number of dipoles, but also by using the filtered coupled dipole-option for the polarizability. This halved the relative errors in cross sections.

  7. πN scattering and γN → Nπ photoproduction within the unitary improved Born approximation

    Science.gov (United States)

    Mariano, A.

    2007-07-01

    Following the programme of describing consistently several processes where the isobar Δ(1232 MeV) nucleon resonance appears as an intermediate state, in this work we propose to unitarize our old improved Born approximation already used to describe successfully π+p elastic and radiative scattering, to treat pion photoproduction. First we add the effect of final state interactions and make a new determination of the mass, width and the coupling constant to the pion-nucleon state of the Δ resonance. Then extending the model for pion photoproduction and using the resonance parameters determined previously, we are able to define effective form factors (at k2γ = 0) for the γN → Δ vertex with values GM = 2.97 ± 0.08 and GE = 0.055 ± 0.010, by fitting the data for the M3/21+ and E3/21+ multipoles. These values are fully consistent with recent chiral effective field theory calculations, and using them we can predict satisfactorily the data for other multipoles and the photoproduction cross section. Finally, we intend a model-independent determination of the bare form factors making a dynamical dressing of the vertex, getting G0M = 1.69 ± 0.02, G0E = 0.028 ± 0.008 and R0EM = -1.67 ± 0.45%, which are compared with different quark models.

  8. User's manual for EXALPHA (a code for calculating electronic properties of molecules). [Muscatel code, multiply scattered electron approximation

    Energy Technology Data Exchange (ETDEWEB)

    Jones, H.D.

    1976-06-01

    The EXALPHA procedures provide a simplified method for running the MUSCATEL computer code, which in turn is used for calculating electronic properties of simple molecules and atomic clusters, based on the multiply scattered electron approximation for the wave equations. The use of the EXALPHA procedures to set up a run of MUSCATEL is described.

  9. Circumstances under which various approximate relativistic and nonrelativistic theories yield accurate Compton scattering doubly differential cross sections at high photon energy

    International Nuclear Information System (INIS)

    LaJohn, L A; Pratt, R H

    2009-01-01

    We discuss the increase in error with increasing nuclear charge Z in the use of the relativistic impulse approximation (RIA) for the calculation of Compton K-shell scattering doubly differential cross sections (DDCS). We also show that nonrelativistic (nr) expressions can be used to obtain accurate peak region DDCS at scattering angles less than about 35 0 even at incident photon energies ω i exceeding 1 MeV, if Z<30. This is possible because in the Compton peak region, as θ→0, a low momentum transfer limit is being approached.

  10. Tunneling effects in electromagnetic wave scattering by nonspherical particles: A comparison of the Debye series and physical-geometric optics approximations

    International Nuclear Information System (INIS)

    Bi, Lei; Yang, Ping

    2016-01-01

    The accuracy of the physical-geometric optics (PG-O) approximation is examined for the simulation of electromagnetic scattering by nonspherical dielectric particles. This study seeks a better understanding of the tunneling effect on the phase matrix by employing the invariant imbedding method to rigorously compute the zeroth-order Debye series, from which the tunneling efficiency and the phase matrix corresponding to the diffraction and external reflection are obtained. The tunneling efficiency is shown to be a factor quantifying the relative importance of the tunneling effect over the Fraunhofer diffraction near the forward scattering direction. Due to the tunneling effect, different geometries with the same projected cross section might have different diffraction patterns, which are traditionally assumed to be identical according to the Babinet principle. For particles with a fixed orientation, the PG-O approximation yields the external reflection pattern with reasonable accuracy, but ordinarily fails to predict the locations of peaks and minima in the diffraction pattern. The larger the tunneling efficiency, the worse the PG-O accuracy is at scattering angles less than 90°. If the particles are assumed to be randomly oriented, the PG-O approximation yields the phase matrix close to the rigorous counterpart, primarily due to error cancellations in the orientation-average process. Furthermore, the PG-O approximation based on an electric field volume-integral equation is shown to usually be much more accurate than the Kirchhoff surface integral equation at side-scattering angles, particularly when the modulus of the complex refractive index is close to unity. Finally, tunneling efficiencies are tabulated for representative faceted particles. - Highlights: • Concepts of diffraction, reflection and tunneling are refined. • The diffraction together with reflection is rigorously treated. • An improved invariant imbedding method is employed to compute the Debye

  11. Mean free paths and in-medium scattering cross sections of energetic nucleons in neutron-rich nucleonic matter within the relativistic impulse approximation

    International Nuclear Information System (INIS)

    Jiang Weizhou; Li Baoan; Chen Liewen

    2007-01-01

    The mean free paths and in-medium scattering cross sections of energetic nucleons in neutron-rich nucleonic matter are investigated using the nucleon optical potential obtained within the relativistic impulse approximation with the empirical nucleon-nucleon scattering amplitudes and the nuclear densities obtained in the relativistic mean-field model. It is found that the isospin-splitting of nucleon mean free paths, sensitive to the imaginary part of the symmetry potential, changes its sign at certain high kinetic energy. The in-medium nucleon-nucleon cross sections are analytically and numerically demonstrated to be essentially independent of the isospin asymmetry of the medium and increase linearly with density in the high-energy region where the relativistic impulse approximation is applicable

  12. Tunneling effects in electromagnetic wave scattering by nonspherical particles: A comparison of the Debye series and physical-geometric optics approximations

    Science.gov (United States)

    Bi, Lei; Yang, Ping

    2016-07-01

    The accuracy of the physical-geometric optics (PG-O) approximation is examined for the simulation of electromagnetic scattering by nonspherical dielectric particles. This study seeks a better understanding of the tunneling effect on the phase matrix by employing the invariant imbedding method to rigorously compute the zeroth-order Debye series, from which the tunneling efficiency and the phase matrix corresponding to the diffraction and external reflection are obtained. The tunneling efficiency is shown to be a factor quantifying the relative importance of the tunneling effect over the Fraunhofer diffraction near the forward scattering direction. Due to the tunneling effect, different geometries with the same projected cross section might have different diffraction patterns, which are traditionally assumed to be identical according to the Babinet principle. For particles with a fixed orientation, the PG-O approximation yields the external reflection pattern with reasonable accuracy, but ordinarily fails to predict the locations of peaks and minima in the diffraction pattern. The larger the tunneling efficiency, the worse the PG-O accuracy is at scattering angles less than 90°. If the particles are assumed to be randomly oriented, the PG-O approximation yields the phase matrix close to the rigorous counterpart, primarily due to error cancellations in the orientation-average process. Furthermore, the PG-O approximation based on an electric field volume-integral equation is shown to usually be much more accurate than the Kirchhoff surface integral equation at side-scattering angles, particularly when the modulus of the complex refractive index is close to unity. Finally, tunneling efficiencies are tabulated for representative faceted particles.

  13. SCATTER

    International Nuclear Information System (INIS)

    Broome, J.

    1965-11-01

    The programme SCATTER is a KDF9 programme in the Egtran dialect of Fortran to generate normalized angular distributions for elastically scattered neutrons from data input as the coefficients of a Legendre polynomial series, or from differential cross-section data. Also, differential cross-section data may be analysed to produce Legendre polynomial coefficients. Output on cards punched in the format of the U.K. A. E. A. Nuclear Data Library is optional. (author)

  14. Unconventional application of the two-flux approximation for the calculation of the Ambartsumyan-Chandrasekhar function and the angular spectrum of the backward-scattered radiation for a semi-infinite isotropically scattering medium

    Science.gov (United States)

    Remizovich, V. S.

    2010-06-01

    It is commonly accepted that the Schwarzschild-Schuster two-flux approximation (1905, 1914) can be employed only for the calculation of the energy characteristics of the radiation field (energy density and energy flux density) and cannot be used to characterize the angular distribution of radiation field. However, such an inference is not valid. In several cases, one can calculate the radiation intensity inside matter and the reflected radiation with the aid of this simplest approximation in the transport theory. In this work, we use the results of the simplest one-parameter variant of the two-flux approximation to calculate the angular distribution (reflection function) of the radiation reflected by a semi-infinite isotropically scattering dissipative medium when a relatively broad beam is incident on the medium at an arbitrary angle relative to the surface. We do not employ the invariance principle and demonstrate that the reflection function exhibits the multiplicative property. It can be represented as a product of three functions: the reflection function corresponding to the single scattering and two identical h functions, which have the same physical meaning as the Ambartsumyan-Chandrasekhar function ( H) has. This circumstance allows a relatively easy derivation of simple analytical expressions for the H function, total reflectance, and reflection function. We can easily determine the relative contribution of the true single scattering in the photon backscattering at an arbitrary probability of photon survival Λ. We compare all of the parameters of the backscattered radiation with the data resulting from the calculations using the exact theory of Ambartsumyan, Chandrasekhar, et al., which was developed decades after the two-flux approximation. Thus, we avoid the application of fine mathematical methods (the Wiener-Hopf method, the Case method of singular functions, etc.) and obtain simple analytical expressions for the parameters of the scattered radiation

  15. Experimental and theoretical study of light scattering by individual mature red blood cells by use of scanning flow cytometry and a discrete dipole approximation.

    Science.gov (United States)

    Yurkin, Maxim A; Semyanov, Konstantin A; Tarasov, Peter A; Chernyshev, Andrei V; Hoekstra, Alfons G; Maltsev, Valeri P

    2005-09-01

    Elastic light scattering by mature red blood cells (RBCs) was theoretically and experimentally analyzed by use of the discrete dipole approximation (DDA) and scanning flow cytometry (SFC), respectively. SFC permits measurement of the angular dependence of the light-scattering intensity (indicatrix) of single particles. A mature RBC is modeled as a biconcave disk in DDA simulations of light scattering. We have studied the effect of RBC orientation related to the direction of the light incident upon the indicatrix. Numerical calculations of indicatrices for several axis ratios and volumes of RBC have been carried out. Comparison of the simulated indicatrices and indicatrices measured by SFC showed good agreement, validating the biconcave disk model for a mature RBC. We simulated the light-scattering output signals from the SFC with the DDA for RBCs modeled as a disk-sphere and as an oblate spheroid. The biconcave disk, the disk-sphere, and the oblate spheroid models have been compared for two orientations, i.e., face-on and rim-on incidence, relative to the direction of the incident beam. Only the oblate spheroid model for rim-on incidence gives results similar to those of the rigorous biconcave disk model.

  16. Determination of low-energy parameters of neutron-proton scattering in the the shape-parameter approximation from present-day experimental data

    International Nuclear Information System (INIS)

    Babenko, V. A.; Petrov, N. M.

    2010-01-01

    On the basis of the total cross sections for neutron-proton scattering in the region of laboratory energies below 150 keV, the value of σ 0 = 20.4288(146) b was obtained for the total cross sections for neutron-proton scattering at zero energy. This value is in very good agreement with the experimental cross sections obtained by Houke and Hurst, but it is at odds with Dilg's experimental cross section. By using the value that we found for σ 0 and the experimental values of the neutron-proton coherent scattering length f, the deuteron binding energy ε t , the deuteron effective radius ρ t (-ε t , -ε t ), and the total cross section in the region of energies below 5 MeV, the following values were found in the shape-parameter approximation for the low-energy parameters of neutron-proton scattering in the spin-triplet and spin-singlet states: a t = 5.4114(27) fm, r 0t = 1.7606(35) fm, v 2t = 0.157 fm 3 , a s = -23.7154(80) fm, r 0s = 2.706(67) fm, and v 2s = 0.491 fm 3 .

  17. Theory of magnetic neutron small-angle scattering using the dynamical theory of diffraction instead of the Born approximation. I

    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.)

  18. New approximations for the interference term applied to the calculation of scattering cross section of the {sup 238} U isotope

    Energy Technology Data Exchange (ETDEWEB)

    Palma, Daniel Artur Pinheiro [Centro Federal de Educacao Tecnologica de Quimica de Nilopolis, RJ (Brazil)]. E-mails: dpalma@cefeteq.br; Martinez, Aquilino Senra; Goncalves, Alessandro C. [Universidade Federal do Rio de Janeiro (UFRJ), RJ (Brazil). Coordenacao dos Programas de Pos-Graduacao em Engenharia (COPPE). Programa de Engenharia Nuclear]. E-mail: agoncalves@con.ufrj.br; aquilino@lmp.ufrj.br

    2008-07-01

    The calculation of the Doppler broadening function and the interference term are very important in the generation of nuclear data. Recent papers have proposed analytical formulations for both functions and, despite their being simple and precise, they contain the error function with a complex argument. With the intention of simplifying the mathematical treatment two approximations are proposed in this paper. The first one consists of using an expansion in the form of series to treat the error function. The other approximation is based on simplifications in the differential equations that govern the Doppler broadening function. For validation purpose the result obtained is compared to the one obtained in the calculation of the cross sections for isotope {sup 238}U for different resonances. Results obtained have proved satisfactory from the standpoint of accuracy. (author)

  19. New approximations for the interference term applied to the calculation of scattering cross section of the 238 U isotope

    International Nuclear Information System (INIS)

    Palma, Daniel Artur Pinheiro; Martinez, Aquilino Senra; Goncalves, Alessandro C.

    2008-01-01

    The calculation of the Doppler broadening function and the interference term are very important in the generation of nuclear data. Recent papers have proposed analytical formulations for both functions and, despite their being simple and precise, they contain the error function with a complex argument. With the intention of simplifying the mathematical treatment two approximations are proposed in this paper. The first one consists of using an expansion in the form of series to treat the error function. The other approximation is based on simplifications in the differential equations that govern the Doppler broadening function. For validation purpose the result obtained is compared to the one obtained in the calculation of the cross sections for isotope 238 U for different resonances. Results obtained have proved satisfactory from the standpoint of accuracy. (author)

  20. The cross section for inclusive deep inelastic scattering in the impulse approximation: scale invariance and mass problems

    International Nuclear Information System (INIS)

    Nataf, R.

    1982-06-01

    The non-perturbative calculation of inclusive D.I.S. is made in a parton model different from the ''naive'' one upon two points: 1) the struck quark is off-shell (impulse approximation), 2) kinematical correlations between partons are taken into account. At low Q 2 (4 to 20 GeV 2 ) the best target mass correction is the Nachtmann one [fr

  1. Contactless diagnostics of biophysical parameters of skin and blood on the basis of approximating functions for radiation fluxes scattered by skin

    Energy Technology Data Exchange (ETDEWEB)

    Lisenko, S A; Kugeiko, M M [Belarusian State University, Minsk (Belarus)

    2014-03-28

    Approximating expressions are derived to calculate spectral and spatial characteristics of diffuse reflection of light from a two-layer medium mimicking human skin. The effectiveness of the use of these expressions in the optical diagnosis of skin biophysical parameters (tissue scattering parameters, concentration of melanin in the epidermis, concentration of total haemoglobin and bilirubin in the tissues of the dermis) and content of haemoglobin derivatives in blood (oxy-, deoxy-, met-, carboxy- and sulfhaemoglobin) is analysed numerically. The methods are proposed to determine in realtime these parameters without contact of the measuring instrument with the patient's body. (biophotonics)

  2. Contactless diagnostics of biophysical parameters of skin and blood on the basis of approximating functions for radiation fluxes scattered by skin

    Science.gov (United States)

    Lisenko, S. A.; Kugeiko, M. M.

    2014-03-01

    Approximating expressions are derived to calculate spectral and spatial characteristics of diffuse reflection of light from a two-layer medium mimicking human skin. The effectiveness of the use of these expressions in the optical diagnosis of skin biophysical parameters (tissue scattering parameters, concentration of melanin in the epidermis, concentration of total haemoglobin and bilirubin in the tissues of the dermis) and content of haemoglobin derivatives in blood (oxy-, deoxy-, met-, carboxy- and sulfhaemoglobin) is analysed numerically. The methods are proposed to determine in realtime these parameters without contact of the measuring instrument with the patient's body.

  3. Quantum interference in grazing scattering of swift He atoms from LiF(0 0 1) surfaces: Surface eikonal approximation

    Energy Technology Data Exchange (ETDEWEB)

    Gravielle, M.S. [Instituto de Astronomia y Fisica del Espacio, CONICET, Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires (Argentina); Dpto. de Fisica, FCEN, Universidad de Buenos Aires, Buenos Aires (Argentina)], E-mail: msilvia@iafe.uba.ar; Miraglia, J.E. [Instituto de Astronomia y Fisica del Espacio, CONICET, Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires (Argentina); Dpto. de Fisica, FCEN, Universidad de Buenos Aires, Buenos Aires (Argentina)

    2009-02-15

    This work deals with the interference effects recently observed in grazing collisions of few-keV atoms with insulator surfaces. The process is studied within a distorted-wave method, the surface eikonal approximation, based on the use of the eikonal wave function and involving axial channeled trajectories with different initial conditions. The theory is applied to helium atoms impinging on a LiF(0 0 1) surface along the <1 1 0> direction. The role played by the projectile polarization and the surface rumpling is investigated. We found that when both effects are included, the proposed eikonal approach provides angular projectile spectra in good agreement with the experimental findings.

  4. Quantum interference in grazing scattering of swift He atoms from LiF(0 0 1) surfaces: Surface eikonal approximation

    International Nuclear Information System (INIS)

    Gravielle, M.S.; Miraglia, J.E.

    2009-01-01

    This work deals with the interference effects recently observed in grazing collisions of few-keV atoms with insulator surfaces. The process is studied within a distorted-wave method, the surface eikonal approximation, based on the use of the eikonal wave function and involving axial channeled trajectories with different initial conditions. The theory is applied to helium atoms impinging on a LiF(0 0 1) surface along the direction. The role played by the projectile polarization and the surface rumpling is investigated. We found that when both effects are included, the proposed eikonal approach provides angular projectile spectra in good agreement with the experimental findings.

  5. Some remarks on off-shell scattering in the eikonal approximation and applications to semi-inclusive reactions

    International Nuclear Information System (INIS)

    Rinat, A.S.; Taragin, M.F.

    1997-01-01

    Using the Abel inversion for the eikonal phase as function of the interaction we derive simple integral relations between half and on-shell eikonal phases. A frequently used short-range approximation for the half off-shell phase and profile appears supported by the above-mentioned relation. We work out some examples and also address the half off-shell eikonal phase pertinent to a diffractive amplitude. The latter is relevant for a calculation of selected transparencies T of nuclei for a proton, knocked-out in selected semi-inclusive A(e,e'p)X reactions. Some numerical results for T are given. (orig.)

  6. Program POD; A computer code to calculate nuclear elastic scattering cross sections with the optical model and neutron inelastic scattering cross sections by the distorted-wave born approximation

    International Nuclear Information System (INIS)

    Ichihara, Akira; Kunieda, Satoshi; Chiba, Satoshi; Iwamoto, Osamu; Shibata, Keiichi; Nakagawa, Tsuneo; Fukahori, Tokio; Katakura, Jun-ichi

    2005-07-01

    The computer code, POD, was developed to calculate angle-differential cross sections and analyzing powers for shape-elastic scattering for collisions of neutron or light ions with target nucleus. The cross sections are computed with the optical model. Angle-differential cross sections for neutron inelastic scattering can also be calculated with the distorted-wave Born approximation. The optical model potential parameters are the most essential inputs for those model computations. In this program, the cross sections and analyzing powers are obtained by using the existing local or global parameters. The parameters can also be inputted by users. In this report, the theoretical formulas, the computational methods, and the input parameters are explained. The sample inputs and outputs are also presented. (author)

  7. Evaluation of interatomic potentials for rainbow scattering under axial channeling at KCl(0 0 1) surface by three-dimensional computer simulations based on binary collision approximation

    Energy Technology Data Exchange (ETDEWEB)

    Takeuchi, Wataru, E-mail: take@sp.ous.ac.jp

    2017-05-01

    The rainbow angles corresponding to prominent peaks in the angular distributions of scattered projectiles with small angle, attributed to rainbow scattering (RS), under axial surface channeling conditions are strongly influenced by the interatomic potentials between projectiles and target atoms. The dependence of rainbow angles on normal energy of projectile energy to the target surface, being experimentally obtained by Specht et al. for RS of He, N, Ne and Ar atoms under 〈1 0 0〉 and 〈1 1 0〉 axial channeling conditions at a KCl(0 0 1) surface with projectile energies of 1–60 keV, was evaluated by the three-dimensional computer simulations using the ACOCT code based on the binary collision approximation with interatomic pair potentials. Good agreement between the ACOCT results using the ZBL pair potential and the individual pair potentials calculated from Hartree-Fock (HF) wave functions and the experimental ones was found for RS of He, N and Ne atoms from the atomic rows along 〈1 0 0〉 direction. For 〈1 1 0〉 direction, the ACOCT results employing the Moliere pair potential with adjustable screening length of O’Connor-Biersack (OB) formula, the ZBL pair potential and the individual HF pair potentials except for Ar → KCl using the OB pair potential are nearly in agreement with the experimental ones.

  8. Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. II. By a spheroidal particle with end-on incidence.

    Science.gov (United States)

    Xu, Feng; Ren, Kuan Fang; Cai, Xiaoshu; Shen, Jianqi

    2006-07-10

    On the basis of our previous work on the extension of the geometrical-optics approximation to Gaussian beam scattering by a spherical particle, we present a further extension of the method to the scattering of a transparent or absorbing spheroidal particle with the same symmetric axis as the incident beam. As was done for the spherical particle, the phase shifts of the emerging rays due to focal lines, optical path, and total reflection are carefully considered. The angular position of the geometric rainbow of primary order is theoretically predicted. Compared with our results, the Möbius prediction of the rainbow angle has a discrepancy of less than 0.5 degrees for a spheroidal droplet of aspect radio kappa within 0.95 and 1.05 and less than 2 degrees for kappa within 0.89 and 1.11. The flux ratio index F, which qualitatively indicates the effect of a surface wave, is also studied and found to be dependent on the size, refractive index, and surface curvature of the particle.

  9. Evaluation of interatomic potentials for noble gas atoms from rainbow scattering under axial channeling at Ag(1 1 1) surface by computer simulations based on binary collision approximation

    Energy Technology Data Exchange (ETDEWEB)

    Takeuchi, Wataru, E-mail: take@sp.ous.ac.jp

    2016-01-01

    The rainbow angles corresponding to pronounced peaks in the angular distributions of scattered projectiles with small angle, attributed to rainbow scattering (RS), under axial surface channeling conditions are strongly dependent on the interatomic potentials between projectiles and target atoms. The dependence of rainbow angles on normal energy of projectile energy to the target surface that has been experimentally obtained by Schüller and Winter (SW) (2007) for RS of He, Ne and Ar atoms from a Ag(1 1 1) surface with projectile energies of 3–60 keV was evaluated by the three-dimensional computer simulations using the ACOCT code based on the binary collision approximation with interatomic pair potentials. Consequently, the ACOCT results employing the Moliere pair potential with screening length correction close to adjustable one of O’Connor and Biersack (OB) formula are almost in agreement with the experimental ones, being self-consistent with the SW’s ones analyzed by computer simulations of classical trajectory calculations as RS from corrugated equipotential planes based on continuum potentials including the Moliere pair potential with screening length correction of the OB formula.

  10. Low-momentum-transfer nonrelativistic limit of the relativistic impulse approximation expression for Compton-scattering doubly differential cross sections and characterization of their relativistic contributions

    International Nuclear Information System (INIS)

    LaJohn, L. A.

    2010-01-01

    The nonrelativistic (nr) impulse approximation (NRIA) expression for Compton-scattering doubly differential cross sections (DDCS) for inelastic photon scattering is recovered from the corresponding relativistic expression (RIA) of Ribberfors [Phys. Rev. B 12, 2067 (1975)] in the limit of low momentum transfer (q→0), valid even at relativistic incident photon energies ω 1 >m provided that the average initial momentum of the ejected electron i > is not too high, that is, i > b 1 >m using nr expressions when θ is small. For example, a 1% accuracy can be obtained when ω 1 =1 MeV if θ 1 increases into the MeV range, the maximum θ at which an accurate Compton peak can be obtained from nr expressions approaches closer to zero, because the θ at which the relativistic shift of CP to higher energy is greatest, which starts at 180 deg. when ω 1 min ,ρ rel ) (where p min is the relativistic version of the z component of the momentum of the initial electron and ρ rel is the relativistic charge density) and K(p min ) on p min . This characterization approach was used as a guide for making the nr QED S-matrix expression for the Compton peak kinematically relativistic. Such modified nr expressions can be more readily applied to large systems than the fully relativistic version.

  11. Evidences for two scales in hadrons

    International Nuclear Information System (INIS)

    Kopeliovich, B. Z.; Potashnikova, I. K.; Schmidt, Ivan; Povh, B.

    2007-01-01

    Some unusual features observed in hadronic collisions at high energies can be understood assuming that gluons in hadrons are located within small spots occupying only about 10% of the hadrons' area. Such a conjecture about the presence of two scales in hadrons helps to explain the following: why diffractive gluon radiation is so suppressed; why the triple-Pomeron coupling shows no t dependence; why total hadronic cross sections rise so slowly with energy; why diffraction cones shrink so slowly, and why α P ' R ' ; why the transition from hard to soft regimes in the structure functions occurs at rather large Q 2 ; why the observed Cronin effect at collider energies is so weak; why hard reactions sensitive to primordial parton motion (direct photon, Drell-Yan dileptons, heavy flavors, back-to-back dihadrons, seagull effect, etc.) demand such a large transverse momenta of the projectile partons, which is not explained by next-to-leading order calculations; why the onset of nuclear shadowing for gluons is so delayed compared to quarks; and why shadowing is so weak

  12. Flow through a Two-Scale Porosity Material

    Directory of Open Access Journals (Sweden)

    A. G. Andersson

    2009-01-01

    Full Text Available Flow through a two-scale porous medium is here investigated by a unique comparison between simulations performed with computational fluid dynamics and the boundary element method with microparticle image velocimetry in model geometries.

  13. Exact and approximate multiple diffraction calculations

    International Nuclear Information System (INIS)

    Alexander, Y.; Wallace, S.J.; Sparrow, D.A.

    1976-08-01

    A three-body potential scattering problem is solved in the fixed scatterer model exactly and approximately to test the validity of commonly used assumptions of multiple scattering calculations. The model problem involves two-body amplitudes that show diffraction-like differential scattering similar to high energy hadron-nucleon amplitudes. The exact fixed scatterer calculations are compared to Glauber approximation, eikonal-expansion results and a noneikonal approximation

  14. A two-scale roughness model for the gloss of coated paper

    Science.gov (United States)

    Elton, N. J.

    2008-08-01

    A model for gloss is developed for surfaces with two-scale random roughness where one scale lies in the wavelength region (microroughness) and the other in the geometrical optics limit (macroroughness). A number of important industrial materials such as coated and printed paper and some paints exhibit such two-scale rough surfaces. Scalar Kirchhoff theory is used to describe scattering in the wavelength region and a facet model used for roughness features much greater than the wavelength. Simple analytical expressions are presented for the gloss of surfaces with Gaussian, modified and intermediate Lorentzian distributions of surface slopes, valid for gloss at high angle of incidence. In the model, gloss depends only on refractive index, rms microroughness amplitude and the FWHM of the surface slope distribution, all of which may be obtained experimentally. Model predictions are compared with experimental results for a range of coated papers and gloss standards, and found to be in fair agreement within model limitations.

  15. Compton scattering

    International Nuclear Information System (INIS)

    Botto, D.J.; Pratt, R.H.

    1979-05-01

    The current status of Compton scattering, both experimental observations and the theoretical predictions, is examined. Classes of experiments are distinguished and the results obtained are summarized. The validity of the incoherent scattering function approximation and the impulse approximation is discussed. These simple theoretical approaches are compared with predictions of the nonrelativistic dipole formula of Gavrila and with the relativistic results of Whittingham. It is noted that the A -2 based approximations fail to predict resonances and an infrared divergence, both of which have been observed. It appears that at present the various available theoretical approaches differ significantly in their predictions and that further and more systematic work is required

  16. Compton scattering

    Energy Technology Data Exchange (ETDEWEB)

    Botto, D.J.; Pratt, R.H.

    1979-05-01

    The current status of Compton scattering, both experimental observations and the theoretical predictions, is examined. Classes of experiments are distinguished and the results obtained are summarized. The validity of the incoherent scattering function approximation and the impulse approximation is discussed. These simple theoretical approaches are compared with predictions of the nonrelativistic dipole formula of Gavrila and with the relativistic results of Whittingham. It is noted that the A/sup -2/ based approximations fail to predict resonances and an infrared divergence, both of which have been observed. It appears that at present the various available theoretical approaches differ significantly in their predictions and that further and more systematic work is required.

  17. Two-scale approach to oscillatory singularly perturbed transport equations

    CERN Document Server

    Frénod, Emmanuel

    2017-01-01

    This book presents the classical results of the two-scale convergence theory and explains – using several figures – why it works. It then shows how to use this theory to homogenize ordinary differential equations with oscillating coefficients as well as oscillatory singularly perturbed ordinary differential equations. In addition, it explores the homogenization of hyperbolic partial differential equations with oscillating coefficients and linear oscillatory singularly perturbed hyperbolic partial differential equations. Further, it introduces readers to the two-scale numerical methods that can be built from the previous approaches to solve oscillatory singularly perturbed transport equations (ODE and hyperbolic PDE) and demonstrates how they can be used efficiently. This book appeals to master’s and PhD students interested in homogenization and numerics, as well as to the Iter community.

  18. Prestack wavefield approximations

    KAUST Repository

    Alkhalifah, Tariq

    2013-01-01

    The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.

  19. Prestack wavefield approximations

    KAUST Repository

    Alkhalifah, Tariq

    2013-09-01

    The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.

  20. The Backscattering Phase Function for a Sphere with a Two-Scale Relief of Rough Surface

    Science.gov (United States)

    Klass, E. V.

    2017-12-01

    The backscattering of light from spherical surfaces characterized by one and two-scale roughness reliefs has been investigated. The analysis is performed using the three-dimensional Monte-Carlo program POKS-RG (geometrical-optics approximation), which makes it possible to take into account the roughness of objects under study by introducing local geometries of different levels. The geometric module of the program is aimed at describing objects by equations of second-order surfaces. One-scale roughness is set as an ensemble of geometric figures (convex or concave halves of ellipsoids or cones). The two-scale roughness is modeled by convex halves of ellipsoids, with surface containing ellipsoidal pores. It is shown that a spherical surface with one-scale convex inhomogeneities has a flatter backscattering phase function than a surface with concave inhomogeneities (pores). For a sphere with two-scale roughness, the dependence of the backscattering intensity is found to be determined mostly by the lower-level inhomogeneities. The influence of roughness on the dependence of the backscattering from different spatial regions of spherical surface is analyzed.

  1. On Two-Scale Modelling of Heat and Mass Transfer

    International Nuclear Information System (INIS)

    Vala, J.; Stastnik, S.

    2008-01-01

    Modelling of macroscopic behaviour of materials, consisting of several layers or components, whose microscopic (at least stochastic) analysis is available, as well as (more general) simulation of non-local phenomena, complicated coupled processes, etc., requires both deeper understanding of physical principles and development of mathematical theories and software algorithms. Starting from the (relatively simple) example of phase transformation in substitutional alloys, this paper sketches the general formulation of a nonlinear system of partial differential equations of evolution for the heat and mass transfer (useful in mechanical and civil engineering, etc.), corresponding to conservation principles of thermodynamics, both at the micro- and at the macroscopic level, and suggests an algorithm for scale-bridging, based on the robust finite element techniques. Some existence and convergence questions, namely those based on the construction of sequences of Rothe and on the mathematical theory of two-scale convergence, are discussed together with references to useful generalizations, required by new technologies.

  2. On Two-Scale Modelling of Heat and Mass Transfer

    Science.gov (United States)

    Vala, J.; Št'astník, S.

    2008-09-01

    Modelling of macroscopic behaviour of materials, consisting of several layers or components, whose microscopic (at least stochastic) analysis is available, as well as (more general) simulation of non-local phenomena, complicated coupled processes, etc., requires both deeper understanding of physical principles and development of mathematical theories and software algorithms. Starting from the (relatively simple) example of phase transformation in substitutional alloys, this paper sketches the general formulation of a nonlinear system of partial differential equations of evolution for the heat and mass transfer (useful in mechanical and civil engineering, etc.), corresponding to conservation principles of thermodynamics, both at the micro- and at the macroscopic level, and suggests an algorithm for scale-bridging, based on the robust finite element techniques. Some existence and convergence questions, namely those based on the construction of sequences of Rothe and on the mathematical theory of two-scale convergence, are discussed together with references to useful generalizations, required by new technologies.

  3. Approximate Likelihood

    CERN Multimedia

    CERN. Geneva

    2015-01-01

    Most physics results at the LHC end in a likelihood ratio test. This includes discovery and exclusion for searches as well as mass, cross-section, and coupling measurements. The use of Machine Learning (multivariate) algorithms in HEP is mainly restricted to searches, which can be reduced to classification between two fixed distributions: signal vs. background. I will show how we can extend the use of ML classifiers to distributions parameterized by physical quantities like masses and couplings as well as nuisance parameters associated to systematic uncertainties. This allows for one to approximate the likelihood ratio while still using a high dimensional feature vector for the data. Both the MEM and ABC approaches mentioned above aim to provide inference on model parameters (like cross-sections, masses, couplings, etc.). ABC is fundamentally tied Bayesian inference and focuses on the “likelihood free” setting where only a simulator is available and one cannot directly compute the likelihood for the dat...

  4. Diophantine approximation

    CERN Document Server

    Schmidt, Wolfgang M

    1980-01-01

    "In 1970, at the U. of Colorado, the author delivered a course of lectures on his famous generalization, then just established, relating to Roth's theorem on rational approxi- mations to algebraic numbers. The present volume is an ex- panded and up-dated version of the original mimeographed notes on the course. As an introduction to the author's own remarkable achievements relating to the Thue-Siegel-Roth theory, the text can hardly be bettered and the tract can already be regarded as a classic in its field."(Bull.LMS) "Schmidt's work on approximations by algebraic numbers belongs to the deepest and most satisfactory parts of number theory. These notes give the best accessible way to learn the subject. ... this book is highly recommended." (Mededelingen van het Wiskundig Genootschap)

  5. Two-scale modelling for hydro-mechanical damage

    International Nuclear Information System (INIS)

    Frey, J.; Chambon, R.; Dascalu, C.

    2010-01-01

    Document available in extended abstract form only. Excavation works for underground storage create a damage zone for the rock nearby and affect its hydraulics properties. This degradation, already observed by laboratory tests, can create a leading path for fluids. The micro fracture phenomenon, which occur at a smaller scale and affect the rock permeability, must be fully understood to minimize the transfer process. Many methods can be used in order to take into account the microstructure of heterogeneous materials. Among them a method has been developed recently. Instead of using a constitutive equation obtained by phenomenological considerations or by some homogenization techniques, the representative elementary volume (R.E.V.) is modelled as a structure and the links between a prescribed kinematics and the corresponding dual forces are deduced numerically. This yields the so called Finite Element square method (FE2). In a numerical point of view, a finite element model is used at the macroscopic level, and for each Gauss point, computations on the microstructure gives the usual results of a constitutive law. This numerical approach is now classical in order to properly model some materials such as composites and the efficiency of such numerical homogenization process has been shown, and allows numerical modelling of deformation processes associated with various micro-structural changes. The aim of this work is to describe trough such a method, damage of the rock with a two scale hydro-mechanical model. The rock damage at the macroscopic scale is directly link with an analysis on the microstructure. At the macroscopic scale a two phase's problem is studied. A solid skeleton is filled up by a filtrating fluid. It is necessary to enforce two balance equation and two mass conservation equations. A classical way to deal with such a problem is to work with the balance equation of the whole mixture, and the mass fluid conservation written in a weak form, the mass

  6. Two-scale large deviations for chemical reaction kinetics through second quantization path integral

    International Nuclear Information System (INIS)

    Li, Tiejun; Lin, Feng

    2016-01-01

    Motivated by the study of rare events for a typical genetic switching model in systems biology, in this paper we aim to establish the general two-scale large deviations for chemical reaction systems. We build a formal approach to explicitly obtain the large deviation rate functionals for the considered two-scale processes based upon the second quantization path integral technique. We get three important types of large deviation results when the underlying two timescales are in three different regimes. This is realized by singular perturbation analysis to the rate functionals obtained by the path integral. We find that the three regimes possess the same deterministic mean-field limit but completely different chemical Langevin approximations. The obtained results are natural extensions of the classical large volume limit for chemical reactions. We also discuss its implication on the single-molecule Michaelis–Menten kinetics. Our framework and results can be applied to understand general multi-scale systems including diffusion processes. (paper)

  7. A manifestly reciprocal theory of scattering in the presence of elastic media

    International Nuclear Information System (INIS)

    Wurmser, D.

    1996-01-01

    The role of elastic waves in the scattering problem is examined in the context of modern field theory. This effort builds upon a previously published, and since successfully applied formalism for solving the acoustic and electromagnetic scattering problems. It specifically addresses the scattering of acoustic waves from a fluid-solid interface, as well as the scattering of elastodynamic waves from surfaces satisfying the zero-displacement, stress-free, and solid endash solid boundary conditions. Expressions for the change in the scattering amplitude due to a perturbation in the scattering surface are derived directly from the requirement of time reversal symmetry (also known as reciprocity). These results constitute formal statements of the composite (or two-scale) model. In a typical application, the perturbation usually corresponds to Bragg scattering and is treated statistically, while the reference surface provides tilt, shadowing, and multiple scattering, and is usually treated deterministically. Used in this way, the new formalism effectively allows existing numerical and operator expansion methods to be used to calculate the scattering from rougher and/or higher dimensional surfaces than would otherwise be possible. An alternate application of the formalism is illustrated using the fluid-solid boundary as an example. A new manifestly reciprocal expression for the scattering amplitude is presented, as are the small slope and open-quote open-quote local close-quote close-quote two-scale approximations for this problem. (By local, it is meant that only local phenomena such as the tilt of the reference surface are automatically included. However, since the result is manifestly reciprocal, it is fairly straightforward to incorporate a non-local effect such as shadowing.) During the course of the discussion, the classical scattering problem is reexamined from an entirely new perspective

  8. Electron-atom scattering

    International Nuclear Information System (INIS)

    McCarthy, I.E.

    1991-07-01

    The coupled-channels-optical method has been implemented using two different approximations to the optical potential. The half-on-shell optical potential involves drastic approximations for numerical feasibility but still gives a good semiquantitative description of the effect of uncoupled channels on electron scattering from hydrogen, helium and sodium. The distorted-wave optical potential makes no approximations other than the weak coupling approximation for uncoupled channels. In applications to hydrogen and sodium it shows promise of describing scattering phenomena excellently at all energies. 27 refs., 5 figs

  9. Diophantine approximation and badly approximable sets

    DEFF Research Database (Denmark)

    Kristensen, S.; Thorn, R.; Velani, S.

    2006-01-01

    . The classical set Bad of `badly approximable' numbers in the theory of Diophantine approximation falls within our framework as do the sets Bad(i,j) of simultaneously badly approximable numbers. Under various natural conditions we prove that the badly approximable subsets of Omega have full Hausdorff dimension...

  10. Characterization of two-scale gradient Young measures and application to homogenization

    OpenAIRE

    Babadjian, Jean-Francois; Baia, Margarida; Santos, Pedro M.

    2006-01-01

    This work is devoted to the study of two-scale gradient Young measures naturally arising in nonlinear elasticity homogenization problems. Precisely, a characterization of this class of measures is derived and an integral representation formula for homogenized energies, whose integrands satisfy very weak regularity assumptions, is obtained in terms of two-scale gradient Young measures.

  11. On an extension of the method of two-scale convergence and its applications

    International Nuclear Information System (INIS)

    Zhikov, V V

    2000-01-01

    The concept of two-scale convergence associated with a fixed periodic Borel measure μ is introduced. In the case when dμ=dx is Lebesgue measure on the torus convergence in the sense of Nguetseng-Allaire is obtained. The main properties of two-scale convergence are revealed by the simultaneous consideration of a sequence of functions and a sequence of their gradients. An application of two-scale convergence to the homogenization of some problems in the theory of porous media (the double-porosity model) is presented. A mathematical notion of 'softly or weakly coupled parallel flows' is worked out. A homogenized operator is constructed and the convergence result itself is interpreted as a 'strong two-scale resolvent convergence'. Problems concerning the behaviour of the spectrum under homogenization are touched upon in this connection

  12. Uniform analytic approximation of Wigner rotation matrices

    Science.gov (United States)

    Hoffmann, Scott E.

    2018-02-01

    We derive the leading asymptotic approximation, for low angle θ, of the Wigner rotation matrix elements, dm1m2 j(θ ) , uniform in j, m1, and m2. The result is in terms of a Bessel function of integer order. We numerically investigate the error for a variety of cases and find that the approximation can be useful over a significant range of angles. This approximation has application in the partial wave analysis of wavepacket scattering.

  13. Analysis of corrections to the eikonal approximation

    Science.gov (United States)

    Hebborn, C.; Capel, P.

    2017-11-01

    Various corrections to the eikonal approximations are studied for two- and three-body nuclear collisions with the goal to extend the range of validity of this approximation to beam energies of 10 MeV/nucleon. Wallace's correction does not improve much the elastic-scattering cross sections obtained at the usual eikonal approximation. On the contrary, a semiclassical approximation that substitutes the impact parameter by a complex distance of closest approach computed with the projectile-target optical potential efficiently corrects the eikonal approximation. This opens the possibility to analyze data measured down to 10 MeV/nucleon within eikonal-like reaction models.

  14. Cross plane scattering correction

    International Nuclear Information System (INIS)

    Shao, L.; Karp, J.S.

    1990-01-01

    Most previous scattering correction techniques for PET are based on assumptions made for a single transaxial plane and are independent of axial variations. These techniques will incorrectly estimate the scattering fraction for volumetric PET imaging systems since they do not take the cross-plane scattering into account. In this paper, the authors propose a new point source scattering deconvolution method (2-D). The cross-plane scattering is incorporated into the algorithm by modeling a scattering point source function. In the model, the scattering dependence both on axial and transaxial directions is reflected in the exponential fitting parameters and these parameters are directly estimated from a limited number of measured point response functions. The authors' results comparing the standard in-plane point source deconvolution to the authors' cross-plane source deconvolution show that for a small source, the former technique overestimates the scatter fraction in the plane of the source and underestimate the scatter fraction in adjacent planes. In addition, the authors also propose a simple approximation technique for deconvolution

  15. Resistivity of strong-scattering alloys: Absence of localization and success of coherent-potential approximation confirmed by exact supercell calculations in V/sub 1-//sub x/Al/sub x/

    International Nuclear Information System (INIS)

    Brown, R.H.; Allen, P.B.; Nicholson, D.M.; Butler, W.H.

    1989-01-01

    A supercell procedure for exact evaluation of the one-electron Kubo-Greenwood formula is applied to the resistivity rho of V/sub 1-//sub x/Al/sub x/ alloys and compared with a Korringa-Kohn-Rostoker coherent-potential approximation calculation. The results of these calculations agree well, consistent with the observation of delocalized eigenstates, in spite of the very high resistivity, rho≅200 μΩ cm

  16. Thermal-neutron multiple scattering: critical double scattering

    International Nuclear Information System (INIS)

    Holm, W.A.

    1976-01-01

    A quantum mechanical formulation for multiple scattering of thermal-neutrons from macroscopic targets is presented and applied to single and double scattering. Critical nuclear scattering from liquids and critical magnetic scattering from ferromagnets are treated in detail in the quasielastic approximation for target systems slightly above their critical points. Numerical estimates are made of the double scattering contribution to the critical magnetic cross section using relevant parameters from actual experiments performed on various ferromagnets. The effect is to alter the usual Lorentzian line shape dependence on neutron wave vector transfer. Comparison with corresponding deviations in line shape resulting from the use of Fisher's modified form of the Ornstein-Zernike spin correlations within the framework of single scattering theory leads to values for the critical exponent eta of the modified correlations which reproduce the effect of double scattering. In addition, it is shown that by restricting the range of applicability of the multiple scattering theory from the outset to critical scattering, Glauber's high energy approximation can be used to provide a much simpler and more powerful description of multiple scattering effects. When sufficiently close to the critical point, it provides a closed form expression for the differential cross section which includes all orders of scattering and has the same form as the single scattering cross section with a modified exponent for the wave vector transfer

  17. Deep inelastic neutron scattering

    International Nuclear Information System (INIS)

    Mayers, J.

    1989-03-01

    The report is based on an invited talk given at a conference on ''Neutron Scattering at ISIS: Recent Highlights in Condensed Matter Research'', which was held in Rome, 1988, and is intended as an introduction to the techniques of Deep Inelastic Neutron Scattering. The subject is discussed under the following topic headings:- the impulse approximation I.A., scaling behaviour, kinematical consequences of energy and momentum conservation, examples of measurements, derivation of the I.A., the I.A. in a harmonic system, and validity of the I.A. in neutron scattering. (U.K.)

  18. Exploring the Validity Range of the Polarimetric Two-Scale Two-Component Model for Soil Moisture Retrieval by Using AGRISAR Data

    Science.gov (United States)

    Di Martino, Gerardo; Iodice, Antonio; Natale, Antonio; Riccio, Daniele; Ruello, Giuseppe

    2015-04-01

    The recently proposed polarimetric two-scale two- component model (PTSTCM) in principle allows us obtaining a reasonable estimation of the soil moisture even in moderately vegetated areas, where the volumetric scattering contribution is non-negligible, provided that the surface component is dominant and the double-bounce component is negligible. Here we test the PTSTCM validity range by applying it to polarimetric SAR data acquired on areas for which, at the same times of SAR acquisitions, ground measurements of soil moisture were performed. In particular, we employ the AGRISAR'06 database, which includes data from several fields covering a period that spans all the phases of vegetation growth.

  19. Diffuse scattering in Ih ice

    International Nuclear Information System (INIS)

    Wehinger, Björn; Krisch, Michael; Bosak, Alexeï; Chernyshov, Dmitry; Bulat, Sergey; Ezhov, Victor

    2014-01-01

    Single crystals of ice Ih, extracted from the subglacial Lake Vostok accretion ice layer (3621 m depth) were investigated by means of diffuse x-ray scattering and inelastic x-ray scattering. The diffuse scattering was identified as mainly inelastic and rationalized in the frame of ab initio calculations for the ordered ice XI approximant. Together with Monte-Carlo modelling, our data allowed reconsidering previously available neutron diffuse scattering data of heavy ice as the sum of thermal diffuse scattering and static disorder contribution. (paper)

  20. Assessing Self-Efficacy in Infant Care: A Comparison of Two Scales

    Directory of Open Access Journals (Sweden)

    Tassanee Prasopkittikun, RN, PhD

    2008-09-01

    Conclusion: The findings suggest that correlations between SICS and two different response formats do not reach the criteria for use as alternatives to each other. However, further research is needed, with particular emphasis on the investigation of construct validity and comparisons between the two scales.

  1. Quasi-potential and Two-Scale Large Deviation Theory for Gillespie Dynamics

    KAUST Repository

    Li, Tiejun; Li, Fangting; Li, Xianggang; Lu, Cheng

    2016-01-01

    theory for Gillespie-type jump dynamics. In the application to a typical genetic switching model, the two-scale large deviation theory is developed to take into account the fast switching of DNA states. The comparison with other proposals are also

  2. Modulated Pade approximant

    International Nuclear Information System (INIS)

    Ginsburg, C.A.

    1980-01-01

    In many problems, a desired property A of a function f(x) is determined by the behaviour of f(x) approximately equal to g(x,A) as x→xsup(*). In this letter, a method for resuming the power series in x of f(x) and approximating A (modulated Pade approximant) is presented. This new approximant is an extension of a resumation method for f(x) in terms of rational functions. (author)

  3. Pade approximant calculations for neutron escape probability

    International Nuclear Information System (INIS)

    El Wakil, S.A.; Saad, E.A.; Hendi, A.A.

    1984-07-01

    The neutron escape probability from a non-multiplying slab containing internal source is defined in terms of a functional relation for the scattering function for the diffuse reflection problem. The Pade approximant technique is used to get numerical results which compare with exact results. (author)

  4. Sparse approximation with bases

    CERN Document Server

    2015-01-01

    This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications.  The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and do...

  5. Correlation in atomic scattering

    International Nuclear Information System (INIS)

    McGuire, J.H.

    1987-01-01

    Correlation due to the Coulomb interactions between electrons in many-electron targets colliding with charged particles is formulated, and various approximate probability amplitudes are evaluated. In the limit that the electron-electron, 1/r/sub i//sub j/, correlation interactions are ignored or approximated by central potentials, the independent-electron approximation is obtained. Two types of correlations, or corrections to the independent-electron approximation due to 1/r/sub i//sub j/ terms, are identified: namely, static and scattering correlation. Static correlation is that contained in the asymptotic, e.g., bound-state, wave functions. Scattering correlation, arising from correlation in the scattering operator, is new and is considered in some detail. Expressions for a scattering correlation amplitude, static correlation or rearrangement amplitude, and independent-electron or direct amplitude are derived at high collision velocity and compared. At high velocities the direct and rearrangement amplitudes dominate. At very high velocities, ν, the rearrangement amplitude falls off less rapidly with ν than the direct amplitude which, however, is dominant as electron-electron correlation tends to zero. Comparisons with experimental observations are discussed

  6. Polarization phenomena in inelastic scattering

    International Nuclear Information System (INIS)

    Verhaar, B.J.

    1974-01-01

    An attempt is made to clarify the principles of inelastic scattering using the distorted wave Born approximation, concentrating on inelastic proton scattering. The principle aspects and merits of the microscopic description and the necessity of including the N-N spin orbit force are discussed. (7 figures) (U.S.)

  7. Gravitational Bhabha scattering

    International Nuclear Information System (INIS)

    Santos, A F; Khanna, Faqir C

    2017-01-01

    Gravitoelectromagnetism (GEM) as a theory for gravity has been developed similar to the electromagnetic field theory. A weak field approximation of Einstein theory of relativity is similar to GEM. This theory has been quantized. Traditional Bhabha scattering, electron–positron scattering, is based on quantized electrodynamics theory. Usually the amplitude is written in terms of one photon exchange process. With the development of quantized GEM theory, the scattering amplitude will have an additional component based on an exchange of one graviton at the lowest order of perturbation theory. An analysis will provide the relative importance of the two amplitudes for Bhabha scattering. This will allow an analysis of the relative importance of the two amplitudes as the energy of the exchanged particles increases. (paper)

  8. Approximate symmetries of Hamiltonians

    Science.gov (United States)

    Chubb, Christopher T.; Flammia, Steven T.

    2017-08-01

    We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.

  9. High frequency and pulse scattering physical acoustics

    CERN Document Server

    Pierce, Allan D

    1992-01-01

    High Frequency and Pulse Scattering investigates high frequency and pulse scattering, with emphasis on the phenomenon of echoes from objects. Geometrical and catastrophe optics methods in scattering are discussed, along with the scattering of sound pulses and the ringing of target resonances. Caustics and associated diffraction catastrophes are also examined.Comprised of two chapters, this volume begins with a detailed account of geometrically based approximation methods in scattering theory, focusing on waves transmitted through fluid and elastic scatterers and glory scattering; surface ray r

  10. Mean Field Limits for Interacting Diffusions in a Two-Scale Potential

    Science.gov (United States)

    Gomes, S. N.; Pavliotis, G. A.

    2018-06-01

    In this paper, we study the combined mean field and homogenization limits for a system of weakly interacting diffusions moving in a two-scale, locally periodic confining potential, of the form considered in Duncan et al. (Brownian motion in an N-scale periodic potential, arXiv:1605.05854, 2016b). We show that, although the mean field and homogenization limits commute for finite times, they do not, in general, commute in the long time limit. In particular, the bifurcation diagrams for the stationary states can be different depending on the order with which we take the two limits. Furthermore, we construct the bifurcation diagram for the stationary McKean-Vlasov equation in a two-scale potential, before passing to the homogenization limit, and we analyze the effect of the multiple local minima in the confining potential on the number and the stability of stationary solutions.

  11. Second-order two-scale method for bending behaviors of composite plate with periodic configuration

    International Nuclear Information System (INIS)

    Zhu Guoqing; Cui Junzhi

    2010-01-01

    In this paper, the second-order two-scale analysis method for bending behaviors of the plate made from composites with 3-D periodic configuration is presented by means of construction way. It can capture the microscopic 3-D mechanics behaviors caused from 3-D micro-structures. First, directly starting from the 3-D elastic plate model of composite materials with 3-D periodic configuration, three cell models are defined, and correspondingly the three classes of cell functions only defined on 3 normalized cells are constructed. And then, the effective homogenization parameters of composites are calculated from those local functions, it leads to a 2-D homogenized laminar plate problem. Next, to solve it the homogenization solution is obtained. Finally, the second-order two-scale solution is constructed from the micro-cell functions and the homogenization solution.

  12. Classical trajectory in non-relativistic scattering

    International Nuclear Information System (INIS)

    Williams, A.C.

    1978-01-01

    With the statistical interpretation of quantum mechanics as a guide, the classical trajectory is incorporated into quantum scattering theory. The Feynman path integral formalism is used as a starting point, and classical transformation theory is applied to the phase of the wave function so derived. This approach is then used to derive an expression for the scattering amplitude for potential scattering. It is found that the amplitude can be expressed in an impact parameter representation similar to the Glauber formalism. Connections are then made to the Glauber approximation and to semiclassical approximations derived from the Feynman path integral formalism. In extending this analysis to projectile-nucleus scattering, an approximation scheme is given with the first term being the same as in Glauber's multiple scattering theory. Higher-order approximations, thus, are found to give corrections to the fixed scatterer form of the impulse approximation inherent in the Glauber theory

  13. Approximating distributions from moments

    Science.gov (United States)

    Pawula, R. F.

    1987-11-01

    A method based upon Pearson-type approximations from statistics is developed for approximating a symmetric probability density function from its moments. The extended Fokker-Planck equation for non-Markov processes is shown to be the underlying foundation for the approximations. The approximation is shown to be exact for the beta probability density function. The applicability of the general method is illustrated by numerous pithy examples from linear and nonlinear filtering of both Markov and non-Markov dichotomous noise. New approximations are given for the probability density function in two cases in which exact solutions are unavailable, those of (i) the filter-limiter-filter problem and (ii) second-order Butterworth filtering of the random telegraph signal. The approximate results are compared with previously published Monte Carlo simulations in these two cases.

  14. CONTRIBUTIONS TO RATIONAL APPROXIMATION,

    Science.gov (United States)

    Some of the key results of linear Chebyshev approximation theory are extended to generalized rational functions. Prominent among these is Haar’s...linear theorem which yields necessary and sufficient conditions for uniqueness. Some new results in the classic field of rational function Chebyshev...Furthermore a Weierstrass type theorem is proven for rational Chebyshev approximation. A characterization theorem for rational trigonometric Chebyshev approximation in terms of sign alternation is developed. (Author)

  15. Approximation techniques for engineers

    CERN Document Server

    Komzsik, Louis

    2006-01-01

    Presenting numerous examples, algorithms, and industrial applications, Approximation Techniques for Engineers is your complete guide to the major techniques used in modern engineering practice. Whether you need approximations for discrete data of continuous functions, or you''re looking for approximate solutions to engineering problems, everything you need is nestled between the covers of this book. Now you can benefit from Louis Komzsik''s years of industrial experience to gain a working knowledge of a vast array of approximation techniques through this complete and self-contained resource.

  16. Usefulness of bound-state approximations in reaction theory

    International Nuclear Information System (INIS)

    Adhikari, S.K.

    1981-01-01

    A bound-state approximation when applied to certain operators, such as the many-body resolvent operator for a two-body fragmentation channel, in many-body scattering equations, reduces such equations to equivalent two-body scattering equations which are supposed to provide a good description of the underlying physical process. In this paper we test several variants of bound-state approximations in the soluble three-boson Amado model and find that such approximations lead to weak and unacceptable kernels for the equivalent two-body scattering equations and hence to a poor description of the underlying many-body process

  17. The binary collision approximation: Background and introduction

    International Nuclear Information System (INIS)

    Robinson, M.T.

    1992-08-01

    The binary collision approximation (BCA) has long been used in computer simulations of the interactions of energetic atoms with solid targets, as well as being the basis of most analytical theory in this area. While mainly a high-energy approximation, the BCA retains qualitative significance at low energies and, with proper formulation, gives useful quantitative information as well. Moreover, computer simulations based on the BCA can achieve good statistics in many situations where those based on full classical dynamical models require the most advanced computer hardware or are even impracticable. The foundations of the BCA in classical scattering are reviewed, including methods of evaluating the scattering integrals, interaction potentials, and electron excitation effects. The explicit evaluation of time at significant points on particle trajectories is discussed, as are scheduling algorithms for ordering the collisions in a developing cascade. An approximate treatment of nearly simultaneous collisions is outlined and the searching algorithms used in MARLOWE are presented

  18. On transparent potentials: a Born approximation study

    International Nuclear Information System (INIS)

    Coudray, C.

    1980-01-01

    In the frame of the scattering inverse problem at fixed energy, a class of potentials transparent in Born approximation is obtained. All these potentials are spherically symmetric and are oscillating functions of the reduced radial variable. Amongst them, the Born approximation of the transparent potential of the Newton-Sabatier method is found. In the same class, quasi-transparent potentials are exhibited. Very general features of potentials transparent in Born approximation are then stated. And bounds are given for the exact scattering amplitudes corresponding to most of the potentials previously exhibited. These bounds, obtained at fixed energy, and for large values of the angular momentum, are found to be independent on the energy

  19. Expectation Consistent Approximate Inference

    DEFF Research Database (Denmark)

    Opper, Manfred; Winther, Ole

    2005-01-01

    We propose a novel framework for approximations to intractable probabilistic models which is based on a free energy formulation. The approximation can be understood from replacing an average over the original intractable distribution with a tractable one. It requires two tractable probability dis...

  20. Ordered cones and approximation

    CERN Document Server

    Keimel, Klaus

    1992-01-01

    This book presents a unified approach to Korovkin-type approximation theorems. It includes classical material on the approximation of real-valuedfunctions as well as recent and new results on set-valued functions and stochastic processes, and on weighted approximation. The results are notonly of qualitative nature, but include quantitative bounds on the order of approximation. The book is addressed to researchers in functional analysis and approximation theory as well as to those that want to applythese methods in other fields. It is largely self- contained, but the readershould have a solid background in abstract functional analysis. The unified approach is based on a new notion of locally convex ordered cones that are not embeddable in vector spaces but allow Hahn-Banach type separation and extension theorems. This concept seems to be of independent interest.

  1. Scaling laws governing the multiple scattering of diatomic molecules under Coulomb explosion

    International Nuclear Information System (INIS)

    Sigmund, P.

    1992-01-01

    The trajectories of fast molecules during and after penetration through foils are governed by Coulomb explosion and distorted by multiple scattering and other penetration phenomena. A scattering event may cause the energy available for Coulomb explosion to increase or decrease, and angular momentum may be transferred to the molecule. Because of continuing Coulomb explosion inside and outside the target foil, the transmission pattern recorded at a detector far away from the target is not just a linear superposition of Coulomb explosion and multiple scattering. The velocity distribution of an initially monochromatic and well-collimated, but randomly oriented, beam of molecular ions is governed by a generalization of the standard Bothe-Landau integral that governs the multiple scattering of atomic ions. Emphasis has been laid on the distribution in relative velocity and, in particular, relative energy. The statistical distributions governing the longitudinal motion (i.e., the relative motion along the molecular axis) and the rotational motion can be scaled into standard multiple-scattering distributions of atomic ions. The two scaling laws are very different. For thin target foils, the significance of rotational energy transfer is enhanced by an order of magnitude compared to switched-off Coulomb explosion. A distribution for the total relative energy (i.e., longitudinal plus rotational motion) has also been found, but its scaling behavior is more complex. Explicit examples given for all three distributions refer to power-law scattering. As a first approximation, scattering events undergone by the two atoms in the molecule were assumed uncorrelated. A separate section has been devoted to an estimate of the effect of impact-parameter correlation on the multiple scattering of penetrating molecules

  2. Nonresonant approximations to the optical potential

    International Nuclear Information System (INIS)

    Kowalski, K.L.

    1982-01-01

    A new class of approximations to the optical potential, which includes those of the multiple-scattering variety, is investigated. These approximations are constructed so that the optical potential maintains the correct unitarity properties along with a proper treatment of nucleon identity. The special case of nucleon-nucleus scattering with complete inclusion of Pauli effects is studied in detail. The treatment is such that the optical potential receives contributions only from subsystems embedded in their own physically correct antisymmetrized subspaces. It is found that a systematic development of even the lowest-order approximations requires the use of the off-shell extension due to Alt, Grassberger, and Sandhas along with a consistent set of dynamical equations for the optical potential. In nucleon-nucleus scattering a lowest-order optical potential is obtained as part of a systematic, exact, inclusive connectivity expansion which is expected to be useful at moderately high energies. This lowest-order potential consists of an energy-shifted (trho)-type term with three-body kinematics plus a heavy-particle exchange or pickup term. The natural appearance of the exchange term additivity in the optical potential clarifies the role of the elastic distortion in connection with the treatment of these processes. The relationship of the relevant aspects of the present analysis of the optical potential to conventional multiple scattering methods is discussed

  3. Approximate and renormgroup symmetries

    Energy Technology Data Exchange (ETDEWEB)

    Ibragimov, Nail H. [Blekinge Institute of Technology, Karlskrona (Sweden). Dept. of Mathematics Science; Kovalev, Vladimir F. [Russian Academy of Sciences, Moscow (Russian Federation). Inst. of Mathematical Modeling

    2009-07-01

    ''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)

  4. Approximate and renormgroup symmetries

    International Nuclear Information System (INIS)

    Ibragimov, Nail H.; Kovalev, Vladimir F.

    2009-01-01

    ''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)

  5. Approximations of Fuzzy Systems

    Directory of Open Access Journals (Sweden)

    Vinai K. Singh

    2013-03-01

    Full Text Available A fuzzy system can uniformly approximate any real continuous function on a compact domain to any degree of accuracy. Such results can be viewed as an existence of optimal fuzzy systems. Li-Xin Wang discussed a similar problem using Gaussian membership function and Stone-Weierstrass Theorem. He established that fuzzy systems, with product inference, centroid defuzzification and Gaussian functions are capable of approximating any real continuous function on a compact set to arbitrary accuracy. In this paper we study a similar approximation problem by using exponential membership functions

  6. General Rytov approximation.

    Science.gov (United States)

    Potvin, Guy

    2015-10-01

    We examine how the Rytov approximation describing log-amplitude and phase fluctuations of a wave propagating through weak uniform turbulence can be generalized to the case of turbulence with a large-scale nonuniform component. We show how the large-scale refractive index field creates Fermat rays using the path integral formulation for paraxial propagation. We then show how the second-order derivatives of the Fermat ray action affect the Rytov approximation, and we discuss how a numerical algorithm would model the general Rytov approximation.

  7. Quasi-potential and Two-Scale Large Deviation Theory for Gillespie Dynamics

    KAUST Repository

    Li, Tiejun

    2016-01-07

    The construction of energy landscape for bio-dynamics is attracting more and more attention recent years. In this talk, I will introduce the strategy to construct the landscape from the connection to rare events, which relies on the large deviation theory for Gillespie-type jump dynamics. In the application to a typical genetic switching model, the two-scale large deviation theory is developed to take into account the fast switching of DNA states. The comparison with other proposals are also discussed. We demonstrate different diffusive limits arise when considering different regimes for genetic translation and switching processes.

  8. The degenerate-internal-states approximation for cold collisions

    NARCIS (Netherlands)

    Maan, A.C.; Tiesinga, E.; Stoof, H.T.C.; Verhaar, B.J.

    1990-01-01

    The Degenerate-Internal-States approximation as well as its first-order correction are shown to provide a convenient method for calculating elastic and inelastic collision amplitudes for low temperature atomic scattering.

  9. Geometric approximation algorithms

    CERN Document Server

    Har-Peled, Sariel

    2011-01-01

    Exact algorithms for dealing with geometric objects are complicated, hard to implement in practice, and slow. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms tend to be simple, fast, and more robust than their exact counterparts. This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are also surveyed. Other topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings. The topics covered are relatively independent and are supplemented by exercises. Close to 200 color figures are included in the text to illustrate proofs and ideas.

  10. INTOR cost approximation

    International Nuclear Information System (INIS)

    Knobloch, A.F.

    1980-01-01

    A simplified cost approximation for INTOR parameter sets in a narrow parameter range is shown. Plausible constraints permit the evaluation of the consequences of parameter variations on overall cost. (orig.) [de

  11. Impulse approximation in solid helium

    International Nuclear Information System (INIS)

    Glyde, H.R.

    1985-01-01

    The incoherent dynamic form factor S/sub i/(Q, ω) is evaluated in solid helium for comparison with the impulse approximation (IA). The purpose is to determine the Q values for which the IA is valid for systems such a helium where the atoms interact via a potential having a steeply repulsive but not infinite hard core. For 3 He, S/sub i/(Q, ω) is evaluated from first principles, beginning with the pair potential. The density of states g(ω) is evaluated using the self-consistent phonon theory and S/sub i/(Q,ω) is expressed in terms of g(ω). For solid 4 He resonable models of g(ω) using observed input parameters are used to evaluate S/sub i/(Q,ω). In both cases S/sub i/(Q, ω) is found to approach the impulse approximation S/sub IA/(Q, ω) closely for wave vector transfers Q> or approx. =20 A -1 . The difference between S/sub i/ and S/sub IA/, which is due to final state interactions of the scattering atom with the remainder of the atoms in the solid, is also predominantly antisymmetric in (ω-ω/sub R/), where ω/sub R/ is the recoil frequency. This suggests that the symmetrization procedure proposed by Sears to eliminate final state contributions should work well in solid helium

  12. Quasiresonant scattering

    International Nuclear Information System (INIS)

    Hategan, Cornel; Comisel, Horia; Ionescu, Remus A.

    2004-01-01

    The quasiresonant scattering consists from a single channel resonance coupled by direct interaction transitions to some competing reaction channels. A description of quasiresonant Scattering, in terms of generalized reduced K-, R- and S- Matrix, is developed in this work. The quasiresonance's decay width is, due to channels coupling, smaller than the width of the ancestral single channel resonance (resonance's direct compression). (author)

  13. Thomson Scattering

    NARCIS (Netherlands)

    Donne, A. J. H.

    1994-01-01

    Thomson scattering is a very powerful diagnostic which is applied at nearly every magnetic confinement device. Depending on the experimental conditions different plasma parameters can be diagnosed. When the wave vector is much larger than the plasma Debye length, the total scattered power is

  14. Approximation and Computation

    CERN Document Server

    Gautschi, Walter; Rassias, Themistocles M

    2011-01-01

    Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanovia, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational alg

  15. Efficiency of the Needle Probe Test for Evaluation of Thermal Conductivity of Composite Materials: Two-Scale Analysis

    Directory of Open Access Journals (Sweden)

    Łydżba Dariusz

    2014-03-01

    Full Text Available The needle probe test, as a thermal conductivity measurement method, has become very popular in recent years. In the present study, the efficiency of this methodology, for the case of composite materials, is investigated based on the numerical simulations. The material under study is a two-phase composite with periodic microstructure of “matrix-inclusion” type. Two-scale analysis, incorporating micromechanics approach, is performed. First, the effective thermal conductivity of the composite considered is found by the solution of the appropriate boundary value problem stated for the single unit cell. Next, numerical simulations of the needle probe test are carried out. In this case, two different locations of the measuring sensor are considered. It is shown that the “equivalent” conductivity, derived from the probe test, is strongly affected by the location of the sensor. Moreover, comparing the results obtained for different scales, one can notice that the “equivalent” conductivity cannot be interpreted as the effective one for the composites considered. Hence, a crude approximation of the effective property is proposed based on the volume fractions of constituents and the equivalent conductivities derived from different sensor locations.

  16. Approximate kernel competitive learning.

    Science.gov (United States)

    Wu, Jian-Sheng; Zheng, Wei-Shi; Lai, Jian-Huang

    2015-03-01

    Kernel competitive learning has been successfully used to achieve robust clustering. However, kernel competitive learning (KCL) is not scalable for large scale data processing, because (1) it has to calculate and store the full kernel matrix that is too large to be calculated and kept in the memory and (2) it cannot be computed in parallel. In this paper we develop a framework of approximate kernel competitive learning for processing large scale dataset. The proposed framework consists of two parts. First, it derives an approximate kernel competitive learning (AKCL), which learns kernel competitive learning in a subspace via sampling. We provide solid theoretical analysis on why the proposed approximation modelling would work for kernel competitive learning, and furthermore, we show that the computational complexity of AKCL is largely reduced. Second, we propose a pseudo-parallelled approximate kernel competitive learning (PAKCL) based on a set-based kernel competitive learning strategy, which overcomes the obstacle of using parallel programming in kernel competitive learning and significantly accelerates the approximate kernel competitive learning for large scale clustering. The empirical evaluation on publicly available datasets shows that the proposed AKCL and PAKCL can perform comparably as KCL, with a large reduction on computational cost. Also, the proposed methods achieve more effective clustering performance in terms of clustering precision against related approximate clustering approaches. Copyright © 2014 Elsevier Ltd. All rights reserved.

  17. The second Born approximation of electron–argon elastic scattering ...

    Indian Academy of Sciences (India)

    [7] D Nehari, J Holmes, K M Dunseath and M Terao-Dunseath, J. Phys. B43, 025203 (2010). [8] B A Harak, L Ladino and N L S Martin, Bull. Am. Phys. Soc. 55, 5 (2010). [9] M Ghalim and F Mastour, J. Phys. B32, 3783 (1999). [10] S T Zhang, J Chen and S M Li, Can. J. Phys. 80, 969 (2002). Pramana – J. Phys., Vol. 78, No.

  18. Scattered data approximation by regular grid weighted smoothing

    Indian Academy of Sciences (India)

    Bibin Francis

    2018-02-07

    Feb 7, 2018 ... proposed method earlier, is one of the recent advancements in developing ... Department of Science and Technology, Government of. India, under Grant .... Springer Science & Business Media, New York, USA. [35] Harten A ...

  19. Two scale damage model and related numerical issues for thermo-mechanical high cycle fatigue

    International Nuclear Information System (INIS)

    Desmorat, R.; Kane, A.; Seyedi, M.; Sermage, J.P.

    2007-01-01

    On the idea that fatigue damage is localized at the microscopic scale, a scale smaller than the mesoscopic one of the Representative Volume Element (RVE), a three-dimensional two scale damage model has been proposed for High Cycle Fatigue applications. It is extended here to aniso-thermal cases and then to thermo-mechanical fatigue. The modeling consists in the micro-mechanics analysis of a weak micro-inclusion subjected to plasticity and damage embedded in an elastic meso-element (the RVE of continuum mechanics). The consideration of plasticity coupled with damage equations at micro-scale, altogether with Eshelby-Kroner localization law, allows to compute the value of microscopic damage up to failure for any kind of loading, 1D or 3D, cyclic or random, isothermal or aniso-thermal, mechanical, thermal or thermo-mechanical. A robust numerical scheme is proposed in order to make the computations fast. A post-processor for damage and fatigue (DAMAGE-2005) has been developed. It applies to complex thermo-mechanical loadings. Examples of the representation by the two scale damage model of physical phenomena related to High Cycle Fatigue are given such as the mean stress effect, the non-linear accumulation of damage. Examples of thermal and thermo-mechanical fatigue as well as complex applications on real size testing structure subjected to thermo-mechanical fatigue are detailed. (authors)

  20. [The development and validation of two scales on retribution practices: PRG-13 and PRE-21].

    Science.gov (United States)

    Boada-Grau, Joan; Costa-Solé, Jordi; Gil-Ripoll, Carme; Vigil-Colet, Andreu

    2012-01-01

    The present study outlines the development process of two scales that measure general and specific retribution practices in organisations. Historically, retribution has been the subject of research of other social sciences such as Sociology and Business Administration. In Psychology, and more specifically in Work and Organisational Psychology, there are hardly any studies or inventories designed to evaluate retribution practices. In order to accomplish the objectives, a sample of 237 employees was selected, 42.6% of whom were women and 57.4% were men. We performed and exploratory factorial analysis using principal axis factoring as extraction method and an oblique rotation (oblimin) to analyse the two scales. The former is made up of four factors and the latter is a two-factor scale. The reliability coefficients of the six subscales we obtained ranged between .72 and .89. External validity was analysed using the correlations obtained between the two inventories and the Balanced Scorecard. The two tools were found to be two potentially useful scales to evaluate retribution practices.

  1. Two-scale characterization of deformation-induced anisotropy of polycrystalline metals

    International Nuclear Information System (INIS)

    Watanabe, Ikumu; Terada, Kenjiro

    2004-01-01

    The anisotropic macro-scale mechanical behavior of polycrystalline metals is characterized by incorporating the micro-scale constitutive model of single crystal plasticity into the two-scale modeling based on the mathematical homogenization theory. The two-scale simulations are conducted to analyze the macro-scale anisotropy induced by micro-scale plastic deformation of the polycrystalline aggregate. In the simulations, the micro-scale representative volume element (RVE) of a polycrystalline aggregate is uniformly loaded in one direction, unloaded to macroscopically zero stress in a certain stage of deformation and then re-loaded in the different directions. The last re-loading calculations provide different macro-scale responses of the RVE, which can be the appearance of material anisotropy. We then try to examine the effects of the intergranular and intragranular behaviors on the anisotropy by means of various illustrations of plastic deformation process in stead of the use of pole figures for the change of crystallographic orientations

  2. Electron scattering off nuclei

    International Nuclear Information System (INIS)

    Gattone, A.O.

    1989-01-01

    Two recently developed aspects related to the scattering of electrons off nuclei are presented. On the one hand, a model is introduced which emphasizes the relativistic aspects of the problem in the impulse approximation, by demanding strict maintenance of the algebra of the Poincare group. On the other hand, the second model aims at a more sophisticated description of the nuclear response in the case of collective excitations. Basically, it utilizes the RPA formalism with a new development which enables a more careful treatment of the states in the continuum as is the case for the giant resonances. Applications of both models to the description of elastic scattering, inelastic scattering to discrete levels, giant resonances and the quasi-elastic region are discussed. (Author) [es

  3. Electromagnetic scattering theory

    Science.gov (United States)

    Bird, J. F.; Farrell, R. A.

    1986-01-01

    Electromagnetic scattering theory is discussed with emphasis on the general stochastic variational principle (SVP) and its applications. The stochastic version of the Schwinger-type variational principle is presented, and explicit expressions for its integrals are considered. Results are summarized for scalar wave scattering from a classic rough-surface model and for vector wave scattering from a random dielectric-body model. Also considered are the selection of trial functions and the variational improvement of the Kirchhoff short-wave approximation appropriate to large size-parameters. Other applications of vector field theory discussed include a general vision theory and the analysis of hydromagnetism induced by ocean motion across the geomagnetic field. Levitational force-torque in the magnetic suspension of the disturbance compensation system (DISCOS), now deployed in NOVA satellites, is also analyzed using the developed theory.

  4. Scattering theory

    International Nuclear Information System (INIS)

    Sitenko, A.

    1991-01-01

    This book emerged out of graduate lectures given by the author at the University of Kiev and is intended as a graduate text. The fundamentals of non-relativistic quantum scattering theory are covered, including some topics, such as the phase-function formalism, separable potentials, and inverse scattering, which are not always coverded in textbooks on scattering theory. Criticisms of the text are minor, but the reviewer feels an inadequate index is provided and the citing of references in the Russian language is a hindrance in a graduate text

  5. On Covering Approximation Subspaces

    Directory of Open Access Journals (Sweden)

    Xun Ge

    2009-06-01

    Full Text Available Let (U';C' be a subspace of a covering approximation space (U;C and X⊂U'. In this paper, we show that and B'(X⊂B(X∩U'. Also, iff (U;C has Property Multiplication. Furthermore, some connections between outer (resp. inner definable subsets in (U;C and outer (resp. inner definable subsets in (U';C' are established. These results answer a question on covering approximation subspace posed by J. Li, and are helpful to obtain further applications of Pawlak rough set theory in pattern recognition and artificial intelligence.

  6. Analytic nuclear scattering theories

    International Nuclear Information System (INIS)

    Di Marzio, F.; University of Melbourne, Parkville, VIC

    1999-01-01

    A wide range of nuclear reactions are examined in an analytical version of the usual distorted wave Born approximation. This new approach provides either semi analytic or fully analytic descriptions of the nuclear scattering processes. The resulting computational simplifications, when used within the limits of validity, allow very detailed tests of both nuclear interaction models as well as large basis models of nuclear structure to be performed

  7. Probing the two-scale-factor universality hypothesis by exact rotation symmetry-breaking mechanism

    Energy Technology Data Exchange (ETDEWEB)

    Neto, J.F.S.; Lima, K.A.L.; Carvalho, P.R.S. [Universidade Federal do Piaui, Departamento de Fisica, Teresina, PI (Brazil); Sena-Junior, M.I. [Universidade de Pernambuco, Escola Politecnica de Pernambuco, Recife, PE (Brazil); Universidade Federal de Alagoas, Instituto de Fisica, Maceio, AL (Brazil)

    2017-12-15

    We probe the two-scale-factor universality hypothesis by evaluating, firstly explicitly and analytically at the one-loop order, the loop quantum corrections to the amplitude ratios for O(N)λφ{sup 4} scalar field theories with rotation symmetry breaking in three distinct and independent methods in which the rotation symmetry-breaking mechanism is treated exactly. We show that the rotation symmetry-breaking amplitude ratios turn out to be identical in the three methods and equal to their respective rotation symmetry-breaking ones, although the amplitudes themselves, in general, depend on the method employed and on the rotation symmetry-breaking parameter. At the end, we show that all these results can be generalized, through an inductive process based on a general theorem emerging from the exact calculation, to any loop level and physically interpreted based on symmetry ideas. (orig.)

  8. On Convex Quadratic Approximation

    NARCIS (Netherlands)

    den Hertog, D.; de Klerk, E.; Roos, J.

    2000-01-01

    In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of

  9. Approximating The DCM

    DEFF Research Database (Denmark)

    Madsen, Rasmus Elsborg

    2005-01-01

    The Dirichlet compound multinomial (DCM), which has recently been shown to be well suited for modeling for word burstiness in documents, is here investigated. A number of conceptual explanations that account for these recent results, are provided. An exponential family approximation of the DCM...

  10. Approximation by Cylinder Surfaces

    DEFF Research Database (Denmark)

    Randrup, Thomas

    1997-01-01

    We present a new method for approximation of a given surface by a cylinder surface. It is a constructive geometric method, leading to a monorail representation of the cylinder surface. By use of a weighted Gaussian image of the given surface, we determine a projection plane. In the orthogonal...

  11. An Efficient Two-Scale Hybrid Embedded Fracture Model for Shale Gas Simulation

    KAUST Repository

    Amir, Sahar Z.

    2016-12-27

    Natural and hydraulic fractures existence and state differs on a reservoir-by-reservoir or even on a well-by-well basis leading to the necessity of exploring the flow regimes variations with respect to the diverse fracture-network shapes forged. Conventional Dual-Porosity Dual-Permeability (DPDP) schemes are not adequate to model such complex fracture-network systems. To overcome this difficulty, in this paper, an iterative Hybrid Embedded multiscale (two-scale) Fracture model (HEF) is applied on a derived fit-for-purpose shale gas model. The HEF model involves splitting the fracture computations into two scales: 1) fine-scale solves for the flux exchange parameter within each grid cell; 2) coarse-scale solves for the pressure applied to the domain grid cells using the flux exchange parameter computed at each grid cell from the fine-scale. After that, the D dimensions matrix pressure and the (D-1) lower dimensional fracture pressure are solved as a system to apply the matrix-fracture coupling. HEF model combines the DPDP overlapping continua concept, the DFN lower dimensional fractures concept, the HFN hierarchical fracture concept, and the CCFD model simplicity. As for the fit-for-purpose shale gas model, various fit-for-purpose shale gas models can be derived using any set of selected properties plugged in one of the most popularly used proposed literature models as shown in the appendix. Also, this paper shows that shale extreme low permeability cause flow behavior to be dominated by the structure and magnitude of high permeability fractures.

  12. An Efficient Two-Scale Hybrid Embedded Fracture Model for Shale Gas Simulation

    KAUST Repository

    Amir, Sahar Z.; Sun, Shuyu

    2016-01-01

    Natural and hydraulic fractures existence and state differs on a reservoir-by-reservoir or even on a well-by-well basis leading to the necessity of exploring the flow regimes variations with respect to the diverse fracture-network shapes forged. Conventional Dual-Porosity Dual-Permeability (DPDP) schemes are not adequate to model such complex fracture-network systems. To overcome this difficulty, in this paper, an iterative Hybrid Embedded multiscale (two-scale) Fracture model (HEF) is applied on a derived fit-for-purpose shale gas model. The HEF model involves splitting the fracture computations into two scales: 1) fine-scale solves for the flux exchange parameter within each grid cell; 2) coarse-scale solves for the pressure applied to the domain grid cells using the flux exchange parameter computed at each grid cell from the fine-scale. After that, the D dimensions matrix pressure and the (D-1) lower dimensional fracture pressure are solved as a system to apply the matrix-fracture coupling. HEF model combines the DPDP overlapping continua concept, the DFN lower dimensional fractures concept, the HFN hierarchical fracture concept, and the CCFD model simplicity. As for the fit-for-purpose shale gas model, various fit-for-purpose shale gas models can be derived using any set of selected properties plugged in one of the most popularly used proposed literature models as shown in the appendix. Also, this paper shows that shale extreme low permeability cause flow behavior to be dominated by the structure and magnitude of high permeability fractures.

  13. Critical scattering

    International Nuclear Information System (INIS)

    Stirling, W.G.; Perry, S.C.

    1996-01-01

    We outline the theoretical and experimental background to neutron scattering studies of critical phenomena at magnetic and structural phase transitions. The displacive phase transition of SrTiO 3 is discussed, along with examples from recent work on magnetic materials from the rare-earth (Ho, Dy) and actinide (NpAs, NpSb, USb) classes. The impact of synchrotron X-ray scattering is discussed in conclusion. (author) 13 figs., 18 refs

  14. Numerical analysis of a main crack interactions with micro-defects/inhomogeneities using two-scale generalized/extended finite element method

    Science.gov (United States)

    Malekan, Mohammad; Barros, Felício B.

    2017-12-01

    Generalized or extended finite element method (G/XFEM) models the crack by enriching functions of partition of unity type with discontinuous functions that represent well the physical behavior of the problem. However, this enrichment functions are not available for all problem types. Thus, one can use numerically-built (global-local) enrichment functions to have a better approximate procedure. This paper investigates the effects of micro-defects/inhomogeneities on a main crack behavior by modeling the micro-defects/inhomogeneities in the local problem using a two-scale G/XFEM. The global-local enrichment functions are influenced by the micro-defects/inhomogeneities from the local problem and thus change the approximate solution of the global problem with the main crack. This approach is presented in detail by solving three different linear elastic fracture mechanics problems for different cases: two plane stress and a Reissner-Mindlin plate problems. The numerical results obtained with the two-scale G/XFEM are compared with the reference solutions from the analytical, numerical solution using standard G/XFEM method and ABAQUS as well, and from the literature.

  15. An improved saddlepoint approximation.

    Science.gov (United States)

    Gillespie, Colin S; Renshaw, Eric

    2007-08-01

    Given a set of third- or higher-order moments, not only is the saddlepoint approximation the only realistic 'family-free' technique available for constructing an associated probability distribution, but it is 'optimal' in the sense that it is based on the highly efficient numerical method of steepest descents. However, it suffers from the problem of not always yielding full support, and whilst [S. Wang, General saddlepoint approximations in the bootstrap, Prob. Stat. Lett. 27 (1992) 61.] neat scaling approach provides a solution to this hurdle, it leads to potentially inaccurate and aberrant results. We therefore propose several new ways of surmounting such difficulties, including: extending the inversion of the cumulant generating function to second-order; selecting an appropriate probability structure for higher-order cumulants (the standard moment closure procedure takes them to be zero); and, making subtle changes to the target cumulants and then optimising via the simplex algorithm.

  16. Prestack traveltime approximations

    KAUST Repository

    Alkhalifah, Tariq Ali

    2011-01-01

    Most prestack traveltime relations we tend work with are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multi-focusing or double square-root (DSR) and the common reflection stack (CRS) equations. Using the DSR equation, I analyze the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I derive expansion based solutions of this eikonal based on polynomial expansions in terms of the reflection and dip angles in a generally inhomogenous background medium. These approximate solutions are free of singularities and can be used to estimate travetimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. A Marmousi example demonstrates the usefulness of the approach. © 2011 Society of Exploration Geophysicists.

  17. Topology, calculus and approximation

    CERN Document Server

    Komornik, Vilmos

    2017-01-01

    Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér, Stieltjes, and Turán. The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdős and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Carathéodory's definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations. Students of both pure an...

  18. Approximate Bayesian recursive estimation

    Czech Academy of Sciences Publication Activity Database

    Kárný, Miroslav

    2014-01-01

    Roč. 285, č. 1 (2014), s. 100-111 ISSN 0020-0255 R&D Projects: GA ČR GA13-13502S Institutional support: RVO:67985556 Keywords : Approximate parameter estimation * Bayesian recursive estimation * Kullback–Leibler divergence * Forgetting Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 4.038, year: 2014 http://library.utia.cas.cz/separaty/2014/AS/karny-0425539.pdf

  19. Approximating Preemptive Stochastic Scheduling

    OpenAIRE

    Megow Nicole; Vredeveld Tjark

    2009-01-01

    We present constant approximative policies for preemptive stochastic scheduling. We derive policies with a guaranteed performance ratio of 2 for scheduling jobs with release dates on identical parallel machines subject to minimizing the sum of weighted completion times. Our policies as well as their analysis apply also to the recently introduced more general model of stochastic online scheduling. The performance guarantee we give matches the best result known for the corresponding determinist...

  20. Optimization and approximation

    CERN Document Server

    Pedregal, Pablo

    2017-01-01

    This book provides a basic, initial resource, introducing science and engineering students to the field of optimization. It covers three main areas: mathematical programming, calculus of variations and optimal control, highlighting the ideas and concepts and offering insights into the importance of optimality conditions in each area. It also systematically presents affordable approximation methods. Exercises at various levels have been included to support the learning process.

  1. Possible role of double scattering in electron-atom scattering in a laser field

    International Nuclear Information System (INIS)

    Rabadan, I.; Mendez, L.; Dickinson, A.S.

    1996-01-01

    By considering observations of double-scattering effects in the excitation of the 2 1 P level of He, gas density values estimated for the laser-assisted elastic scattering experiments of Wallbank and Holmes (1993, 1994a,b) for which the Kroll-Watson approximation appears to fail. Using comparable densities for He and lower densities for Ar, and assuming the Kroll-Watson approximation for single-scattering events, differential cross sections are calculated including double scattering for laser-assisted scattering for a range of energies and scattering angles. Comparison with the observed values shows that double-scattering effects can give a semi-quantitative explanation of the apparent breakdown of the Kroll-Watson approximation in both He and Ar. (author)

  2. Light Scattering by Optically Soft Particles Theory and Applications

    CERN Document Server

    Sharma, Subodh K

    2006-01-01

    The present monograph deals with a particular class of approximation methods in the context of light scattering by small particles. This class of approximations has been termed as eikonal or soft particle approximations. The eikonal approximation was studied extensively in the potential scattering and then adopted in optical scattering problems. In this context, the eikonal and other soft particle approximations pertain to scatterers whose relative refractive index compared to surrounding medium is close to unity. The study of these approximations is very important because soft particles occur abundantly in nature. For example, the particles that occur in ocean optics, biomedical optics, atmospheric optics and in many industrial applications can be classified as soft particles. This book was written in recognition of the long-standing and current interest in the field of scattering approximations for soft particles. It should prove to be a useful addition for researchers in the field of light scattering.

  3. Cyclic approximation to stasis

    Directory of Open Access Journals (Sweden)

    Stewart D. Johnson

    2009-06-01

    Full Text Available Neighborhoods of points in $mathbb{R}^n$ where a positive linear combination of $C^1$ vector fields sum to zero contain, generically, cyclic trajectories that switch between the vector fields. Such points are called stasis points, and the approximating switching cycle can be chosen so that the timing of the switches exactly matches the positive linear weighting. In the case of two vector fields, the stasis points form one-dimensional $C^1$ manifolds containing nearby families of two-cycles. The generic case of two flows in $mathbb{R}^3$ can be diffeomorphed to a standard form with cubic curves as trajectories.

  4. On the WKBJ approximation

    International Nuclear Information System (INIS)

    El Sawi, M.

    1983-07-01

    A simple approach employing properties of solutions of differential equations is adopted to derive an appropriate extension of the WKBJ method. Some of the earlier techniques that are commonly in use are unified, whereby the general approximate solution to a second-order homogeneous linear differential equation is presented in a standard form that is valid for all orders. In comparison to other methods, the present one is shown to be leading in the order of iteration, and thus possibly has the ability of accelerating the convergence of the solution. The method is also extended for the solution of inhomogeneous equations. (author)

  5. The relaxation time approximation

    International Nuclear Information System (INIS)

    Gairola, R.P.; Indu, B.D.

    1991-01-01

    A plausible approximation has been made to estimate the relaxation time from a knowledge of the transition probability of phonons from one state (r vector, q vector) to other state (r' vector, q' vector), as a result of collision. The relaxation time, thus obtained, shows a strong dependence on temperature and weak dependence on the wave vector. In view of this dependence, relaxation time has been expressed in terms of a temperature Taylor's series in the first Brillouin zone. Consequently, a simple model for estimating the thermal conductivity is suggested. the calculations become much easier than the Callaway model. (author). 14 refs

  6. Polynomial approximation on polytopes

    CERN Document Server

    Totik, Vilmos

    2014-01-01

    Polynomial approximation on convex polytopes in \\mathbf{R}^d is considered in uniform and L^p-norms. For an appropriate modulus of smoothness matching direct and converse estimates are proven. In the L^p-case so called strong direct and converse results are also verified. The equivalence of the moduli of smoothness with an appropriate K-functional follows as a consequence. The results solve a problem that was left open since the mid 1980s when some of the present findings were established for special, so-called simple polytopes.

  7. Finite elements and approximation

    CERN Document Server

    Zienkiewicz, O C

    2006-01-01

    A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o

  8. Hierarchical Stereo Matching in Two-Scale Space for Cyber-Physical System

    Directory of Open Access Journals (Sweden)

    Eunah Choi

    2017-07-01

    Full Text Available Dense disparity map estimation from a high-resolution stereo image is a very difficult problem in terms of both matching accuracy and computation efficiency. Thus, an exhaustive disparity search at full resolution is required. In general, examining more pixels in the stereo view results in more ambiguous correspondences. When a high-resolution image is down-sampled, the high-frequency components of the fine-scaled image are at risk of disappearing in the coarse-resolution image. Furthermore, if erroneous disparity estimates caused by missing high-frequency components are propagated across scale space, ultimately, false disparity estimates are obtained. To solve these problems, we introduce an efficient hierarchical stereo matching method in two-scale space. This method applies disparity estimation to the reduced-resolution image, and the disparity result is then up-sampled to the original resolution. The disparity estimation values of the high-frequency (or edge component regions of the full-resolution image are combined with the up-sampled disparity results. In this study, we extracted the high-frequency areas from the scale-space representation by using difference of Gaussian (DoG or found edge components, using a Canny operator. Then, edge-aware disparity propagation was used to refine the disparity map. The experimental results show that the proposed algorithm outperforms previous methods.

  9. Hierarchical Stereo Matching in Two-Scale Space for Cyber-Physical System.

    Science.gov (United States)

    Choi, Eunah; Lee, Sangyoon; Hong, Hyunki

    2017-07-21

    Dense disparity map estimation from a high-resolution stereo image is a very difficult problem in terms of both matching accuracy and computation efficiency. Thus, an exhaustive disparity search at full resolution is required. In general, examining more pixels in the stereo view results in more ambiguous correspondences. When a high-resolution image is down-sampled, the high-frequency components of the fine-scaled image are at risk of disappearing in the coarse-resolution image. Furthermore, if erroneous disparity estimates caused by missing high-frequency components are propagated across scale space, ultimately, false disparity estimates are obtained. To solve these problems, we introduce an efficient hierarchical stereo matching method in two-scale space. This method applies disparity estimation to the reduced-resolution image, and the disparity result is then up-sampled to the original resolution. The disparity estimation values of the high-frequency (or edge component) regions of the full-resolution image are combined with the up-sampled disparity results. In this study, we extracted the high-frequency areas from the scale-space representation by using difference of Gaussian (DoG) or found edge components, using a Canny operator. Then, edge-aware disparity propagation was used to refine the disparity map. The experimental results show that the proposed algorithm outperforms previous methods.

  10. A Two-Scale Reduced Model for Darcy Flow in Fractured Porous Media

    KAUST Repository

    Chen, Huangxin

    2016-06-01

    In this paper, we develop a two-scale reduced model for simulating the Darcy flow in two-dimensional porous media with conductive fractures. We apply the approach motivated by the embedded fracture model (EFM) to simulate the flow on the coarse scale, and the effect of fractures on each coarse scale grid cell intersecting with fractures is represented by the discrete fracture model (DFM) on the fine scale. In the DFM used on the fine scale, the matrix-fracture system are resolved on unstructured grid which represents the fractures accurately, while in the EFM used on the coarse scale, the flux interaction between fractures and matrix are dealt with as a source term, and the matrix-fracture system can be resolved on structured grid. The Raviart-Thomas mixed finite element methods are used for the solution of the coupled flows in the matrix and the fractures on both fine and coarse scales. Numerical results are presented to demonstrate the efficiency of the proposed model for simulation of flow in fractured porous media.

  11. 'Speaking up' about patient safety concerns and unprofessional behaviour among residents: validation of two scales.

    Science.gov (United States)

    Martinez, William; Etchegaray, Jason M; Thomas, Eric J; Hickson, Gerald B; Lehmann, Lisa Soleymani; Schleyer, Anneliese M; Best, Jennifer A; Shelburne, Julia T; May, Natalie B; Bell, Sigall K

    2015-11-01

    To develop and test the psychometric properties of two new survey scales aiming to measure the extent to which the clinical environment supports speaking up about (a) patient safety concerns and (b) unprofessional behaviour. Residents from six large US academic medical centres completed an anonymous, electronic survey containing questions regarding safety culture and speaking up about safety and professionalism concerns. Confirmatory factor analysis supported two separate, one-factor speaking up climates (SUCs) among residents; one focused on patient safety concerns (SUC-Safe scale) and the other focused on unprofessional behaviour (SUC-Prof scale). Both scales had good internal consistency (Cronbach's α>0.70) and were unique from validated safety and teamwork climate measures (rspeaking up behaviour about safety and professionalism concerns (r=0.21, pspeaking up behaviour among residents. These two scales may fill an existing gap in residency and safety culture assessments by measuring the openness of communication about safety and professionalism concerns, two important aspects of safety culture that are under-represented in existing metrics. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://group.bmj.com/group/rights-licensing/permissions.

  12. Two-scale correlation and energy cascade in three-dimensional turbulent flows

    International Nuclear Information System (INIS)

    Huang, Y X; Schmitt, F G; Gagne, Y

    2014-01-01

    In this paper, we propose a high-order harmonic-free methodology, namely arbitrary-order Hilbert spectral analysis, to estimate the two-scale correlation (TSC). When applied to fully developed turbulent velocity, we find that the scale-dependent Hilbert energy satisfies a lognormal distribution on both the inertial and dissipation ranges. The maximum probability density function of the logarithm of the Hilbert energy obeys a power law with a scaling exponent γ ≃ 0.33 in the inertial range. For the measured TSC, we observe a logarithmic correlation law with an experimental exponent α ≃ 0.37 on both the inertial and dissipation ranges. The correlation itself is found to be self-similar with respect to the distance between the two considered scales and a central frequency ω c in the logarithm space. An empirical nonlinear and nonlocal triad-scale interaction formula is proposed to describe the observed TSC. This triadic interaction can be interpreted as experimental evidence of a small-scale nonlinear and nonlocal coupling inside the self-similarity of the Richardson–Kolmogorov phenomenological cascade picture. (paper)

  13. A two-scale model for correlation between B cell VDJ usage in zebrafish

    Science.gov (United States)

    Pan, Keyao; Deem, Michael

    2011-03-01

    The zebrafish (Danio rerio) is one of the model animals for study of immunology. The dynamics of the adaptive immune system in zebrafish is similar to that in higher animals. In this work, we built a two-scale model to simulate the dynamics of B cells in primary and secondary immune reactions in zebrafish and to explain the reported correlation between VDJ usage of B cell repertoires in distinct zebrafish. The first scale of the model consists of a generalized NK model to simulate the B cell maturation process in the 10-day primary immune response. The second scale uses a delay ordinary differential equation system to model the immune responses in the 6-month lifespan of zebrafish. The generalized NK model shows that mature B cells specific to one antigen mostly possess a single VDJ recombination. The probability that mature B cells in two zebrafish have the same VDJ recombination increases with the B cell population size or the B cell selection intensity and decreases with the B cell hypermutation rate. The ODE model shows a distribution of correlation in the VDJ usage of the B cell repertoires in two six-month-old zebrafish that is highly similar to that from experiment. This work presents a simple theory to explain the experimentally observed correlation in VDJ usage of distinct zebrafish B cell repertoires after an immune response.

  14. Approximate Bayesian computation.

    Directory of Open Access Journals (Sweden)

    Mikael Sunnåker

    Full Text Available Approximate Bayesian computation (ABC constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. ABC methods bypass the evaluation of the likelihood function. In this way, ABC methods widen the realm of models for which statistical inference can be considered. ABC methods are mathematically well-founded, but they inevitably make assumptions and approximations whose impact needs to be carefully assessed. Furthermore, the wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years and in particular for the analysis of complex problems arising in biological sciences (e.g., in population genetics, ecology, epidemiology, and systems biology.

  15. Compton scattering revisited

    Energy Technology Data Exchange (ETDEWEB)

    Pratt, R.H., E-mail: rpratt@pitt.ed [Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260 (United States); LaJohn, L.A., E-mail: lal18@pitt.ed [Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260 (United States); Florescu, V., E-mail: flor@barutu.fizica.unibuc.r [Centre for Advanced Quantum Physics, University of Bucharest, MG-11 Bucharest-Magurele, 077125 Magurele (Romania); Suric, T., E-mail: suric@irb.h [R. Boskovic Institute, Bijenicka 54, 10000 Zagreb (Croatia); Chatterjee, B.K., E-mail: barun_k_chatterjee@yahoo.co [Department of Physics, Bose Institute, Kolkata 700009 (India); Roy, S.C., E-mail: suprakash.roy@gmail.co [Department of Physics, Bose Institute, Kolkata 700009 (India)

    2010-02-15

    We review the standard theory of Compton scattering from bound electrons, and we describe recent findings that require modification of the usual understanding, noting the nature of consequences for experiment. The subject began with Compton and scattering from free electrons. Experiment actually involved bound electrons, and this was accommodated with the use of impulse approximation (IA), which described inelastic scattering from bound electrons in terms of scattering from free electrons. This was good for the Compton peak but failed for soft final photons. The standard theory was formalized by Eisenberger and Platzman (EP) [1970. Phys. Rev. A 2, 415], whose work also suggested why impulse approximation was better than one would expect, for doubly differential cross sections (DDCS), but not for triply differential cross sections (TDCS). A relativistic version of IA (RIA) was worked out by Ribberfors [1975. Phys. Rev. B 12, 2067]. And Suric et al. [1991. Phys. Rev. Lett. 67, 189] and Bergstrom et al. [1993. Phys. Rev. A 48, 1134] developed a full relativistic second order S-matrix treatment, not making impulse approximation, but within independent particle approximation (IPA). Newer developments in the theory of Compton scattering include: (1) Demonstration that the EP estimates of the validity of IA are incorrect, although the qualitative conclusion remains unchanged; IA is not to be understood as the first term in a standard series expansion. (2) The greater validity of IA for DDCS than for the TDCS, which when integrated give DDCS, is related to the existence of a sum rule, only valid for DDCS. (3) The so-called 'asymmetry' of a Compton profile is primarily to be understood as simply the shift of the peak position in the profile; symmetric and anti-symmetric deviations from a shifted Compton profile are very small, except for high Z inner shells where further p{sup -}>.A{sup -}> effects come into play. (4) Most relativistic effects, except at low

  16. Compton scattering revisited

    International Nuclear Information System (INIS)

    Pratt, R.H.; LaJohn, L.A.; Florescu, V.; Suric, T.; Chatterjee, B.K.; Roy, S.C.

    2010-01-01

    We review the standard theory of Compton scattering from bound electrons, and we describe recent findings that require modification of the usual understanding, noting the nature of consequences for experiment. The subject began with Compton and scattering from free electrons. Experiment actually involved bound electrons, and this was accommodated with the use of impulse approximation (IA), which described inelastic scattering from bound electrons in terms of scattering from free electrons. This was good for the Compton peak but failed for soft final photons. The standard theory was formalized by Eisenberger and Platzman (EP) [1970. Phys. Rev. A 2, 415], whose work also suggested why impulse approximation was better than one would expect, for doubly differential cross sections (DDCS), but not for triply differential cross sections (TDCS). A relativistic version of IA (RIA) was worked out by Ribberfors [1975. Phys. Rev. B 12, 2067]. And Suric et al. [1991. Phys. Rev. Lett. 67, 189] and Bergstrom et al. [1993. Phys. Rev. A 48, 1134] developed a full relativistic second order S-matrix treatment, not making impulse approximation, but within independent particle approximation (IPA). Newer developments in the theory of Compton scattering include: (1) Demonstration that the EP estimates of the validity of IA are incorrect, although the qualitative conclusion remains unchanged; IA is not to be understood as the first term in a standard series expansion. (2) The greater validity of IA for DDCS than for the TDCS, which when integrated give DDCS, is related to the existence of a sum rule, only valid for DDCS. (3) The so-called 'asymmetry' of a Compton profile is primarily to be understood as simply the shift of the peak position in the profile; symmetric and anti-symmetric deviations from a shifted Compton profile are very small, except for high Z inner shells where further p → .A → effects come into play. (4) Most relativistic effects, except at low energies, are to be

  17. Evaluation of Fresnel's corrections to the eikonal approximation by the separabilization method

    International Nuclear Information System (INIS)

    Musakhanov, M.M.; Zubarev, A.L.

    1975-01-01

    Method of separabilization of potential over the Schroedinger approximate solutions, leading to Schwinger's variational principle for scattering amplitude, is suggested. The results are applied to calculation of the Fresnel corrections to the Glauber approximation

  18. The random phase approximation

    International Nuclear Information System (INIS)

    Schuck, P.

    1985-01-01

    RPA is the adequate theory to describe vibrations of the nucleus of very small amplitudes. These vibrations can either be forced by an external electromagnetic field or can be eigenmodes of the nucleus. In a one dimensional analogue the potential corresponding to such eigenmodes of very small amplitude should be rather stiff otherwise the motion risks to be a large amplitude one and to enter a region where the approximation is not valid. This means that nuclei which are supposedly well described by RPA must have a very stable groundstate configuration (must e.g. be very stiff against deformation). This is usually the case for doubly magic nuclei or close to magic nuclei which are in the middle of proton and neutron shells which develop a very stable groundstate deformation; we take the deformation as an example but there are many other possible degrees of freedom as, for example, compression modes, isovector degrees of freedom, spin degrees of freedom, and many more

  19. The quasilocalized charge approximation

    International Nuclear Information System (INIS)

    Kalman, G J; Golden, K I; Donko, Z; Hartmann, P

    2005-01-01

    The quasilocalized charge approximation (QLCA) has been used for some time as a formalism for the calculation of the dielectric response and for determining the collective mode dispersion in strongly coupled Coulomb and Yukawa liquids. The approach is based on a microscopic model in which the charges are quasilocalized on a short-time scale in local potential fluctuations. We review the conceptual basis and theoretical structure of the QLC approach and together with recent results from molecular dynamics simulations that corroborate and quantify the theoretical concepts. We also summarize the major applications of the QLCA to various physical systems, combined with the corresponding results of the molecular dynamics simulations and point out the general agreement and instances of disagreement between the two

  20. One-dimensional conduction through supporting electrolytes: two-scale cathodic Debye layer.

    Science.gov (United States)

    Almog, Yaniv; Yariv, Ehud

    2011-10-01

    Supporting-electrolyte solutions comprise chemically inert cations and anions, produced by salt dissolution, together with a reactive ionic species that may be consumed and generated on bounding ion-selective surfaces (e.g., electrodes or membranes). Upon application of an external voltage, a Faraday current is thereby established. It is natural to analyze this ternary-system process through a one-dimensional transport problem, employing the thin Debye-layer limit. Using a simple model of ideal ion-selective membranes, we have recently addressed this problem for moderate voltages [Yariv and Almog, Phys. Rev. Lett. 105, 176101 (2010)], predicting currents that scale as a fractional power of Debye thickness. We address herein the complementary problem of moderate currents. We employ matched asymptotic expansions, separately analyzing the two inner thin Debye layers adjacent to the ion-selective surfaces and the outer electroneutral region outside them. A straightforward calculation following comparable singular-perturbation analyses of binary systems is frustrated by the prediction of negative ionic concentrations near the cathode. Accompanying numerical simulations, performed for small values of Debye thickness, indicate a number unconventional features occurring at that region, such as inert-cation concentration amplification and electric-field intensification. The current-voltage correlation data of the electrochemical cell, obtained from compilation of these simulations, does not approach a limit as the Debye thickness vanishes. Resolution of these puzzles reveals a transformation of the asymptotic structure of the cathodic Debye layer. This reflects the emergence of an internal boundary layer, adjacent to the cathode, wherein field and concentration scaling differs from those of the Gouy-Chapman theory. The two-scale feature of the cathodic Debye layer is manifested through a logarithmic voltage scaling with Debye thickness. Accounting for this scaling, the

  1. Deep inelastic scattering

    International Nuclear Information System (INIS)

    Zakharov, V.I.

    1977-01-01

    The present status of the quark-parton-gluon picture of deep inelastic scattering is reviewed. The general framework is mostly theoretical and covers investigations since 1970. Predictions of the parton model and of the asymptotically free field theories are compared with experimental data available. The valence quark approximation is concluded to be valid in most cases, but fails to account for the data on the total momentum transfer. On the basis of gluon corrections introduced to the parton model certain predictions concerning both the deep inelastic structure functions and form factors are made. The contributions of gluon exchanges and gluon bremsstrahlung are highlighted. Asymptotic freedom is concluded to be very attractive and provide qualitative explanation to some experimental observations (scaling violations, breaking of the Drell-Yan-West type relations). Lepton-nuclear scattering is pointed out to be helpful in probing the nature of nuclear forces and studying the space-time picture of the parton model

  2. Two Scales, Hybrid Model for Soils, Involving Artificial Neural Network and Finite Element Procedure

    Directory of Open Access Journals (Sweden)

    Krasiński Marcin

    2015-02-01

    Full Text Available A hybrid ANN-FE solution is presented as a result of two level analysis of soils: a level of a laboratory sample and a level of engineering geotechnical problem. Engineering properties of soils (sands are represented directly in the form of ANN (this is in contrast with our former paper where ANN approximated constitutive relationships. Initially the ANN is trained with Duncan formula (Duncan and Chang [2], then it is re-trained (calibrated with some available experimental data, specific for the soil considered. The obtained approximation of the constitutive parameters is used directly in finite element method at the level of a single element at the scale of the laboratory sample to check the correct representation of the laboratory test. Then, the finite element that was successfully tested at the level of laboratory sample is used at the macro level to solve engineering problems involving the soil for which it was calibrated.

  3. Development of the relativistic impulse approximation

    International Nuclear Information System (INIS)

    Wallace, S.J.

    1985-01-01

    This talk contains three parts. Part I reviews the developments which led to the relativistic impulse approximation for proton-nucleus scattering. In Part II, problems with the impulse approximation in its original form - principally the low energy problem - are discussed and traced to pionic contributions. Use of pseudovector covariants in place of pseudoscalar ones in the NN amplitude provides more satisfactory low energy results, however, the difference between pseudovector and pseudoscalar results is ambiguous in the sense that it is not controlled by NN data. Only with further theoretical input can the ambiguity be removed. Part III of the talk presents a new development of the relativistic impulse approximation which is the result of work done in the past year and a half in collaboration with J.A. Tjon. A complete NN amplitude representation is developed and a complete set of Lorentz invariant amplitudes are calculated based on a one-meson exchange model and appropriate integral equations. A meson theoretical basis for the important pair contributions to proton-nucleus scattering is established by the new developments. 28 references

  4. Approximate quantum Markov chains

    CERN Document Server

    Sutter, David

    2018-01-01

    This book is an introduction to quantum Markov chains and explains how this concept is connected to the question of how well a lost quantum mechanical system can be recovered from a correlated subsystem. To achieve this goal, we strengthen the data-processing inequality such that it reveals a statement about the reconstruction of lost information. The main difficulty in order to understand the behavior of quantum Markov chains arises from the fact that quantum mechanical operators do not commute in general. As a result we start by explaining two techniques of how to deal with non-commuting matrices: the spectral pinching method and complex interpolation theory. Once the reader is familiar with these techniques a novel inequality is presented that extends the celebrated Golden-Thompson inequality to arbitrarily many matrices. This inequality is the key ingredient in understanding approximate quantum Markov chains and it answers a question from matrix analysis that was open since 1973, i.e., if Lieb's triple ma...

  5. Prestack traveltime approximations

    KAUST Repository

    Alkhalifah, Tariq Ali

    2012-05-01

    Many of the explicit prestack traveltime relations used in practice are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multifocusing, based on the double square-root (DSR) equation, and the common reflection stack (CRS) approaches. Using the DSR equation, I constructed the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I recasted the eikonal in terms of the reflection angle, and thus, derived expansion based solutions of this eikonal in terms of the difference between the source and receiver velocities in a generally inhomogenous background medium. The zero-order term solution, corresponding to ignoring the lateral velocity variation in estimating the prestack part, is free of singularities and can be used to estimate traveltimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. The higher-order terms include limitations for horizontally traveling waves, however, we can readily enforce stability constraints to avoid such singularities. In fact, another expansion over reflection angle can help us avoid these singularities by requiring the source and receiver velocities to be different. On the other hand, expansions in terms of reflection angles result in singularity free equations. For a homogenous background medium, as a test, the solutions are reasonably accurate to large reflection and dip angles. A Marmousi example demonstrated the usefulness and versatility of the formulation. © 2012 Society of Exploration Geophysicists.

  6. Two-Scale 13C Metabolic Flux Analysis for Metabolic Engineering.

    Science.gov (United States)

    Ando, David; Garcia Martin, Hector

    2018-01-01

    Accelerating the Design-Build-Test-Learn (DBTL) cycle in synthetic biology is critical to achieving rapid and facile bioengineering of organisms for the production of, e.g., biofuels and other chemicals. The Learn phase involves using data obtained from the Test phase to inform the next Design phase. As part of the Learn phase, mathematical models of metabolic fluxes give a mechanistic level of comprehension to cellular metabolism, isolating the principle drivers of metabolic behavior from the peripheral ones, and directing future experimental designs and engineering methodologies. Furthermore, the measurement of intracellular metabolic fluxes is specifically noteworthy as providing a rapid and easy-to-understand picture of how carbon and energy flow throughout the cell. Here, we present a detailed guide to performing metabolic flux analysis in the Learn phase of the DBTL cycle, where we show how one can take the isotope labeling data from a 13 C labeling experiment and immediately turn it into a determination of cellular fluxes that points in the direction of genetic engineering strategies that will advance the metabolic engineering process.For our modeling purposes we use the Joint BioEnergy Institute (JBEI) Quantitative Metabolic Modeling (jQMM) library, which provides an open-source, python-based framework for modeling internal metabolic fluxes and making actionable predictions on how to modify cellular metabolism for specific bioengineering goals. It presents a complete toolbox for performing different types of flux analysis such as Flux Balance Analysis, 13 C Metabolic Flux Analysis, and it introduces the capability to use 13 C labeling experimental data to constrain comprehensive genome-scale models through a technique called two-scale 13 C Metabolic Flux Analysis (2S- 13 C MFA) [1]. In addition to several other capabilities, the jQMM is also able to predict the effects of knockouts using the MoMA and ROOM methodologies. The use of the jQMM library is

  7. Elastic scattering

    International Nuclear Information System (INIS)

    Leader, Elliot

    1991-01-01

    With very few unexplained results to challenge conventional ideas, physicists have to look hard to search for gaps in understanding. An area of physics which offers a lot more than meets the eye is elastic and diffractive scattering where particles either 'bounce' off each other, emerging unscathed, or just graze past, emerging relatively unscathed. The 'Blois' workshops provide a regular focus for this unspectacular, but compelling physics, attracting highly motivated devotees

  8. Neutron scattering

    International Nuclear Information System (INIS)

    1991-02-01

    The annual report on hand gives an overview of the research work carried out in the Laboratory for Neutron Scattering (LNS) of the ETH Zuerich in 1990. Using the method of neutron scattering, it is possible to examine in detail the static and dynamic properties of the condensed material. In accordance with the multidisciplined character of the method, the LNS has for years maintained a system of intensive co-operation with numerous institutes in the areas of biology, chemistry, solid-state physics, crystallography and materials research. In 1990 over 100 scientists from more than 40 research groups both at home and abroad took part in the experiments. It was again a pleasure to see the number of graduate students present, who were studying for a doctorate and who could be introduced into the neutron scattering during their stay at the LNS and thus were in the position to touch on central ways of looking at a problem in their dissertation using this modern experimental method of solid-state research. In addition to the numerous and interesting ways of formulating the questions to explain the structure, nowadays the scientific programme increasingly includes particularly topical studies in connection with high temperature-supraconductors and materials research

  9. Scattering theory

    CERN Document Server

    Friedrich, Harald

    2016-01-01

    This corrected and updated second edition of "Scattering Theory" presents a concise and modern coverage of the subject. In the present treatment, special attention is given to the role played by the long-range behaviour of the projectile-target interaction, and a theory is developed, which is well suited to describe near-threshold bound and continuum states in realistic binary systems such as diatomic molecules or molecular ions. It is motivated by the fact that experimental advances have shifted and broadened the scope of applications where concepts from scattering theory are used, e.g. to the field of ultracold atoms and molecules, which has been experiencing enormous growth in recent years, largely triggered by the successful realization of Bose-Einstein condensates of dilute atomic gases in 1995. The book contains sections on special topics such as near-threshold quantization, quantum reflection, Feshbach resonances and the quantum description of scattering in two dimensions. The level of abstraction is k...

  10. SAM revisited: uniform semiclassical approximation with absorption

    International Nuclear Information System (INIS)

    Hussein, M.S.; Pato, M.P.

    1986-01-01

    The uniform semiclassical approximation is modified to take into account strong absorption. The resulting theory, very similar to the one developed by Frahn and Gross is used to discuss heavy-ion elastic scattering at intermediate energies. The theory permits a reasonably unambiguos separation of refractive and diffractive effects. The systems 12 C+ 12 C and 12 C+ 16 O, which seem to exhibit a remnant of a nuclear rainbow at E=20 Mev/N, are analysed with theory which is built directly on a model for the S-matrix. Simple relations between the fit S-matrix and the underlying complex potential are derived. (Author) [pt

  11. Elastic scattering of slow positrons by helium

    International Nuclear Information System (INIS)

    Amusia, M.Ya.; Cherepkov, N.A.; Chernysheva, L.V.; Shapiro, S.G.

    1976-01-01

    The s-, p-, d- and f-wave phaseshifts for elastic scattering of slow positrons by He are calculated using a simplified version of the random phase approximation with exchange, with virtual positronium formation effect taken into account. (author)

  12. Elastic and inelastic heavy ion scattering

    International Nuclear Information System (INIS)

    Toepffer, C.; University of the Witwatersrand, Johannesburg; Richter, A.

    1977-02-01

    In the field of elastic and inelastic heavy ion scattering, the following issues are dealt with: semiclassical descriptive approximations, optical potentials, barriers, critical radii and angular momenta, excitation functions and the application to superheavy ions and high energies. (WL) [de

  13. Recent results in Rayleigh scattering

    International Nuclear Information System (INIS)

    Kahane, S.; Shahal, O.; Moreh, R.; Ben-Gurion Univ. of the Negev, Beer-Sheva

    1997-01-01

    New measurements of Rayleigh scattering, employing neutron capture γ rays are presented. Experimental conditions are achieved such that the Rayleigh contribution is dominant and much larger than other competing coherent process. A detailed comparison with the modified relativistic form factor approximation (MRFF) is made. It is found that MRFF overestimates the true cross sections by 3-4%. (author)

  14. Quasi-elastic scattering

    International Nuclear Information System (INIS)

    Pizzi, J.R.

    1975-01-01

    In a first part, the kinematical conditions which are chosen to study quasi free scattering reactions are presented, as well as the impulse approximation which is used to interpret the experimental data. Then, the evolution of the study of these reactions in the last few years is analyzed. Three recent experiments are presented and discussed. Two of them deal with α-clusters studied by (p,pα) reaction at 157 and 600MeV. The third is concerned with d, t and 3 He clusters studied by (p,px) reaction at 75MeV [fr

  15. Chaotic scattering and quantum dynamics

    International Nuclear Information System (INIS)

    Doron, Eyal.

    1992-11-01

    The main concern of this thesis is the application of the semiclassical approximation to quantum chaotic scattering systems. We deal with two separate, although interconnected, subjects. The first subject dealt with is the semiclassical characterization of the fluctuations of the S matrix. A particular important parameter is the magnetic field B, and we show how the correlation length and line shape of S matrix elements under a change of B may be derived. An effect which is present in many physical wave systems is absorption of energy flux. We show how absorption affects both the reflectivity and the scattering phase and time delay of a scattering system. In the second part of the thesis, we show how the formalism and results obtained from chaotic scattering can be applied to the investigation of closed chaotic systems, and in particular to chaotic billiards. The semiclassical expansion for billiards is presented. In the last part of the thesis we deal with the statistics of S matrices of chaotic scattering systems. The main message of this work is that scattering matrix, and its classical counterpart the Poincare Scattering Map can be used to yield a powerful formulation of the quantum mechanical dynamics of bounded systems. (author)

  16. Self-similar factor approximants

    International Nuclear Information System (INIS)

    Gluzman, S.; Yukalov, V.I.; Sornette, D.

    2003-01-01

    The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving an improved type of approximants. The derivation is based on the self-similar approximation theory, which presents the passage from one approximant to another as the motion realized by a dynamical system with the property of group self-similarity. The derived approximants, because of their form, are called self-similar factor approximants. These complement the obtained earlier self-similar exponential approximants and self-similar root approximants. The specific feature of self-similar factor approximants is that their control functions, providing convergence of the computational algorithm, are completely defined from the accuracy-through-order conditions. These approximants contain the Pade approximants as a particular case, and in some limit they can be reduced to the self-similar exponential approximants previously introduced by two of us. It is proved that the self-similar factor approximants are able to reproduce exactly a wide class of functions, which include a variety of nonalgebraic functions. For other functions, not pertaining to this exactly reproducible class, the factor approximants provide very accurate approximations, whose accuracy surpasses significantly that of the most accurate Pade approximants. This is illustrated by a number of examples showing the generality and accuracy of the factor approximants even when conventional techniques meet serious difficulties

  17. Heating of field-reversed plasma rings estimated with two scaling models

    Energy Technology Data Exchange (ETDEWEB)

    Shearer, J.W.

    1978-05-18

    Scaling calculations are presented of the one temperature heating of a field-reversed plasma ring. Two sharp-boundary models of the ring are considered: the long thin approximation and a pinch model. Isobaric, adiabatic, and isovolumetric cases are considered, corresponding to various ways of heating the plasma in a real experiment by using neutral beams, or by raising the magnetic field. It is found that the shape of the plasma changes markedly with heating. The least sensitive shape change (as a function of temperature) is found for the isovolumetric heating case, which can be achieved by combining neutral beam heating with compression. The complications introduced by this heating problem suggest that it is desirable, if possible, to create a field reversed ring which is already quite hot, rather than cold.

  18. Diffractive scattering

    CERN Document Server

    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.

  19. Diffractive Scattering

    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)

  20. 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

  1. International Conference Approximation Theory XV

    CERN Document Server

    Schumaker, Larry

    2017-01-01

    These proceedings are based on papers presented at the international conference Approximation Theory XV, which was held May 22–25, 2016 in San Antonio, Texas. The conference was the fifteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 146 participants. The book contains longer survey papers by some of the invited speakers covering topics such as compressive sensing, isogeometric analysis, and scaling limits of polynomials and entire functions of exponential type. The book also includes papers on a variety of current topics in Approximation Theory drawn from areas such as advances in kernel approximation with applications, approximation theory and algebraic geometry, multivariate splines for applications, practical function approximation, approximation of PDEs, wavelets and framelets with applications, approximation theory in signal processing, compressive sensing, rational interpolation, spline approximation in isogeometric analysis, a...

  2. Quasi-elastic shadowing in nucleus-nucleus elastic scattering

    Energy Technology Data Exchange (ETDEWEB)

    Dymarz, R; Malecki, A [Institute of Nuclear Physics, Krakow (Poland); Gluski, K [Institute of Nuclear Research, Warsaw (Poland); Picchi, P [Turin Univ. (Italy). Ist. di Fisica; Consiglio Nazionale delle Ricerche, Turin (Italy). Lab. di Cosmo-Geofisica)

    1979-01-06

    The complete evaluation of the Glauber multiple-scattering series for nucleus-nucleus collisions is a very difficult task and that is why various approximate formulae were proposed. In this work some of these approximations are discussed.

  3. Two-Scale Modelling of Effects of Microstructure and Thermomechanical Properties on Dynamic Performance of an Aluminium Alloy

    Science.gov (United States)

    2010-09-01

    Influences of microstructure and properties of an aluminium alloy on resistance to dynamic perforation are predicted using a decoupled multiscale ... simulated performance. Library parameters typical for aluminium alloys (Kohn, 1969) are used for the macroscopic equation of state of Al 2139, details of...Two-Scale Modelling of Effects of Microstructure and Thermomechanical Properties on Dynamic Performance of an Aluminium Alloy by J. D

  4. Hierarchical low-rank approximation for high dimensional approximation

    KAUST Repository

    Nouy, Anthony

    2016-01-01

    Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.

  5. Hierarchical low-rank approximation for high dimensional approximation

    KAUST Repository

    Nouy, Anthony

    2016-01-07

    Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.

  6. Wigner representation in scattering problems

    International Nuclear Information System (INIS)

    Remler, E.A.

    1975-01-01

    The basic equations of quantum scattering are translated into the Wigner representation. This puts quantum mechanics in the form of a stochastic process in phase space. Instead of complex valued wavefunctions and transition matrices, one now works with real-valued probability distributions and source functions, objects more responsive to physical intuition. Aside from writing out certain necessary basic expressions, the main purpose is to develop and stress the interpretive picture associated with this representation and to derive results used in applications published elsewhere. The quasiclassical guise assumed by the formalism lends itself particularly to approximations of complex multiparticle scattering problems is laid. The foundation for a systematic application of statistical approximations to such problems. The form of the integral equation for scattering as well as its mulitple scattering expansion in this representation are derived. Since this formalism remains unchanged upon taking the classical limit, these results also constitute a general treatment of classical multiparticle collision theory. Quantum corrections to classical propogators are discussed briefly. The basic approximation used in the Monte Carlo method is derived in a fashion that allows for future refinement and includes bound state production. The close connection that must exist between inclusive production of a bound state and of its constituents is brought out in an especially graphic way by this formalism. In particular one can see how comparisons between such cross sections yield direct physical insight into relevant production mechanisms. A simple illustration of scattering by a bound two-body system is treated. Simple expressions for single- and double-scattering contributions to total and differential cross sections, as well as for all necessary shadow corrections thereto, are obtained and compared to previous results of Glauber and Goldberger

  7. Nernst effect beyond the relaxation-time approximation

    OpenAIRE

    Pikulin, D. I.; Hou, Chang-Yu; Beenakker, C. W. J.

    2011-01-01

    Motivated by recent interest in the Nernst effect in cuprate superconductors, we calculate this magneto-thermo-electric effect for an arbitrary (anisotropic) quasiparticle dispersion relation and elastic scattering rate. The exact solution of the linearized Boltzmann equation is compared with the commonly used relaxation-time approximation. We find qualitative deficiencies of this approximation, to the extent that it can get the sign wrong of the Nernst coefficient. Ziman's improvement of the...

  8. Characterization of porous materials by small-angle scattering

    Indian Academy of Sciences (India)

    With the availability of ultra small-angle scattering instruments, one can investigate porous materials in the sub-micron length scale. Because of the increased accessible length scale vis-a-vis the multiple scattering effect, conventional data analysis procedures based on single scattering approximation quite often fail.

  9. Forms of Approximate Radiation Transport

    CERN Document Server

    Brunner, G

    2002-01-01

    Photon radiation transport is described by the Boltzmann equation. Because this equation is difficult to solve, many different approximate forms have been implemented in computer codes. Several of the most common approximations are reviewed, and test problems illustrate the characteristics of each of the approximations. This document is designed as a tutorial so that code users can make an educated choice about which form of approximate radiation transport to use for their particular simulation.

  10. Electron scattering off palladium isotopes

    International Nuclear Information System (INIS)

    Laan, J.B. van der.

    1986-01-01

    The low-lying states of the even Pd isotopes are characterized by vibrator-like properties. In this thesis the results of an electron scattering experiment on the Pd isotopes, designed to study the description of such nuclei in the Anharmonic Vibrator Model (AVM) and the Interacting Boson Approximation (IBA), are presented and discussed. Data have been taken at the high-resolution electron scattering facility of NIKHEF-K and covered a momentum-transfer range of 0.4 to 2.5 fm -1 . (Auth.)

  11. Approximation by planar elastic curves

    DEFF Research Database (Denmark)

    Brander, David; Gravesen, Jens; Nørbjerg, Toke Bjerge

    2016-01-01

    We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good initial guess for the approximating curve. A gradient......-driven optimization is then used to find the approximating elastic curve....

  12. Exact constants in approximation theory

    CERN Document Server

    Korneichuk, N

    1991-01-01

    This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base

  13. International Conference Approximation Theory XIV

    CERN Document Server

    Schumaker, Larry

    2014-01-01

    This volume developed from papers presented at the international conference Approximation Theory XIV,  held April 7–10, 2013 in San Antonio, Texas. The proceedings contains surveys by invited speakers, covering topics such as splines on non-tensor-product meshes, Wachspress and mean value coordinates, curvelets and shearlets, barycentric interpolation, and polynomial approximation on spheres and balls. Other contributed papers address a variety of current topics in approximation theory, including eigenvalue sequences of positive integral operators, image registration, and support vector machines. This book will be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related approximation areas.

  14. The Nonrelativistic Scattering States of the Deng-Fan Potential

    Directory of Open Access Journals (Sweden)

    Bentol Hoda Yazarloo

    2013-01-01

    Full Text Available The approximately analytical scattering state solution of the Schrodinger equation is obtained for the Deng-Fan potential by using an approximation scheme to the centrifugal term. Energy eigenvalues, normalized wave functions, and scattering phase shifts are calculated. We consider and verify two special cases: the l=0 and the s-wave Hulthén potential.

  15. Scattering of acoustic waves by small crustaceans

    Science.gov (United States)

    Andreeva, I. B.; Tarasov, L. L.

    2003-03-01

    Features of underwater sound scattering by small crustaceans are considered. The scattering data are obtained with the use of unique instrumentation that allows one to measure quantitative scattering characteristics (backscattering cross sections and angular scattering patterns) for crustaceans of different sizes, at different frequencies (20 200 kHz) and different insonification aspects. A computational model of crustaceans is considered with allowance for both the soft tissues of the main massive part of the animal's body and the stiff armour. The model proves to be advantageous for explaining some scattering features observed in the experiments. The scattering cross sections of crustaceans measured by other researchers are presented in a unified form appropriate for comparison. Based on such a quantitative comparison, relatively simple approximate empirical formulas are proposed for estimating the backscattering cross sections of small (within several centimeters) marine crustaceans in a broad frequency range.

  16. Scattered radiation in fan beam imaging systems

    International Nuclear Information System (INIS)

    Johns, P.C.; Yaffe, M.

    1982-01-01

    Scatter-to-primary energy fluence ratios (S/P) have been studied for fan x-ray beams as used in CT scanners and slit projection radiography systems. The dependence of S/P on phantom diameter, distance from phantom to image receptor, and kilovoltage is presented. An empirical equation is given that predicts S/P over a wide range of fan beam imaging configurations. For CT body scans on a 4th-generation machine, S/P is approximately 5%. Scattered radiation can produce a significant cupping artefact in CT images which is similar to that due to beam hardening. When multiple slices are used in scanned slit radiography, they can be arranged such that the increase in S/P is negligible. Calculations of scatter-to-primary ratios for first order scattering showed that for fan beams the contribution of coherent scatter is comparable to or greater than that of incoherent first scatter

  17. Neutron scattering. Lectures

    International Nuclear Information System (INIS)

    Brueckel, Thomas; Heger, Gernot; Richter, Dieter; Roth, Georg; Zorn, Reiner

    2012-01-01

    The following topics are dealt with: Neutron scattering in contemporary research, neutron sources, symmetry of crystals, diffraction, nanostructures investigated by small-angle neutron scattering, the structure of macromolecules, spin dependent and magnetic scattering, structural analysis, neutron reflectometry, magnetic nanostructures, inelastic scattering, strongly correlated electrons, dynamics of macromolecules, applications of neutron scattering. (HSI)

  18. The scattering matrix element of the three body reactive collision

    International Nuclear Information System (INIS)

    Morsy, M.W.; Hilal, A.A.; El-Sabagh, M.A.

    1980-08-01

    The optical model approximation has been applied to a previously derived set of coupled equations representing the dynamics of the three-body reactive scattering. The Schroedinger equation obtained describing the scattering problem has then been solved by inserting the effective mass approximation. The asymptotic requirements for both the entrance and exit channels, respectively, have been supplied to give the scattering matrix element of the reactive collision. (author)

  19. Linear systems formulation of scattering theory for rough surfaces with arbitrary incident and scattering angles.

    Science.gov (United States)

    Krywonos, Andrey; Harvey, James E; Choi, Narak

    2011-06-01

    Scattering effects from microtopographic surface roughness are merely nonparaxial diffraction phenomena resulting from random phase variations in the reflected or transmitted wavefront. Rayleigh-Rice, Beckmann-Kirchhoff. or Harvey-Shack surface scatter theories are commonly used to predict surface scatter effects. Smooth-surface and/or paraxial approximations have severely limited the range of applicability of each of the above theoretical treatments. A recent linear systems formulation of nonparaxial scalar diffraction theory applied to surface scatter phenomena resulted first in an empirically modified Beckmann-Kirchhoff surface scatter model, then a generalized Harvey-Shack theory that produces accurate results for rougher surfaces than the Rayleigh-Rice theory and for larger incident and scattered angles than the classical Beckmann-Kirchhoff and the original Harvey-Shack theories. These new developments simplify the analysis and understanding of nonintuitive scattering behavior from rough surfaces illuminated at arbitrary incident angles.

  20. Conference on Abstract Spaces and Approximation

    CERN Document Server

    Szökefalvi-Nagy, B; Abstrakte Räume und Approximation; Abstract spaces and approximation

    1969-01-01

    The present conference took place at Oberwolfach, July 18-27, 1968, as a direct follow-up on a meeting on Approximation Theory [1] held there from August 4-10, 1963. The emphasis was on theoretical aspects of approximation, rather than the numerical side. Particular importance was placed on the related fields of functional analysis and operator theory. Thirty-nine papers were presented at the conference and one more was subsequently submitted in writing. All of these are included in these proceedings. In addition there is areport on new and unsolved problems based upon a special problem session and later communications from the partici­ pants. A special role is played by the survey papers also presented in full. They cover a broad range of topics, including invariant subspaces, scattering theory, Wiener-Hopf equations, interpolation theorems, contraction operators, approximation in Banach spaces, etc. The papers have been classified according to subject matter into five chapters, but it needs littl...

  1. Scattering of electromagnetic waves by a traversable wormhole

    Directory of Open Access Journals (Sweden)

    B. Nasr Esfahani

    2005-09-01

    Full Text Available   Replacing the wormhole geometry with an equivalent medium using the perturbation theory of scattering and the Born approximation, we have calculated the differential scattering cross section of electromagnetic waves by a traversable wormhole. It is shown that scattering at long wavelenghts can essentially distinguish wormhole from ordinary scattering object. Some of the zeros of the scattering cross section are determined which can be used for estimating the radius of the throat of wormholes. The known result that in this kind of scattering the linear polarization remains unchanged is verified here.

  2. Practical model for the calculation of multiply scattered lidar returns

    International Nuclear Information System (INIS)

    Eloranta, E.W.

    1998-01-01

    An equation to predict the intensity of the multiply scattered lidar return is presented. Both the scattering cross section and the scattering phase function can be specified as a function of range. This equation applies when the cloud particles are larger than the lidar wavelength. This approximation considers photon trajectories with multiple small-angle forward-scattering events and one large-angle scattering that directs the photon back toward the receiver. Comparisons with Monte Carlo simulations, exact double-scatter calculations, and lidar data demonstrate that this model provides accurate results. copyright 1998 Optical Society of America

  3. SCATTERING FROM RAMIFIED POLYMERIC SYSTEMS

    Directory of Open Access Journals (Sweden)

    M.Benhamou

    2004-01-01

    Full Text Available Here, of great interest to us is a quantitative study of the scattering properties from ramified polymeric systems of arbitrary topology. We consider three types of systems, namely ramified polymers in solution, ramified polymer blends, or ternary mixtures made of two ramified polymers of different chemical nature immersed in a good solvent. To achieve the goal of the study, use is made of the Random Phase Approximation. First we determine the exact expression of the form factor of an ideal ramified polymer of any topology, from which we extract the exact expression of its gyration radius. Using the classical Zimm's formulae and the exact form factor, we determine all scattering properties of these three types of ramified polymeric systems. The main conclusion is that ramification of the chains induces drastic changes of the scattering properties.

  4. Certain theories of multiple scattering in random media of discrete scatterers

    International Nuclear Information System (INIS)

    Olsen, R.L.; Kharadly, M.M.Z.; Corr, D.G.

    1976-01-01

    New information is presented on the accuracy of the heuristic approximations in two important theories of multiple scattering in random media of discrete scatterers: Twersky's ''free-space'' and ''two-space scatterer'' formalisms. Two complementary approaches, based primarily on a one-dimensional model and the one-dimensional forms of the theories, are used. For scatterer distributions of low average density, the ''heuristic'' asymptotic forms for the coherent field and the incoherent intensity are compared with asymptotic forms derived from a systematic analysis of the multiple scattering processes. For distributions of higher density, both in the average number of scatterers per wavelength and in the degree of packing of finite-size scatterers, the analysis is carried out ''experimentally'' by means of a Monte Carlo computer simulation. Approximate series expressions based on the systematic approach are numerically evaluated along with the heuristic expressions. The comparison (for both forward- and back-scattered field moments) is made for the worst-case conditions of strong multiple scattering for which the theories have not previously been evaluated. Several significant conclusions are drawn which have certain practical implications: in application of the theories to describe some of the scattering phenomena which occur in the troposphere, and in the further evaluation of the theories using experiments on physical models

  5. Some results in Diophantine approximation

    DEFF Research Database (Denmark)

    Pedersen, Steffen Højris

    the basic concepts on which the papers build. Among other it introduces metric Diophantine approximation, Mahler’s approach on algebraic approximation, the Hausdorff measure, and properties of the formal Laurent series over Fq. The introduction ends with a discussion on Mahler’s problem when considered......This thesis consists of three papers in Diophantine approximation, a subbranch of number theory. Preceding these papers is an introduction to various aspects of Diophantine approximation and formal Laurent series over Fq and a summary of each of the three papers. The introduction introduces...

  6. Limitations of shallow nets approximation.

    Science.gov (United States)

    Lin, Shao-Bo

    2017-10-01

    In this paper, we aim at analyzing the approximation abilities of shallow networks in reproducing kernel Hilbert spaces (RKHSs). We prove that there is a probability measure such that the achievable lower bound for approximating by shallow nets can be realized for all functions in balls of reproducing kernel Hilbert space with high probability, which is different with the classical minimax approximation error estimates. This result together with the existing approximation results for deep nets shows the limitations for shallow nets and provides a theoretical explanation on why deep nets perform better than shallow nets. Copyright © 2017 Elsevier Ltd. All rights reserved.

  7. Self-consistent approximations beyond the CPA: Part II

    International Nuclear Information System (INIS)

    Kaplan, T.; Gray, L.J.

    1982-01-01

    This paper concentrates on a self-consistent approximation for random alloys developed by Kaplan, Leath, Gray, and Diehl. The construction of the augmented space formalism for a binary alloy is sketched, and the notation to be used derived. Using the operator methods of the augmented space, the self-consistent approximation is derived for the average Green's function, and for evaluating the self-energy, taking into account the scattering by clusters of excitations. The particular cluster approximation desired is derived by treating the scattering by the excitations with S /SUB T/ exactly. Fourier transforms on the disorder-space clustersite labels solve the self-consistent set of equations. Expansion to short range order in the alloy is also discussed. A method to reduce the problem to a computationally tractable form is described

  8. Scattering Solar Thermal Concentrators

    Energy Technology Data Exchange (ETDEWEB)

    Giebink, Noel C. [Pennsylvania State Univ., State College, PA (United States)

    2015-01-31

    This program set out to explore a scattering-based approach to concentrate sunlight with the aim of improving collector field reliability and of eliminating wind loading and gross mechanical movement through the use of a stationary collection optic. The approach is based on scattering sunlight from the focal point of a fixed collection optic into the confined modes of a sliding planar waveguide, where it is transported to stationary tubular heat transfer elements located at the edges. Optical design for the first stage of solar concentration, which entails focusing sunlight within a plane over a wide range of incidence angles (>120 degree full field of view) at fixed tilt, led to the development of a new, folded-path collection optic that dramatically out-performs the current state-of-the-art in scattering concentration. Rigorous optical simulation and experimental testing of this collection optic have validated its performance. In the course of this work, we also identified an opportunity for concentrating photovoltaics involving the use of high efficiency microcells made in collaboration with partners at the University of Illinois. This opportunity exploited the same collection optic design as used for the scattering solar thermal concentrator and was therefore pursued in parallel. This system was experimentally demonstrated to achieve >200x optical concentration with >70% optical efficiency over a full day by tracking with <1 cm of lateral movement at fixed latitude tilt. The entire scattering concentrator waveguide optical system has been simulated, tested, and assembled at small scale to verify ray tracing models. These models were subsequently used to predict the full system optical performance at larger, deployment scale ranging up to >1 meter aperture width. Simulations at an aperture widths less than approximately 0.5 m with geometric gains ~100x predict an overall optical efficiency in the range 60-70% for angles up to 50 degrees from normal. However, the

  9. Bidirectional optical scattering facility

    Data.gov (United States)

    Federal Laboratory Consortium — Goniometric optical scatter instrument (GOSI)The bidirectional reflectance distribution function (BRDF) quantifies the angular distribution of light scattered from a...

  10. Random phase approximation in relativistic approach

    International Nuclear Information System (INIS)

    Ma Zhongyu; Yang Ding; Tian Yuan; Cao Ligang

    2009-01-01

    Some special issues of the random phase approximation(RPA) in the relativistic approach are reviewed. A full consistency and proper treatment of coupling to the continuum are responsible for the successful application of the RPA in the description of dynamical properties of finite nuclei. The fully consistent relativistic RPA(RRPA) requires that the relativistic mean filed (RMF) wave function of the nucleus and the RRPA correlations are calculated in a same effective Lagrangian and the consistent treatment of the Dirac sea of negative energy states. The proper treatment of the single particle continuum with scattering asymptotic conditions in the RMF and RRPA is discussed. The full continuum spectrum can be described by the single particle Green's function and the relativistic continuum RPA is established. A separable form of the paring force is introduced in the relativistic quasi-particle RPA. (authors)

  11. Polarized constituent quarks in NLO approximation

    International Nuclear Information System (INIS)

    Khorramian, Ali N.; Tehrani, S. Atashbar; Mirjalili, A.

    2006-01-01

    The valon representation provides a basis between hadrons and quarks, in terms of which the bound-state and scattering properties of hadrons can be united and described. We studied polarized valon distributions which have an important role in describing the spin dependence of parton distribution in leading and next-to-leading order approximation. Convolution integral in frame work of valon model as a useful tool, was used in polarized case. To obtain polarized parton distributions in a proton we need to polarized valon distribution in a proton and polarized parton distributions inside the valon. We employed Bernstein polynomial averages to get unknown parameters of polarized valon distributions by fitting to available experimental data

  12. Electron scattering by hydrogen atoms

    International Nuclear Information System (INIS)

    Fujii, D.H.

    1981-02-01

    A variational method to calculate the differential cross section of the electron-hydrogen atom scattering process is presented. The second Born approximation is calculated, through a variational calculation using the energy and electronic charge simultaneously as parameters, in order to calculate the differential cross section which is written in a fractional form according to the Schwinger variational principle. Effects due to the electron change are included in the calculations. (L.C.) [pt

  13. Multichannel Thomson scattering apparatus

    International Nuclear Information System (INIS)

    Bretz, N.; Dimock, D.; Foote, V.; Johnson, D.; Long, D.; Tolnas, E.

    1977-07-01

    A Thomson scattering apparatus for measuring the electron temperature and density along a 90 cm diameter of the PLT plasma has been built. A wide angle objective images the 3 mm x 900 mm ruby laser beam onto an image dissector which rearranges the 300 : 1 image to 20 : 1 forming the input slit of a spectrometer. The stigmatic spectrometer provides 20 wavelength elements of approximately 70 A each. A micro-channel-plate image intensifier optically coupled to a cooled SIT tube provides detection with single frame linearity and 1000 : 1 dynamic range. Spatial profiles of N/sub e/ and T/sub e/ in the range 10 13 - 10 14 cm -3 and 0.05 - 3 keV have an accuracy of 30 √10 13 /N/sub e/ (cm -3 ) percent per 1.2 cm element

  14. Spherical Approximation on Unit Sphere

    Directory of Open Access Journals (Sweden)

    Eman Samir Bhaya

    2018-01-01

    Full Text Available In this paper we introduce a Jackson type theorem for functions in LP spaces on sphere And study on best approximation of  functions in  spaces defined on unit sphere. our central problem is to describe the approximation behavior of functions in    spaces for  by modulus of smoothness of functions.

  15. Approximate circuits for increased reliability

    Science.gov (United States)

    Hamlet, Jason R.; Mayo, Jackson R.

    2015-08-18

    Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.

  16. Finite-rank potential that reproduces the Pade approximant

    International Nuclear Information System (INIS)

    Tani, S.

    1979-01-01

    If a scattering potential is of a finite rank, say N, the exact solution of the problem can be obtained from the Born series, if the potential strength is within the radius of convergence; the exact solution can be obtained from the analytical continuation of the formal Born series outside the radius of convergence. Beyond the first 2N terms of the Born series, an individual term of the Born series depends on the first 2N terms, and the [N/N] Pade approximant and the exact solution agree with each other. The above-mentioned features of a finite-rank problem are relevant to scattering theory in general, because most scattering problems may be handled as an extension of the rank-N problem, in which the rank N tends to infinity. The foregoing aspects of scattering theory will be studied in depth in the present paper, and in so doing we proceed in the opposite direction. Namely, given a potential, we calculate the first 2N terms of the Born series for the K matrix and the first N terms of the Born series for the wave function. Using these data, a special rank-N potential is constructed in such a way that it reproduces the [N/N] Pade approximant of the K matrix of the original scattering problem. One great advantage of obtaining such a rank-N potential is that the wave function of the system may be approximated in the same spirit as done for the K matrix; hence, we can introduce a new approximation method for dealing with an off-shell T matrix. A part of the mathematical work is incomplete, but the physical aspects are thoroughly discussed

  17. Approximate Dynamic Programming: Combining Regional and Local State Following Approximations.

    Science.gov (United States)

    Deptula, Patryk; Rosenfeld, Joel A; Kamalapurkar, Rushikesh; Dixon, Warren E

    2018-06-01

    An infinite-horizon optimal regulation problem for a control-affine deterministic system is solved online using a local state following (StaF) kernel and a regional model-based reinforcement learning (R-MBRL) method to approximate the value function. Unlike traditional methods such as R-MBRL that aim to approximate the value function over a large compact set, the StaF kernel approach aims to approximate the value function in a local neighborhood of the state that travels within a compact set. In this paper, the value function is approximated using a state-dependent convex combination of the StaF-based and the R-MBRL-based approximations. As the state enters a neighborhood containing the origin, the value function transitions from being approximated by the StaF approach to the R-MBRL approach. Semiglobal uniformly ultimately bounded (SGUUB) convergence of the system states to the origin is established using a Lyapunov-based analysis. Simulation results are provided for two, three, six, and ten-state dynamical systems to demonstrate the scalability and performance of the developed method.

  18. Soft Gluon Radiation off Heavy Quarks beyond Eikonal Approximation

    International Nuclear Information System (INIS)

    Mazumder, Surasree; Bhattacharyya, Trambak; Abir, Raktim

    2016-01-01

    We calculate the soft gluon radiation spectrum off heavy quarks (HQs) interacting with light quarks (LQs) beyond small angle scattering (eikonality) approximation and thus generalize the dead-cone formula of heavy quarks extensively used in the literatures of Quark-Gluon Plasma (QGP) phenomenology to the large scattering angle regime which may be important in the energy loss of energetic heavy quarks in the deconfined Quark-Gluon Plasma medium. In the proper limits, we reproduce all the relevant existing formulae for the gluon radiation distribution off energetic quarks, heavy or light, used in the QGP phenomenology.

  19. Impact parameter dynamics in quantum theory in large angle scattering

    International Nuclear Information System (INIS)

    Andriyanov, A.A.

    1975-01-01

    High energy behaviour of a free particle Green's function is studied for construction of the scattering amplitude. The main part of the Green's function is determined by eikonal scattering along the mean moment and by the total scattering along the transfered momentum. This ''impact'' approximation may be included as a first approximation in the iteration scheme for the scattering amplitude along the mean momentum, i.e. the ''impact'' perturbation theory. With the help of the ''impact'' approximation an expansion of the scattering amplitude in the impact parameter depending on interaction is obtained. These expansions are more correct than the eikonal expansions at large angle scattering. The results are illustrated grafically foe the exponential and the Yukawa potentials

  20. The efficiency of Flory approximation

    International Nuclear Information System (INIS)

    Obukhov, S.P.

    1984-01-01

    The Flory approximation for the self-avoiding chain problem is compared with a conventional perturbation theory expansion. While in perturbation theory each term is averaged over the unperturbed set of configurations, the Flory approximation is equivalent to the perturbation theory with the averaging over the stretched set of configurations. This imposes restrictions on the integration domain in higher order terms and they can be treated self-consistently. The accuracy δν/ν of Flory approximation for self-avoiding chain problems is estimated to be 2-5% for 1 < d < 4. (orig.)

  1. Geometrical effects in X-mode scattering

    International Nuclear Information System (INIS)

    Bretz, N.

    1986-10-01

    One technique to extend microwave scattering as a probe of long wavelength density fluctuations in magnetically confined plasmas is to consider the launching and scattering of extraordinary (X-mode) waves nearly perpendicular to the field. When the incident frequency is less than the electron cyclotron frequency, this mode can penetrate beyond the ordinary mode cutoff at the plasma frequency and avoid significant distortions from density gradients typical of tokamak plasmas. In the more familiar case, where the incident and scattered waves are ordinary, the scattering is isotropic perpendicular to the field. However, because the X-mode polarization depends on the frequency ratios and the ray angle to the magnetic field, the coupling between the incident and scattered waves is complicated. This geometrical form factor must be unfolded from the observed scattering in order to interpret the scattering due to density fluctuations alone. The geometrical factor is calculated here for the special case of scattering perpendicular to the magnetic field. For frequencies above the ordinary mode cutoff the scattering is relatively isotropic, while below cutoff there are minima in the forward and backward directions which go to zero at approximately half the ordinary mode cutoff density

  2. Neutron scattering. Lectures

    Energy Technology Data Exchange (ETDEWEB)

    Brueckel, Thomas; Heger, Gernot; Richter, Dieter; Roth, Georg; Zorn, Reiner [eds.

    2010-07-01

    The following topics are dealt with: Neutron sources, symmetry of crystals, diffraction, nanostructures investigated by small-angle neutron scattering, the structure of macromolecules, spin dependent and magnetic scattering, structural analysis, neutron reflectometry, magnetic nanostructures, inelastic scattering, strongly correlated electrons, dynamics of macromolecules, applications of neutron scattering. (HSI)

  3. Neutron scattering. Lectures

    International Nuclear Information System (INIS)

    Brueckel, Thomas; Heger, Gernot; Richter, Dieter; Roth, Georg; Zorn, Reiner

    2013-01-01

    The following topics are dealt with: Neutron sources, symmetry of crystals, nanostructures investigated by small-angle neutron scattering, structure of macromolecules, spin dependent and magnetic scattering, structural analysis, neutron reflectometry, magnetic nanostructures, inelastic neutron scattering, strongly correlated electrons, polymer dynamics, applications of neutron scattering. (HSI)

  4. Neutron scattering. Lectures

    International Nuclear Information System (INIS)

    Brueckel, Thomas; Heger, Gernot; Richter, Dieter; Roth, Georg; Zorn, Reiner

    2010-01-01

    The following topics are dealt with: Neutron sources, symmetry of crystals, diffraction, nanostructures investigated by small-angle neutron scattering, the structure of macromolecules, spin dependent and magnetic scattering, structural analysis, neutron reflectometry, magnetic nanostructures, inelastic scattering, strongly correlated electrons, dynamics of macromolecules, applications of neutron scattering. (HSI)

  5. Multiple scattering of ions in polyatomic materials

    International Nuclear Information System (INIS)

    Eastham, D.A.

    1980-01-01

    The equations which determine small angle multiple scattering in the thin polyatomic layers are evaluated numerically for certain cases. A simple approximate method for calculating the scattering in terms of an average target charge which is a function of the target thickness is given and compared with the exact numerical value. The results agree to better than 5% over a wide range of target composition and thickness. (orig.)

  6. Approximate Implicitization Using Linear Algebra

    Directory of Open Access Journals (Sweden)

    Oliver J. D. Barrowclough

    2012-01-01

    Full Text Available We consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore well suited to floating-point implementation in computer-aided geometric design (CAGD systems. We unify the approaches under the names of commonly known polynomial basis functions and consider various theoretical and practical aspects of the algorithms. We offer new methods for a least squares approach to approximate implicitization using orthogonal polynomials, which tend to be faster and more numerically stable than some existing algorithms. We propose several simple propositions relating the properties of the polynomial bases to their implicit approximation properties.

  7. Rollout sampling approximate policy iteration

    NARCIS (Netherlands)

    Dimitrakakis, C.; Lagoudakis, M.G.

    2008-01-01

    Several researchers have recently investigated the connection between reinforcement learning and classification. We are motivated by proposals of approximate policy iteration schemes without value functions, which focus on policy representation using classifiers and address policy learning as a

  8. Weighted approximation with varying weight

    CERN Document Server

    Totik, Vilmos

    1994-01-01

    A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.

  9. Framework for sequential approximate optimization

    NARCIS (Netherlands)

    Jacobs, J.H.; Etman, L.F.P.; Keulen, van F.; Rooda, J.E.

    2004-01-01

    An object-oriented framework for Sequential Approximate Optimization (SAO) isproposed. The framework aims to provide an open environment for thespecification and implementation of SAO strategies. The framework is based onthe Python programming language and contains a toolbox of Python

  10. Diffraction scattering of strongly bound system

    International Nuclear Information System (INIS)

    Kuzmichev, V.E.

    1982-04-01

    The scattering of a hadron on a strongly bound system of two hadrons (dihadron) is considered in the high-energy limit for the relative hadron-dihadron motion. The dihadron scatterer motion and the internal interaction are included in our consideration. It is shown that only small values of the internal transfer momentum of dihadron particles bring the principal contribution to the three-particle propagator in eikonal approximation. On the basis of the exact analytical solution of the integral equation for the total Green function the scattering amplitude is derived. It is shown that the scattering amplitude contains only single, double, and triple scattering terms. The three new terms to the Glauber formula for the total cross section are obtained. These terms decrease both the true total hadron-hadron cross section and the screening correction. (orig.)

  11. Radiofrequency encoded angular-resolved light scattering

    DEFF Research Database (Denmark)

    Buckley, Brandon W.; Akbari, Najva; Diebold, Eric D.

    2015-01-01

    The sensitive, specific, and label-free classification of microscopic cells and organisms is one of the outstanding problems in biology. Today, instruments such as the flow cytometer use a combination of light scatter measurements at two distinct angles to infer the size and internal complexity...... of cells at rates of more than 10,000 per second. However, by examining the entire angular light scattering spectrum it is possible to classify cells with higher resolution and specificity. Current approaches to performing these angular spectrum measurements all have significant throughput limitations...... Encoded Angular-resolved Light Scattering (REALS), this technique multiplexes angular light scattering in the radiofrequency domain, such that a single photodetector captures the entire scattering spectrum from a particle over approximately 100 discrete incident angles on a single shot basis. As a proof...

  12. Inelastic scattering of fast electrons by crystals

    International Nuclear Information System (INIS)

    Allen, L.J.; Josefsson, T.W.

    1995-01-01

    Generalized fundamental equations for electron diffraction in crystals, which include the effect of inelastic scattering described by a nonlocal interaction, are derived. An expression is obtained for the cross section for any specific type of inelastic scattering (e.g. inner-shell ionization, Rutherford backscattering). This result takes into account all other (background) inelastic scattering in the crystal leading to absorption from the dynamical Bragg-reflected beams, in practice mainly due to thermal diffuse scattering. There is a contribution to the cross section from all absorbed electrons, which form a diffuse background, as well as from the dynamical electrons. The approximations involved, assuming that the interactions leading to inelastic scattering can be described by a local potential are discussed, together with the corresponding expression for the cross section. It is demonstrated by means of an example for K-shell electron energy loss spectroscopy that nonlocal effects can be significant. 47 refs., 4 figs

  13. The reactive content of the proton-nucleus impulse - approximation Dirac optical potential

    International Nuclear Information System (INIS)

    Carlson, B.V.; Isidro Filho, M.P.; Hussein, M.S.

    1984-01-01

    The total reaction cross sections for intermediate energy proton scattering on 40 Ca and 208 Pb are calculated within the Dirac-Eikonal formalism. Comparison with data indicate that the recently proposed impulse-approximation Dirac optical potential for nucleon-nucleus scattering, is not absorptive enough. (Author) [pt

  14. Approximative Krieger-Nelkin orientation averaging and anisotropy of water molecules vibrations

    International Nuclear Information System (INIS)

    Markovic, M.I.

    1974-01-01

    Quantum-mechanics approach of water molecules dynamics should be taken into account for precise theoretical calculation of differential scattering cross sections of neutrons. Krieger and Nelkin have proposed an approximate method for averaging orientation of molecules regarding directions of incoming and scattered neutron. This paper shows that this approach can be successfully applied for general shape of water molecule vibration anisotropy

  15. A Monte Carlo evaluation of analytical multiple scattering corrections for unpolarised neutron scattering and polarisation analysis data

    International Nuclear Information System (INIS)

    Mayers, J.; Cywinski, R.

    1985-03-01

    Some of the approximations commonly used for the analytical estimation of multiple scattering corrections to thermal neutron elastic scattering data from cylindrical and plane slab samples have been tested using a Monte Carlo program. It is shown that the approximations are accurate for a wide range of sample geometries and scattering cross-sections. Neutron polarisation analysis provides the most stringent test of multiple scattering calculations as multiply scattered neutrons may be redistributed not only geometrically but also between the spin flip and non spin flip scattering channels. A very simple analytical technique for correcting for multiple scattering in neutron polarisation analysis has been tested using the Monte Carlo program and has been shown to work remarkably well in most circumstances. (author)

  16. Neutron scattering. Lectures

    Energy Technology Data Exchange (ETDEWEB)

    Brueckel, Thomas; Heger, Gernot; Richter, Dieter; Roth, Georg; Zorn, Reiner (eds.)

    2010-07-01

    The following topics are dealt with: Neutron sources, neutron properties and elastic scattering, correlation functions measured by scattering experiments, symmetry of crystals, applications of neutron scattering, polarized-neutron scattering and polarization analysis, structural analysis, magnetic and lattice excitation studied by inelastic neutron scattering, macromolecules and self-assembly, dynamics of macromolecules, correlated electrons in complex transition-metal oxides, surfaces, interfaces, and thin films investigated by neutron reflectometry, nanomagnetism. (HSI)

  17. Neutron scattering. Lectures

    International Nuclear Information System (INIS)

    Brueckel, Thomas; Heger, Gernot; Richter, Dieter; Roth, Georg; Zorn, Reiner

    2010-01-01

    The following topics are dealt with: Neutron sources, neutron properties and elastic scattering, correlation functions measured by scattering experiments, symmetry of crystals, applications of neutron scattering, polarized-neutron scattering and polarization analysis, structural analysis, magnetic and lattice excitation studied by inelastic neutron scattering, macromolecules and self-assembly, dynamics of macromolecules, correlated electrons in complex transition-metal oxides, surfaces, interfaces, and thin films investigated by neutron reflectometry, nanomagnetism. (HSI)

  18. Efficient Fixed-Offset GPR Scattering Analysis

    DEFF Research Database (Denmark)

    Meincke, Peter; Chen, Xianyao

    2004-01-01

    The electromagnetic scattering by buried three-dimensional penetrable objects, as involved in the analysis of ground penetrating radar systems, is calculated using the extended Born approximation. The involved scattering tensor is calculated using fast Fourier transforms (FFT's). We incorporate...... in the scattering calculation the correct radiation patterns of the ground penetrating radar antennas by using their plane-wave transmitting and receiving spectra. Finally, we derive an efficient FFT-based method to analyze a fixed-offset configuration in which the location of the transmitting antenna is different...

  19. Monte Carlo simulations of neutron scattering instruments

    International Nuclear Information System (INIS)

    Aestrand, Per-Olof; Copenhagen Univ.; Lefmann, K.; Nielsen, K.

    2001-01-01

    A Monte Carlo simulation is an important computational tool used in many areas of science and engineering. The use of Monte Carlo techniques for simulating neutron scattering instruments is discussed. The basic ideas, techniques and approximations are presented. Since the construction of a neutron scattering instrument is very expensive, Monte Carlo software used for design of instruments have to be validated and tested extensively. The McStas software was designed with these aspects in mind and some of the basic principles of the McStas software will be discussed. Finally, some future prospects are discussed for using Monte Carlo simulations in optimizing neutron scattering experiments. (R.P.)

  20. Medium energy hadron scattering from nuclei

    International Nuclear Information System (INIS)

    Ginocchio, J.N.; Wenes, G.

    1986-01-01

    The Glauber approximation for medium energy scattering of hadronic projectiles from nuclei is combined with the interacting boson model of nuclei to produce a transition matrix for elastic and inelastic scattering in algebraic form which includes coupling to all the intermediate states. We present closed form analytic expresions for the transition matrix elements for the three dynamical symmetries of the interacting boson model; that is for, a spherical quadrupole vibrator, a γ unstable rotor, and both prolate and oblate axially symmetric rotors. We give examples of application of this formalism to proton scattering from 154 Sm and 154 Gd. 27 refs., 5 figs., 1 tab

  1. Light-scattering theory of diffraction.

    Science.gov (United States)

    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.

  2. Approximate quantum differential cross section for the F + HD → HF + D and DF + H reactions

    International Nuclear Information System (INIS)

    Lee, K.T.; Bowman, J.M.

    1982-01-01

    In a previous paper we proposed a novel way to obtain approximate quantum mechanical differential cross sections. Here, we use this approximate method to study the reactions F + HD(nu = 0) → FH(nu' = 2) + D and F + DH(nu = 0) → DF(nu' = 3) + H. Backward and forward scattering are found for the first reaction and only backward scattering for the second one. These results agree qualitatively with experiment. 1 figure

  3. The Role of Mesonic Degrees of Freedom in Scattering of Hardrons on Nuclei

    DEFF Research Database (Denmark)

    Kofoed-Hansen, O.

    1978-01-01

    The Glauber multiple scattering is reviewed, its experimental success described and its essential approximations enumerated. A simple harmonic oscillator model of mesonic degrees of freedom is constructed and Glauber scattering evaluated. The difficulties in fitting experimental amplitude data va...

  4. Direct numerical reconstruction of conductivities in three dimensions using scattering transforms

    DEFF Research Database (Denmark)

    Bikowski, Jutta; Knudsen, Kim; Mueller, Jennifer L

    2011-01-01

    A direct three-dimensional EIT reconstruction algorithm based on complex geometrical optics solutions and a nonlinear scattering transform is presented and implemented for spherically symmetric conductivity distributions. The scattering transform is computed both with a Born approximation and from...

  5. Nuclear Hartree-Fock approximation testing and other related approximations

    International Nuclear Information System (INIS)

    Cohenca, J.M.

    1970-01-01

    Hartree-Fock, and Tamm-Dancoff approximations are tested for angular momentum of even-even nuclei. Wave functions, energy levels and momenta are comparatively evaluated. Quadripole interactions are studied following the Elliott model. Results are applied to Ne 20 [pt

  6. Validation of two scales for measuring participation and perceived stigma in Chinese community-based rehabilitation programs.

    Science.gov (United States)

    Chung, Eva Yin-Han; Lam, Gigi

    2018-05-29

    The World Health Organization has asserted the importance of enhancing participation of people with disabilities within the International Classification of Functioning, Disability and Health framework. Participation is regarded as a vital outcome in community-based rehabilitation. The actualization of the right to participate is limited by social stigma and discrimination. To date, there is no validated instrument for use in Chinese communities to measure participation restriction or self-perceived stigma. This study aimed to translate and validate the Participation Scale and the Explanatory Model Interview Catalogue (EMIC) Stigma Scale for use in Chinese communities with people with physical disabilities. The Chinese versions of the Participation Scale and the EMIC stigma scale were administered to 264 adults with physical disabilities. The two scales were examined separately. The reliability analysis was studied in conjunction with the construct validity. Reliability analysis was conducted to assess the internal consistency and item-total correlation. Exploratory factor analysis was conducted to investigate the latent patterns of relationships among variables. A Rasch model analysis was conducted to test the dimensionality, internal validity, item hierarchy, and scoring category structure of the two scales. Both the Participation Scale and the EMIC stigma scale were confirmed to have good internal consistency and high item-total correlation. Exploratory factor analysis revealed the factor structure of the two scales, which demonstrated the fitting of a pattern of variables within the studied construct. The Participation Scale was found to be multidimensional, whereas the EMIC stigma scale was confirmed to be unidimensional. The item hierarchies of the Participation Scale and the EMIC stigma scale were discussed and were regarded as compatible with the cultural characteristics of Chinese communities. The Chinese versions of the Participation Scale and the EMIC

  7. Semi-classical approximation to path integrals - phases and catastrophes

    International Nuclear Information System (INIS)

    Levit, S.

    1977-01-01

    Problems of phases and catastrophes were encountered when trying to apply the classical S-matrix theory to the scattering phenomena in nuclear physics. The path integral formulation provided a suitable basis for the treatment of these and related problems. Within conventional mathematical language it was possible to give practical prescriptions and discuss their limitations. Since the semi-classical (stationary phase) approximation is commonly used in any application of the path integral method, the results are not restricted to the scattering problems and may be of general interest. The derivation of the uniform approximations in the energy representation should use the exact path integral expression as the starting point, rather than performing Fourier transforms on the expressions derived in the present lecture. (B.G.)

  8. Shearlets and Optimally Sparse Approximations

    DEFF Research Database (Denmark)

    Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q

    2012-01-01

    Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient analysis is the provision of optimally sparse approximations...... optimally sparse approximations of this model class in 2D as well as 3D. Even more, in contrast to all other directional representation systems, a theory for compactly supported shearlet frames was derived which moreover also satisfy this optimality benchmark. This chapter shall serve as an introduction...... to and a survey about sparse approximations of cartoon-like images by band-limited and also compactly supported shearlet frames as well as a reference for the state-of-the-art of this research field....

  9. Diophantine approximation and Dirichlet series

    CERN Document Server

    Queffélec, Hervé

    2013-01-01

    This self-contained book will benefit beginners as well as researchers. It is devoted to Diophantine approximation, the analytic theory of Dirichlet series, and some connections between these two domains, which often occur through the Kronecker approximation theorem. Accordingly, the book is divided into seven chapters, the first three of which present tools from commutative harmonic analysis, including a sharp form of the uncertainty principle, ergodic theory and Diophantine approximation to be used in the sequel. A presentation of continued fraction expansions, including the mixing property of the Gauss map, is given. Chapters four and five present the general theory of Dirichlet series, with classes of examples connected to continued fractions, the famous Bohr point of view, and then the use of random Dirichlet series to produce non-trivial extremal examples, including sharp forms of the Bohnenblust-Hille theorem. Chapter six deals with Hardy-Dirichlet spaces, which are new and useful Banach spaces of anal...

  10. Approximations to camera sensor noise

    Science.gov (United States)

    Jin, Xiaodan; Hirakawa, Keigo

    2013-02-01

    Noise is present in all image sensor data. Poisson distribution is said to model the stochastic nature of the photon arrival process, while it is common to approximate readout/thermal noise by additive white Gaussian noise (AWGN). Other sources of signal-dependent noise such as Fano and quantization also contribute to the overall noise profile. Question remains, however, about how best to model the combined sensor noise. Though additive Gaussian noise with signal-dependent noise variance (SD-AWGN) and Poisson corruption are two widely used models to approximate the actual sensor noise distribution, the justification given to these types of models are based on limited evidence. The goal of this paper is to provide a more comprehensive characterization of random noise. We concluded by presenting concrete evidence that Poisson model is a better approximation to real camera model than SD-AWGN. We suggest further modification to Poisson that may improve the noise model.

  11. Rational approximations for tomographic reconstructions

    International Nuclear Information System (INIS)

    Reynolds, Matthew; Beylkin, Gregory; Monzón, Lucas

    2013-01-01

    We use optimal rational approximations of projection data collected in x-ray tomography to improve image resolution. Under the assumption that the object of interest is described by functions with jump discontinuities, for each projection we construct its rational approximation with a small (near optimal) number of terms for a given accuracy threshold. This allows us to augment the measured data, i.e., double the number of available samples in each projection or, equivalently, extend (double) the domain of their Fourier transform. We also develop a new, fast, polar coordinate Fourier domain algorithm which uses our nonlinear approximation of projection data in a natural way. Using augmented projections of the Shepp–Logan phantom, we provide a comparison between the new algorithm and the standard filtered back-projection algorithm. We demonstrate that the reconstructed image has improved resolution without additional artifacts near sharp transitions in the image. (paper)

  12. Approximation methods in probability theory

    CERN Document Server

    Čekanavičius, Vydas

    2016-01-01

    This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function. Emphasising the correct usage of the methods presented, each step required for the proofs is examined in detail. As a result, this textbook provides valuable tools for proving approximation theorems. While Approximation Methods in Probability Theory will appeal to everyone interested in limit theorems of probability theory, the book is particularly aimed at graduate students who have completed a standard intermediate course in probability theory. Furthermore, experienced researchers wanting to enlarge their toolkit will also find this book useful.

  13. Significance of multiple scattering in imaging through turbid media

    International Nuclear Information System (INIS)

    Zardecki, A.; Gerstl, S.A.W.

    1986-01-01

    The degradation of image quality in a turbid medium is analyzed within the framework of the small-angle approximation, the diffusion approximation, and a rigorous two-dimensional radiative transfer equation. These three approaches allow us to emphasize different aspects of the imaging problem when multiple scattering effects are important. For a medium with a forward-peaked phase function, the separation of multiple scattering into a series of scatterings of various order provides a fruitful technique. The use of the diffusion approximation and transport theory extends the determination of the modulation transfer function to a turbid medium with an arbitrary degree of anisotropy

  14. Approximate reasoning in physical systems

    International Nuclear Information System (INIS)

    Mutihac, R.

    1991-01-01

    The theory of fuzzy sets provides excellent ground to deal with fuzzy observations (uncertain or imprecise signals, wavelengths, temperatures,etc.) fuzzy functions (spectra and depth profiles) and fuzzy logic and approximate reasoning. First, the basic ideas of fuzzy set theory are briefly presented. Secondly, stress is put on application of simple fuzzy set operations for matching candidate reference spectra of a spectral library to an unknown sample spectrum (e.g. IR spectroscopy). Thirdly, approximate reasoning is applied to infer an unknown property from information available in a database (e.g. crystal systems). Finally, multi-dimensional fuzzy reasoning techniques are suggested. (Author)

  15. Face Recognition using Approximate Arithmetic

    DEFF Research Database (Denmark)

    Marso, Karol

    Face recognition is image processing technique which aims to identify human faces and found its use in various different fields for example in security. Throughout the years this field evolved and there are many approaches and many different algorithms which aim to make the face recognition as effective...... processing applications the results do not need to be completely precise and use of the approximate arithmetic can lead to reduction in terms of delay, space and power consumption. In this paper we examine possible use of approximate arithmetic in face recognition using Eigenfaces algorithm....

  16. Approximated treatment of the Pauli principle effects in elastic collisons

    International Nuclear Information System (INIS)

    Schechter, H.

    1984-08-01

    Exact microscopic methods like the RGM (Resonanting Group Method) and the GCM (Generator Coordinate Method) and approximate methods like the OCM (Orthogonality Condition Model) are used to study the effects of Pauli Principle in α- 16 O elastic scattering. Using V2 and BL nucleon-nucleon interactions, nucleus-nucleus effective potentials are obtained from RGM 'exact' wave functions and also from an approximate method developed previoulsy. Using these potentials in the OCM Saito Equation phase-shifts are calculated for partial waves Λ = 0, 1, ... 11, in the energy range 0 [pt

  17. Approximate representations of propagators in an external field

    International Nuclear Information System (INIS)

    Fried, H.M.

    1979-01-01

    A method of forming approximate representations for propagators with external field dependence is suggested and discussed in the context of potential scattering. An integro-differential equation in D+1 variables, where D represents the dimensionality of Euclidian space-time, is replaced by a Volterra equation in one variable. Approximate solutions to the latter provide a generalization of the Bloch-Nordsieck representation, containing the effects of all powers of hard-potential interactions, each modified by a characteristic soft-potential dependence [fr

  18. Role of eikonal approximation in the infrared domain

    Energy Technology Data Exchange (ETDEWEB)

    Banerjee, H; Sharma, S K [Saha Inst. of Nuclear Physics, Calcutta (India); Mallik, S [Bern Univ. (Switzerland). Inst. fuer Theoretische Physik

    1977-01-31

    It is shown that the infrared limit of amplitudes for ladder diagrams in spinor electrodynamics is given by eikonal approximation correctly upto terms of relative O(/t/sup(1/2)/ssup(1/2)) only if one also makes the 'small-angle assumption'. Leading corrections to eikonal amplitude contain s-channel poles which do not have Coulomb analogue. For fixed angle scattering the leading infrared contribution of ladder diagrams is obtained.

  19. The role of eikonal approximation in the infrared domain

    International Nuclear Information System (INIS)

    Banerjee, H.; Sharma, S.K.; Mallik, S.

    1977-01-01

    It is shown that the infrared limit of amplitudes for ladder diagrams in spinor electrodynamics is given by eikonal approximation correctly upto terms of relative O(/t/sup(1/2)/ssup(1/2)) only if one also makes the 'small-angle assumption'. Leading corrections to eikonal amplitude contain s-channel poles which do not have Coulomb analogue. For fixed angle scattering the leading infrared contribution of ladder diagrams is obtained. (Auth.)

  20. Validity of the Glauber approximation with account of the deuteron quark structure

    International Nuclear Information System (INIS)

    Zakharov, B.G.; Kopeliovich, B.Z.

    1985-01-01

    Corrections to the hadron-deuteron elastic scattering amplitude due to the deuteron quark structore are calculated. The two-gluon pomeron model which provides a good description of the hadron-hardron scattering data has been used. It is shown that the Glauber approximation with elastic corrections provides with a good description of the data on the total and differential pd-scattering cross sections, if the admixture of the six-quark bag state in the deuteron S 6 wave function is small ( 6 approximately 0.8 fm

  1. Scattering and multiple scattering in disordered materials

    International Nuclear Information System (INIS)

    Weaver, R.L.; Butler, W.H.

    1992-01-01

    The papers in this section were presented at a joint session of symposium V on Applications of Multiple Scattering Theory and of Symposium P on Disordered Systems. They show that the ideas of scattering theory can help us to understand a very broad class of phenomena

  2. Approximate Reanalysis in Topology Optimization

    DEFF Research Database (Denmark)

    Amir, Oded; Bendsøe, Martin P.; Sigmund, Ole

    2009-01-01

    In the nested approach to structural optimization, most of the computational effort is invested in the solution of the finite element analysis equations. In this study, the integration of an approximate reanalysis procedure into the framework of topology optimization of continuum structures...

  3. Approximate Matching of Hierarchial Data

    DEFF Research Database (Denmark)

    Augsten, Nikolaus

    -grams of a tree are all its subtrees of a particular shape. Intuitively, two trees are similar if they have many pq-grams in common. The pq-gram distance is an efficient and effective approximation of the tree edit distance. We analyze the properties of the pq-gram distance and compare it with the tree edit...

  4. Approximation of Surfaces by Cylinders

    DEFF Research Database (Denmark)

    Randrup, Thomas

    1998-01-01

    We present a new method for approximation of a given surface by a cylinder surface. It is a constructive geometric method, leading to a monorail representation of the cylinder surface. By use of a weighted Gaussian image of the given surface, we determine a projection plane. In the orthogonal...

  5. Approximation properties of haplotype tagging

    Directory of Open Access Journals (Sweden)

    Dreiseitl Stephan

    2006-01-01

    Full Text Available Abstract Background Single nucleotide polymorphisms (SNPs are locations at which the genomic sequences of population members differ. Since these differences are known to follow patterns, disease association studies are facilitated by identifying SNPs that allow the unique identification of such patterns. This process, known as haplotype tagging, is formulated as a combinatorial optimization problem and analyzed in terms of complexity and approximation properties. Results It is shown that the tagging problem is NP-hard but approximable within 1 + ln((n2 - n/2 for n haplotypes but not approximable within (1 - ε ln(n/2 for any ε > 0 unless NP ⊂ DTIME(nlog log n. A simple, very easily implementable algorithm that exhibits the above upper bound on solution quality is presented. This algorithm has running time O((2m - p + 1 ≤ O(m(n2 - n/2 where p ≤ min(n, m for n haplotypes of size m. As we show that the approximation bound is asymptotically tight, the algorithm presented is optimal with respect to this asymptotic bound. Conclusion The haplotype tagging problem is hard, but approachable with a fast, practical, and surprisingly simple algorithm that cannot be significantly improved upon on a single processor machine. Hence, significant improvement in computatational efforts expended can only be expected if the computational effort is distributed and done in parallel.

  6. All-Norm Approximation Algorithms

    NARCIS (Netherlands)

    Azar, Yossi; Epstein, Leah; Richter, Yossi; Woeginger, Gerhard J.; Penttonen, Martti; Meineche Schmidt, Erik

    2002-01-01

    A major drawback in optimization problems and in particular in scheduling problems is that for every measure there may be a different optimal solution. In many cases the various measures are different ℓ p norms. We address this problem by introducing the concept of an All-norm ρ-approximation

  7. Truthful approximations to range voting

    DEFF Research Database (Denmark)

    Filos-Ratsika, Aris; Miltersen, Peter Bro

    We consider the fundamental mechanism design problem of approximate social welfare maximization under general cardinal preferences on a finite number of alternatives and without money. The well-known range voting scheme can be thought of as a non-truthful mechanism for exact social welfare...

  8. On badly approximable complex numbers

    DEFF Research Database (Denmark)

    Esdahl-Schou, Rune; Kristensen, S.

    We show that the set of complex numbers which are badly approximable by ratios of elements of , where has maximal Hausdorff dimension. In addition, the intersection of these sets is shown to have maximal dimension. The results remain true when the sets in question are intersected with a suitably...

  9. Approximate reasoning in decision analysis

    Energy Technology Data Exchange (ETDEWEB)

    Gupta, M M; Sanchez, E

    1982-01-01

    The volume aims to incorporate the recent advances in both theory and applications. It contains 44 articles by 74 contributors from 17 different countries. The topics considered include: membership functions; composite fuzzy relations; fuzzy logic and inference; classifications and similarity measures; expert systems and medical diagnosis; psychological measurements and human behaviour; approximate reasoning and decision analysis; and fuzzy clustering algorithms.

  10. Rational approximation of vertical segments

    Science.gov (United States)

    Salazar Celis, Oliver; Cuyt, Annie; Verdonk, Brigitte

    2007-08-01

    In many applications, observations are prone to imprecise measurements. When constructing a model based on such data, an approximation rather than an interpolation approach is needed. Very often a least squares approximation is used. Here we follow a different approach. A natural way for dealing with uncertainty in the data is by means of an uncertainty interval. We assume that the uncertainty in the independent variables is negligible and that for each observation an uncertainty interval can be given which contains the (unknown) exact value. To approximate such data we look for functions which intersect all uncertainty intervals. In the past this problem has been studied for polynomials, or more generally for functions which are linear in the unknown coefficients. Here we study the problem for a particular class of functions which are nonlinear in the unknown coefficients, namely rational functions. We show how to reduce the problem to a quadratic programming problem with a strictly convex objective function, yielding a unique rational function which intersects all uncertainty intervals and satisfies some additional properties. Compared to rational least squares approximation which reduces to a nonlinear optimization problem where the objective function may have many local minima, this makes the new approach attractive.

  11. Pythagorean Approximations and Continued Fractions

    Science.gov (United States)

    Peralta, Javier

    2008-01-01

    In this article, we will show that the Pythagorean approximations of [the square root of] 2 coincide with those achieved in the 16th century by means of continued fractions. Assuming this fact and the known relation that connects the Fibonacci sequence with the golden section, we shall establish a procedure to obtain sequences of rational numbers…

  12. Ultrafast Approximation for Phylogenetic Bootstrap

    NARCIS (Netherlands)

    Bui Quang Minh, [No Value; Nguyen, Thi; von Haeseler, Arndt

    Nonparametric bootstrap has been a widely used tool in phylogenetic analysis to assess the clade support of phylogenetic trees. However, with the rapidly growing amount of data, this task remains a computational bottleneck. Recently, approximation methods such as the RAxML rapid bootstrap (RBS) and

  13. Compton-scatter tissue densitometry: calculation of single and multiple scatter photon fluences

    International Nuclear Information System (INIS)

    Battista, J.J.; Bronskill, M.J.

    1978-01-01

    The accurate measurement of in vivo electron densities by the Compton-scatter method is limited by attenuations and multiple scattering in the patient. Using analytic and Monte Carlo calculation methods, the Clarke tissue density scanner has been modelled for incident monoenergetic photon energies from 300 to 2000 keV and for mean scattering angles of 30 to 130 degrees. For a single detector focussed to a central position in a uniform water phantom (25 x 25 x 25 cm 3 ) it has been demonstrated that: (1) Multiple scatter contamination is an inherent limitation of the Compton-scatter method of densitometry which can be minimised, but not eliminated, by improving the energy resolution of the scattered radiation detector. (2) The choice of the incident photon energy is a compromise between the permissible radiation dose to the patient and the tolerable level of multiple scatter contamination. For a mean scattering angle of 40 degrees, the intrinsic multiple-single scatter ratio decreases from 64 to 35%, and the radiation dose (per measurement) increases from 1.0 to 4.1 rad, as the incident photon energy increases from 300 to 2000 keV. These doses apply to a sampled volume of approximately 0.3 cm 3 and an electron density precision of 0.5%. (3) The forward scatter densitometer configuration is optimum, minimising both the dose and the multiple scatter contamination. For an incident photon energy of 1250 keV, the intrinsic multiple-single scatter ratio reduces from 122 to 27%, and the dose reduces from 14.3 to 1.2 rad, as the mean scattering angle decreases from 130 to 30 degrees. These calculations have been confirmed by experimental measurements. (author)

  14. Periodic instantons and scattering amplitudes

    International Nuclear Information System (INIS)

    Khlebnikov, S.Yu.; Rubakov, V.A.; Tinyakov, P.G.

    1991-04-01

    We discuss the role of periodic euclidean solutions with two turning points and zero winding number (periodic instantons) in instanton induced processes below the sphaleron energy E sph . We find that the periodic instantons describe certain multiparticle scattering events leading to the transitions between topologically distinct vacua. Both the semiclassical amplitudes and inital and final states of these transitions are determined by the periodic instantons. Furthermore, the corresponding probabilities are maximal among all states of given energy. We show that at E ≤ E sph , the periodic instantons can be approximated by infinite chains of ordinary instantons and anti-instantons, and they naturally emerge as deformations of the zero energy instanton. In the framework of 2d abelian Higgs model and 4d electroweak theory we show, however, that there is not obvious relation between periodic instantons and two-particle scattering amplitudes. (orig.)

  15. Depth distribution of multiple order X-ray scatter

    International Nuclear Information System (INIS)

    Yao Weiguang; Leszczynski, Konrad

    2008-01-01

    Scatter can significantly affect quality of projectional X-ray radiographs and tomographic reconstructions. With this in mind, we examined some of the physical properties of multiple orders of scatter of X-ray photons traversing through a layer of scattering media such as water. Using Monte Carlo techniques, we investigated depth distributions of interactions between incident X-ray photons and water before the resulting scattered photons reach the detector plane. Effects of factors such as radiation field size, air gap, thickness of the layer of scattering medium and X-ray energy, on the scatter were included in the scope of this study. The following scatter characteristics were observed: (1) for a layer of scattering material corresponding to the typical subject thickness in medical imaging, frequency distribution of locations of the last scattering interaction increases approximately exponentially with depth, and the higher the order of scatter or the energy of the incident photon, the narrower is the distribution; (2) for the second order scatter, the distribution of locations of the first interaction is more uniform than that of the last interaction and is dependent on the energy of the primary photons. Theoretical proofs for some of these properties are given. These properties are important to better understanding of effects of scatter on the radiographic and tomographic imaging process and to developing effective methods for scatter correction

  16. SIMSAS - a window based software package for simulation and analysis of multiple small-angle scattering data

    International Nuclear Information System (INIS)

    Jayaswal, B.; Mazumder, S.

    1998-09-01

    Small-angle scattering data from strong scattering systems, e.g. porous materials, cannot be analysed invoking single scattering approximation as specimen needed to replicate the bulk matrix in essential properties are too thick to validate the approximation. The presence of multiple scattering is indicated by invalidity of the functional invariance property of the observed scattering profile with variation of sample thickness and/or wave length of the probing radiation. This article delineates how non accounting of multiple scattering affects the results of analysis and then how to correct the data for its effect. It deals with an algorithm to extract single scattering profile from small-angle scattering data affected by multiple scattering. The algorithm can process the scattering data and deduce single scattering profile in absolute scale. A software package, SIMSAS, is introduced for executing this inversion step. This package is useful both to simulate and to analyse multiple small-angle scattering data. (author)

  17. Neutron scattering from fractals

    DEFF Research Database (Denmark)

    Kjems, Jørgen; Freltoft, T.; Richter, D.

    1986-01-01

    The scattering formalism for fractal structures is presented. Volume fractals are exemplified by silica particle clusters formed either from colloidal suspensions or by flame hydrolysis. The determination of the fractional dimensionality through scattering experiments is reviewed, and recent small...

  18. Scatter from optical components

    International Nuclear Information System (INIS)

    Stover, J.C.

    1989-01-01

    This book is covered under the following topics: measurement and analysis techniques; BRDF standards, comparisons, and anomalies; scatter measurement of several materials; scatter from contaminations; and optical system contamination: effects, measurement, and control

  19. Lateral displacement in small angle multiple scattering

    Energy Technology Data Exchange (ETDEWEB)

    Bichsel, H.; Hanson, K.M.; Schillaci, K.M. (Los Alamos National Lab., NM (USA))

    1982-07-01

    Values have been calculated for the average lateral displacement in small angle multiple scattering of protons with energies of several hundred MeV. The calculations incorporate the Moliere distribution which does not make the gaussian approximations of the distribution in projected angle and lateral deflections. Compared to other published data, such approximations can lead to errors in the lateral displacement of up to 10% in water.

  20. Multi-scale approximation of Vlasov equation

    International Nuclear Information System (INIS)

    Mouton, A.

    2009-09-01

    One of the most important difficulties of numerical simulation of magnetized plasmas is the existence of multiple time and space scales, which can be very different. In order to produce good simulations of these multi-scale phenomena, it is recommended to develop some models and numerical methods which are adapted to these problems. Nowadays, the two-scale convergence theory introduced by G. Nguetseng and G. Allaire is one of the tools which can be used to rigorously derive multi-scale limits and to obtain new limit models which can be discretized with a usual numerical method: this procedure is so-called a two-scale numerical method. The purpose of this thesis is to develop a two-scale semi-Lagrangian method and to apply it on a gyrokinetic Vlasov-like model in order to simulate a plasma submitted to a large external magnetic field. However, the physical phenomena we have to simulate are quite complex and there are many questions without answers about the behaviour of a two-scale numerical method, especially when such a method is applied on a nonlinear model. In a first part, we develop a two-scale finite volume method and we apply it on the weakly compressible 1D isentropic Euler equations. Even if this mathematical context is far from a Vlasov-like model, it is a relatively simple framework in order to study the behaviour of a two-scale numerical method in front of a nonlinear model. In a second part, we develop a two-scale semi-Lagrangian method for the two-scale model developed by E. Frenod, F. Salvarani et E. Sonnendrucker in order to simulate axisymmetric charged particle beams. Even if the studied physical phenomena are quite different from magnetic fusion experiments, the mathematical context of the one-dimensional paraxial Vlasov-Poisson model is very simple for establishing the basis of a two-scale semi-Lagrangian method. In a third part, we use the two-scale convergence theory in order to improve M. Bostan's weak-* convergence results about the finite

  1. Improving the wide resonance approximation

    International Nuclear Information System (INIS)

    Aboustta, Mohamed A.; Martinez, Aquilino S.

    1999-01-01

    A resonance is considered wide if its practical width, in energy, exceeds the average energy loss per collision, E(1-α A )/2, of the absorbing material. When the mass number, A, is taken infinite, the scattering produces only a change in the direction of motion of the neutron and not in its energy. Based on this assumption, the integral in the slowing-down equation describing the contribution of the resonant absorber is evaluated by taking its limit when α A →1. This work questions the necessity to take such a limit and shows that it is still possible to obtain a simple and more accurate expression for the integral without taking such limit

  2. Improving the wide resonance approximation

    Energy Technology Data Exchange (ETDEWEB)

    Aboustta, Mohamed A.; Martinez, Aquilino S

    1999-03-01

    A resonance is considered wide if its practical width, in energy, exceeds the average energy loss per collision, E(1-{alpha}{sub A})/2, of the absorbing material. When the mass number, A, is taken infinite, the scattering produces only a change in the direction of motion of the neutron and not in its energy. Based on this assumption, the integral in the slowing-down equation describing the contribution of the resonant absorber is evaluated by taking its limit when {alpha}{sub A}{yields}1. This work questions the necessity to take such a limit and shows that it is still possible to obtain a simple and more accurate expression for the integral without taking such limit.

  3. Electron scattering from tetrahydrofuran

    International Nuclear Information System (INIS)

    Fuss, M C; Sanz, A G; García, G; Muñoz, A; Oller, J C; Blanco, F; Do, T P T; Brunger, M J; Almeida, D; Limão-Vieira, P

    2012-01-01

    Electron scattering from Tetrahydrofuran (C 4 H 8 O) was investigated over a wide range of energies. Following a mixed experimental and theoretical approach, total scattering, elastic scattering and ionization cross sections as well as electron energy loss distributions were obtained.

  4. Neutron-proton scattering

    International Nuclear Information System (INIS)

    Doll, P.

    1990-02-01

    Neutron-proton scattering as fundamental interaction process below and above hundred MeV is discussed. Quark model inspired interactions and phenomenological potential models are described. The seminar also indicates the experimental improvements for achieving new precise scattering data. Concluding remarks indicate the relevance of nucleon-nucleon scattering results to finite nuclei. (orig.) [de

  5. Neutron Scattering Software

    Science.gov (United States)

    Home Page | Facilities | Reference | Software | Conferences | Announcements | Mailing Lists Neutron Scattering Banner Neutron Scattering Software A new portal for neutron scattering has just been established sets KUPLOT: data plotting and fitting software ILL/TAS: Matlab probrams for analyzing triple axis data

  6. Magnetic photon scattering

    International Nuclear Information System (INIS)

    Lovesey, S.W.

    1987-05-01

    The report reviews, at an introductory level, the theory of photon scattering from condensed matter. Magnetic scattering, which arises from first-order relativistic corrections to the Thomson scattering amplitude, is treated in detail and related to the corresponding interaction in the magnetic neutron diffraction amplitude. (author)

  7. Polarized Neutron Scattering

    OpenAIRE

    Roessli, B.; Böni, P.

    2000-01-01

    The technique of polarized neutron scattering is reviewed with emphasis on applications. Many examples of the usefulness of the method in various fields of physics are given like the determination of spin density maps, measurement of complex magnetic structures with spherical neutron polarimetry, inelastic neutron scattering and separation of coherent and incoherent scattering with help of the generalized XYZ method.

  8. Beyond the random phase approximation

    DEFF Research Database (Denmark)

    Olsen, Thomas; Thygesen, Kristian S.

    2013-01-01

    We assess the performance of a recently proposed renormalized adiabatic local density approximation (rALDA) for ab initio calculations of electronic correlation energies in solids and molecules. The method is an extension of the random phase approximation (RPA) derived from time-dependent density...... functional theory and the adiabatic connection fluctuation-dissipation theorem and contains no fitted parameters. The new kernel is shown to preserve the accurate description of dispersive interactions from RPA while significantly improving the description of short-range correlation in molecules, insulators......, and metals. For molecular atomization energies, the rALDA is a factor of 7 better than RPA and a factor of 4 better than the Perdew-Burke-Ernzerhof (PBE) functional when compared to experiments, and a factor of 3 (1.5) better than RPA (PBE) for cohesive energies of solids. For transition metals...

  9. Hydrogen: Beyond the Classic Approximation

    International Nuclear Information System (INIS)

    Scivetti, Ivan

    2003-01-01

    The classical nucleus approximation is the most frequently used approach for the resolution of problems in condensed matter physics.However, there are systems in nature where it is necessary to introduce the nuclear degrees of freedom to obtain a correct description of the properties.Examples of this, are the systems with containing hydrogen.In this work, we have studied the resolution of the quantum nuclear problem for the particular case of the water molecule.The Hartree approximation has been used, i.e. we have considered that the nuclei are distinguishable particles.In addition, we have proposed a model to solve the tunneling process, which involves the resolution of the nuclear problem for configurations of the system away from its equilibrium position

  10. Approximation errors during variance propagation

    International Nuclear Information System (INIS)

    Dinsmore, Stephen

    1986-01-01

    Risk and reliability analyses are often performed by constructing and quantifying large fault trees. The inputs to these models are component failure events whose probability of occuring are best represented as random variables. This paper examines the errors inherent in two approximation techniques used to calculate the top event's variance from the inputs' variance. Two sample fault trees are evaluated and several three dimensional plots illustrating the magnitude of the error over a wide range of input means and variances are given

  11. WKB approximation in atomic physics

    International Nuclear Information System (INIS)

    Karnakov, Boris Mikhailovich

    2013-01-01

    Provides extensive coverage of the Wentzel-Kramers-Brillouin approximation and its applications. Presented as a sequence of problems with highly detailed solutions. Gives a concise introduction for calculating Rydberg states, potential barriers and quasistationary systems. This book has evolved from lectures devoted to applications of the Wentzel-Kramers-Brillouin- (WKB or quasi-classical) approximation and of the method of 1/N -expansion for solving various problems in atomic and nuclear physics. The intent of this book is to help students and investigators in this field to extend their knowledge of these important calculation methods in quantum mechanics. Much material is contained herein that is not to be found elsewhere. WKB approximation, while constituting a fundamental area in atomic physics, has not been the focus of many books. A novel method has been adopted for the presentation of the subject matter, the material is presented as a succession of problems, followed by a detailed way of solving them. The methods introduced are then used to calculate Rydberg states in atomic systems and to evaluate potential barriers and quasistationary states. Finally, adiabatic transition and ionization of quantum systems are covered.

  12. Interference scattering effects on intermediate resonance absorption at operating temperatures

    International Nuclear Information System (INIS)

    Goldstein, R.

    1975-01-01

    Resonance integrals may be accurately calculated using the intermediate resonance (IR) approximation. Results are summarized for the case of an absorber with given potential scattering cross sections and interference scattering parameter admixed with a non absorbing moderator of given cross section and located in a narrow resonance moderating medium. From the form of the IR solutions, it is possible to make some general observations about effects of interference scattering on resonance absorption. 2 figures

  13. ns-ms excitation of alkali atoms in the Glauber approximation

    International Nuclear Information System (INIS)

    Barros, H.G. de P.L. de

    1980-05-01

    An expression for the scattering amplitude in the Glauber approximation for ns-ms electronic excitation of alkali atoms is obtained. The interaction potential between the incident electron, the core electrons and N-1 protons is approximated by an appropriate spherical potential. (Author) [pt

  14. Self-consistent approximation for muffin-tin models of random substitutional alloys with environmental disorder

    International Nuclear Information System (INIS)

    Kaplan, T.; Gray, L.J.

    1984-01-01

    The self-consistent approximation of Kaplan, Leath, Gray, and Diehl is applied to models for substitutional random alloys with muffin-tin potentials. The particular advantage of this approximation is that, in addition to including cluster scattering, the muffin-tin potentials in the alloy can depend on the occupation of the surrounding sites (i.e., environmental disorder is included)

  15. Effective exchange potentials for electronically inelastic scattering

    International Nuclear Information System (INIS)

    Schwenke, D.W.; Staszewska, G.; Truhlar, D.G.

    1983-01-01

    We propose new methods for solving the electron scattering close coupling equations employing equivalent local exchange potentials in place of the continuum-multiconfiguration-Hartree--Fock-type exchange kernels. The local exchange potentials are Hermitian. They have the correct symmetry for any symmetries of excited electronic states included in the close coupling expansion, and they have the same limit at very high energy as previously employed exchange potentials. Comparison of numerical calculations employing the new exchange potentials with the results obtained with the standard nonlocal exchange kernels shows that the new exchange potentials are more accurate than the local exchange approximations previously available for electronically inelastic scattering. We anticipate that the new approximations will be most useful for intermediate-energy electronically inelastic electron--molecule scattering

  16. Inelastic scattering to collective states in double-magic nuclei

    International Nuclear Information System (INIS)

    Wambach, J.

    1979-06-01

    The paper discusses several aspects of inelastic scattering to collective states in the framework of the 'Shell Model RPA Approximation' with special emphasis on the analysis of giant resonance states. (orig./WL) [de

  17. Rainbows: Mie computations and the Airy approximation.

    Science.gov (United States)

    Wang, R T; van de Hulst, H C

    1991-01-01

    Efficient and accurate computation of the scattered intensity pattern by the Mie formulas is now feasible for size parameters up to x = 50,000 at least, which in visual light means spherical drops with diameters up to 6 mm. We present a method for evaluating the Mie coefficients from the ratios between Riccati-Bessel and Neumann functions of successive order. We probe the applicability of the Airy approximation, which we generalize to rainbows of arbitrary p (number of internal reflections = p - 1), by comparing the Mie and Airy intensity patterns. Millimeter size water drops show a match in all details, including the position and intensity of the supernumerary maxima and the polarization. A fairly good match is still seen for drops of 0.1 mm. A small spread in sizes helps to smooth out irrelevant detail. The dark band between the rainbows is used to test more subtle features. We conclude that this band contains not only externally reflected light (p = 0) but also a sizable contribution f rom the p = 6 and p = 7 rainbows, which shift rapidly with wavelength. The higher the refractive index, the closer both theories agree on the first primary rainbow (p = 2) peak for drop diameters as small as 0.02 mm. This may be useful in supporting experimental work.

  18. High energy proton-nucleus scattering

    International Nuclear Information System (INIS)

    Beurtey, R.M.

    1977-01-01

    This paper is restricted to an overall global criticism of what has been produced, experimentally and theoretically, during the past ten years, concerning elastic proton scattering at intermediate energy: theoretical models and approximations, phenomenological analysis, criticisms and suggestions on experimental methods

  19. Minimizing the scattering of a nonmagnetic cloak

    DEFF Research Database (Denmark)

    Zhang, Jingjing; Luo, Yu; Mortensen, Asger

    2010-01-01

    Nonmagnetic cloak offers a feasible way to achieve invisibility at optical frequencies using materials with only electric responses. In this letter, we suggest an approximation of the ideal nonmagnetic cloak and quantitatively study its electromagnetic characteristics using a full-wave scattering...

  20. The Bateman method for multichannel scattering theory

    International Nuclear Information System (INIS)

    Kim, Y. E.; Kim, Y. J.; Zubarev, A. L.

    1997-01-01

    Accuracy and convergence of the Bateman method are investigated for calculating the transition amplitude in multichannel scattering theory. This approximation method is applied to the calculation of elastic amplitude. The calculated results are remarkably accurate compared with those of exactly solvable multichannel model

  1. e--H scattering at intermediate energies

    International Nuclear Information System (INIS)

    Ghosh, A.S.

    1978-01-01

    The effect of exchange is included explicitly in the framework of simplified form of the fixed scatterer approximation as proposed by Ghosh. Inclusion of exchange is found to improve the results for the differential cross section appreciably when comparisons are made with the measured values. The computational labour involved is very reasonable. (author)

  2. Long-Wavelength Phonon Scattering in Nonpolar Semiconductors

    DEFF Research Database (Denmark)

    Lawætz, Peter

    1969-01-01

    The long-wavelength acoustic- and optical-phonon scattering of carriers in nonpolar semiconductors is considered from a general point of view. The deformation-potential approximation is defined and it is shown that long-range electrostatic forces give a nontrivial correction to the scattering...... of the very-short-range nature of interactions in a covalent semiconductor....

  3. The Harwell back-scattering spectrometer

    International Nuclear Information System (INIS)

    Windsor, C.G.; Bunce, L.J.; Borcherds, P.H.; Cole, I.; Fitzmaurice, M.; Johnson, D.A.G.; Sinclair, R.N.

    1976-01-01

    Neutron diffraction spectra in which both high resolution (Δ Q/Q approximately equal to 0.003) and high intensity are maintained up to scattering vectors as high as 30A -1 (sin theta/lambda = 2.5) have been obtained with the back-scattering spectrometer (BSS) recently installed on the Harwell electron linac. The theory behind the spectrometer design is described, and it is shown how the above resolution requirement leads to its basic features of a 12m incident flight path, a 2m scattering flight path and a scattering angle (2theta) acceptance from 165 0 to 175 0 . Examples of the resolution, intensity and background are given. It is shown that the problem of frame overlap may be overcome by using an absorbing filter. (author)

  4. Theory of neutron scattering in disordered alloys

    International Nuclear Information System (INIS)

    Yussouff, M.; Mookerjee, A.

    1984-08-01

    A comprehensive theory of thermal neutron scattering in disordered alloys is presented here. We consider in detail the case of substitutional random binary alloy with random changes in mass and force constants; and for all values of the concentration. The cluster CPA formalism in argumented space developed here is free from analytical difficulties for the Green function, performs correct averaging over random atomic scattering lengths and employs a self-consistent medium for the calculations. For easy computation, we describe the graphical representation of the resolvent where the approximation steps can be depicted as closed paths in augmented space. Our results for scattering cross sections, both coherent and incoherent, include new types of terms and these lead to asymmetric line shapes for the coherent scattering. (author)

  5. Toward a new polyethylene scattering law determined using inelastic neutron scattering

    International Nuclear Information System (INIS)

    Lavelle, C.M.; Liu, C.-Y.; Stone, M.B.

    2013-01-01

    Monte Carlo neutron transport codes such as MCNP rely on accurate data for nuclear physics cross-sections to produce accurate results. At low energy, this takes the form of scattering laws based on the dynamic structure factor, S(Q,E). High density polyethylene (HDPE) is frequently employed as a neutron moderator at both high and low temperatures, however the only cross-sections available are for ambient temperatures (∼300K), and the evaluation has not been updated in quite some time. In this paper we describe inelastic neutron scattering measurements on HDPE at 5 and 294 K which are used to improve the scattering law for HDPE. We review some of the past HDPE scattering laws, describe the experimental methods, and compare computations using these models to the measured S(Q,E). The total cross-section is compared to available data, and the treatment of the carbon secondary scatterer as a free gas is assessed. We also discuss the use of the measurement itself as a scattering law via the one phonon approximation. We show that a scattering law computed using a more detailed model for the Generalized Density of States (GDOS) compares more favorably to this experiment, suggesting that inelastic neutron scattering can play an important role in both the development and validation of new scattering laws for Monte Carlo work. -- Highlights: ► Polyethylene at 5 K and 300 K is measured using inelastic neutron scattering (INS). ► Measurements conducted at the Wide Angular-Range Chopper Spectrometer at SNS. ► Several models for Polyethylene are compared to measurements. ► Improvements to existing models for the polyethylene scattering law are suggested. ► INS is shown to be highly valuable tool for scattering law development

  6. Radiative transfer in disc galaxies - V. The accuracy of the KB approximation

    Science.gov (United States)

    Lee, Dukhang; Baes, Maarten; Seon, Kwang-Il; Camps, Peter; Verstocken, Sam; Han, Wonyong

    2016-12-01

    We investigate the accuracy of an approximate radiative transfer technique that was first proposed by Kylafis & Bahcall (hereafter the KB approximation) and has been popular in modelling dusty late-type galaxies. We compare realistic galaxy models calculated with the KB approximation with those of a three-dimensional Monte Carlo radiative transfer code SKIRT. The SKIRT code fully takes into account of the contribution of multiple scattering whereas the KB approximation calculates only single scattered intensity and multiple scattering components are approximated. We find that the KB approximation gives fairly accurate results if optically thin, face-on galaxies are considered. However, for highly inclined (I ≳ 85°) and/or optically thick (central face-on optical depth ≳1) galaxy models, the approximation can give rise to substantial errors, sometimes, up to ≳40 per cent. Moreover, it is also found that the KB approximation is not always physical, sometimes producing infinite intensities at lines of sight with high optical depth in edge-on galaxy models. There is no `simple recipe' to correct the errors of the KB approximation that is universally applicable to any galaxy models. Therefore, it is recommended that the full radiative transfer calculation be used, even though it is slower than the KB approximation.

  7. High-energy expansion for nuclear multiple scattering

    International Nuclear Information System (INIS)

    Wallace, S.J.

    1975-01-01

    The Watson multiple scattering series is expanded to develop the Glauber approximation plus systematic corrections arising from three (1) deviations from eikonal propagation between scatterings, (2) Fermi motion of struck nucleons, and (3) the kinematic transformation which relates the many-body scattering operators of the Watson series to the physical two-body scattering amplitude. Operators which express effects ignored at the outset to obtain the Glauber approximation are subsequently reintroduced via perturbation expansions. Hence a particular set of approximations is developed which renders the sum of the Watson series to the Glauber form in the center of mass system, and an expansion is carried out to find leading order corrections to that summation. Although their physical origins are quite distinct, the eikonal, Fermi motion, and kinematic corrections produce strikingly similar contributions to the scattering amplitude. It is shown that there is substantial cancellation between their effects and hence the Glauber approximation is more accurate than the individual approximations used in its derivation. It is shown that the leading corrections produce effects of order (2kR/subc/) -1 relative to the double scattering term in the uncorrected Glauber amplitude, hk being momentum and R/subc/ the nuclear char []e radius. The leading order corrections are found to be small enough to validate quatitative analyses of experimental data for many intermediate to high energy cases and for scattering angles not limited to the very forward region. In a Gaussian model, the leading corrections to the Glauber amplitude are given as convenient analytic expressions

  8. Green function and scattering amplitudes in many dimensional space

    International Nuclear Information System (INIS)

    Fabre de la Ripelle, M.

    1991-06-01

    Methods for solving scattering are studied in many dimensional space. Green function and scattering amplitudes are given in terms of the requested asymptotic behaviour of the wave function. The Born approximation and the optical theorem are derived in many dimensional space. Phase-shift analysis are developed for hypercentral potentials and for non-hypercentral potentials with the hyperspherical adiabatic approximation. (author) 16 refs., 3 figs

  9. Green functions and scattering amplitudes in many-dimensional space

    International Nuclear Information System (INIS)

    Fabre de la Ripelle, M.

    1993-01-01

    Methods for solving scattering are studied in many-dimensional space. Green function and scattering amplitudes are given in terms of the required asymptotic behaviour of the wave function. The Born approximation and the optical theorem are derived in many-dimensional space. Phase-shift analyses are performed for hypercentral potentials and for non-hypercentral potentials by use of the hyperspherical adiabatic approximation. (author)

  10. Approximate solutions to Mathieu's equation

    Science.gov (United States)

    Wilkinson, Samuel A.; Vogt, Nicolas; Golubev, Dmitry S.; Cole, Jared H.

    2018-06-01

    Mathieu's equation has many applications throughout theoretical physics. It is especially important to the theory of Josephson junctions, where it is equivalent to Schrödinger's equation. Mathieu's equation can be easily solved numerically, however there exists no closed-form analytic solution. Here we collect various approximations which appear throughout the physics and mathematics literature and examine their accuracy and regimes of applicability. Particular attention is paid to quantities relevant to the physics of Josephson junctions, but the arguments and notation are kept general so as to be of use to the broader physics community.

  11. Approximate Inference for Wireless Communications

    DEFF Research Database (Denmark)

    Hansen, Morten

    This thesis investigates signal processing techniques for wireless communication receivers. The aim is to improve the performance or reduce the computationally complexity of these, where the primary focus area is cellular systems such as Global System for Mobile communications (GSM) (and extensions...... to the optimal one, which usually requires an unacceptable high complexity. Some of the treated approximate methods are based on QL-factorization of the channel matrix. In the work presented in this thesis it is proven how the QL-factorization of frequency-selective channels asymptotically provides the minimum...

  12. Quantum tunneling beyond semiclassical approximation

    International Nuclear Information System (INIS)

    Banerjee, Rabin; Majhi, Bibhas Ranjan

    2008-01-01

    Hawking radiation as tunneling by Hamilton-Jacobi method beyond semiclassical approximation is analysed. We compute all quantum corrections in the single particle action revealing that these are proportional to the usual semiclassical contribution. We show that a simple choice of the proportionality constants reproduces the one loop back reaction effect in the spacetime, found by conformal field theory methods, which modifies the Hawking temperature of the black hole. Using the law of black hole mechanics we give the corrections to the Bekenstein-Hawking area law following from the modified Hawking temperature. Some examples are explicitly worked out.

  13. Generalized Gradient Approximation Made Simple

    International Nuclear Information System (INIS)

    Perdew, J.P.; Burke, K.; Ernzerhof, M.

    1996-01-01

    Generalized gradient approximations (GGA close-quote s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. copyright 1996 The American Physical Society

  14. Electron--molecule scattering in momentum space

    International Nuclear Information System (INIS)

    Ritchie, B.

    1979-01-01

    We examine the Fourier transform of the Schroedinger equation for electron--molecule scattering, treated as potential scattering from a multicenter distribution of charged fixed in space. When the angle theta between R,the internuclear vector of a diatomic target, and q, the momentum transfer, is held fixed during the collision, then the directions of incidence and scattering are fixed relative to R. The process is then described as having a dynamical dependence on the magnitude of q, q, from which the scattering angle is determined, and a parametric dependence on q's direction relative to R. This approximation is used routinely at high energies in the calculation of the Born amplitude. Fixed--nuclei coordinate--space studies suggest that this approximation can be extended to low energies, provided the amplitude is taken from the solution of the integral equation of momentum space rather than from its inhomogeneity, proportional to the Born amplitude. We constrain R to be in the same direction relative to q', a virtual momentum transfer belonging to the kernel, as it is to q.Calculations are performed for the e, H 2 scattering in the static approximation, and cross sections averaged over theta/sub R/ are shown to be in good agreement with cross sections calculated by use of coupled spherical and coupled spheroidal partial wave theories. The angular distribution in the static approximation is also calculated at an incident energy close to 7 eV, where exchange is relatively unimportant. This result is in reasonably good agreement with that of R matrix theory in the static--exchange approximation. The extension of the theory to treat exchange is formulated and discussed. Also its extension to treat more complicated molecular targets is discussed

  15. Finite approximations in fluid mechanics

    International Nuclear Information System (INIS)

    Hirschel, E.H.

    1986-01-01

    This book contains twenty papers on work which was conducted between 1983 and 1985 in the Priority Research Program ''Finite Approximations in Fluid Mechanics'' of the German Research Society (Deutsche Forschungsgemeinschaft). Scientists from numerical mathematics, fluid mechanics, and aerodynamics present their research on boundary-element methods, factorization methods, higher-order panel methods, multigrid methods for elliptical and parabolic problems, two-step schemes for the Euler equations, etc. Applications are made to channel flows, gas dynamical problems, large eddy simulation of turbulence, non-Newtonian flow, turbomachine flow, zonal solutions for viscous flow problems, etc. The contents include: multigrid methods for problems from fluid dynamics, development of a 2D-Transonic Potential Flow Solver; a boundary element spectral method for nonstationary viscous flows in 3 dimensions; navier-stokes computations of two-dimensional laminar flows in a channel with a backward facing step; calculations and experimental investigations of the laminar unsteady flow in a pipe expansion; calculation of the flow-field caused by shock wave and deflagration interaction; a multi-level discretization and solution method for potential flow problems in three dimensions; solutions of the conservation equations with the approximate factorization method; inviscid and viscous flow through rotating meridional contours; zonal solutions for viscous flow problems

  16. Plasma Physics Approximations in Ares

    International Nuclear Information System (INIS)

    Managan, R. A.

    2015-01-01

    Lee & More derived analytic forms for the transport properties of a plasma. Many hydro-codes use their formulae for electrical and thermal conductivity. The coefficients are complex functions of Fermi-Dirac integrals, Fn( μ/θ ), the chemical potential, μ or ζ = ln(1+e μ/θ ), and the temperature, θ = kT. Since these formulae are expensive to compute, rational function approximations were fit to them. Approximations are also used to find the chemical potential, either μ or ζ . The fits use ζ as the independent variable instead of μ/θ . New fits are provided for A α (ζ ),A β (ζ ), ζ, f(ζ ) = (1 + e -μ/θ )F 1/2 (μ/θ), F 1/2 '/F 1/2 , F c α , and F c β . In each case the relative error of the fit is minimized since the functions can vary by many orders of magnitude. The new fits are designed to exactly preserve the limiting values in the non-degenerate and highly degenerate limits or as ζ→ 0 or ∞. The original fits due to Lee & More and George Zimmerman are presented for comparison.

  17. A 'range test' for determining scatterers with unknown physical properties

    Science.gov (United States)

    Potthast, Roland; Sylvester, John; Kusiak, Steven

    2003-06-01

    We describe a new scheme for determining the convex scattering support of an unknown scatterer when the physical properties of the scatterers are not known. The convex scattering support is a subset of the scatterer and provides information about its location and estimates for its shape. For convex polygonal scatterers the scattering support coincides with the scatterer and we obtain full shape reconstructions. The method will be formulated for the reconstruction of the scatterers from the far field pattern for one or a few incident waves. The method is non-iterative in nature and belongs to the type of recently derived generalized sampling schemes such as the 'no response test' of Luke-Potthast. The range test operates by testing whether it is possible to analytically continue a far field to the exterior of any test domain Omegatest. By intersecting the convex hulls of various test domains we can produce a minimal convex set, the convex scattering support of which must be contained in the convex hull of the support of any scatterer which produces that far field. The convex scattering support is calculated by testing the range of special integral operators for a sampling set of test domains. The numerical results can be used as an approximation for the support of the unknown scatterer. We prove convergence and regularity of the scheme and show numerical examples for sound-soft, sound-hard and medium scatterers. We can apply the range test to non-convex scatterers as well. We can conclude that an Omegatest which passes the range test has a non-empty intersection with the infinity-support (the complement of the unbounded component of the complement of the support) of the true scatterer, but cannot find a minimal set which must be contained therein.

  18. Electron-atom scattering at intermediate energies

    International Nuclear Information System (INIS)

    Kingston, A.E.; Walters, H.R.J.

    1982-01-01

    The problems of intermediate energy scattering are approached from the low and high energy ends. At low intermediate energies difficulties associated with the use of pseudostates and correlation terms are discussed, special consideration being given to nonphysical pseudoresonances. Perturbation methods appropriate to high intermediate energies are described and attempts to extend these high energy approximations down to low intermediate energies are studied. It is shown how the importance of electron exchange effects develops with decreasing energy. The problem of assessing the 'effective completeness' of pseudostate sets at intermediate energies is mentioned and an instructive analysis of a 2p pseudostate approximation to elastic e - -H scattering is given. It is suggested that at low energies the Pauli Exclusion Principle can act to hide short range defects in pseudostate approximations. (author)

  19. Effect of neutron anisotropic scattering in fast reactor analysis

    International Nuclear Information System (INIS)

    Chiba, Gou

    2004-01-01

    Numerical tests were performed about an effect of a neutron anisotropic scattering on criticality in the Sn transport calculation. The simplest approximation, the consistent P approximation and the extended transport approximation were compared with each other in one-dimensional slab fast reactor models. JAERI fast set which has been used for fast reactor analyses is inadequate to evaluate the effect because it doesn't include the scattering matrices and the self-shielding factors to calculate the group-averaged cross sections weighted by the higher-order moment of angular flux. In the present study, the sub-group method was used to evaluate the group-averaged cross sections. Results showed that the simplest approximation is inadequate and the transport approximation is effective for evaluating the anisotropic scattering. (author)

  20. Approximating the minimum cycle mean

    Directory of Open Access Journals (Sweden)

    Krishnendu Chatterjee

    2013-07-01

    Full Text Available We consider directed graphs where each edge is labeled with an integer weight and study the fundamental algorithmic question of computing the value of a cycle with minimum mean weight. Our contributions are twofold: (1 First we show that the algorithmic question is reducible in O(n^2 time to the problem of a logarithmic number of min-plus matrix multiplications of n-by-n matrices, where n is the number of vertices of the graph. (2 Second, when the weights are nonnegative, we present the first (1 + ε-approximation algorithm for the problem and the running time of our algorithm is ilde(O(n^ω log^3(nW/ε / ε, where O(n^ω is the time required for the classic n-by-n matrix multiplication and W is the maximum value of the weights.

  1. Nonlinear approximation with dictionaries I. Direct estimates

    DEFF Research Database (Denmark)

    Gribonval, Rémi; Nielsen, Morten

    2004-01-01

    We study various approximation classes associated with m-term approximation by elements from a (possibly) redundant dictionary in a Banach space. The standard approximation class associated with the best m-term approximation is compared to new classes defined by considering m-term approximation w...

  2. Approximate cohomology in Banach algebras | Pourabbas ...

    African Journals Online (AJOL)

    We introduce the notions of approximate cohomology and approximate homotopy in Banach algebras and we study the relation between them. We show that the approximate homotopically equivalent cochain complexes give the same approximate cohomologies. As a special case, approximate Hochschild cohomology is ...

  3. Scattering with polarized neutrons

    International Nuclear Information System (INIS)

    Schweizer, J.

    2007-01-01

    In the history of neutron scattering, it was shown very soon that the use of polarized neutron beams brings much more information than usual scattering with unpolarized neutrons. We shall develop here the different scattering methods that imply polarized neutrons: 1) polarized beams without polarization analysis, the flipping ratio method; 2) polarized beams with a uniaxial polarization analysis; 3) polarized beams with a spherical polarization analysis. For all these scattering methods, we shall give examples of the physical problems which can been solved by these methods, particularly in the field of magnetism: investigation of complex magnetic structures, investigation of spin or magnetization densities in metals, insulators and molecular compounds, separation of magnetic and nuclear scattering, investigation of magnetic properties of liquids and amorphous materials and even, for non magnetic material, separation between coherent and incoherent scattering. (author)

  4. Incoherent quasielastic neutron scattering from plastic crystals

    International Nuclear Information System (INIS)

    Bee, M.; Amoureux, J.P.

    1980-01-01

    The aim of this paper is to present some applications of a method indicated by Sears in order to correct for multiple scattering. The calculations were performed in the particular case of slow neutron incoherent quasielastic scattering from organic plastic crystals. First, an exact calculation (up to second scattering) is compared with the results of a Monte Carlo simulation technique. Then, an approximation is developed on the basis of a rotational jump model which allows a further analytical treatment. The multiple scattering is expressed in terms of generalized structure factors (which can be regarded as self convolutions of first order structure factors taking into account the instrumental geometry) and lorentzian functions the widths of which are linear combinations of the jump rates. Three examples are given. Two of them correspond to powder samples while in the third we are concerned with the case of a single crystalline slab. In every case, this approximation is shown to be a good approach to the multiple scattering evaluation, its main advantage being the possibility of applying it without any preliminary knowledge of the correlation times for rotational jumps. (author)

  5. Neutron scattering and magnetism

    International Nuclear Information System (INIS)

    Mackintosh, A.R.

    1983-01-01

    Those properties of the neutron which make it a unique tool for the study of magnetism are described. The scattering of neutrons by magnetic solids is briefly reviewed, with emphasis on the information on the magnetic structure and dynamics which is inherent in the scattering cross-section. The contribution of neutron scattering to our understanding of magnetic ordering, excitations and phase transitions is illustrated by experimental results on a variety of magnetic crystals. (author)

  6. Stationary theory of scattering

    International Nuclear Information System (INIS)

    Kato, T.

    1977-01-01

    A variant of the stationary methods is described, and it is shown that it is useful in a wide range of problems, including scattering, by long-range potentials, two-space scattering, and multichannel scattering. The method is based on the notion of spectral forms. The paper is restricted to the simplest case of continuous spectral forms defined on a Banach space embedded in the basic Hilbert space. (P.D.)

  7. Introduction to neutron scattering

    Energy Technology Data Exchange (ETDEWEB)

    Fischer, W E [Paul Scherrer Inst. (PSI), Villigen (Switzerland)

    1996-11-01

    We give here an introduction to the theoretical principles of neutron scattering. The relationship between scattering- and correlation-functions is particularly emphasized. Within the framework of linear response theory (justified by the weakness of the basic interaction) the relation between fluctuation and dissipation is discussed. This general framework explains the particular power of neutron scattering as an experimental method. (author) 4 figs., 4 refs.

  8. Compton profiles by inelastic ion-electron scattering

    International Nuclear Information System (INIS)

    Boeckl, H.; Bell, F.

    1983-01-01

    It is shown that Compton profiles (CP) can be measured by inelastic ion-electron scattering. Within the impulse approximation the binary-encounter peak (BEP) reflects the CP of the target atom whereas the electron-loss peak (ELP) is given by projectile CP's. Evaluation of experimental data reveals that inelastic ion-electron scattering might be a promising method to supply inelastic electron or photon scattering for the determination of target CP's. The measurement of projectile CP's is unique to ion scattering since one gains knowledge about wave-function effects because of the high excitation degree of fast heavy-ion projectiles

  9. Debye-Waller Factor in Neutron Scattering by Ferromagnetic Metals

    Science.gov (United States)

    Paradezhenko, G. V.; Melnikov, N. B.; Reser, B. I.

    2018-04-01

    We obtain an expression for the neutron scattering cross section in the case of an arbitrary interaction of the neutron with the crystal. We give a concise, simple derivation of the Debye-Waller factor as a function of the scattering vector and the temperature. For ferromagnetic metals above the Curie temperature, we estimate the Debye-Waller factor in the range of scattering vectors characteristic of polarized magnetic neutron scattering experiments. In the example of iron, we compare the results of harmonic and anharmonic approximations.

  10. A finite range coupled channel Born approximation code

    International Nuclear Information System (INIS)

    Nagel, P.; Koshel, R.D.

    1978-01-01

    The computer code OUKID calculates differential cross sections for direct transfer nuclear reactions in which multistep processes, arising from strongly coupled inelastic states in both the target and residual nuclei, are possible. The code is designed for heavy ion reactions where full finite range and recoil effects are important. Distorted wave functions for the elastic and inelastic scattering are calculated by solving sets of coupled differential equations using a Matrix Numerov integration procedure. These wave functions are then expanded into bases of spherical Bessel functions by the plane-wave expansion method. This approach allows the six-dimensional integrals for the transition amplitude to be reduced to products of two one-dimensional integrals. Thus, the inelastic scattering is treated in a coupled channel formalism while the transfer process is treated in a finite range born approximation formalism. (Auth.)

  11. Scattering from black holes

    International Nuclear Information System (INIS)

    Futterman, J.A.H.; Handler, F.A.; Matzner, R.A.

    1987-01-01

    This book provides a comprehensive treatment of the propagation of waves in the presence of black holes. While emphasizing intuitive physical thinking in their treatment of the techniques of analysis of scattering, the authors also include chapters on the rigorous mathematical development of the subject. Introducing the concepts of scattering by considering the simplest, scalar wave case of scattering by a spherical (Schwarzschild) black hole, the book then develops the formalism of spin weighted spheroidal harmonics and of plane wave representations for neutrino, electromagnetic, and gravitational scattering. Details and results of numerical computations are given. The techniques involved have important applications (references are given) in acoustical and radar imaging

  12. Quantum theory of scattering

    CERN Document Server

    Wu Ta You

    1962-01-01

    This volume addresses the broad formal aspects and applications of the quantum theory of scattering in atomic and nuclear collisions. An encyclopedic source of pioneering work, it serves as a text for students and a reference for professionals in the fields of chemistry, physics, and astrophysics. The self-contained treatment begins with the general theory of scattering of a particle by a central field. Subsequent chapters explore particle scattering by a non-central field, collisions between composite particles, the time-dependent theory of scattering, and nuclear reactions. An examinati

  13. Scattering of radio frequency waves by blob-filaments

    International Nuclear Information System (INIS)

    Myra, J. R.; D'Ippolito, D. A.

    2010-01-01

    Radio frequency waves used for heating and current drive in magnetic confinement experiments must traverse the scrape-off-layer (SOL) and edge plasma before reaching the core. The edge and SOL plasmas are strongly turbulent and intermittent in both space and time. As a first approximation, the SOL can be treated as a tenuous background plasma upon which denser filamentary field-aligned blobs of plasma are superimposed. The blobs are approximately stationary on the rf time scale. The scattering of plane waves in the ion-cyclotron to lower-hybrid frequency range from a cylindrical blob is treated here in the cold plasma fluid model. Scattering widths are derived for incident fast and slow waves, and the scattered power fraction is estimated. Processes such as scattering-induced mode conversion, scattering resonances, and shadowing are investigated.

  14. Simplified solutions of the Cox-Thompson inverse scattering method at fixed energy

    International Nuclear Information System (INIS)

    Palmai, Tamas; Apagyi, Barnabas; Horvath, Miklos

    2008-01-01

    Simplified solutions of the Cox-Thompson inverse quantum scattering method at fixed energy are derived if a finite number of partial waves with only even or odd angular momenta contribute to the scattering process. Based on new formulae various approximate methods are introduced which also prove applicable to the generic scattering events

  15. Probing the phase of the elastic pp scattering amplitude with vortex proton beams

    International Nuclear Information System (INIS)

    Ivanov, I. P.

    2013-01-01

    We show that colliding vortex proton beams instead of (approximate) plane waves can lead to a direct measurement of how the overall phase of the scattering amplitude changes with the scattering angle. In elastic pp scattering, this will open a novel way to measure the parameter ρ(t) and probe the real part of the Pomeron.

  16. Probing the phase of the elastic pp scattering amplitude with vortex proton beams

    Energy Technology Data Exchange (ETDEWEB)

    Ivanov, I. P. [IFPA, Universite de Liege, Allee du 6 Aout 17, batiment B5a, 4000 Liege, Belgium Sobolev Institute of Mathematics, Koptyug avenue 4, 630090, Novosibirsk (Russian Federation)

    2013-04-15

    We show that colliding vortex proton beams instead of (approximate) plane waves can lead to a direct measurement of how the overall phase of the scattering amplitude changes with the scattering angle. In elastic pp scattering, this will open a novel way to measure the parameter {rho}(t) and probe the real part of the Pomeron.

  17. An inverse-scattering approach to the physics of transition metals ...

    African Journals Online (AJOL)

    A method is developed for the deduction of a transition metal ion potential from a knowledge of the phase-shift. The method used is based the distorted plane – wave scattering approximation for the deduction of non singular potentials from scattering phase shifts in an inverse scattering approach. The resulting electron ...

  18. Responsividade e exigência: duas escalas para avaliar estilos parentais Respondingness and demandingness: two scales to evaluate parenting styles

    Directory of Open Access Journals (Sweden)

    Fabiana T. da Costa

    2000-01-01

    Full Text Available O objetivo deste estudo foi traduzir e adaptar duas escalas que avaliam as dimensões de responsividade e exigência parentais com adolescentes, as quais permitem a classificação de quatro estilos parentais. As escalas foram aplicadas a 378 adolescentes, tendo apresentado índices de consistência interna adequados (alpha entre 0,70 e 0,83. Análises de variância revelaram que a exigência materna percebida foi maior do que a paterna entre adolescentes de ambos os sexos, mas as garotas perceberam níveis de exigência (materna e paterna mais altos do que os garotos. A responsividade materna observada foi superior à paterna para ambos os sexos, porém as mulheres atribuíram escores de responsividade mais altos às suas mães do que os homens. Não houve diferenças entre os sexos quanto ao nível de responsividade paterna. A proporção de estilos parentais observada nesta amostra foi 13,3% (autoritário, 36,7% (autoritativo, 14,5% (indulgente e 35,5% (negligente, sugerindo que nossa cultura não é tão permissiva quanto se supõe usualmente.The aim of this study was to translate and adapt two scales of parental responsiveness and demandingness to Portuguese (Brazil. According to these scales levels, it is possible to categorize four parenting styles. The scales were administred to 378 adolescents of both sexes and showed satisfactory reliability coefficients (alpha between 0,70 and 0,83. Analysis of variance indicated that perceived mothers’ demandingness was greater than fathers’ for both sexes, but girls observed higher levels of parental demandingness than boys. Both males and females attributed higher scores of responsiveness to their mothers than to their fathers, but girls scored higher on mothers’ responsiveness than boys. No significant differences between sexes were found for fathers’ level of responsiveness. The frequency of parenting styles observed in this sample was 13,3% (authoritarian, 36,7% (authoritative, 14

  19. An In Vitro Evaluation of Alumina, Zirconia, and Lithium Disilicate Surface Roughness Caused by Two Scaling Instruments.

    Science.gov (United States)

    Vigolo, Paolo; Buzzo, Ottavia; Buzzo, Maurizio; Mutinelli, Sabrina

    2017-02-01

    Plaque control is crucial for the prevention of inflammatory periodontal disease. Hand scaling instruments have been shown to be efficient for the removal of plaque; however, routine periodontal prophylactic procedures may modify the surface profile of restorative materials. The purpose of this study was to assess in vitro the changes in roughness of alumina, zirconia, and lithium disilicate surfaces treated by two hand scaling instruments. Forty-eight alumina specimens, 48 zirconia specimens, and 48 lithium disilicate specimens, were selected. All specimens were divided into three groups of 16 each; one group for each material was considered the control group and no scaling procedures were performed; the second group of each material was exposed to scaling with steel curettes simulating standard clinical conditions; the third group of each material was exposed to scaling with titanium curettes. After scaling, the surface roughness of the specimens was evaluated with a profilometer. First, a statistical test was carried out to evaluate the difference in surface roughness before the scaling procedure of the three materials was effected (Kruskal-Wallis test). Subsequently, the effect of curette material (steel and titanium) on roughness difference and roughness ratio was analyzed throughout the entire sample and within each material group, and a nonparametric test for dependent values was conducted (Wilcoxon signed-rank test). Finally, the roughness ratios of the three material groups were compared by means of a Kruskal-Wallis test and a Wilcoxon signed-rank test. Upon completion of profilometric evaluation, representative specimens from each group were prepared for SEM evaluation to evaluate the effects of the two scaling systems on the different surfaces qualitatively. After scaling procedure, the roughness profile value increased in all disks. Classifying the full sample according to curette used, the roughness of the disks treated with a steel curette reached a

  20. Diffuse neutron scattering signatures of rough films

    International Nuclear Information System (INIS)

    Pynn, R.; Lujan, M. Jr.

    1992-01-01

    Patterns of diffuse neutron scattering from thin films are calculated from a perturbation expansion based on the distorted-wave Born approximation. Diffuse fringes can be categorised into three types: those that occur at constant values of the incident or scattered neutron wavevectors, and those for which the neutron wavevector transfer perpendicular to the film is constant. The variation of intensity along these fringes can be used to deduce the spectrum of surface roughness for the film and the degree of correlation between the film's rough surfaces

  1. Enhanced ionized impurity scattering in nanowires

    Science.gov (United States)

    Oh, Jung Hyun; Lee, Seok-Hee; Shin, Mincheol

    2013-06-01

    The electronic resistivity in silicon nanowires is investigated by taking into account scattering as well as the donor deactivation from the dielectric mismatch. The effects of poorly screened dopant atoms from the dielectric mismatch and variable carrier density in nanowires are found to play a crucial role in determining the nanowire resistivity. Using Green's function method within the self-consistent Born approximation, it is shown that donor deactivation and ionized impurity scattering combined with the charged interface traps successfully to explain the increase in the resistivity of Si nanowires while reducing the radius, measured by Björk et al. [Nature Nanotech. 4, 103 (2009)].

  2. Coupled channel theory of pion--deuteron reaction applied to threshold scattering

    International Nuclear Information System (INIS)

    Mizutani, T.; Koltun, D.S.

    1977-01-01

    Scattering and absorption of pions by a nuclear target are treated together in a coupled channel theory. The theory is developed explicitly for the problem of pion scattering and absorption by a deuteron. The equations are presented in terms of the integral equations of three-body scattering theory. The method is then applied in an approximate from to calculate the contribution of pion absorption to the scattering length for pion--deuteron scattering. The sensitivity of the calculated results to the model assumptions and approximations is investigated

  3. Big geo data surface approximation using radial basis functions: A comparative study

    Science.gov (United States)

    Majdisova, Zuzana; Skala, Vaclav

    2017-12-01

    Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for big scattered datasets in n-dimensional space. It is a non-separable approximation, as it is based on the distance between two points. This method leads to the solution of an overdetermined linear system of equations. In this paper the RBF approximation methods are briefly described, a new approach to the RBF approximation of big datasets is presented, and a comparison for different Compactly Supported RBFs (CS-RBFs) is made with respect to the accuracy of the computation. The proposed approach uses symmetry of a matrix, partitioning the matrix into blocks and data structures for storage of the sparse matrix. The experiments are performed for synthetic and real datasets.

  4. Discrete Ordinates Approximations to the First- and Second-Order Radiation Transport Equations

    International Nuclear Information System (INIS)

    FAN, WESLEY C.; DRUMM, CLIFTON R.; POWELL, JENNIFER L. email wcfan@sandia.gov

    2002-01-01

    The conventional discrete ordinates approximation to the Boltzmann transport equation can be described in a matrix form. Specifically, the within-group scattering integral can be represented by three components: a moment-to-discrete matrix, a scattering cross-section matrix and a discrete-to-moment matrix. Using and extending these entities, we derive and summarize the matrix representations of the second-order transport equations

  5. Discrete Ordinates Approximations to the First- and Second-Order Radiation Transport Equations

    CERN Document Server

    Fan, W C; Powell, J L

    2002-01-01

    The conventional discrete ordinates approximation to the Boltzmann transport equation can be described in a matrix form. Specifically, the within-group scattering integral can be represented by three components: a moment-to-discrete matrix, a scattering cross-section matrix and a discrete-to-moment matrix. Using and extending these entities, we derive and summarize the matrix representations of the second-order transport equations.

  6. Scattering of electromagnetic waves from a half-space of randomly distributed discrete scatterers and polarized backscattering ratio law

    Science.gov (United States)

    Zhu, P. Y.

    1991-01-01

    The effective-medium approximation is applied to investigate scattering from a half-space of randomly and densely distributed discrete scatterers. Starting from vector wave equations, an approximation, called effective-medium Born approximation, a particular way, treating Green's functions, and special coordinates, of which the origin is set at the field point, are used to calculate the bistatic- and back-scatterings. An analytic solution of backscattering with closed form is obtained and it shows a depolarization effect. The theoretical results are in good agreement with the experimental measurements in the cases of snow, multi- and first-year sea-ice. The root product ratio of polarization to depolarization in backscattering is equal to 8; this result constitutes a law about polarized scattering phenomena in the nature.

  7. Measurement of pressure ridges in SAR images of sea ice - Preliminary results on scattering theory

    Science.gov (United States)

    Vesecky, J. F.; Smith, M. P.; Daida, J. M.; Samadani, R.; Camiso, J. C.

    1992-01-01

    Sea ice ridges and keels (hummocks and bummocks) are important in sea ice research for both scientific and practical reasons. A long-term objective is to make quantitative measurements of sea ice ridges using synthetic aperture radar (SAR) images. The preliminary results of a scattering model for sea ice ridge are reported. The approach is through the ridge height variance spectrum Psi(K), where K is the spatial wavenumber, and the two-scale scattering model. The height spectrum model is constructed to mimic height statistics observed with an airborne optical laser. The spectrum model is used to drive a two-scale scattering model. Model results for ridges observed at C- and X-band yield normalized radar cross sections that are 10 to 15 dB larger than the observed cross sections of multiyear ice over the range of angles of incidence from 10 to 70 deg.

  8. Using function approximation to determine neural network accuracy

    International Nuclear Information System (INIS)

    Wichman, R.F.; Alexander, J.

    2013-01-01

    Many, if not most, control processes demonstrate nonlinear behavior in some portion of their operating range and the ability of neural networks to model non-linear dynamics makes them very appealing for control. Control of high reliability safety systems, and autonomous control in process or robotic applications, however, require accurate and consistent control and neural networks are only approximators of various functions so their degree of approximation becomes important. In this paper, the factors affecting the ability of a feed-forward back-propagation neural network to accurately approximate a non-linear function are explored. Compared to pattern recognition using a neural network for function approximation provides an easy and accurate method for determining the network's accuracy. In contrast to other techniques, we show that errors arising in function approximation or curve fitting are caused by the neural network itself rather than scatter in the data. A method is proposed that provides improvements in the accuracy achieved during training and resulting ability of the network to generalize after training. Binary input vectors provided a more accurate model than with scalar inputs and retraining using a small number of the outlier x,y pairs improved generalization. (author)

  9. Extended quasiparticle approximation for relativistic electrons in plasmas

    Directory of Open Access Journals (Sweden)

    V.G.Morozov

    2006-01-01

    Full Text Available Starting with Dyson equations for the path-ordered Green's function, it is shown that the correlation functions for relativistic electrons (positrons in a weakly coupled non-equilibrium plasmas can be decomposed into sharply peaked quasiparticle parts and off-shell parts in a rather general form. To leading order in the electromagnetic coupling constant, this decomposition yields the extended quasiparticle approximation for the correlation functions, which can be used for the first principle calculation of the radiation scattering rates in QED plasmas.

  10. Validity of PEC Approximation for On-Body Propagation

    DEFF Research Database (Denmark)

    Kammersgaard, Nikolaj Peter Iversen; Kvist, Søren Helstrup; Thaysen, Jesper

    2016-01-01

    Many articles on on-body propagation assumes that the human body can be approximated by a perfect electric conductor (PEC) instead of the actual constitutive parameters of the human body, which is that of a lossy dielectric. This assumption is investigated in this article through comparison...... of the scattering of a plane wave at oblique incidence by a PEC and a lossy dielectric cylinder. The investigation shows that the validity of the assumption depends on the polarization of the plane wave, the angle of incidence, and the region of interest....

  11. Neutrino-nucleus cross section in the impulse approximation regime

    International Nuclear Information System (INIS)

    Benhar, Omar; Farina, Nicola

    2005-01-01

    In the impulse approximation regime the nuclear response to a weakly interacting probe can be written in terms of the measured nucleon structure functions and the target spectral function, yielding the energy and momentum distribution of the constituent nucleons. We discuss a calculation of charged current neutrino-oxygen interactions in the quasielastic channel, carried out within nuclear many body theory. The proposed approach, extensively and successfully employed in the analysis of electron-nucleus scattering data, allows for a parameter free prediction of the neutrino-nucleus cross section, whose quantitative understanding will be critical to the analysis of the next generation of high precision neutrino oscillation experiments

  12. Pion-pion scattering

    International Nuclear Information System (INIS)

    Kuehnelt, H.

    1975-01-01

    We discuss a few properties of scattering amplitudes proved within the framework of the field theory and their significance in the derivation of quantitative statements. The state of the boundaries for the scattering lengths is to be especially discussed as well as the question as to how far it is possible to exclude various solutions from phase displacement analyses. (orig./LH) [de

  13. Modelling Hyperboloid Sound Scattering

    DEFF Research Database (Denmark)

    Burry, Jane; Davis, Daniel; Peters, Brady

    2011-01-01

    The Responsive Acoustic Surfaces workshop project described here sought new understandings about the interaction between geometry and sound in the arena of sound scattering. This paper reports on the challenges associated with modelling, simulating, fabricating and measuring this phenomenon using...... both physical and digital models at three distinct scales. The results suggest hyperboloid geometry, while difficult to fabricate, facilitates sound scattering....

  14. Incoherent Thomson scattering

    NARCIS (Netherlands)

    Donne, A. J. H.

    1996-01-01

    Thomson scattering is a very powerful diagnostic which is applied at nearly every magnetic confinement device. Depending on the experimental conditions different plasma parameters can be diagnosed. When the wave vector is much larger than the plasma Debye length, the total scattered power is

  15. Concentric layered Hermite scatterers

    Science.gov (United States)

    Astheimer, Jeffrey P.; Parker, Kevin J.

    2018-05-01

    The long wavelength limit of scattering from spheres has a rich history in optics, electromagnetics, and acoustics. Recently it was shown that a common integral kernel pertains to formulations of weak spherical scatterers in both acoustics and electromagnetic regimes. Furthermore, the relationship between backscattered amplitude and wavenumber k was shown to follow power laws higher than the Rayleigh scattering k2 power law, when the inhomogeneity had a material composition that conformed to a Gaussian weighted Hermite polynomial. Although this class of scatterers, called Hermite scatterers, are plausible, it may be simpler to manufacture scatterers with a core surrounded by one or more layers. In this case the inhomogeneous material property conforms to a piecewise continuous constant function. We demonstrate that the necessary and sufficient conditions for supra-Rayleigh scattering power laws in this case can be stated simply by considering moments of the inhomogeneous function and its spatial transform. This development opens an additional path for construction of, and use of scatterers with unique power law behavior.

  16. A modified linear algebraic approach to electron scattering using cubic splines

    International Nuclear Information System (INIS)

    Kinney, R.A.

    1986-01-01

    A modified linear algebraic approach to the solution of the Schrodiner equation for low-energy electron scattering is presented. The method uses a piecewise cubic-spline approximation of the wavefunction. Results in the static-potential and the static-exchange approximations for e - +H s-wave scattering are compared with unmodified linear algebraic and variational linear algebraic methods. (author)

  17. Schwinger variational principle in scattering problems of charged particles on mesic atoms and atoms

    International Nuclear Information System (INIS)

    Belyaev, V.B.; Zubarev, A.L.; Podkopaev, A.P.

    1978-01-01

    The Schwinger variational principle is applied to solve the problems of atomic physics. A separable approximation for a Hamiltonian of a bound subsystem is used. The length of e + H-scattering and the elastic p(dμ)-scattering cross section are calculated in the second Born approximation

  18. Eikonal representation of N-body Coulomb scattering amplitudes

    International Nuclear Information System (INIS)

    Fried, H.M.; Kang, K.; McKellar, B.H.J.

    1983-01-01

    A new technique for the construction of N-body Coulomb scattering amplitudes is proposed, suggested by the simplest case of N = 2: Calculate the scattering amplitude in eikonal approximation, discard the infinite phase factors which appear upon taking the limit of a Coulomb potential, and treat the remainder as an amplitude whose absolute value squared produces the exact, Coulomb differential cross section. The method easily generalizes to the N-body Coulomb problem for elastic scattering, and for inelastic rearrangement scattering of Coulomb bound states. We give explicit results for N = 3 and 4; in the N = 3 case we extract amplitudes for the processes (12)+3->1+2+3 (breakup), (12)+3->1+(23) (rearrangement), and (12)+3→(12)'+3 (inelastic scattering) as residues at the appropriate poles in the free-free amplitude. The method produces scattering amplitudes f/sub N/ given in terms of explicit quadratures over (N-2) 2 distinct integrands

  19. Application of Van Hove theory to fast neutron inelastic scattering

    International Nuclear Information System (INIS)

    Stanicicj, V.

    1974-11-01

    The Vane Hove general theory of the double differential scattering cross section has been used to derive the particular expressions of the inelastic fast neutrons scattering kernel and scattering cross section. Since the considered energies of incoming neutrons being less than 10 MeV, it enables to use the Fermi gas model of nucleons. In this case it was easy to derive an analytical expression for the time-dependent correlation function of the nucleus. Further, by using an impulse approximation and a short-collision time approach, it was possible to derive the analytical expression of the scattering kernel and scattering cross section for the fast neutron inelastic scattering. The obtained expressions have been used for Fe nucleus. It has been shown a surprising agreement with the experiments. The main advantage of this theory is in its simplicity for some practical calculations and for some theoretical investigations of nuclear processes

  20. On seismic interferometry, the generalized optical theorem, and the scattering matrix of a point scatterer

    NARCIS (Netherlands)

    Wapenaar, C.P.A.; Slob, E.C.; Snieder, R.

    2010-01-01

    We have analyzed the far-field approximation of the Green's function representation for seismic interferometry. By writing each of the Green's functions involved in the correlation process as a superposition of a direct wave and a scattered wave, the Green's function representation is rewritten as a

  1. Introductory theory of neutron scattering

    International Nuclear Information System (INIS)

    Gunn, J.M.F.

    1986-12-01

    The paper comprises a set of six lecture notes which were delivered to the summer school on 'Neutron Scattering at a pulsed source', Rutherford Laboratory, United Kingdom, 1986. The lectures concern the physical principles of neutron scattering. The topics of the lectures include: diffraction, incoherent inelastic scattering, connection with the Schroedinger equation, magnetic scattering, coherent inelastic scattering, and surfaces and neutron optics. (UK)

  2. Compton scatter correction for planner scintigraphic imaging

    Energy Technology Data Exchange (ETDEWEB)

    Vaan Steelandt, E; Dobbeleir, A; Vanregemorter, J [Algemeen Ziekenhuis Middelheim, Antwerp (Belgium). Dept. of Nuclear Medicine and Radiotherapy

    1995-12-01

    A major problem in nuclear medicine is the image degradation due to Compton scatter in the patient. Photons emitted by the radioactive tracer scatter in collision with electrons of the surrounding tissue. Due to the resulting loss of energy and change in direction, the scattered photons induce an object dependant background on the images. This results in a degradation of the contrast of warm and cold lesions. Although theoretically interesting, most of the techniques proposed in literature like the use of symmetrical photopeaks can not be implemented on the commonly used gamma camera due to the energy/linearity/sensitivity corrections applied in the detector. A method for a single energy isotope based on existing methods with adjustments towards daily practice and clinical situations is proposed. It is assumed that the scatter image, recorded from photons collected within a scatter window adjacent to the photo peak, is a reasonable close approximation of the true scatter component of the image reconstructed from the photo peak window. A fraction `k` of the image using the scatter window is subtracted from the image recorded in the photo peak window to produce the compensated image. The principal matter of the method is the right value for the factor `k`, which is determined in a mathematical way and confirmed by experiments. To determine `k`, different kinds of scatter media are used and are positioned in different ways in order to simulate a clinical situation. For a secondary energy window from 100 to 124 keV below a photo peak window from 126 to 154 keV, a value of 0.7 is found. This value has been verified using both an antropomorph thyroid phantom and the Rollo contrast phantom.

  3. Diffuse scattering of neutrons

    International Nuclear Information System (INIS)

    Novion, C.H. de.

    1981-02-01

    The use of neutron scattering to study atomic disorder in metals and alloys is described. The diffuse elastic scattering of neutrons by a perfect crystal lattice leads to a diffraction spectrum with only Bragg spreads. the existence of disorder in the crystal results in intensity and position modifications to these spreads, and above all, to the appearance of a low intensity scatter between Bragg peaks. The elastic scattering of neutrons is treated in this text, i.e. by measuring the number of scattered neutrons having the same energy as the incident neutrons. Such measurements yield information on the static disorder in the crystal and time average fluctuations in composition and atomic displacements [fr

  4. Inelastic Light Scattering Processes

    Science.gov (United States)

    Fouche, Daniel G.; Chang, Richard K.

    1973-01-01

    Five different inelastic light scattering processes will be denoted by, ordinary Raman scattering (ORS), resonance Raman scattering (RRS), off-resonance fluorescence (ORF), resonance fluorescence (RF), and broad fluorescence (BF). A distinction between fluorescence (including ORF and RF) and Raman scattering (including ORS and RRS) will be made in terms of the number of intermediate molecular states which contribute significantly to the scattered amplitude, and not in terms of excited state lifetimes or virtual versus real processes. The theory of these processes will be reviewed, including the effects of pressure, laser wavelength, and laser spectral distribution on the scattered intensity. The application of these processes to the remote sensing of atmospheric pollutants will be discussed briefly. It will be pointed out that the poor sensitivity of the ORS technique cannot be increased by going toward resonance without also compromising the advantages it has over the RF technique. Experimental results on inelastic light scattering from I(sub 2) vapor will be presented. As a single longitudinal mode 5145 A argon-ion laser line was tuned away from an I(sub 2) absorption line, the scattering was observed to change from RF to ORF. The basis, of the distinction is the different pressure dependence of the scattered intensity. Nearly three orders of magnitude enhancement of the scattered intensity was measured in going from ORF to RF. Forty-seven overtones were observed and their relative intensities measured. The ORF cross section of I(sub 2) compared to the ORS cross section of N2 was found to be 3 x 10(exp 6), with I(sub 2) at its room temperature vapor pressure.

  5. A mathematical formulation of the Mahaux-Weidenmueller formula for the scattering matrix

    International Nuclear Information System (INIS)

    Christiansen, T J; Zworski, M

    2009-01-01

    This paper gives a mathematical exposition of a formula for the scattering matrix for a manifold with infinite cylindrical ends or a waveguide. This formula is well known in the physics literature and we show that a variant of this formula gives the scattering matrix of the mathematics literature. Moreover, we bound the difference between the scattering matrix and an approximation of it computed using a finite rank approximation of the interaction matrix.

  6. Influence of scattering processes on electron quantum states in nanowires

    Directory of Open Access Journals (Sweden)

    Pozdnyakov Dmitry

    2007-01-01

    Full Text Available AbstractIn the framework of quantum perturbation theory the self-consistent method of calculation of electron scattering rates in nanowires with the one-dimensional electron gas in the quantum limit is worked out. The developed method allows both the collisional broadening and the quantum correlations between scattering events to be taken into account. It is an alternativeper seto the Fock approximation for the self-energy approach based on Green’s function formalism. However this approach is free of mathematical difficulties typical to the Fock approximation. Moreover, the developed method is simpler than the Fock approximation from the computational point of view. Using the approximation of stable one-particle quantum states it is proved that the electron scattering processes determine the dependence of electron energy versus its wave vector.

  7. Lorentz violation, gravitoelectromagnetic field and Bhabha scattering

    Science.gov (United States)

    Santos, A. F.; Khanna, Faqir C.

    2018-01-01

    Lorentz symmetry is a fundamental symmetry in the Standard Model (SM) and in General Relativity (GR). This symmetry holds true for all models at low energies. However, at energies near the Planck scale, it is conjectured that there may be a very small violation of Lorentz symmetry. The Standard Model Extension (SME) is a quantum field theory that includes a systematic description of Lorentz symmetry violations in all sectors of particle physics and gravity. In this paper, SME is considered to study the physical process of Bhabha Scattering in the Gravitoelectromagnetism (GEM) theory. GEM is an important formalism that is valid in a suitable approximation of general relativity. A new nonminimal coupling term that violates Lorentz symmetry is used in this paper. Differential cross-section for gravitational Bhabha scattering is calculated. The Lorentz violation contributions to this GEM scattering cross-section are small and are similar in magnitude to the case of the electromagnetic field.

  8. The basic physics of neutron scattering experiments

    International Nuclear Information System (INIS)

    Mezei, F.

    1999-01-01

    The basic physical principles behind the well-established but also developing practice of neutron scattering experiments are presented. A few examples are given either to illustrate the physical principles or to give an idea of the variety, importance or magnitude of various phenomena. The evolution of neutron scattering experimental techniques is investigated from a special aspect: the increasing capability of taking into account more and more important and sometimes decisive finer details by using more and more realistic mathematical models of the evolution of the neutrons from birth do death, eventually passing by the sample and being scattered more than one times. Working with such numerical 'virtual instruments' one will have to go far beyond notions like resolution function, convolution etc, and actually eliminate a large number of approximations currently in use. (K.A.)

  9. Raman scattering in the atmospheres of the major planets

    International Nuclear Information System (INIS)

    Cochran, W.D.; Trafton, L.M.

    1978-01-01

    A method is developed for calculating the rate at which photons are Raman scattered as a function of frequency and depth in an inhomogeneous anisotropically scattering atmosphere. This method is used to determine the effects of Raman scattering by H 2 in the atmospheres of the major planets. Raman scattering causes an insufficient decrease in the blue and ultraviolet to explain the albedos of all of the planets; an additional source of extinction is necessary in this spectral region. Approximately 0.5-2.0% of the blue continuum photons have undergone Raman scattering in the shallow atmospheres of Jupiter and Saturn, while in the deep atmospheres of Uranus and Neptune Raman scattering accounts for abount 10-15% of the blue continuum intensity. The filling in of the cores of solar lines and the production of Raman-shifted ghosts of the Fraunhofer spectrum will be detectable effects in all of the major planets. Raman scattering has a significant influence on the formation and profiles of the strong red and near-infrared CH 4 bands on Uranus and Neptune. The residual intensity in the cores of these bands may be fully explained as a result of Raman scattering by H 2 . This scattering of photons into the cores of saturated absorption bands will cause an underestimate of the abundance of the absorber unless the effects of Raman scattering by H 2 in an inhomogeneous atmosphere are properly included in the analysis

  10. Light scattering studies at UNICAMP

    International Nuclear Information System (INIS)

    Luzzi, R.; Cerdeira, H.A.; Salzberg, J.; Vasconcellos, A.R.; Frota Pessoa, S.; Reis, F.G. dos; Ferrari, C.A.; Algarte, C.A.S.; Tenan, M.A.

    1975-01-01

    Current theoretical studies on light scattering spectroscopy at UNICAMP is presented briefly, such as: inelastic scattering of radiation from a solid state plasma; resonant Ramman scattering; high excitation effects; saturated semiconductors and glasses

  11. Approximation by rational functions as processing method, analysis and transformation of neutron data

    International Nuclear Information System (INIS)

    Gaj, E.V.; Badikov, S.A.; Gusejnov, M.A.; Rabotnov, N.S.

    1988-01-01

    Possible applications of rational functions in the analysis of neutron cross sections, angular distributions and neutron constants generation are described. Results of investigations made in this direction, which have been obtained after the preceding conference in Kiev, are presented: the method of simultaneous treatment of several cross sections for one compound nucleus in the resonance range; the use of the Pade approximation for elastically scattered neutron angular distribution approximation; obtaining of subgroup constants on the basis of rational approximation of cross section functional dependence on dilution cross section; the first experience in function approximation by two variables

  12. Scattering of Electromagnetic Waves by Drift Vortex in Plasma

    International Nuclear Information System (INIS)

    Wang Dong; Chen Yinhua; Wang Ge

    2008-01-01

    In a quasi-two-dimensional model, the scattering of incident ordinary electromagnetic waves by a dipole-electrostatic drift vortex is studied with first-order Born approximation. The distribution of the scattering cross-section and total cross-section are evaluated analytically in different approximate conditions, and the physical interpretations are discussed. When the wavelength of incident wave is much longer than the vortex radius (k i a || 1), it is found that the angle at which the scattering cross-section reaches its maxim depends significantly on the approximation of the parameters of the vortex used. It is also found that the total scattering cross-section has an affinitive relation with the parameters of the plasma, while it is irrelevant to the frequency of the incident wave in a wide range of parameters of the vortex. In a totally different range of parameters when incident wave is in the radar-frequency range (then k i a || 1, the wavelength of incident wave is much shorter than the vortex radius), the numerical procedure is conducted with computer in order to obtain the distribution and the total expression of the scattering cross-section. Then it is found that the total scattering cross-section in the low frequency range is much larger than that in high frequency range, so the scattering is more effective in the low frequency range than in high frequency range.

  13. Migration of scattered teleseismic body waves

    Science.gov (United States)

    Bostock, M. G.; Rondenay, S.

    1999-06-01

    The retrieval of near-receiver mantle structure from scattered waves associated with teleseismic P and S and recorded on three-component, linear seismic arrays is considered in the context of inverse scattering theory. A Ray + Born formulation is proposed which admits linearization of the forward problem and economy in the computation of the elastic wave Green's function. The high-frequency approximation further simplifies the problem by enabling (1) the use of an earth-flattened, 1-D reference model, (2) a reduction in computations to 2-D through the assumption of 2.5-D experimental geometry, and (3) band-diagonalization of the Hessian matrix in the inverse formulation. The final expressions are in a form reminiscent of the classical diffraction stack of seismic migration. Implementation of this procedure demands an accurate estimate of the scattered wave contribution to the impulse response, and thus requires the removal of both the reference wavefield and the source time signature from the raw record sections. An approximate separation of direct and scattered waves is achieved through application of the inverse free-surface transfer operator to individual station records and a Karhunen-Loeve transform to the resulting record sections. This procedure takes the full displacement field to a wave vector space wherein the first principal component of the incident wave-type section is identified with the direct wave and is used as an estimate of the source time function. The scattered displacement field is reconstituted from the remaining principal components using the forward free-surface transfer operator, and may be reduced to a scattering impulse response upon deconvolution of the source estimate. An example employing pseudo-spectral synthetic seismograms demonstrates an application of the methodology.

  14. Virtual neutron scattering experiments

    DEFF Research Database (Denmark)

    Overgaard, Julie Hougaard; Bruun, Jesper; May, Michael

    2017-01-01

    . In the last week of the course, students travel to a large-scale neutron scattering facility to perform real neutron scattering experiments. Through student interviews and survey answers, we argue, that the virtual training prepares the students to engage more fruitfully with experiments by letting them focus......We describe how virtual experiments can be utilized in a learning design that prepares students for hands-on experiments at large-scale facilities. We illustrate the design by showing how virtual experiments are used at the Niels Bohr Institute in a master level course on neutron scattering...

  15. Scattering on magnetic monopoles

    International Nuclear Information System (INIS)

    Petry, H.R.

    1980-01-01

    The time-dependent scattering theory of charged particles on magnetic monopoles is investigated within a mathematical frame-work, which duely pays attention to the fact that the wavefunctions of the scattered particles are sections in a non-trivial complex line-bundle. It is found that Moeller operators have to be defined in a way which takes into account the peculiar long-range behaviour of the monopole field. Formulas for the scattering matrix and the differential cross-section are derived, and, as a by-product, a momentum space picture for particles, which are described by sections in the underlying complex line-bundle, is presented. (orig.)

  16. Neutron scattering from a substitutional mass defect

    International Nuclear Information System (INIS)

    Williams, R.D.; Lovesey, S.W.

    1985-06-01

    The dynamic structure factor is calculated for a low concentration of light mass scatterers substituted in a cubic crystal matrix. A new numerical method for the exact calculation is demonstrated. A local density of states for the low momentum transfer limit, and the shifts and widths of the oscillator peaks in the high momentum transfer limit are derived. The limitations of an approximation which decouples the defect from the lattice is discussed. (author)

  17. Proton scattering at intermediate energies

    International Nuclear Information System (INIS)

    Chaumeaux, A.; Layly, V.; Schaeffer, R.

    1977-01-01

    This article is devoted to the analysis of the most recent Saclay data of elastic and inelastic proton scattering on nuclei at incident energies around 1GeV ( 16 O, the Ca isotopes, the Ni isotopes, 90 Zr and 208 Pb). Various theories (Impulse or Glauber approximation) are comapred. It is shown that the reaction mechanism is very well understood at 1GeV and that, at these energies, absorption and distortion is small enough, so one can extract nuclear densities from the experiment. In particular, the shape of the neutron densities is given, and compared to the Hartree-Fock predictions. The uncertainties, especially in the determination of the neutron radii are discussed [fr

  18. Monopole scattering with a twist

    International Nuclear Information System (INIS)

    Houghton, C.J.; Sutcliffe, P.M.

    1996-01-01

    By imposing certain combined inversion and rotation symmetries on the rational maps for SU(2) BPS monopoles we construct geodesics in the monopole moduli space. In the moduli space approximation these geodesics describe a novel kind of monopole scattering. During these scattering processes axial symmetry is instantaneously attained and, in some, monopoles with the symmetries of the regular solids are formed. The simplest example corresponds to a charge three monopole invariant under a combined inversion and 90 circle rotation symmetry. In this example three well-separated collinear unit charge monopoles coalesce to form first a tetrahedron, then a torus, then the dual tetrahedron and finally separate again along the same axis of motion. We explicitly construct the spectral curves in this case and use a numerical ADHMN construction to compute the energy density at various times during the motion. We find that the dynamics of the zeros of the Higgs field is extremely rich and we discover a new phenomenon; there exist charge k SU(2) BPS monopoles with more than k zeros of the Higgs field. (orig.)

  19. On the convergence of multigroup discrete-ordinates approximations

    International Nuclear Information System (INIS)

    Victory, H.D. Jr.; Allen, E.J.; Ganguly, K.

    1987-01-01

    Our analysis is divided into two distinct parts which we label for convenience as Part A and Part B. In Part A, we demonstrate that the multigroup discrete-ordinates approximations are well-defined and converge to the exact transport solution in any subcritical setting. For the most part, we focus on transport in two-dimensional Cartesian geometry. A Nystroem technique is used to extend the discrete ordinates multigroup approximates to all values of the angular and energy variables. Such an extension enables us to employ collectively compact operator theory to deduce stability and convergence of the approximates. In Part B, we perform a thorough convergence analysis for the multigroup discrete-ordinates method for an anisotropically-scattering subcritical medium in slab geometry. The diamond-difference and step-characteristic spatial approximation methods are each studied. The multigroup neutron fluxes are shown to converge in a Banach space setting under realistic smoothness conditions on the solution. This is the first thorough convergence analysis for the fully-discretized multigroup neutron transport equations

  20. On the mathematical treatment of the Born-Oppenheimer approximation

    International Nuclear Information System (INIS)

    Jecko, Thierry

    2014-01-01

    Motivated by the paper by Sutcliffe and Woolley [“On the quantum theory of molecules,” J. Chem. Phys. 137, 22A544 (2012)], we present the main ideas used by mathematicians to show the accuracy of the Born-Oppenheimer approximation for molecules. Based on mathematical works on this approximation for molecular bound states, in scattering theory, in resonance theory, and for short time evolution, we give an overview of some rigorous results obtained up to now. We also point out the main difficulties mathematicians are trying to overcome and speculate on further developments. The mathematical approach does not fit exactly to the common use of the approximation in Physics and Chemistry. We criticize the latter and comment on the differences, contributing in this way to the discussion on the Born-Oppenheimer approximation initiated by Sutcliffe and Woolley. The paper neither contains mathematical statements nor proofs. Instead, we try to make accessible mathematically rigourous results on the subject to researchers in Quantum Chemistry or Physics

  1. On the mathematical treatment of the Born-Oppenheimer approximation

    Energy Technology Data Exchange (ETDEWEB)

    Jecko, Thierry, E-mail: thierry.jecko@u-cergy.fr [AGM, UMR 8088 du CNRS, Université de Cergy-Pontoise, Département de mathématiques, site de Saint Martin, 2 avenue Adolphe Chauvin, F-95000 Pontoise (France)

    2014-05-15

    Motivated by the paper by Sutcliffe and Woolley [“On the quantum theory of molecules,” J. Chem. Phys. 137, 22A544 (2012)], we present the main ideas used by mathematicians to show the accuracy of the Born-Oppenheimer approximation for molecules. Based on mathematical works on this approximation for molecular bound states, in scattering theory, in resonance theory, and for short time evolution, we give an overview of some rigorous results obtained up to now. We also point out the main difficulties mathematicians are trying to overcome and speculate on further developments. The mathematical approach does not fit exactly to the common use of the approximation in Physics and Chemistry. We criticize the latter and comment on the differences, contributing in this way to the discussion on the Born-Oppenheimer approximation initiated by Sutcliffe and Woolley. The paper neither contains mathematical statements nor proofs. Instead, we try to make accessible mathematically rigourous results on the subject to researchers in Quantum Chemistry or Physics.

  2. The P1approximation in the transport of beta rays

    International Nuclear Information System (INIS)

    Legarda, F.; Idoeta, R.; Herranz, M.

    1994-01-01

    A validation test for the p1 approximation to the linear transport of electrons in planar geometry has been performed. The p1 approximation is shown to be a good option for the description of the transport of beta rays with endpoint energies between 400kev and 3.5Mev through aluminium foils . This approximation together with the use of only elastic interactions of electrons with atoms has found good agreement with experimental results . A calculation has been made of the fraction of transmitted electrons through foils, solving the transport equation for planar geometry in the p1 approximation and assuming that only elastic scattering processes take place. The boundary condition at the entrance of the foil was a collimated beta source, while at the end of the foil has been adopted a vaccum boundary condition.Sources considered are those for which experimental and calculated spectrum shapes are known to agree. The calculated fractional transmission through different absorber thicknesses is found to have an exponential shape . Besides this fact the attenuation coefficients found ,when compared with those empirically obtained, agree to within 5%. 1 fig.; 4 refs. (author)

  3. Electron scattering from pyrimidine

    International Nuclear Information System (INIS)

    Colmenares, Rafael; Fuss, Martina C; García, Gustavo; Oller, Juan C; Muñoz, Antonio; Blanco, Francisco; Almeida, Diogo; Limão-Vieira, Paulo

    2014-01-01

    Electron scattering from pyrimidine (C 4 H 4 N 2 ) was investigated over a wide range of energies. Following different experimental and theoretical approaches, total, elastic and ionization cross sections as well as electron energy loss distributions were obtained.

  4. Applied electromagnetic scattering theory

    CERN Document Server

    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...

  5. Scattering by bound nucleons

    International Nuclear Information System (INIS)

    Tezuka, Hirokazu.

    1984-10-01

    Scattering of a particle by bound nucleons is discussed. Effects of nucleons that are bound in a nucleus are taken as a structure function. The way how to calculate the structure function is given. (author)

  6. LIDAR Thomson scattering

    International Nuclear Information System (INIS)

    1991-07-01

    This collection contains 21 papers on the application and development of LIDAR (Light Detection and Ranging) Thomson scattering techniques for the determination of spatially resolved electron temperature and density in magnetic confinement experiments, particularly tokamaks. Refs, figs and tabs

  7. Magnetic electron scattering

    International Nuclear Information System (INIS)

    Peterson, G.A.

    1989-01-01

    We briefly review some of the motivations, early results, and techniques of magnetic elastic and inelastic electron-nucleus scattering. We then discuss recent results, especially those acquired at high momentum transfers. 50 refs., 19 figs

  8. Deep inelastic lepton scattering

    International Nuclear Information System (INIS)

    Nachtmann, O.

    1977-01-01

    Deep inelastic electron (muon) nucleon and neutrino nucleon scattering as well as electron positron annihilation into hadrons are reviewed from a theoretical point of view. The emphasis is placed on comparisons of quantum chromodynamics with the data. (orig.) [de

  9. Factorized distorted wave approximation for the (e,2e) reaction on atoms : noncoplanar symmetric

    International Nuclear Information System (INIS)

    Dixon, A.J.; McCarthy, I.E.; Noble, C.J.; Weigold, E.

    1977-02-01

    Angular and energy correlations for electrons produced in the ionization of neon and xenon by electrons with energies between 400eV and 2.5 keV have been measured using symmetric noncoplanar kinematics. The reaction yields information about the atomic orbitals and their correlations when analysed with the distorted-wave off-shell impulse approximation. In the past either plane waves or various eikonal approximations have been used for the distorted waves, and in the cases where the eikonal parameters are approximately related to the elastic scattering the spectroscopic sum rule has been approximately verified. In the present work calculations have also been carried out using partial-wave-expanded optical model wave functions which describe the elastic scattering in detail. (Author)

  10. Atmospheric scattering corrections to solar radiometry

    International Nuclear Information System (INIS)

    Box, M.A.; Deepak, A.

    1979-01-01

    Whenever a solar radiometer is used to measure direct solar radiation, some diffuse sky radiation invariably enters the detector's field of view along with the direct beam. Therefore, the atmospheric optical depth obtained by the use of Bouguer's transmission law (also called Beer-Lambert's law), that is valid only for direct radiation, needs to be corrected by taking account of the scattered radiation. In this paper we shall discuss the correction factors needed to account for the diffuse (i.e., singly and multiply scattered) radiation and the algorithms developed for retrieving aerosol size distribution from such measurements. For a radiometer with a small field of view (half-cone angle 0 ) and relatively clear skies (optical depths <0.4), it is shown that the total diffuse contributions represents approximately l% of the total intensity. It is assumed here that the main contributions to the diffuse radiation within the detector's view cone are due to single scattering by molecules and aerosols and multiple scattering by molecules alone, aerosol multiple scattering contributions being treated as negligibly small. The theory and the numerical results discussed in this paper will be helpful not only in making corrections to the measured optical depth data but also in designing improved solar radiometers

  11. Small angle neutron scattering

    International Nuclear Information System (INIS)

    Bernardini, G.; Cherubini, G.; Fioravanti, A.; Olivi, A.

    1976-09-01

    A method for the analysis of the data derived from neutron small angle scattering measurements has been accomplished in the case of homogeneous particles, starting from the basic theory without making any assumption on the form of particle size distribution function. The experimental scattering curves are interpreted with the aid the computer by means of a proper routine. The parameters obtained are compared with the corresponding ones derived from observations at the transmission electron microscope

  12. Pp scattering at SIN

    International Nuclear Information System (INIS)

    Aprile-Giboni, E.; Cantale, G.; Hausammann, R.

    1983-01-01

    Using the PM1 polarized proton beam at SIN and a polarized target, the elastic pp scattering as well as the inelastic channel pp → π + d have been studied between 400 and 600 MeV. For the elastic reaction, a sufficient number of spin dependent parameters has been measured in order to do a direct reconstruction of the scattering matrix between 38 0 /sub cm/ and 90 0 /sub cm/. 10 references, 6 figures

  13. Trajectory averaging for stochastic approximation MCMC algorithms

    KAUST Repository

    Liang, Faming

    2010-01-01

    to the stochastic approximation Monte Carlo algorithm [Liang, Liu and Carroll J. Amer. Statist. Assoc. 102 (2007) 305-320]. The application of the trajectory averaging estimator to other stochastic approximationMCMC algorithms, for example, a stochastic

  14. Reduction of Linear Programming to Linear Approximation

    OpenAIRE

    Vaserstein, Leonid N.

    2006-01-01

    It is well known that every Chebyshev linear approximation problem can be reduced to a linear program. In this paper we show that conversely every linear program can be reduced to a Chebyshev linear approximation problem.

  15. Some relations between entropy and approximation numbers

    Institute of Scientific and Technical Information of China (English)

    郑志明

    1999-01-01

    A general result is obtained which relates the entropy numbers of compact maps on Hilbert space to its approximation numbers. Compared with previous works in this area, it is particularly convenient for dealing with the cases where the approximation numbers decay rapidly. A nice estimation between entropy and approximation numbers for noncompact maps is given.

  16. Axiomatic Characterizations of IVF Rough Approximation Operators

    Directory of Open Access Journals (Sweden)

    Guangji Yu

    2014-01-01

    Full Text Available This paper is devoted to the study of axiomatic characterizations of IVF rough approximation operators. IVF approximation spaces are investigated. The fact that different IVF operators satisfy some axioms to guarantee the existence of different types of IVF relations which produce the same operators is proved and then IVF rough approximation operators are characterized by axioms.

  17. An approximation for kanban controlled assembly systems

    NARCIS (Netherlands)

    Topan, E.; Avsar, Z.M.

    2011-01-01

    An approximation is proposed to evaluate the steady-state performance of kanban controlled two-stage assembly systems. The development of the approximation is as follows. The considered continuous-time Markov chain is aggregated keeping the model exact, and this aggregate model is approximated

  18. Operator approximant problems arising from quantum theory

    CERN Document Server

    Maher, Philip J

    2017-01-01

    This book offers an account of a number of aspects of operator theory, mainly developed since the 1980s, whose problems have their roots in quantum theory. The research presented is in non-commutative operator approximation theory or, to use Halmos' terminology, in operator approximants. Focusing on the concept of approximants, this self-contained book is suitable for graduate courses.

  19. LIGHT SCATTERING BY FRACTAL DUST AGGREGATES. I. ANGULAR DEPENDENCE OF SCATTERING

    Energy Technology Data Exchange (ETDEWEB)

    Tazaki, Ryo [Department of Astronomy, Graduate School of Science, Kyoto University, Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto 606-8502 (Japan); Tanaka, Hidekazu [Astronomical Institute, Tohoku University, 6-3 Aramaki, Aoba-ku, Sendai 980-8578 (Japan); Okuzumi, Satoshi; Nomura, Hideko [Department of Earth and Planetary Sciences, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551 (Japan); Kataoka, Akimasa, E-mail: rtazaki@kusastro.kyoto-u.ac.jp [Institute for Theoretical Astrophysics, Heidelberg University, Albert-Ueberle-Strasse 2, D-69120 Heidelberg (Germany)

    2016-06-01

    In protoplanetary disks, micron-sized dust grains coagulate to form highly porous dust aggregates. Because the optical properties of these aggregates are not completely understood, it is important to investigate how porous dust aggregates scatter light. In this study, the light scattering properties of porous dust aggregates were calculated using a rigorous method, the T -matrix method, and the results were then compared with those obtained using the Rayleigh–Gans–Debye (RGD) theory and Mie theory with the effective medium approximation (EMT). The RGD theory is applicable to moderately large aggregates made of nearly transparent monomers. This study considered two types of porous dust aggregates—ballistic cluster–cluster agglomerates (BCCAs) and ballistic particle–cluster agglomerates. First, the angular dependence of the scattered intensity was shown to reflect the hierarchical structure of dust aggregates; the large-scale structure of the aggregates is responsible for the intensity at small scattering angles, and their small-scale structure determines the intensity at large scattering angles. Second, it was determined that the EMT underestimates the backward scattering intensity by multiple orders of magnitude, especially in BCCAs, because the EMT averages the structure within the size of the aggregates. It was concluded that the RGD theory is a very useful method for calculating the optical properties of BCCAs.

  20. Determination of X-ray anomalous scattering in silicon

    International Nuclear Information System (INIS)

    Cusatis, C.

    1987-01-01

    The linear attenuation coeficient for X-ray in silicon was measured with approximately 0,1% accuracy, for 6 diferent wavelenghts of caracteristic radiation. From these result the imaginary parts of the atomic scattering factors, for silicon and for those wavelenghts, were obtained with the same accuracy. The results are compared with the most recent published values. The proposed method to avoid Rayleigh scattering can be used for any type of ''perfect'' crystal. (author) [pt

  1. Differential cross sections for neutrino scattering on 12C

    International Nuclear Information System (INIS)

    Kolbe, E.

    1996-01-01

    Differential cross sections for neutrino scattering on 12 C are calculated within the (continuum) random phase approximation model. The charged current (ν e ,e - ) and (ν μ ,μ - ) capture reactions on 12 C are measured by the LSND Collaboration at LAMPF. We investigate and discuss the merits of such studies, especially the information that can be extracted from data for differential neutrino scattering cross sections. copyright 1996 The American Physical Society

  2. Multiple pole in the electron--hydrogen-atom scattering amplitude

    International Nuclear Information System (INIS)

    Amusia, M.Y.; Kuchiev, M.Y.

    1982-01-01

    It is demonstrated that the amplitude for electron--hydrogen-atom forward scattering has the third-order pole at the point E = -13.6 eV, E being the energy of the incident electron. The coefficients which characterize the pole are calculated exactly. The invalidity of the Born approximation is proved. The contribution of the pole singularity to the dispersion relation for the scattering amplitude is discussed

  3. True many-particle scattering theory in oscillator representation

    International Nuclear Information System (INIS)

    Smirnov, Yu.F.; Shirokov, A.M.

    1988-01-01

    The scattering theory in oscillator representation in case of true multiparticle scattering (TMS) is generalized. All necessary expressions to construct a wave function of several particles system in a discrete or continuous spectra at TMS approximation are obtained. Essential advantage of the method suggested lies in the fact that the most difficult part: construction and diagonolization of the Hamiltonian cutted matrix is to be carried out only once, and then the wave function can be calculated at any designed energy. 23 refs

  4. Accuracy of the discrete dipole approximation for simulation of optical properties of gold nanoparticles

    NARCIS (Netherlands)

    Yurkin, M.A.; de Kanter, D.; Hoekstra, A.G.

    2010-01-01

    We studied the accuracy of the discrete dipole approximation (DDA) for simulations of absorption and scattering spectra by gold nanoparticles (spheres, cubes, and rods ranging in size from 10 to 100 nm). We varied the dipole resolution and applied two DDA formulations, employing the standard lattice

  5. Beyond the Born approximation. The case of very long polymer chains adsorbed at an interface

    International Nuclear Information System (INIS)

    Guiselin, O.; Jannink, G.; Cloizeaux, J. des

    1991-01-01

    Two experimental evidences are discussed of the reflectance discontinuity associated with very long adsorbed polymer chains. It is shown that the Born approximation is not valid in this case. The anomalous low reflectivity is compared to the Ramsauer-Townsend effect in the scattering of slow electrons by rare-gas atoms. (author) 15 refs.; 6 figs

  6. The interacting boson approximation and the spectroscopy of the even Cadmium and Tin isotopes

    International Nuclear Information System (INIS)

    Morrison, I.; Smith, R.

    1981-01-01

    Within the framework of the Interacting Boson Approximation (IBA), the authors investigate, using the even-mass isotopes Cd 108 to Cd 116 and Sn 116 to Sn 124 , whether a single two-boson interaction can describe the energy, B(E2), quadrupole moment and some inelastic nucleon scattering systematics of these nuclei

  7. The discrete-dipole-approximation code ADDA: capabilities and known limitations

    NARCIS (Netherlands)

    Yurkin, M.A.; Hoekstra, A.G.

    2011-01-01

    The open-source code ADDA is described, which implements the discrete dipole approximation (DDA), a method to simulate light scattering by finite 3D objects of arbitrary shape and composition. Besides standard sequential execution, ADDA can run on a multiprocessor distributed-memory system,

  8. Advantages of using gyrotron scattering for alpha particle diagnostics

    International Nuclear Information System (INIS)

    Woskoboinikow, P.P.; Cohn, D.R.; Machuzak, J.S.; Myer, R.C.; Rhee, R.Y.

    1987-07-01

    Millimeter-wave gyrotron collective Thomson scattering can be an effective diagnostic technique for the study of alpha particle behavior in ignited plasmas. The measurement of alpha particle density, velocity distribution, and alpha particle induced plasma instabilities can be accomplished with both spatial and temporal resolution. Advantages include long pulse operation which can make possible very high signal to noise ratios and use of millimeter waves which maximizes the Doppler shifted scattered signal in WHz -1 and makes possible scattering angles up to 180 0 . Extraordinary mode scattering at approximately 60 and 200 GHz would be used in TFTR and CIT respectively, and 140 GHz ordinary mode scattering in JET. 8 refs., 1 fig

  9. Bistable scattering in graphene-coated dielectric nanowires.

    Science.gov (United States)

    Li, Rujiang; Wang, Huaping; Zheng, Bin; Dehdashti, Shahram; Li, Erping; Chen, Hongsheng

    2017-06-22

    In nonlinear plasmonics, the switching threshold of optical bistability is limited by the weak nonlinear responses from the conventional Kerr dielectric media. Considering the giant nonlinear susceptibility of graphene, here we develop a nonlinear scattering model under the mean field approximation and study the bistable scattering in graphene-coated dielectric nanowires based on the semi-analytical solutions. We find that the switching intensities of bistable scattering can be smaller than 1 MW cm -2 at the working frequency. To further decrease the switching intensities, we show that the most important factor that restricts the bistable scattering is the relaxation time of graphene. Our work not only reveals some general characteristics of graphene-based bistable scattering, but also provides a guidance to further applications of optical bistability in the high speed all-optical signal processing.

  10. Deconvolution of shift-variant broadening for Compton scatter imaging

    International Nuclear Information System (INIS)

    Evans, Brian L.; Martin, Jeffrey B.; Roggemann, Michael C.

    1999-01-01

    A technique is presented for deconvolving shift-variant Doppler broadening of singly Compton scattered gamma rays from their recorded energy distribution. Doppler broadening is important in Compton scatter imaging techniques employing gamma rays with energies below roughly 100 keV. The deconvolution unfolds an approximation to the angular distribution of scattered photons from their recorded energy distribution in the presence of statistical noise and background counts. Two unfolding methods are presented, one based on a least-squares algorithm and one based on a maximum likelihood algorithm. Angular distributions unfolded from measurements made on small scattering targets show less evidence of Compton broadening. This deconvolution is shown to improve the quality of filtered backprojection images in multiplexed Compton scatter tomography. Improved sharpness and contrast are evident in the images constructed from unfolded signals

  11. Mapping moveout approximations in TI media

    KAUST Repository

    Stovas, Alexey; Alkhalifah, Tariq Ali

    2013-01-01

    Moveout approximations play a very important role in seismic modeling, inversion, and scanning for parameters in complex media. We developed a scheme to map one-way moveout approximations for transversely isotropic media with a vertical axis of symmetry (VTI), which is widely available, to the tilted case (TTI) by introducing the effective tilt angle. As a result, we obtained highly accurate TTI moveout equations analogous with their VTI counterparts. Our analysis showed that the most accurate approximation is obtained from the mapping of generalized approximation. The new moveout approximations allow for, as the examples demonstrate, accurate description of moveout in the TTI case even for vertical heterogeneity. The proposed moveout approximations can be easily used for inversion in a layered TTI medium because the parameters of these approximations explicitly depend on corresponding effective parameters in a layered VTI medium.

  12. Analytical approximation of neutron physics data

    International Nuclear Information System (INIS)

    Badikov, S.A.; Vinogradov, V.A.; Gaj, E.V.; Rabotnov, N.S.

    1984-01-01

    The method for experimental neutron-physical data analytical approximation by rational functions based on the Pade approximation is suggested. It is shown that the existence of the Pade approximation specific properties in polar zones is an extremely favourable analytical property essentially extending the convergence range and increasing its rate as compared with polynomial approximation. The Pade approximation is the particularly natural instrument for resonance curve processing as the resonances conform to the complex poles of the approximant. But even in a general case analytical representation of the data in this form is convenient and compact. Thus representation of the data on the neutron threshold reaction cross sections (BOSPOR constant library) in the form of rational functions lead to approximately twenty fold reduction of the storaged numerical information as compared with the by-point calculation at the same accWracy

  13. A unified approach to the Darwin approximation

    International Nuclear Information System (INIS)

    Krause, Todd B.; Apte, A.; Morrison, P. J.

    2007-01-01

    There are two basic approaches to the Darwin approximation. The first involves solving the Maxwell equations in Coulomb gauge and then approximating the vector potential to remove retardation effects. The second approach approximates the Coulomb gauge equations themselves, then solves these exactly for the vector potential. There is no a priori reason that these should result in the same approximation. Here, the equivalence of these two approaches is investigated and a unified framework is provided in which to view the Darwin approximation. Darwin's original treatment is variational in nature, but subsequent applications of his ideas in the context of Vlasov's theory are not. We present here action principles for the Darwin approximation in the Vlasov context, and this serves as a consistency check on the use of the approximation in this setting

  14. Mapping moveout approximations in TI media

    KAUST Repository

    Stovas, Alexey

    2013-11-21

    Moveout approximations play a very important role in seismic modeling, inversion, and scanning for parameters in complex media. We developed a scheme to map one-way moveout approximations for transversely isotropic media with a vertical axis of symmetry (VTI), which is widely available, to the tilted case (TTI) by introducing the effective tilt angle. As a result, we obtained highly accurate TTI moveout equations analogous with their VTI counterparts. Our analysis showed that the most accurate approximation is obtained from the mapping of generalized approximation. The new moveout approximations allow for, as the examples demonstrate, accurate description of moveout in the TTI case even for vertical heterogeneity. The proposed moveout approximations can be easily used for inversion in a layered TTI medium because the parameters of these approximations explicitly depend on corresponding effective parameters in a layered VTI medium.

  15. An Approximate Approach to Automatic Kernel Selection.

    Science.gov (United States)

    Ding, Lizhong; Liao, Shizhong

    2016-02-02

    Kernel selection is a fundamental problem of kernel-based learning algorithms. In this paper, we propose an approximate approach to automatic kernel selection for regression from the perspective of kernel matrix approximation. We first introduce multilevel circulant matrices into automatic kernel selection, and develop two approximate kernel selection algorithms by exploiting the computational virtues of multilevel circulant matrices. The complexity of the proposed algorithms is quasi-linear in the number of data points. Then, we prove an approximation error bound to measure the effect of the approximation in kernel matrices by multilevel circulant matrices on the hypothesis and further show that the approximate hypothesis produced with multilevel circulant matrices converges to the accurate hypothesis produced with kernel matrices. Experimental evaluations on benchmark datasets demonstrate the effectiveness of approximate kernel selection.

  16. Bounded-Degree Approximations of Stochastic Networks

    Energy Technology Data Exchange (ETDEWEB)

    Quinn, Christopher J.; Pinar, Ali; Kiyavash, Negar

    2017-06-01

    We propose algorithms to approximate directed information graphs. Directed information graphs are probabilistic graphical models that depict causal dependencies between stochastic processes in a network. The proposed algorithms identify optimal and near-optimal approximations in terms of Kullback-Leibler divergence. The user-chosen sparsity trades off the quality of the approximation against visual conciseness and computational tractability. One class of approximations contains graphs with speci ed in-degrees. Another class additionally requires that the graph is connected. For both classes, we propose algorithms to identify the optimal approximations and also near-optimal approximations, using a novel relaxation of submodularity. We also propose algorithms to identify the r-best approximations among these classes, enabling robust decision making.

  17. Theory of direct scattering of neutral and charged atoms

    Science.gov (United States)

    Franco, V.

    1979-01-01

    The theory for direct elastic and inelastic collisions between composite atomic systems formulated within the framework of the Glauber approximation is presented. It is shown that the phase-shift function is the sum of a point Coulomb contribution and of an expression in terms of the known electron-hydrogen-atom and proton-hydrogen-atom phase shift function. The scattering amplitude is reexpressed, the pure Coulomb scattering in the case of elastic collisions between ions is isolated, and the exact optical profile function is approximated by a first-order expansion in Glauber theory which takes into account some multiple collisions. The approximate optical profile function terms corresponding to interactions involving one and two electrons are obtained in forms of Meijer G functions and as a one-dimensional integral, and for collisions involving one or two neutral atoms, the scattering amplitude is further reduced to a simple closed-form expression.

  18. A general framework and review of scatter correction methods in cone beam CT. Part 2: Scatter estimation approaches

    International Nuclear Information System (INIS)

    Ruehrnschopf and, Ernst-Peter; Klingenbeck, Klaus

    2011-01-01

    The main components of scatter correction procedures are scatter estimation and a scatter compensation algorithm. This paper completes a previous paper where a general framework for scatter compensation was presented under the prerequisite that a scatter estimation method is already available. In the current paper, the authors give a systematic review of the variety of scatter estimation approaches. Scatter estimation methods are based on measurements, mathematical-physical models, or combinations of both. For completeness they present an overview of measurement-based methods, but the main topic is the theoretically more demanding models, as analytical, Monte-Carlo, and hybrid models. Further classifications are 3D image-based and 2D projection-based approaches. The authors present a system-theoretic framework, which allows to proceed top-down from a general 3D formulation, by successive approximations, to efficient 2D approaches. A widely useful method is the beam-scatter-kernel superposition approach. Together with the review of standard methods, the authors discuss their limitations and how to take into account the issues of object dependency, spatial variance, deformation of scatter kernels, external and internal absorbers. Open questions for further investigations are indicated. Finally, the authors refer on some special issues and applications, such as bow-tie filter, offset detector, truncated data, and dual-source CT.

  19. Variational lower bound on the scattering length

    International Nuclear Information System (INIS)

    Rosenberg, L.; Spruch, L.

    1975-01-01

    The scattering length A characterizes the zero-energy scattering of one system by another. It was shown some time ago that a variational upper bound on A could be obtained using methods, of the Rayleigh-Ritz type, which are commonly employed to obtain upper bounds on energy eigenvalues. Here we formulate a method for obtaining a variational lower bound on A. Once again the essential idea is to express the scattering length as a variational estimate plus an error term and then to reduce the problem of bounding the error term to one involving bounds on energy eigenvalues. In particular, the variational lower bound on A is rigorously established provided a certin modified Hamiltonian can be shown to have no discrete states lying below the level of the continuum threshold. It is unfortunately true that necessary conditions for the existence of bound states are not available for multiparticle systems in general. However, in the case of positron-atom scattering the adiabatic approximation can be introduced as an (essentially) solvable comparison problem to rigorously establish the nonexistence of bound states of the modified Hamiltonian. It has recently been shown how the validity of the variational upper bound on A can be maintained when the target ground-state wave function is imprecisely known. Similar methods can be used to maintain the variational lower bound on A. Since the bound is variational, the error in the calculated scattering length will be of second order in the error in the wave function. The use of the adiabatic approximation in the present context places no limitation in principle on the accuracy achievable

  20. Pion inelastic scattering and the pion-nucleus effective interaction

    International Nuclear Information System (INIS)

    Carr, J.A.

    1983-01-01

    This work examines pion inelastic scattering with the primary purpose of gaining a better understanding of the properties of the pion-nucleus interaction. The main conclusion of the work is that an effective interaction which incorporates the most obvious theoretical corrections to the impulse approximation does a good job of explaining pion elastic and inelastic scattering from zero to 200 MeV without significant adjustments to the strength parameters of the force. Watson's multiple scattering theory is used to develop a theoretical interaction starting from the free pion-nucleon interaction. Elastic scattering was used to calibrate the isoscalar central interaction. It was found that the impulse approximation did poorly at low energy, while the multiple scattering corrections gave good agreement with all of the data after a few minor adjustments in the force. The distorted wave approximation for the inelastic transition matrix elements are evaluated for both natural and unnatural parity excitations. The isoscalar natural parity transitions are used to test the reaction theory, and it is found that the effective interaction calibrated by elastic scattering produces good agreement with the inelastic data. Calculations are also shown for other inelastic and charge exchange reactions. It appears that the isovector central interaction is reasonable, but the importance of medium corrections cannot be determined. The unnatural parity transitions are also reasonably described by the theoretical estimate of the spin-orbit interaction, but not enough systematic data exists to reach a firm conclusion