Rytov approximation in electron scattering
Krehl, Jonas; Lubk, Axel
2017-06-01
In this work we introduce the Rytov approximation in the scope of high-energy electron scattering with the motivation of developing better linear models for electron scattering. Such linear models play an important role in tomography and similar reconstruction techniques. Conventional linear models, such as the phase grating approximation, have reached their limits in current and foreseeable applications, most importantly in achieving three-dimensional atomic resolution using electron holographic tomography. The Rytov approximation incorporates propagation effects which are the most pressing limitation of conventional models. While predominately used in the weak-scattering regime of light microscopy, we show that the Rytov approximation can give reasonable results in the inherently strong-scattering regime of transmission electron microscopy.
Born approximation, scattering, and algorithm
Martinez, Alex; Hu, Mengqi; Gu, Haicheng; Qiao, Zhijun
2015-05-01
In the past few decades, there were many imaging algorithms designed in the case of the absence of multiple scattering. Recently, we discussed an algorithm for removing high order scattering components from collected data. This paper is a continuation of our previous work. First, we investigate the current state of multiple scattering in SAR. Then, we revise our method and test it. Given an estimate of our target reflectivity, we compute the multi scattering effects in the target region for various frequencies. Furthermore, we propagate this energy through free space towards our antenna, and remove it from the collected data.
On Born approximation in black hole scattering
Energy Technology Data Exchange (ETDEWEB)
Batic, D. [University of West Indies, Department of Mathematics, Kingston (Jamaica); Kelkar, N.G.; Nowakowski, M. [Universidad de los Andes, Departamento de Fisica, Bogota (Colombia)
2011-12-15
A massless field propagating on spherically symmetric black hole metrics such as the Schwarzschild, Reissner-Nordstroem and Reissner-Nordstroem-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. (orig.)
Polarimetric entropy of the ocean surface with a two-scale scattering model
Institute of Scientific and Technical Information of China (English)
WANG Wenguang; LI Haiyan; SONG Xingai
2014-01-01
The relationships among an ocean wave spectrum, a fully polarimetric coherence matrix, and radar pa-rameters are deduced with an electromagnetic wave theory. Furthermore, the relationship between the polarimetric entropy and ocean wave spectrum is established based on the definition of entropy and a two-scale scattering model of the ocean surface. It is the first time that the polarimetric entropy of the ocean surface is presented in theory. Meanwhile, the relationships among the fully polarimetric entropy and the parameters related to radar and ocean are discussed. The study is the basis of further monitoring targets on the ocean surface and deriving oceanic information with the entropy from the ocean surface. The con-trast enhancement between human-made targets and the ocean surface with the entropy is presented with quad-pol airborne synthetic aperture radar (AIRSAR) data.
Nanostructures: Scattering beyond the Born approximation
Grigoriev, S. V.; Syromyatnikov, A. V.; Chumakov, A. P.; Grigoryeva, N. A.; Napolskii, K. S.; Roslyakov, I. V.; Eliseev, A. A.; Petukhov, A. V.; Eckerlebe, H.
2010-03-01
The neutron scattering on a two-dimensional ordered nanostructure with the third nonperiodic dimension can go beyond the Born approximation. In our model supported by the exact theoretical solution a well-correlated hexagonal porous structure of anodic aluminum oxide films acts as a peculiar two-dimensional grating for the coherent neutron wave. The thickness of the film L (length of pores) plays important role in the transition from the weak to the strong scattering regimes. It is shown that the coherency of the standard small-angle neutron scattering setups suits to the geometry of the studied objects and often affects the intensity of scattering. The proposed theoretical solution can be applied in the small-angle neutron diffraction experiments with flux lines in superconductors, periodic arrays of magnetic or superconducting nanowires, as well as in small-angle diffraction experiments on synchrotron radiation.
Yueh, S. H.; Nghiem, S. V.; Kwok, R.; Li, F. K.
1993-01-01
Recently, it has been observed that the brightness temperatures of sea surfaces correlate with the azimuth angle of the ocean wind vector, indicating that ocean wind direction can not only be retrieved from the microwave backscatter, but also from the brightness temperature measurements. In this paper, comparison of the theoretical result calculated from a two-scale emission and scattering model with the Seasat and SSM/I model functions and aircraft measurements is presented and potential applications of microwave polarimetry are discussed. In our two-scale model, the modified reflectivities of large scale surfaces are calculated by extending the small perturbation method to the second order for small scale perturbation with anisotropic directional spectrum. It was found that the modified reflectivities derived from the second-order scattered field agree excellently well with the results obtained from a Monte Carlo simulation technique which numerically calculates the polarimetric reflectivities of one-dimensional random rough surfaces with a power-law spectrum. Without the second-order correction, the modified reflectivities of the rough surfaces are significantly over-estimated and sign errors are observed in the third and fourth Stokes parameters for thermal emissions. The surface spectrum parameters and two-scale cutoff are selected so that the calculated scattering and emission signatures agree with the reported model functions for Seasat and SSM/I. Subsequently, the polarimetric signatures of sea surfaces are illustrated to indicate the possibility of reducing the number of azimuthal looks required for spaceborne sensors in the remote sensing of ocean wind by using the polarimetric information. Furthermore, it is found that contrary to the dependence of backscattering coefficients on incidence angles, polarimetric brightness temperatures display a stronger wind direction dependence in the near nadir-looking direction than away from nadir. Finally, we discuss
Scattering of electromagnetic wave by dielectric cylinder in eikonal approximation
Syshchenko, V. V.
2016-07-01
The scattering of the plane electromagnetic wave on a spatially extended, fiber lake target is considered. The formula for the scattering cross section is obtained using the approximation analogous to eikonal one in quantum mechanics.
Scattering from rough thin films: discrete-dipole-approximation simulations.
Parviainen, Hannu; Lumme, Kari
2008-01-01
We investigate the wave-optical light scattering properties of deformed thin circular films of constant thickness using the discrete-dipole approximation. Effects on the intensity distribution of the scattered light due to different statistical roughness models, model dependent roughness parameters, and uncorrelated, random, small-scale porosity of the inhomogeneous medium are studied. The suitability of the discrete-dipole approximation for rough-surface scattering problems is evaluated by considering thin films as computationally feasible rough-surface analogs. The effects due to small-scale inhomogeneity of the scattering medium are compared with the analytic approximation by Maxwell Garnett, and the results are found to agree with the approximation.
A Modified Two-scale Microwave Scattering Model for a Dielectric Randomly Rough Surface(in English
Directory of Open Access Journals (Sweden)
Yu Fan
2015-10-01
Full Text Available In this paper, we present a Modified Two-Scale Microwave (MTSM scattering model to describe the scattering coefficient of naturally rough surfaces. The surface roughness is assumed to be Gaussian in the proposed model so that the surface height z(x, y can be split into large- and small-scale components by the wavelet packet transform according to electromagnetic wavelength. We used the Kirchhoff Model(KM and Small Perturbation Method (SPM to estimate the backscattering coefficient of large- and small-scale roughness, respectively. The tilting effect caused by the slope of large-scale roughness was corrected when calculating the contribution of backscattering to small-scale roughness. The backscattering coefficient of the MTSM comprised the total backscattering contributions of surfaces with both scales of roughness. The MTSM was tested and validated using the Advanced Integral Equation Model (AIEM for dielectric randomly rough surfaces. The accuracy of the MTSM showed favorable agreement with AIEM, both when the incident angle was less than 30° (θi<30° and when the surface roughness was small (ks=0.354.
Geometrical optics approximation of light scattering by large air bubbles
Institute of Scientific and Technical Information of China (English)
Haitao Yu; Jianqi Shen; Yuehuan Wei
2008-01-01
For large spherical bubbles in water,geometrical optics approximation is considered a better method for calculating light scattering patterns.In this paper,the basic theory of geometrical optics approximation is clarified.The change of phase for bubbles is calculated when total reflection occurs,which is different from particles with relative refractive indices larger than 1.Verification of the method was achieved by assuming a spherical particle and comparing present results to Mie scattering and Debye calculation.Agreement with the Mie theory was excellent in all directions when the dimensionless size parameter is larger than 50.Limitations of the geometrical optics approximation are also discussed.
Quasielastic electron-deuteron scattering in the weak binding approximation
Energy Technology Data Exchange (ETDEWEB)
Ethier, Jacob J. [William and Mary College, JLAB; Doshi, Nidhi P. [Carnegie Mellon University; Malace, Simona P. [JLAB; Melnitchouk, Wally [JLAB
2014-06-01
We perform a global analysis of all available electron-deuteron quasielastic scattering data using Q^2-dependent smearing functions that describe inclusive inelastic e-d scattering within the weak binding approximation. We study the dependence of the cross sections on the deuteron wave function and the off-shell extrapolation of the elastic electron-nucleon cross section, which show particular sensitivity at x >> 1. The excellent overall agreement with data over a large range of Q^2 and x suggest a limited need for effects beyond the impulse approximation, with the exception of the very high-x or very low-Q^2 regions, where short-distance effects in the deuteron become more relevant.
Quasielastic electron-deuteron scattering in the weak binding approximation
Energy Technology Data Exchange (ETDEWEB)
Ethier, Jacob J. [William and Mary College, JLAB; Doshi, Nidhi P. [Carnegie Mellon University; Malace, Simona P. [JLAB; Melnitchouk, Wally [JLAB
2014-06-01
We perform a global analysis of all available electron-deuteron quasielastic scattering data using Q^2-dependent smearing functions that describe inclusive inelastic e-d scattering within the weak binding approximation. We study the dependence of the cross sections on the deuteron wave function and the off-shell extrapolation of the elastic electron-nucleon cross section, which show particular sensitivity at x >> 1. The excellent overall agreement with data over a large range of Q^2 and x suggest a limited need for effects beyond the impulse approximation, with the exception of the very high-x or very low-Q^2 regions, where short-distance effects in the deuteron become more relevant.
Coulomb-Born-Oppenheimer approximation in Ps-H scattering
Indian Academy of Sciences (India)
Hasi Ray
2006-02-01
To improve the Coulomb-Born approximation (CBA) theory of ionization in positronium (Ps) and atom scattering, the effect of exchange is introduced. The nine-dimensional exchange amplitude for ionization of Ps in Ps-H scattering is reduced to a two-dimensional integral using the present Coulomb-Born-Oppenheimer approximation (CBOA). The methodology is extremely useful to evaluate ionization parameters for different target systems and for different types of ionization processes. It is then applied to evaluate the Ps-ionization cross-section and to estimate the effect of exchange on Ps-ionization in Ps-H system. We establish the importance of exchange at lower energy region.
Multiple Scattering Model for Optical Coherence Tomography with Rytov Approximation
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.
Parity Violating Electron Scattering in the Relativistic Eikonal Approximation
Institute of Scientific and Technical Information of China (English)
DONG Tie-Kuang; REN Zhong-Zhou
2008-01-01
The parity violating electron scattering is investigated in the relativistic Eikonal approximation. The parity violating asymmetry parameters for many isotopes are calculated. In calculations the proton and neutron densities are obtained from the relativistic mean-field theory. We take Ni isotopes as examples to analyse the behaviour of the parity violating asymmetry parameters. The results show that the parity violating asymmetry parameter is sensitive to the difference between the proton and neutron densities. The amplitude of the parity violating asymmetry parameter increases with the distance between the minima of proton and neutron form factors. Our results are useful for future parity violating electron scattering experiments. By comparing our results with experimental data one can test the validity of the relativistic mean-field theory in calculating the neutron densities of nuclei.
High energy light scattering in the generalized eikonal approximation.
Chen, T W
1989-10-01
The generalized eikonal approximation method is applied to the study of light scattering by a dielectric medium. In this method, the propagation of light inside the medium is assumed to be rectilinear, as in the usual eikonal method, but with a parameterized propagator which is used to include the edge effect and ray optics behavior at the limit of very short wavelengths. The resulting formulas for the intensity and extinction efficiency factor are compared numerically and shown to agree excellently with the exact results for a homogeneous dielectric sphere.
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
annihilation event and undergoing a single scattering at a certain angle. The equations for single scatter calculation are derived using the Single Scatter Simulation approximation. We show that the three-dimensional slice-by-slice filtered backprojection algorithm is applicable for scatter data inversion...
A solution of LIDAR problem in double scattering approximation
Leble, Sergey
2011-01-01
A problem of monoenergetic particles pulse reflection from half-infinite stratified medium is considered in conditions of elastic scattering with absorbtion account. The theory is based on multiple scattering series solution of Kolmogorov equation for one-particle distribution function. The analytical representation for first two terms are given in compact form for a point impulse source and cylindric symmetrical detector. Reading recent articles on the LIDAR sounding of environment (e.g. Atmospheric and Oceanic Optics (2010) 23: 389-395, Kaul, B. V.; Samokhvalov, I. V. http://www.springerlink.com/content/k3p2p3582674xt21/) one recovers standing interest to the related direct and inverse problems. A development of the result fo the case of n-fold scattering and polarization account as well as correspondent convergence series problem solution of the Kolmogorov equation will be published in nearest future.
La Budde, R. A.
1972-01-01
Sampling techniques have been used previously to evaluate Jacobian determinants that occur in classical mechanical descriptions of molecular scattering. These determinants also occur in the quasiclassical approximation. A new technique is described which can be used to evaluate Jacobian determinants which occur in either description. This method is expected to be valuable in the study of reactive scattering using the quasiclassical approximation.
Quantum Theory of (H,H{Sub 2}) Scattering: Approximate Treatments of Reactive Scattering
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.
Separable approximation method for two-body relativistic scattering
Energy Technology Data Exchange (ETDEWEB)
Tandy, P.C.; Thaler, R.M.
1988-03-01
A method for defining a separable approximation to a given interaction within a two-body relativistic equation, such as the Bethe-Salpeter equation, is presented. The rank-N separable representation given here permits exact reproduction of the T matrix on the mass shell and half off the mass shell at N selected bound state and/or continuum values of the invariant mass. The method employed is a four-space generalization of the separable representation developed for Schroedinger interactions by Ernst, Shakin, and Thaler, supplemented by procedures for dealing with the relativistic spin structure in the case of Dirac particles.
Separable approximation method for two-body relativistic scattering
Tandy, P. C.; Thaler, R. M.
1988-03-01
A method for defining a separable approximation to a given interaction within a two-body relativistic equation, such as the Bethe-Salpeter equation, is presented. The rank-N separable representation given here permits exact reproduction of the T matrix on the mass shell and half off the mass shell at N selected bound state and/or continuum values of the invariant mass. The method employed is a four-space generalization of the separable representation developed for Schrödinger interactions by Ernst, Shakin, and Thaler, supplemented by procedures for dealing with the relativistic spin structure in the case of Dirac particles.
A diffusion approximation for ocean wave scatterings by randomly distributed ice floes
Zhao, Xin; Shen, Hayley
2016-11-01
This study presents a continuum approach using a diffusion approximation method to solve the scattering of ocean waves by randomly distributed ice floes. In order to model both strong and weak scattering, the proposed method decomposes the wave action density function into two parts: the transmitted part and the scattered part. For a given wave direction, the transmitted part of the wave action density is defined as the part of wave action density in the same direction before the scattering; and the scattered part is a first order Fourier series approximation for the directional spreading caused by scattering. An additional approximation is also adopted for simplification, in which the net directional redistribution of wave action by a single scatterer is assumed to be the reflected wave action of a normally incident wave into a semi-infinite ice cover. Other required input includes the mean shear modulus, diameter and thickness of ice floes, and the ice concentration. The directional spreading of wave energy from the diffusion approximation is found to be in reasonable agreement with the previous solution using the Boltzmann equation. The diffusion model provides an alternative method to implement wave scattering into an operational wave model.
Padé approximants and their application to scattering from fluid media.
Denis, Max; Tsui, Jing; Thompson, Charles; Chandra, Kavitha
2010-11-01
In this work, a numerical method for modeling the scattered acoustic pressure from fluid occlusions is described. The method is based on the asymptotic series expansion of the pressure expressed in terms of sound speed contrast between the host medium and entrained fluid occlusions. Padé approximants are used to extend the applicability of the result for larger values of sound speed contrast. For scattering from a circular cylinder, an improvement in convergence between the exact and numerical solutions is demonstrated. In the case of scattering from an inhomogeneous medium, a numerical solution with reduced order of Padé approximants is presented.
Proton-Nucleus Scattering Approximations and Implications for LHC Crystal Collimation
Energy Technology Data Exchange (ETDEWEB)
Noble, Robert; /SLAC
2010-06-07
In particle accelerators, scattered protons with energies close to the incident particles may travel considerable distances with the beam before impacting on accelerator components downstream. To analyze such problems, angular deflection and energy loss of scattered particles are the main quantities to be simulated since these lead to changes in the beam's phase space distribution and particle loss. Simple approximations for nuclear scattering processes causing limited energy loss to high-energy protons traversing matter are developed which are suitable for rapid estimates and reduced-description Monte Carlo simulations. The implications for proton loss in the Large Hadron Collider due to nuclear scattering on collimation crystals are discussed.
Electron-Helium Scattering in a Bichromatic Laser Field in the Second-Order Born Approximation
Institute of Scientific and Technical Information of China (English)
ZHOU Bin; LI Shu-Min
2009-01-01
@@ The elastic scattering of electrons in atomic helium assisted by a bichromatic laser field is investigated in the second order Born approximation. The target atom is approximated by a simple screening potential. The dependence of the differential cross section on the relative phase between the two laser components is calculated, and compared with the recent results of first order Born approximation [Sun J F, Liang M C and Zhu Z L 2007Chin. Phys. Lett. 24 2572].
Off-shell scattering amplitudes in the double-logarithmic approximation
Ermolaev, B I; Olness, F; Troyan, S I
2005-01-01
When scattering amplitudes are calculated in the double-logarithmic approximation, it is possible to relate the double-logarithmic on-shell and off-shell amplitudes. Explicit relations are obtained for scattering amplitudes in QED, QCD, and the ElectroWeak Standard Model. The off-shell amplitudes are considered in the hard and the Regge kinematic limits. We compare our results in both the Feynman and Coulomb gauges.
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
Approximate Marginalization of Absorption and Scattering in Fluorescence Diffuse Optical Tomography
Mozumder, Meghdoot; Arridge, Simon; Kaipio, Jari P; d'Andrea, Cosimo; Kolehmainen, Ville
2015-01-01
In fluorescence diffuse optical tomography (fDOT), the reconstruction of the fluorophore concentration inside the target body is usually carried out using a normalized Born approximation model where the measured fluorescent emission data is scaled by measured excitation data. One of the benefits of the model is that it can tolerate inaccuracy in the absorption and scattering distributions that are used in the construction of the forward model to some extent. In this paper, we employ the recently proposed Bayesian approximation error approach to fDOT for compensating for the modeling errors caused by the inaccurately known optical properties of the target in combination with the normalized Born approximation model. The approach is evaluated using a simulated test case with different amount of error in the optical properties. The results show that the Bayesian approximation error approach improves the tolerance of fDOT imaging against modeling errors caused by inaccurately known absorption and scattering of the...
Two-loop Bhabha scattering at high energy beyond leading power approximation
Directory of Open Access Journals (Sweden)
Alexander A. Penin
2016-09-01
Full Text Available We evaluate the two-loop O(me2/s contribution to the wide-angle high-energy electron–positron scattering in the double-logarithmic approximation. The origin and the general structure of the power-suppressed double logarithmic corrections are discussed in detail.
The second Born approximation of electron-argon elastic scattering in a Bichromatic laser field
Zhou, Bin; Wen, Da-Yong
2013-01-01
We study the elastic scattering of atomic argon by electron in the presence of a bichromatic laser field in the second Born approximation. The target atom is approximated by a simple screening potential and the continuum states of the impinging and emitting electrons are described as Volkov states. We evaluate the S-matrix elements numerically. The dependence of differential cross section on the relative phase between the two laser components is presented. The results obtained in the first and second Born approximation are compared and analysed.
Effective potential and off-shell two-body scattering amplitudes in the eikonal approximation
Energy Technology Data Exchange (ETDEWEB)
Bartnik, E.A.; Rek, Z.
1973-12-31
An effective potential is computed for 2-body elastic scattering with the experimental on-shell t-matrices as an input. Nonrelativistic elkonal approximation and locality together with spherical ial are assumed. The explicit form of potential for pp, pi /sup +/p, and pi /sup -/p in the energy range from 5 to 20 GeV is investigated. The half off-shell scattering amplitude is calculated in the potential model. In the position representation this amplitude is found to be asymmetric along the eikonal direction, and an interesting absorption interpretation of this fact is given. (auth)
Analysis of a finite PML approximation to the three dimensional elastic wave scattering problem
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.
Physical explanation of the SLIPI technique by the large scatterer approximation of the RTE
Kristensson, Elias; Kristensson, Gerhard
2017-03-01
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 assess
Three-body scattering problem in the fixed center approximation: the case of attraction
Kudryavtsev, Alexander E; Romanov, Alexander I
2016-01-01
We study 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.
The second Born approximation in electron-helium scattering in a Nd-YAG laser field
Energy Technology Data Exchange (ETDEWEB)
Khalil, D.; Makhoute, A.; Rahali, G.; Zitane, M. [Universite Moulay Ismail, UFR de Physique Atomique, Moleculaire et Optique Appliquee, Faculte des Sciences (Morocco); Rahali, G.; Makhoute, A. [The Abdus Salam International Centre for Theoretical Physics, Trieste (Italy); Maquet, A. [Universite Pierre et Marie Curie, Lab. de Chimie Physique, Matiere et Rayonnement, 75 - Paris (France)
2007-02-15
The dynamics of laser-assisted elastic collisions in helium is studied using the second-order Born approximation. Detailed calculations of the scattering amplitudes are performed by using the Sturmian basis expansion. Differential cross sections for elastic scattering with the net absorption/emission of up to two photons are calculated for collision energies of 5 eV, 10 eV, and 20 eV. We discuss the influence of the low-energy electrons on the differential cross section (DCS) as a function of the scattering angle for selected choices of the laser frequency and the number of photons exchanged between the external field and electron-helium system. (authors)
Low-energy positronium-hydrogen elastic scattering using the six-state close coupling approximation
Energy Technology Data Exchange (ETDEWEB)
Sinha, Prabal K. [Department of Physics, Bangabasi College, 19, Rajkumar Chakraborty Sarani, Calcutta 700 009 (India); Basu, Arindam; Ghosh, A.S. [Department of Theoretical Physics, Indian Association for the Cultivation of Science, Jadavpur, Calcutta 700 032 (India)
2000-07-14
Positronium-hydrogen elastic scattering is investigated using the six-state full close coupling approximation employing the basis set Ps(1s,2s,2p)+H(1s,2s,2p). S-wave singlet and triplet scattering and also the corresponding scattering length and effective range are compared with the corresponding predictions of Drachman and Houston and the Belfast group. We also report phase shifts up to l=2 and the integrated elastic cross sections. Present results indicate that the effect of target excitation as well as the effect of excitations of both the atoms are significant in the energy region considered. We also report the angle integrated Ps(1s)+H(1s){yields}Ps(2p)+H(1s) and Ps(1s)+H(1s){yields}Ps(1s)+H(2p) excitation cross sections. (author)
Konoshonkin, Alexander V.; Kustova, Natalia V.; Borovoi, Anatoli G.
2015-10-01
The open-source beam-splitting code is described which implements the geometric-optics approximation to light scattering by convex faceted particles. This code is written in C++ as a library which can be easy applied to a particular light scattering problem. The code uses only standard components, that makes it to be a cross-platform solution and provides its compatibility to popular Integrated Development Environments (IDE's). The included example of solving the light scattering by a randomly oriented ice crystal is written using Qt 5.1, consequently it is a cross-platform solution, too. Both physical and computational aspects of the beam-splitting algorithm are discussed. Computational speed of the beam-splitting code is obviously higher compared to the conventional ray-tracing codes. A comparison of the phase matrix as computed by our code with the ray-tracing code by A. Macke shows excellent agreement.
Mitchell, D. G.; Roelof, E. C.
1976-01-01
A simplified analytical technique is presented for modeling the interplanetary scintillation of radio sources of finite angular size with a power-law electron-density-fluctuation power spectrum. The simplification results from the representation of the scintillation spectrum in confluent hypergeometric functions. The approximations presented allow fast numerical evaluation of a spectrum for a weakly scattering but extended medium with less than 10% error over the entire spectrum. Parameters describing anisotropic electron irregularities as well as anisotropic source structure are included, and the dependence of the spectrum normalization on the scales of the medium is derived explicitly. The parametric description of the domains of convergence of the approximate expansions also provides a simple conceptualization of the relative contributions of the scattered radiation along the line of sight to the observed spectrum. This is particularly useful for sources of finite angular size. This technique is applied to previously published observations.
Mitchell, D. G.; Roelof, E. C.
1976-01-01
A simplified analytical technique is presented for modeling the interplanetary scintillation of radio sources of finite angular size with a power-law electron-density-fluctuation power spectrum. The simplification results from the representation of the scintillation spectrum in confluent hypergeometric functions. The approximations presented allow fast numerical evaluation of a spectrum for a weakly scattering but extended medium with less than 10% error over the entire spectrum. Parameters describing anisotropic electron irregularities as well as anisotropic source structure are included, and the dependence of the spectrum normalization on the scales of the medium is derived explicitly. The parametric description of the domains of convergence of the approximate expansions also provides a simple conceptualization of the relative contributions of the scattered radiation along the line of sight to the observed spectrum. This is particularly useful for sources of finite angular size. This technique is applied to previously published observations.
Comparison of exact solution with Eikonal approximation for elastic heavy ion scattering
Dubey, Rajendra R.; Khandelwal, Govind S.; Cucinotta, Francis A.; Maung, Khin Maung
1995-01-01
A first-order optical potential is used to calculate the total and absorption cross sections for nucleus-nucleus scattering. The differential cross section is calculated by using a partial-wave expansion of the Lippmann-Schwinger equation in momentum space. The results are compared with solutions in the Eikonal approximation for the equivalent potential and with experimental data in the energy range from 25A to 1000A MeV.
Analysis of a Cartesian PML approximation to acoustic scattering problems in and
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.
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.
Yurkin, Maxim A; Hoekstra, Alfons G
2007-01-01
In this manuscript we investigate the capabilities of the Discrete Dipole Approximation (DDA) to simulate scattering from particles that are much larger than the wavelength of the incident light, and describe an optimized publicly available DDA computer program that processes the large number of dipoles required for such simulations. Numerical simulations of light scattering by spheres with size parameters x up to 160 and 40 for refractive index m=1.05 and 2 respectively are presented and compared with exact results of the Mie theory. Errors of both integral and angle-resolved scattering quantities generally increase with m and show no systematic dependence on x. Computational times increase steeply with both x and m, reaching values of more than 2 weeks on a cluster of 64 processors. The main distinctive feature of the computer program is the ability to parallelize a single DDA simulation over a cluster of computers, which allows it to simulate light scattering by very large particles, like the ones that are...
Accurate and Approximate Calculations of Raman Scattering in the Atmosphere of Neptune
Sromovsky, Lawrence
2015-01-01
Raman scattering by H$_2$ in Neptune's atmosphere has significant effects on its reflectivity for $\\lambda <$ 0.5 $\\mu$m, producing baseline decreases of $\\sim$ 20% in a clear atmosphere and $\\sim$ 10% in a hazy atmosphere. Here we present the first radiation transfer algorithm that includes both polarization and Raman scattering and facilitates computation of spatially resolved spectra. New calculations show that Cochran and Trafton's (1978, Astrophys. J. 219, 756-762) suggestion that light reflected in the deep CH$_4$ bands is mainly Raman scattered is not valid for current estimates of the CH$_4$vertical distribution, which implies only a 4% Raman contribution. Comparisons with IUE, HST, and groundbased observations confirm that high altitude haze absorption is reducing Neptune's geometric albedo by $\\sim$6% in the 0.22-0.26 $\\mu$m range and by $\\sim$13% in the 0.35-0.45 $\\mu$m range. We used accurate calculations to evaluate several approximations of Raman scattering. The Karkoschka (1994, Icarus 111, ...
González-Jiménez, R; Donnelly, T W
2015-01-01
We study parity violation in quasielastic (QE) electron-nucleus scattering using the relativistic impulse approximation. Different fully relativistic approaches have been considered to estimate the effects associated with the final-state interactions. We have computed the parity-violating quasielastic (PVQE) asymmetry and have analyzed its sensitivity to the different ingredients that enter in the description of the reaction mechanism: final-state interactions, nucleon off-shellness effects, current gauge ambiguities. Particular attention has been paid to the description of the weak neutral current form factors. The PVQE asymmetry is proven to be an excellent observable when the goal is to get precise information on the axial-vector sector of the weak neutral current. Specifically, from measurements of the asymmetry at backward scattering angles good knowledge of the radiative corrections entering in the isovector axial-vector sector can be gained. Finally, scaling properties shown by the interference $\\gamma...
2p-2h excitations in neutrino scattering: angular distribution and frozen approximation
Simo, I Ruiz; Amaro, J E; Barbaro, M B; Caballero, J A; Donnelly, T W
2015-01-01
We study the phase-space dependence of 2p-2h excitations in neutrino scattering using the relativistic Fermi gas model. We follow a similar approach to other authors, but focusing in the phase-space properties, comparing with the non-relativistic model. A careful mathematical analysis of the angular distribution function for the outgoing nucleons is performed. Our goals are to optimize the CPU time of the 7D integral to compute the hadron tensor in neutrino scattering, and to conciliate the different relativistic and non relativistic models by describing general properties independently of the two-body current. For some emission angles the angular distribution becomes infinite in the Lab system, and we derive a method to integrate analytically around the divergence. Our results show that the frozen approximation, obtained by neglecting the momenta of the two initial nucleons inside the integral of the hadron tensor, reproduces fairly the exact response functions for constant current matrix elements.
Kocifaj, Miroslav
2011-06-10
The approximate bulk-scattering phase function of a polydisperse system of dust particles is derived in an analytical form. In the theoretical solution, the particle size distribution is modeled by a modified gamma function that can satisfy various media differing in modal radii. Unlike the frequently applied power law, the modified gamma distribution shows no singularity when the particle radius approaches zero. The approximate scattering phase function is related to the parameters of the size distribution function. This is an important advantage compared to the empirical Henyey-Greenstein (HG) approximation, which is a simple function of the average cosine. However, any optimized value of average cosine of the HG function cannot provide the information on particle microphysical characteristics, such as the size distribution function. In this paper, the mapping between average cosine and the parameters of size distribution function is given by a semianalytical expression that is applicable in rapid numerical simulations on various dust populations. In particular, the modal radius and half-width can be quickly estimated using the presented formulas.
Three-cluster breakup in deuteron-deuteron collisions: single-scattering approximation
Deltuva, A
2016-01-01
We present results for the three-cluster breakup in deuteron-deuteron collisions at 130 and 270 MeV deuteron beam energy. The breakup amplitude is calculated using the first term in the Neumann series expansion of the corresponding exact four-nucleon equations. In analogy with nucleon-deuteron breakup where an equivalent approximation is compared with exact calculations, we expect this single-scattering approximation to provide a rough estimation of three-body breakup observables in quasifree configurations. We predict the nucleon-deuteron and deuteron-deuteron three-cluster breakup cross sections to be of a comparable size and thereby question the reliability of the recent experimental data [A. Ramazani-Moghaddam-Arani, Ph.D. thesis, University of Groningen, 2009; A. Ramazani-Moghaddam-Arani et al., EPJ Web of Conferences 3, 04012 (2010)] that is smaller by about three orders of magnitude. We also show that an equivalent single-scattering approximation provides a reasonable description of deuteron-deuteron e...
An approximate factorization method for inverse medium scattering with unknown buried objects
Qu, Fenglong; Yang, Jiaqing; Zhang, Bo
2017-03-01
This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous medium with different kinds of unknown buried objects inside. By constructing a sequence of operators which are small perturbations of the far-field operator in a suitable way, we prove that each operator in this sequence has a factorization satisfying the Range Identity. We then develop an approximate factorization method for recovering the support of the inhomogeneous medium from the far-field data. Finally, numerical examples are provided to illustrate the practicability of the inversion algorithm.
One-loop approximation of Mφller scattering in generalized Krein-space quantization
Institute of Scientific and Technical Information of China (English)
F. PAYANDEH; M. MEHRAFARIN; M. V. TAKOOK
2009-01-01
It has been shown that the negative-norm states necessarily appear in a covariant quantization of the free minimally coupled scalar field in de Sitter spacetime. In this processes ultraviolet and infrared di-vergences have been automatically eliminated. A natural renormalization of the one-loop interacting quantum field in Minkowski spacetime (λψ4) has been achieved through the consideration of the nega-tive-norm states defined in Krein space. It has been shown that the combination of quantum field theory in Krein space together with consideration of quantum metric fluctuation, results in quantum field the-cry without any divergences. Pursuing this approach, we express Wick's theorem and calculate Mφiler scattering in the one-loop approximation in generalized Krein space. The mathematical consequence of this method is the disappearance of the ultraviolet divergence in the one-loop approximation.
One-loop approximation of Mφller scattering in generalized Krein-space quantization
Institute of Scientific and Technical Information of China (English)
F.; PAYANDEH; M.; MEHRAFARIN; M.; V.; TAKOOK
2009-01-01
It has been shown that the negative-norm states necessarily appear in a covariant quantization of the free minimally coupled scalar field in de Sitter spacetime. In this processes ultraviolet and infrared di- vergences have been automatically eliminated. A natural renormalization of the one-loop interacting quantum field in Minkowski spacetime (λφ 4) has been achieved through the consideration of the nega- tive-norm states defined in Krein space. It has been shown that the combination of quantum field theory in Krein space together with consideration of quantum metric fluctuation, results in quantum field the- ory without any divergences. Pursuing this approach, we express Wick’s theorem and calculate Mφller scattering in the one-loop approximation in generalized Krein space. The mathematical consequence of this method is the disappearance of the ultraviolet divergence in the one-loop approximation.
Approximate solutions of some problems of scattering of surface water waves by vertical barriers
Indian Academy of Sciences (India)
A CHOUDHARY; S C MARTHA
2017-05-01
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(ii) a bottom standing barrier. The solutions of the bvps are obtained by utilizing the eigenfunction expansion method, leading to a mathematical problem of solving over-determined systems of linear algebraic equations. The methods of analytical least-square approximation as well as algebraic least-square approximation are employed to solve the corresponding over-determined system of linear algebraic equations and thereby evaluate the physical quantities, namely, the reflection and transmission coefficients. Further, the absolute values of the reflection coefficients are compared to the known results obtained by utilizing a Galerkin type of approximate method after reducing the bvps to integral equations whose complete solutions are difficult to be determined.Various combinations of discretization of the resulting dual series relations obtained in the present analysis are employed to determine the least-square solution.
Krochik, G. M.
1980-02-01
Stimulated Raman scattering of a randomly modulated pump is investigated by the method of successive approximations. This involves expanding solutions in terms of small parameters, which are ratios of the correlation scales of random effects to other characteristic dynamic scales of the problem. Systems of closed equations are obtained for the moments of the amplitudes of the Stokes and pump waves and of the molecular vibrations. These describe the dynamics of the process allowing for changes in the pump intensity and statistics due to a three-wave interaction. By analyzing equations in higher-order approximations, it is possible to establish the conditions of validity of the first (Markov) and second approximations. In particular, it is found that these are valid for pump intensities JL both above and below the critical value Jcr near which the gain begins to increase rapidly and reproduction of the pump spectrum by the Stokes wave is initiated. Solutions are obtained for average intensities of the Stokes wave and molecular vibrations in the first approximation in a constant pump field. It is established that, for JLgtrsimJcr, the Stokes wave undergoes rapid nonsteady-state amplification which is associated with an increase in the amplitude of the molecular vibrations. The results of the calculations show good agreement with known experimental data.
The Born Approximation and Eikonal Approximation of the Quantum Scattering%量子散射的玻恩近似和程函近似
Institute of Scientific and Technical Information of China (English)
徐中辉; 周祥; 廖昱博
2011-01-01
The theory of scattering is a very important part of the quantum mechanics.The Born approximation and Eikonal approximation of the Scattering cross-section are calculated with the Gauss potential and Lenzjensen potential under a particular incident energy.The results show that the bigger the Electronic energy is,the smaller the total scattering crossection is and the weaker the electron scattering of potential field is.There is little influence of potential to the energetic particle about the Lenz-jensen potential.And the majority of scattered particles are concentrated on a narrow range.%散射理论是量子力学的一项重要内容.在规定的入射能量下,分别给定Gauss位势和Lenz-jensen位势,计算了散射总截面的玻恩近似和程函近似.结果表明对于Gauss位势,电子能量越大,总散射截面越小,势场对电子的散射越弱.对于Lenz-jensen位势,势对高能粒子的影响比较小,大部分散射的粒子集中在小角度范围内.
Institute of Scientific and Technical Information of China (English)
余凡; 袁捷
2015-01-01
In this paper, we present a Modified Two-Scale Microwave (MTSM) scattering model to describe the scattering coefficient of naturally rough surfaces. The surface roughness is assumed to be Gaussian in the pro-posed model so that the surface heightz(x,y) can be split into large- and small-scale components by the wave-let packet transform according to electromagnetic wavelength. We used the Kirchhoff Model(KM) and Small Perturbation Method (SPM) to estimate the backscattering coefficient of large- and small-scale roughness, re-spectively. The tilting effect caused by the slope of large-scale roughness was corrected when calculating the contribution of backscattering to small-scale roughness. The backscattering coefficient of the MTSM comprised the total backscattering contributions of surfaces with both scales of roughness. The MTSM was tested and val-idated using the Advanced Integral Equation Model (AIEM) for dielectric randomly rough surfaces. The accur-acy of the MTSM showed favorable agreement with AIEM, both when the incident angle was less than 30° (qi<30°) and when the surface roughness was small (ks=0.354).%该文提出一种新的双尺度(Modified Two-Scale Model, MTSM)粗糙度地表微波散射模型，采用小波包变换的方法将面上的粗糙度(z(x, y))变换到频域进行处理，粗糙度频谱的低频部分代表大尺度分量，高频部分代表小尺度分量，然后分别用基尔霍夫近似和小扰动模型来分别模拟大小尺度的粗糙度，考虑到小尺度的粗糙度是叠于大尺度粗糙度之上，模型在计算小尺度粗糙度的后向散射贡献时还考虑了大尺度起伏造成的几何倾斜。MTSM的解为大尺度粗糙度的基尔霍夫解加上几何倾斜修正后的小尺度粗糙度的小扰动解。最后采用改进的积分方程模型(AIEM)对MTSM做了初步的验证，结果表明在入射角qi<30°，粗糙度较小(ks=0.354)的时候，MTSM有比较好的精度。
Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory
Damour, Thibault
2016-01-01
A novel approach to the Effective One-Body description of gravitationally interacting two-body systems is introduced. This approach is based on the post-Minkowskian approximation scheme (perturbation theory in G, without assuming small velocities), and employs a new dictionary focussing on the functional dependence of the scattering angle on the total energy and the total angular momentum of the system. Using this approach, we prove to all orders in v/c two results that were previously known to hold only to a limited post-Newtonian accuracy: (i) the relativistic gravitational dynamics of a two-body system is equivalent, at first post-Minkowskian order, to the relativistic dynamics of an effective test particle moving in a Schwarzschild metric; and (ii) this equivalence requires the existence of an exactly quadratic map between the real (relativistic) two-body energy and the (relativistic) energy of the effective particle. The same energy map is also shown to apply to the effective one-body description of two ...
Institute of Scientific and Technical Information of China (English)
ZHOU Bin; LI Shu-Min
2010-01-01
@@ We study the elastic scattering of atomic argon by an electron in the presence of a bichromatic laser field in the second Born approximation.The target atom is approximated by a simple screening potential.We explore the dependences of the differential cross sections on the relative phase (φ) between the two components of the radiation field and discuss the influence of the number of photons exchanged on the phase-dependence effect.Moreover,for different scattering angles and incident electron energies,the differential cross sections are notably different.
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 wavefuncti......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...
The second Born approximation of electron–argon elastic scattering in a bichromatic laser ﬁeld
Indian Academy of Sciences (India)
Bin Zhou; Ming-Yang Zheng; Da-Yong Wen
2012-03-01
We study the elastic scattering of atomic argon by electron in the presence of a bichromatic laser ﬁeld in the second Born approximation. The target atom is approximated by a simple screening potential and the continuum states of the impinging and emitting electrons are described as Volkov states. We evaluate the S-matrix elements numerically. The dependence of differential cross-section on the relative phase between the two laser components is presented. The results obtained in the ﬁrst and second Born approximations are compared and analysed.
Raman Scattering at Resonant or Near-Resonant Conditions: A Generalized Short-Time Approximation
Institute of Scientific and Technical Information of China (English)
Abdelsalam Mohammed; Yu-Ping Sun; Quan Miao; Hans (A)gren; Faris Gel'mukhanov
2012-01-01
We investigate the dynamics of resonant Raman scattering in the course of the frequency detuning.The dephasing in the time domain makes the scattering fast when the photon energy is tuned from the absorption resonance.This makes frequency detuning to act as a camera shutter with a regulated scattering duration and provides a practical tool of controlling the scattering time in ordinary stationary measurements.The theory is applied to resonant Raman spectra of a couple of few-mode model systems and to trans-1,3,5-hexatriene and guanine-cytosine (G-C) Watson-Crick base pairs (DNA) molecules.Besides some particular physical effects,the regime of fast scattering leads to a simplification of the spectrum as well as to the scattering theory itself.Strong overtones appear in the Raman spectra when the photon frequency is tuned in the resonant region,while in the mode of fast scattering,the overtones are gradually quenched when the photon frequency is tuned more than one vibrational quantum below the first absorption resonance.The detuning from the resonant region thus leads to a strong purification of the Raman spectrum from the contamination by higher overtones and soft modes and purifies the spectrum also in terms of avoidance of dissociation and interfering fluorescence decay of the resonant state.This makes frequency detuning a very useful practical tool in the analysis of the resonant Raman spectra of complex systems and considerably improves the prospects for using the Raman effect for detection of foreign substances at ultra-low concentrations.
Institute of Scientific and Technical Information of China (English)
无
1998-01-01
The discrete-ordinates method is a simple,accurate and of little computational time solution to predict the radiactive heat transfer in the combustion chambers,In this paper,three-dimension radiative problems for absorbing-emitting-scattering medium are modeled using this method in the rectangular enclosure.And in addition,new discrete-ordinates are developed to study the absorbing-emitting-scattering radiation processes for complex phase function.The reasonable results can be obtained though these new ordinates,yet the deviated results are only obtained through conventional Sn ordinates.
1969-01-01
REFERENCE SIGNA TYPE 564BADAS OSCILLOSCOPE AMLFE I TRIGGER KROHN- HIITE GENERAL RADIO CO. MODEL 4100 TYPE 1396-A OSCILLATOR TONE BURST GENE RATOR...size of the insonified area (-3 d.B) for a grazing angle of 40 deg. The active scattering area for each of the ten data runs is confined to a
Institute of Scientific and Technical Information of China (English)
张德悦; 马富明
2004-01-01
In this paper, we consider the electromagnetic scattering from periodic chiral structures. The structure is periodic in one direction and invariant in another direction. The electromagnetic fields in the chiral medium are governed by the Maxwell equations together with the Drude-Born-Fedorov equations. We simplify the problem to a two-dimensional scattering problem and we show that for all but possibly a discrete set of wave numbers, there is a unique quasi-periodic weak solution to the diffraction problem. The diffraction problem can be solved by finite element method. We also establish uniform error estimates for the finite element method and the error estimates when the truncation of the nonlocal transparent boundary operators takes place.
Karlovets, D V; Serbo, V G
2015-01-01
Laser photons carrying non-zero orbital angular momentum are known and exploited during the last twenty years. Recently it has been demonstrated experimentally that such (twisted) electrons can be produced and even focused to a subnanometer scale. Thus, twisted electrons emerge as a new tool in atomic physics. The state of a twisted electron can be considered as a specific wave packet of plane waves. In the present paper-I we consider elastic scattering of the wave packets of fast non-relativistic particles on a potential field. We obtain simple and convenient formulae for a number of events in such a scattering. The equations derived represent, in fact, generalization of the well-known Born approximation for the case when finite sizes and inhomogeneity of the initial packet should be taken into account. To illustrate the obtained results, we consider two simple models corresponding to scattering of a Gaussian wave packet on the Gaussian potential and on the hydrogen atom. The scattering of twisted electrons ...
Incoherent scatter spectra from plasma of a 13-moment approximation distribution function
Institute of Scientific and Technical Information of China (English)
2008-01-01
The function and physical mechanism of heat flow and the viscous stress in the velocity distribution function expanded by Maxwellian distribution are presented. With the introduction of effective temperature Tf, incoherent scatter spectra from plasma for electromagnetic wave in arbitrary line of sight are given. The effect of asymmetry and anisotropy provided by heat flow and the viscous stress on power spectra is discussed. Radar spectra are calculated for different cases of electric field, direction, collision frequency and temperature. The effect of heat flow and the viscous stress on inversion results is analyzed. With a large electric field, the character of non-Maxwellian must be considered.
Dual Quantum Electrodynamics Dyon-Dyon and Charge-Monopole Scattering in a High-Energy Approximation
Gamberg, L P; Gamberg, Leonard; Milton, Kimball A.
2000-01-01
We develop the quantum field theory of electron-point magnetic monopole interactions and more generally, dyon-dyon interactions, based on the original string-dependent ``nonlocal'' action of Dirac and Schwinger. We demonstrate that a viable nonperturbative quantum field theoretic formulation can be constructed that results in a string {\\em independent} cross section for monopole-electron and dyon-dyon scattering. Such calculations can be done only by using nonperturbative approximations such as the eikonal and not by some mutilation of lowest-order perturbation theory.
Probing phase of a scattering amplitude beyond the plane-wave approximation
Karlovets, Dmitry V
2016-01-01
Within a plane-wave approach, a number of scattering events in a generic collision process is insensitive to an overall complex phase of a transition amplitude, although this phase is extremely important for a number of problems, especially in hadronic physics at the LHC energies. In reality, however, the particles are better described as localized wave packets with the mean momenta $p$, their uncertainties $\\sigma$, and here we show that the observables grow dependent upon this phase if one lays aside the simplified plane-wave model. A relative contribution of the phase to the cross section is generally attenuated by a small factor $\\sigma^2/p^2 \\ll 1$, making its experimental measurement a rather challenging task. We discuss two methods for probing how this phase changes with the transferred momentum $t$, either by colliding two beams at a non-zero impact-parameter (say, $pp \\rightarrow X$) or by employing the states with the non-trivial wave functions, for instance, vortex particles carrying orbital angula...
Gilev, Konstantin V; Eremina, Elena; Yurkin, Maxim A; Maltsev, Valeri P
2010-03-15
The discrete sources method (DSM) and the discrete dipole approximation (DDA) were compared for simulation of light scattering by a red blood cell (RBC) model. We considered RBCs with diameters up to 8 mum (size parameter up to 38), relative refractive indices 1.03 and 1.06, and two different orientations. The agreement in the angle-resolved S(11) element of the Mueller matrix obtained by these methods is generally good, but it deteriorates with increasing scattering angle, diameter and refractive index of a RBC. Based on the DDA simulations with very fine discretization (up to 93 dipoles per wavelength) for a single RBC, we attributed most of the disagreement to the DSM, which results contain high-frequency ripples. For a single orientation of a RBC the DDA is comparable to or faster than the DSM. However, the relation is reversed when a set of particle orientations need to be simulated at once. Moreover, the DSM requires about an order of magnitude less computer memory. At present, application of the DSM for massive calculation of light scattering patterns of RBCs is hampered by its limitations in size parameter of a RBC due to the high number of harmonics used for calculations.
Energy Technology Data Exchange (ETDEWEB)
Novaes, Marcel [Instituto de Física, Universidade Federal de Uberlândia, Av. João Naves de Ávila, 2121, Uberlândia, MG 38408-100 (Brazil)
2015-06-15
We consider S-matrix correlation functions for a chaotic cavity having M open channels, in the absence of time-reversal invariance. Relying on a semiclassical approximation, we compute the average over E of the quantities Tr[S{sup †}(E − ϵ) S(E + ϵ)]{sup n}, for general positive integer n. Our result is an infinite series in ϵ, whose coefficients are rational functions of M. From this, we extract moments of the time delay matrix Q = − iħS{sup †}dS/dE and check that the first 8 of them agree with the random matrix theory prediction from our previous paper [M. Novaes, J. Math. Phys. 56, 062110 (2015)].
Application of asymptotic waveform approximation technique to hybrid FE/BI method for 3D scattering
Institute of Scientific and Technical Information of China (English)
PENG Zhen; SHENG XinQing
2007-01-01
The asymptotic waveform evaluation (AWE) technique is a rational function approximation method in computational mathematics, which is used in many applications in computational electromagnetics. In this paper, the performance of the AWE technique in conjunction with hybrid finite element/boundary integral (FE/BI) method is firstly investigated. The formulation of the AWE applied in hybrid FE/BI method is given in detail. The characteristic implementation of the application of the AWE to the hybrid FE/BI method is discussed. Numerical results demonstrate that the AWE technique can greatly speed up the hybrid FE/BI method to acquire wide-band and wide-angle backscatter radar-cross-section (RCS) by complex targets.
Energy Technology Data Exchange (ETDEWEB)
Rasmussen, C.H.; Rawitscher, G.H.
1977-03-01
A scattering matrix function is defined, which obeys a nonlinear (Riccati) matrix differential equation, containing two coupling potential matrices U and W, which are slowly vanishing, and which are mildly oscillatory and rapidly oscillatory, respectively. The scattering matrix is the limiting value of this scattering function. The equation is first transformed to separate the effects of U and W, this transformation yielding separate equations in each. The long range effects of U and W are included in approximations for the scattering matrix, errors are assessed, and a prescription is outlined for the numerical computation of these approximations. In the case where the effect of W is entirely neglected beyond a certain point, the approximation obtained by Alder and Pauli (Nucl. Phys. 128, 193 (1969)) is recovered. An assessment of the error in this approximation is obtained.
Phillips, D R; Devine, N K
1998-01-01
The electromagnetic interactions of a relativistic two-body bound state are formulated in three dimensions using an equal-time (ET) formalism. This involves a systematic reduction of four-dimensional dynamics to a three-dimensional form by integrating out the time components of relative momenta. A conserved electromagnetic current is developed for the ET formalism. It is shown that consistent truncations of the electromagnetic current and the $NN$ interaction kernel may be made, order-by-order in the coupling constants, such that appropriate Ward-Takahashi identities are satisfied. A meson-exchange model of the $NN$ interaction is used to calculate deuteron vertex functions. Calculations of electromagnetic form factors for elastic scattering of electrons by deuterium are performed using an impulse-approximation current. Negative-energy components of the deuteron's vertex function and retardation effects in the meson-exchange interaction are found to have only minor effects on the deuteron form factors.
Alhalholy, Tareq
2016-01-01
Using the relativistic Eikonal approximation, we study the one and two photon exchange amplitudes in elastic electron-nucleon scattering for the case of transversely polarized nucleons with unpolarized electrons beam. In our approach, we utilize the convolution theory of Fourier transforms and the transverse charge density in transverse momentum space to evaluate the one and two photon exchange Eikonal amplitudes. The results obtained for the $2\\gamma$ amplitude in impact parameter space are compared to the corresponding 4D case. We show that while the one and two photon cross sections are azimuthally symmetric, the interference term between them is azimuthally asymmetric, which is an indication of an azimuthal single spin asymmetry for proton and neutron which can be attributed to the fact that the nucleon charge density is transversely (azimuthally) distorted in the transverse plane for transversely polarized nucleons. In addition, the calculations of the interference term for proton and neutron show agreem...
Meziane, M; Jones, M K; Luo, W; Pentchev, L; Perdrisat, C F; Puckett, A J R; Punjabi, V; Wesselmann, F R; Ahmidouch, A; Albayrak, I; Aniol, K A; Arrington, J; Asaturyan, A; Ates, O; Baghdasaryan, H; Benmokhtar, F; Bertozzi, W; Bimbot, L; Bosted, P; Boeglin, W; Butuceanu, C; Carter, P; Chernenko, S; Christy, E; Commisso, M; Cornejo, J C; Covrig, S; Danagoulian, S; Daniel, A; Davidenko, A; Day, D; Dhamija, S; Dutta, D; Ent, R; Frullani, S; Fenker, H; Frlez, E; Garibaldi, F; Gaskell, D; Gilad, S; Gilman, R; Goncharenko, Y; Hafidi, K; Hamilton, D; Higinbotham, D W; Hinton, W; Horn, T; Hu, B; Huang, J; Huber, G M; Jensen, E; Kang, H; Keppel, C; Khandaker, M; King, P; Kirillov, D; Kohl, M; Kravtsov, V; Kumbartzki, G; Li, Y; Mamyan, V; Margaziotis, D J; Markowitz, P; Marsh, A; Matulenko, Y; Maxwell, J; Mbianda, G; Meekins, D; Melnik, Y; Miller, J; Mkrtchyan, A; Mkrtchyan, H; Moffit, B; Moreno, O; Mulholland, J; Narayan, A; Nuruzzaman,; Nedev, S; Piasetzky, E; Pierce, W; Piskunov, N M; Prok, Y; Ransome, R D; Razin, D S; Reimer, P E; Reinhold, J; Rondon, O; Shabestari, M; Shahinyan, A; Shestermanov, K; Sirca, S; Sitnik, I; Smykov, L; Smith, G; Solovyev, L; Solvignon, P; Subedi, R; Suleiman, R; Tomasi-Gustafsson, E; Vasiliev, A; Vanderhaeghen, M; Veilleux, M; Wojtsekhowski, B B; Wood, S; Ye, Z; Zanevsky, Y; Zhang, X; Zhang, Y; Zheng, X; Zhu, L
2010-01-01
Intensive theoretical and experimental efforts over the past decade have aimed at explaining the discrepancy between data for the proton form factor ratio $G_{Ep}/G_{Mp}$ obtained from cross section and polarization measurements. One possible explanation for this difference is a two-photon-exchange contribution. We report the results of the JLab Hall C $GEp2\\gamma$ experiment, which measured the kinematical dependence of polarization transfer observables in elastic electron-proton scattering at $Q^2=2.5$ GeV$^2$, in search of effects beyond the Born approximation. For a wide range of values of the kinematic factor $\\epsilon$ ($\\epsilon=$0.15, 0.63, and 0.77), the proton polarization component ratio and the longitudinal polarization transfer component were measured with statistical uncertainties of $\\pm$0.01 and $\\pm$0.006 and systematic uncertainties of 0.013 and 0.01, respectively.
Froelich, P.; Weyrich, Wolf
1984-06-01
Basic electrodynamical and collision theory presumptions related to Compton scattering are critically reconsidered (with particular emphasis on identifying the proper transition matrix element effectively controlling the process, and on framing it within time dependent perturbation theory and scattering theory) in order to indicate the main features and the validity of the proposed method. The on-energy-shell transition matrix element governing the cross-sectional formula is obtained from Furry's two-potential formalism, which makes possible a treatment of the primary electron-photon interaction to first order while incorporating the effects of the final state Coulombic interaction to all orders. Furry's procedure, in addition to defining clearly which initial and final states should enter the transition matrix element, also brings additional insight into the nature of the so-called ``sudden impulse approximation.'' A treatment is proposed in which the decisive transition matrix element is obtained without explicit calculation of the distorted continuum solutions implied by Furry's procedure, but is instead extracted from the dispersion relations of the ``beat-frequency'' dependent generalized polarizability by means of the L2 treatment based on the complex-coordinate method. The practical advantage of the method will be its ability to incorporate correlation between the ejected electron and the electrons remaining in the ion.
Liu, Kaijian; Levander, Alan
2013-03-01
Teleseismic imaging techniques utilizing mode converted/scattered waves are gaining importance due to the deployment of increasingly dense broad-band seismograph arrays. Although common-conversion point (CCP) stacking is widely used to determine structure from Ps or Sp scattered wavefields isolated by receiver function (RF) processing, this method is limited due to its assumption of a layered medium: Dipping events and diffractions are not treated correctly. As an extension of previous 2-D generalized Radon transform (GRT) imaging methods, we present a 3-D Kirchhoff-approximate imaging technique to migrate scattered waves in 3-D. We first derive the 3-D migration formula for P-to-S conversions using the GRT solution to the linear inverse elastic wave scattering problem. Then we illustrate the Kirchhoff method using finite-difference synthetic seismograms from several 3-D models. Next, we apply the method to two portable broad-band array data sets in the western United States to image the Mendocino Triple Junction and the High Lava Plains (HLP) crust and uppermost mantle structures. From the HLP data, we construct the Ps transmission coefficient images with three-component Green's functions. The 1.0 and 0.5 Hz images show a continuous undulating Moho, as well as three negative upper-mantle events at 50-80 km depth. Compared to the CCP images, the Moho is more clearly imaged, particularly near 117.5°W-117.8°W at the western edge of the Owyhee Plateau. The three negative events in the upper mantle correlate well with the top of three low-Vs zones (-3 per cent contour) in the Rayleigh wave tomography model. The migrated Ps RF data from Mendocino clearly image the rapid decrease in depth of the lithosphere-asthenosphere boundary from ˜65 km beneath the subducting Gorda Plate to 30-50 km beneath the Coast Ranges slab window. The final image is consistent with, but has higher resolution than the Vs structure determined from joint receiver function/Rayleigh wave
Asenchik, O. D.
2017-02-01
A method of approximate calculation of the interaction inverse matrix in the method of discrete dipoles is proposed. The knowledge of this matrix makes it possible to determine the optical response of a system to the action of an electromagnetic wave with an arbitrary shape, which can be represented as a combination of vector spherical wave functions. The number of calculation operations of the matrix in the proposed method is considerably smaller than in the case of its direct calculation. In the case of a change in the refractive index of scattering particles, two methods of approximate calculation of the interaction inverse matrix are also proposed. This makes it possible to calculate the optical response of systems with new characteristics without direct solving equations of a system with a large dimension. The accuracy of the methods is numerically determined for particles with spherical and cubic shapes. It is shown that the methods are computationally efficient and can be used to calculate the values of polarization vectors inside particles and extinction and absorption cross sections of systems.
Forward hard scattering in hadron-hadron collisions in the energy region approximately 10/sup 14/ eV
Shibata, T
1980-01-01
On the basis of the quark-parton picture, the author derives analytically the cross sections for production of hadrons and gamma rays through forward hard scattering in hadron-hadron collisions in the energy region approximately 10/sup 14/ eV. The author takes account of transverse motions both of partons inside proton (p/sub T/) /sub p to q/, and of hadrons fragmented from quark (gluon) (k/sub T/) /sub 1 to h/. In addition, the effects of scale violation are taken into account. The numerical results thus obtained are compared with cosmic-ray data in the energy region approximately 10/sup 14/ eV, observed at Mt. Chacaltaya by Japan-Brazil emulsion-chamber collaboration. After eliminating carefully the bias effect inherent there, it was found that the theoretical calculations reproduced surprisingly well the cosmic-ray data on large p/sub T gamma / not only in the shape, but also in the absolute value. The production cross sections of pi /sup +/ and K/sup +/ expected from the forthcoming p-p colliding beams wi...
Dolmatov, V K; Cooper, M B; Hunter, M E
2015-01-01
Electron elastic-scattering phase shifts and cross sections along with the differential and total cross sections and polarization of low-frequency bremsstrahlung upon low-energy electron collision with endohedral fullerenes $A$@C$_{60}$ are theoretically scrutinized versus the nature, size and spin of the encapsulated atom $A$. The case-study-atoms $A$ are N, Ar, Cr, Mn, Mo, Tc, Xe, Ba, and Eu. They are thoughtfully picked out of different rows of the periodic table. The study is performed in the framework of a model static approximation. There, both the encapsulated atom $A$ and C$_{60}$ cage are regarded as non-polarizable targets. The C$_{60}$ cage is modeled by an attractive spherical annular potential well. The study provides the most complete initial understanding of how the processes of interest might evolve upon electron collision with various $A$@C$_{60}$. Calculated results identify the most interesting and/or useful future measurements or more rigorous calculations of an electron+$A$@C$_{60}$ colli...
Institute of Scientific and Technical Information of China (English)
Jun Ma; Lixin Guo; Xiangzhe Cheng
2009-01-01
The optical wave scattering from one-dimensional (1D) lossy dielectric Gaussian random rough surface is studied. The tapered incident wave is introduced into the classical Kirchhoff approximation (KA), and the shadowing effect is also taken into account to make the KA results have a high accuracy. The definition of the bistatic scattering coefficient of the modified KA and the method of moment (MOM) are unified. The characteristics of the optical wave scattering from the lossy dielectric Gaussian random rough surface of different parameters are analyzed by implementing MOM.
DEFF Research Database (Denmark)
Posselt, Dorthe; Busch, Peter; Rauscher, Markus
2006-01-01
Grazing-incidence small-angle X-ray or neutron scattering of thin polymer films reveals information about the ordering and preferential orientations of the phase-separated microdomains within the films. The grazing-incidence geometry enhances the surface sensitivity; however, the scattering has t...
Tishkovets, Victor P.; Petrova, Elena V.
2016-10-01
Problems of the theory of light scattering by densely packed discrete random media are analyzed with the model, considering such medium as a semi-infinite layer composed of randomly oriented clusters. Each of the clusters is assumed to be in the far zones of all other clusters. Under this approach, the numerical solution of the radiative transfer equation and the equation for weak localization of waves yields the characteristics of radiation reflected by the medium. Since in these equations an elementary volume of the medium is assumed to be represented by randomly oriented clusters, the near-field effects, as well as the irregular shape and heterogeneity of the scatterers, are partially taken into account. The model results are compared to the currently available laboratory measurements of the intensity and the degree of linear polarization of nonabsorbing samples (MgO, Al2O3, and SiO2) composed the scatterers smaller than the wavelength in size. The scattering characteristics of the samples with different (though not very high) packing densities are considered. In the frames of the applied model, some of the calculated phase profiles of polarization well agree with the measured ones. This allowed us to estimate the relative concentration of scatterers in the media and their sizes. At the same time, the measured phase dependences of intensity are poorly fitted with the models. This suggests that some scattering mechanisms remained beyond the frames the considered model; these mechanisms noticeably influence the intensity of radiation reflected by the medium, while their effect on the linear polarization is negligible.
Institute of Scientific and Technical Information of China (English)
Wei Gao-Feng; Chen Wen-Li; Wang Hong-Ying; Li Yuan-Yuan
2009-01-01
This paper finds the approximate analytical scattering state solutions of the arbitrary l-wave Schrodinger equation for the generalized Hulthén potential by taking an improved new approximate scheme for the centrifugal term. The normalized analytical radial wave functions of the l-wave Schrodinger equation for the generalized Hulthén potential are presented and the corresponding calculation formula of phase shifts is derived. Some useful figures are plotted to show the improved accuracy of the obtained results and two special cases for the standard Hulthén potential and Woods-Saxon potential are also studied briefly.
Energy Technology Data Exchange (ETDEWEB)
Buehring, W.
1983-03-01
Non-relativistic scattering phase shifts, bound state energies, and wave function normalization factors for a screened Coulomb potential of the Hulthen type are presented in the form of relatively simple analytic expressions. These formulae have been obtained by a suitable renormalization procedure applied to the quantities derived from an approximate Schroedinger equation which contains the exact Hulthen potential together with an approximate angular momentum term. When the screening exponent vanishes, our formulae reduce to the exact Coulomb expresions. The interrelation between our formulae and Pratt's analytic perturbation theory for screened Coulomb potentials' is discussed.
Energy Technology Data Exchange (ETDEWEB)
Megias, G.D. [Departamento de Física Atómica, Molecular y Nuclear, Universidad de Sevilla, 41080 Sevilla (Spain); Amaro, J.E. [Departamento de Física Atómica, Molecular y Nuclear and Instituto Carlos I de Física Teorica y Computacional, Universidad de Granada, 18071 Granada (Spain); Barbaro, M.B., E-mail: barbaro@to.infn.it [Dipartimento di Fisica, Università di Torino and INFN, Sezione di Torino, Via P. Giuria 1, 10125 Torino (Italy); Caballero, J.A. [Departamento de Física Atómica, Molecular y Nuclear, Universidad de Sevilla, 41080 Sevilla (Spain); Donnelly, T.W. [Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States)
2013-08-09
We compare the predictions of the SuperScaling model for charged-current quasielastic muonic neutrino and antineutrino scattering from {sup 12}C with experimental data spanning an energy range up to 100 GeV. We discuss the sensitivity of the results to different parametrizations of the nucleon vector and axial-vector form factors. Finally, we show the differences between electron and muon (anti)neutrino cross sections relevant for the νSTORM facility.
Amaro, J E; Caballero, J A; Donnelly, T W; Megias, G D
2013-01-01
We compare the predictions of the SuperScaling model for charged current quasielastic muonic neutrino and antineutrino scattering from $^{12}$C with experimental data spanning an energy range up to 100 GeV. We discuss the sensitivity of the results to different parametrizations of the nucleon vector and axial-vector form factors. Finally, we show the differences between electron and muon (anti-)neutrino cross sections relevant for the $\
Institute of Scientific and Technical Information of China (English)
李祥震; 韩香娥
2011-01-01
On the basis of geometrical optics approximation (GOA) of light scattering by spheres, GOA method of forward scattering by a GI-POF for normally incident plane wave was presented. The convergence factor and the phase shift caused by focal line were deduced in GOA. The nondimensional form of scattering intensity formula of forward scattering by a GI-POF for normally incident plane wave was obtained. Based on the above work, the scattering intensity distribution and calculation speed calculated by GOA was compared with the result calculated by Mie theory. The comparison result shows that GOA can be used to calculate the forward scattering intensity of a GI-POF with normally incident plane wave exactly. And the calculation speed of GOA is higher than that of Mie theory, the GOA method is suitable for the real-time measurement of particle-sizing.%基于球粒子光散射的几何光学近似方法,推导了平面波垂直入射梯度折射率光纤(GI-POF)前向散射的几何光学近似.详细推导了几何光学近似方法中的收敛因子和焦线引起的相位变化,得到了平面波垂直入射到GI-POF时无量纲散射强度公式.在此基础上,将几何光学近似方法计算出的前向散射强度分布和算法的运行速度与Mie理论进行了对比,结果表明:几何光学近似方法可以快速而准确地计算出粒子前向散射分布,适用于粒度的在线测量.
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
Yurkin, Maxim A; Tarasov, Peter A; Chernyshev, Andrei V; Hoekstra, Alfons G; Maltsev, Valeri P
2005-01-01
Elastic light scattering by mature red blood cells (RBCs) was theoretically and experimentally analyzed with the discrete dipole approximation (DDA) and the scanning flow cytometry (SFC), respectively. SFC permits measurement of angular dependence of 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 incident light upon the indicatrix. Numerical calculations of indicatrices for several aspect 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-o...
Cogley, A. C.; Pandey, D. K.; Bergstrom, R. W.
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.
Meziane, M; Brash, E J; Gilman, R; Jones, M K; Luo, W; Pentchev, L; Perdrisat, C F; Puckett, A J R; Punjabi, V; Wesselmann, F R; Ahmidouch, A; Albayrak, I; Aniol, K A; Arrington, J; Asaturyan, A; Ates, O; Baghdasaryan, H; Benmokhtar, F; Bertozzi, W; Bimbot, L; Bosted, P; Boeglin, W; Butuceanu, C; Carter, P; Chernenko, S; Christy, E; Commisso, M; Cornejo, J C; Covrig, S; Danagoulian, S; Daniel, A; Davidenko, A; Day, D; Dhamija, S; Dutta, D; Ent, R; Frullani, S; Fenker, H; Frlez, E; Garibaldi, F; Gaskell, D; Gilad, S; Goncharenko, Y; Hafidi, K; Hamilton, D; Higinbotham, D W; Hinton, W; Horn, T; Hu, B; Huang, J; Huber, G M; Jensen, E; Kang, H; Keppel, C; Khandaker, M; King, P; Kirillov, D; Kohl, M; Kravtsov, V; Kumbartzki, G; Li, Y; Mamyan, V; Margaziotis, D J; Markowitz, P; Marsh, A; Matulenko, Y; Maxwell, J; Mbianda, G; Meekins, D; Melnik, Y; Miller, J; Mkrtchyan, A; Mkrtchyan, H; Moffit, B; Moreno, O; Mulholland, J; Narayan, A; Nuruzzaman; Nedev, S; Piasetzky, E; Pierce, W; Piskunov, N M; Prok, Y; Ransome, R D; Razin, D S; Reimer, P E; Reinhold, J; Rondon, O; Shabestari, M; Shahinyan, A; Shestermanov, K; Širca, S; Sitnik, I; Smykov, L; Smith, G; Solovyev, L; Solvignon, P; Subedi, R; Suleiman, R; Tomasi-Gustafsson, E; Vasiliev, A; Vanderhaeghen, M; Veilleux, M; Wojtsekhowski, B B; Wood, S; Ye, Z; Zanevsky, Y; Zhang, X; Zhang, Y; Zheng, X; Zhu, L
2011-04-01
Intensive theoretical and experimental efforts over the past decade have aimed at explaining the discrepancy between data for the proton electric to magnetic form factor ratio, G(E)/G(M), obtained separately from cross section and polarization transfer measurements. One possible explanation for this difference is a two-photon-exchange contribution. In an effort to search for effects beyond the one-photon-exchange or Born approximation, we report measurements of polarization transfer observables in the elastic H(e[over →],e(')p[over →]) reaction for three different beam energies at a Q(2)=2.5 GeV(2), spanning a wide range of the kinematic parameter ε. The ratio R, which equals μ(p)G(E)/G(M) in the Born approximation, is found to be independent of ε at the 1.5% level. The ε dependence of the longitudinal polarization transfer component P(ℓ) shows an enhancement of (2.3±0.6)% relative to the Born approximation at large ε.
Energy Technology Data Exchange (ETDEWEB)
Meziane, M; Brash, E J; Jones, M K; Luo, W; Pentchev, L; Perdrisat, C F; Puckett, A J.R.; Punjabi, V; Wesselmann, F R; Ahmidouch, A; Albayrak, I; Aniol, K A; Arrington, J; Asaturyan, A; Ates, O; Baghdasaryan, H; Benmokhtar, F; Bertozzi, W; Bimbot, L; Bosted, P; Boeglin, W; Butuceanu, C; Carter, P; Chernenko, S; Christy, E; Commisso, M; Cornejo, J C; Covrig, S; Danagoulian, S; Daniel, A; Davidenko, A; Day, D; Dhamija, S; Dutta, D; Ent, R; Frullani, S; Fenker, H; Frlez, E; Garibaldi, F; Gaskell, D; Gilad, S; Goncharenko, Y; Hafidi, K; Hamilton, D; Higinbothan, D W; Hinton, W; Horn, T; Hu, B; Huang, J; Huber, G M; Jensen, E; Kang, H; Keppel, C; Khandaker, M; King, P; Kirillov, D; Kohl, M; Kravtsov, V; Kumbartzki, G; Li, Y; Mamyan, V; Margaziotis, D J; Markowitz, P; Marsh, A; Matulenko, Y; Maxwell, J; Mbianda, G; Meekins, D; Melnick, Y; Miller, J; Mkrtchyan, A; Mkrtchyan, H; Moffit, B; Moreno, O; Mulholland, J; Narayan, A; Nuruzzaman,; Nedev, S; Piasetzky, E; Pierce, W; Piskunov, N M; Prok, Y; Ransome, R D; Razin, D S; Reimer, P E; Reinhold, J; Rondon, O; Shabestari, M; Shahinyan, A; Shestermanov, K; Sirca, S; Sitnik, I; Smykov, L; Smith, G; Solovyev, L; Solvignon, P; Subedi, R; Suleiman, R; Tomasi-Gustafsson, E; Vasiliev, A; Vanderhaeghen, M; Veilleux, M; Wojtsekhowski, B B; Wood, S; Ye, Z; Zanevsky, Y; Zhang, X; Zhang, Y; Zheng, X; Zhu, L
2011-04-01
Intensive theoretical and experimental efforts over the past decade have aimed at explaining the discrepancy between data for the proton electric to magnetic form factor ratio, $G_{E}/G_{M}$, obtained separately from cross section and polarization transfer measurements. One possible explanation for this difference is a two-photon-exchange (TPEX) contribution. In an effort to search for effects beyond the one-photon-exchange or Born approximation, we report measurements of polarization transfer observables in the elastic $H(\\vec{e},e'\\vec{p})$ reaction for three different beam energies at a fixed squared momentum transfer $Q^2 = 2.5$ GeV$^2$, spanning a wide range of the virtual photon polarization parameter, $\\epsilon$. From these measured polarization observables, we have obtained separately the ratio $R$, which equals $\\mu_p G_{E}/G_{M}$ in the Born approximation, and the longitudinal polarization transfer component $P_\\ell$, with statistical and systematic uncertainties of $\\Delta R \\approx \\pm 0.01 \\mbox{(stat)} \\pm 0.013 \\mbox{(syst)}$ and $\\Delta P_\\ell/P^{Born}_{\\ell} \\approx \\pm 0.006 \\mbox{(stat)}\\pm 0.01 \\mbox{(syst)}$. The ratio $R$ is found to be independent of $\\epsilon$ at the 1.5% level, while the $\\epsilon$ dependence of $P_\\ell$ shows an enhancement of $(2.3 \\pm 0.6) %$ relative to the Born approximation at large $\\epsilon$.
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.
Draine, B. T.; Goodman, Jeremy
1993-01-01
We derive the dispersion relation for electromagnetic waves propagating on a lattice of polarizable points. From this dispersion relation we obtain a prescription for choosing dipole polarizabilities so that an infinite lattice with finite lattice spacing will mimic a continuum with dielectric constant. The discrete dipole approximation is used to calculate scattering and absorption by a finite target by replacing the target with an array of point dipoles. We compare different prescriptions for determining the dipole polarizabilities. We show that the most accurate results are obtained when the lattice dispersion relation is used to set the polarizabilities.
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)
Institute of Scientific and Technical Information of China (English)
Fang SU; Jun-zhi CUI; Zhan XU
2009-01-01
The purpose of this paper is to solve nonselfadjoint elliptic problems with rapidly oscillatory coefficients. A two-order and two-scale approximate solution expression for nonselfadjoint elliptic problems is considered, and the error estimation of the two-order and two-scale approximate solution is derived. The numerical result shows that the presented approximation solution is effective.
Staszewska, G.
1981-06-01
A new approach to the solution of coupled equations involved in electron-ion and electron-atom scattering problems is proposed. This method is a combination of iteration and variation procedures. The main advantage of this method is that exchange terms can be calculated in a direct and straightforward manner. The method is based on the Lippmann-Schwinger equation and does not require trial functions satisfying appropriate boundary conditions. Using the Volterra formulation one can find the solution on an interval determined by the range of the exchange potential and the long-range potential terms can be taken into account by a projection procedure giving the asymptotic value of the reactance matrix. The method is tested on the case of electron-hydrogen atom scattering in the 1s-2s and 1s-2s-2p approximation. We have adapted the method proposed originally by Rayski to obtain solutions of coupled equations involved in electron-ion and electron-atom scattering. As mentioned in section 1 the construction of the method secures an automatic fulfilment of the boundary conditions. It allows an easy calculation of the exchange potential as well as an estimation of the introduced approximation. It gives also a possibility of detecting any spurious convergence. Moreover, it is important that this formalism can be applied in the case of normalized as well as unnormalized initial integral equations. This fact is of special importance in the case of long-range interactions. When the method is used for unnormalized (Volterra) equations it allows application of a very convenient projection procedure for treating the long-range terms in the direct potential. Electron-hydrogen atom collisions are investigated as a numerical illustration of the method. In the 1s-2s approximation the normalized equations were solved, while in the 1s-2s-2p approximation the solution was obtained with the help of Volterra equations and the long-range terms of the direct potential were taken into account
Lagrangian and Hamiltonian two-scale reduction
Giannoulis, Johannes; Mielke, Alexander
2008-01-01
Studying high-dimensional Hamiltonian systems with microstructure, it is an important and challenging problem to identify reduced macroscopic models that describe some effective dynamics on large spatial and temporal scales. This paper concerns the question how reasonable macroscopic Lagrangian and Hamiltonian structures can by derived from the microscopic system. In the first part we develop a general approach to this problem by considering non-canonical Hamiltonian structures on the tangent bundle. This approach can be applied to all Hamiltonian lattices (or Hamiltonian PDEs) and involves three building blocks: (i) the embedding of the microscopic system, (ii) an invertible two-scale transformation that encodes the underlying scaling of space and time, (iii) an elementary model reduction that is based on a Principle of Consistent Expansions. In the second part we exemplify the reduction approach and derive various reduced PDE models for the atomic chain. The reduced equations are either related to long wave...
Institute of Scientific and Technical Information of China (English)
周观珍
2005-01-01
The relationship between the order of approximation by neural network based on scattered threshold value nodes and the neurons involved in a single hidden layer is investigated.The results obtained show that the degree of approximation by the periodic neural network with one hidden layer and scattered threshold value nodes is increased with the increase of the number of neurons hid in hidden layer and the smoothness of excitation function.
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.
Evidences for two scales in hadrons
Kopeliovich, B Z; Povh, B; Schmidt, Ivan
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 hadron's area. Such a conjecture about the presence of two scales in hadrons helps to explain: why diffractive gluon radiation so much suppressed; why the triple-Pomeron coupling shows no t-dependence; why total hadronic cross sections rise with energy so slowly; why diffraction cone shrinks so slowly, and why $\\alpha^\\prime_P\\ll\\alpha^\\prime_R$; 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 di-hadrons, seagull effect, etc.) demand such a large transverse momenta of the projectile partons, which is not explained by NLO calculations; why the onset of nuclear shadowing for gluons is so much de...
A two scale analysis of tight sandstones
Adler, P. M.; Davy, C. A.; Song, Y.; Troadec, D.; Hauss, G.; Skoczylas, F.
2015-12-01
Tight sandstones have a low porosity and a very small permeability K. Available models for K do not compare well with measurements. These sandstones are made of SiO_2 grains, with a typical size of several hundreds of micron. These grains are separated by a network of micro-cracks, with sizes ranging between microns down to tens of nm. Therefore, the structure can be schematized by Voronoi polyhedra separated by plane and permeable polygonal micro-cracks. Our goal is to estimate K based on a two scale analysis and to compare the results to measurements. For a particular sample [2], local measurements on several scales include FIB/SEM [3], CMT and 2D SEM. FIB/SEM is selected because the peak pore size given by Mercury Intrusion Porosimetry is of 350nm. FIB/SEM imaging (with 50 nm voxel size) identifies an individual crack of 180nm average opening, whereas CMT provides a connected porosity (individual crack) for 60 nm voxel size, of 4 micron average opening. Numerical modelling is performed by combining the micro-crack network scale (given by 2D SEM) and the 3D micro-crack scale (given by either FIB/SEM or CMT). Estimates of the micro-crack density are derived from 2D SEM trace maps by counting the intersections with scanlines, the surface density of traces, and the number of fracture intersections. K is deduced by using a semi empirical formula valid for identical, isotropic and uniformly distributed fractures [1]. This value is proportional to the micro-crack transmissivity sigma. Sigma is determined by solving the Stokes equation in the micro-cracks measured by FIB/SEM or CMT. K is obtained by combining the two previous results. Good correlation with measured values on centimetric plugs is found when using sigma from CMT data. The results are discussed and further research is proposed. [1] Adler et al, Fractured porous media, Oxford Univ. Press, 2012. [2] Duan et al, Int. J. Rock Mech. Mining Sci., 65, p75, 2014. [3] Song et al, Marine and Petroleum Eng., 65, p63
Andersen, A C; Pustovit, V N; Niklasson, G A
2001-01-01
Certain dust particles in space are expected to appear as clusters of individual grains. The morphology of these clusters could be fractal or compact. In this paper we study the light scattering by compact and fractal polycrystalline graphite clusters consisting of touching identical spheres. We compare three general methods for computing the extinction of the clusters in the wavelength range 0.1 - 100 micron, namely, a rigorous solution (Gerardy & Ausloos 1982) and two different discrete-dipole approximation methods -- MarCODES (Markel 1998) and DDSCAT (Draine & Flatau 1994). We consider clusters of N = 4, 7, 8, 27,32, 49, 108 and 343 particles of radii either 10 nm or 50 nm, arranged in three different geometries: open fractal (dimension D = 1.77), simple cubic and face-centred cubic. The rigorous solution shows that the extinction of the fractal clusters, with N 5 micron, the rigorous solution indicates that the extinction from fractal and compact clusters are of the same order of magnitude. It wa...
A TWO-SCALE HIGHER-ORDER FINITE ELEMENT DISCRETIZATION FOR SCHRODINGER EQUATION
Institute of Scientific and Technical Information of China (English)
Huajie Chen; Fang Liu; Aihui Zhou
2009-01-01
In this paper,a two-scale higher-order finite element discretization scheme is proposed and analyzed for a Schr(o)dinger equation on tensor product domains.With the scheme,the solution of the eigenvalue problem on a fine grid can be reduced to an eigenvalue problem on a much coarser grid together with some eigenvalue problems on partially fine grids.It is shown theoretically and numerically that the proposed two-scale higher-order scheme not only significantly reduces the number of degrees of freedom but also produces very accurate approximations.
Two-Scale Analysis of Honeycombs Indented by Flat Punch
Asada, Takashi; Tanaka, Yuji; Ohno, Nobutada
The fully implicit incremental homogenization scheme developed by Asada and Ohno (2007) for elastoplastic periodic solids is applied to two-scale analysis of honeycomb blocks subjected to flat punch indentation. To this end, the scheme is rebuilt by introducing half unit cells based on the point-symmetric distributions of stress and strain in unit cells, so that analysis domains in unit cells are reduced by half. Then, by assuming the zigzag and armchair types of cell-arrangements, the two-scale analysis of honeycomb blocks is performed. The corresponding full-scale finite element analysis is also performed to reveal the cell-arrangement dependence of cell deformation in the honeycomb blocks. It is shown that the two-scale analysis is macroscopically successful in spite of microscopic limitations.
Two-Scale Convergence of Unsteady Stokes Type Equations
Signing, Lazarus
2011-01-01
In this paper we study the homogenization of unsteady Stokes type equations in the periodic setting. The usual Laplace operator involved in the classical Stokes equations is here replaced by a linear elliptic differential operator of divergence form with periodically oscillating coefficients. Our mean tool is the well known two-scale convergence method.
Energy Technology Data Exchange (ETDEWEB)
Mekhtiche, A. [Laboratoire SNIRM, Faculté de Physique, Université des Sciences et de la Technologie Houari Boumediene (USTHB), BP 32 El Alia, Bab Ezzouar, Algiers (Algeria); Faculté des Sciences et de la Technologie, Université Yahia Farès de Médéa (Algeria); Khalal-Kouache, K., E-mail: kkouache@yahoo.fr [Laboratoire SNIRM, Faculté de Physique, Université des Sciences et de la Technologie Houari Boumediene (USTHB), BP 32 El Alia, Bab Ezzouar, Algiers (Algeria)
2016-09-01
In this paper, angular distributions of slow H{sup +} ions transmitted through different targets (Al, Ag and Au) are calculated using the model of Sigmund and Winterbon (SW) in the multiple scattering theory. Valdés and Arista (VA) developed a method extending the SW model by including the effect of energy loss in the calculation of angular distributions of transmitted ions. Another method has been proposed for such calculations: one can consider the SW model by using an average value for the energy of the ions inside the target. In this contribution, a new expression is proposed for the mean energy which gives a better agreement with the VA model than the precedent one at low energy. Different potentials have been considered to describe the interaction projectile-target atom in this study and the new expression is found to be independent of the interaction potential.
A two-scale damage model with material length
Dascalu, Cristian
2009-09-01
The Note presents the formulation of a class of two-scale damage models involving a micro-structural length. A homogenization method based on asymptotic developments is employed to deduce the macroscopic damage equations. The damage model completely results from energy-based micro-crack propagation laws, without supplementary phenomenological assumptions. We show that the resulting two-scale model has the property of capturing micro-structural lengths. When damage evolves, the micro-structural length is given by the ratio of the surface density of energy dissipated during the micro-crack growth and the macroscopic damage energy release rate per unit volume of the material. The use of fracture criteria based on resistance curves or power laws for sub-critical growth of micro-cracks leads to quasi-brittle and, respectively, time-dependent damage models. To cite this article: C. Dascalu, C. R. Mecanique 337 (2009).
Saturated versus non-saturated two-scales permeability
Lopez, Elena; Ammar, Amine; Abisset-Chavanne, Emmanuelle; Binetruy, Christophe; Chinesta, Francisco
2016-10-01
A crucial step in many composites manufacturing processes is the impregnation of fibrous medium with the resin. The fundamental property needed to quantify the flow is the permeability of the fibrous medium. Process models require the permeability as input data to predict flow patterns and pressure fields. Efficient numerical techniques are needed to solve homogenization problems with geometrical data coming from high-resolution images, involving two-scales and linear fluids. Within this frame-work, this work addresses the question of how to compute the macroscopic permeability from a microscopic description consisting of a viscous fluid flow model defined in a two-scale porous medium, considering the saturated and unsaturated cases.
Bi-Spectrum Scattering Model for Conducting Randomly Rough Surface
Institute of Scientific and Technical Information of China (English)
刘宁; 李宗谦
2002-01-01
A scattering model is developed to predict the scattering coefficient of a conducting randomly rough surface by analyzing the randomly rough surface in the spectral domain using the bi-spectrum method. For common randomly rough surfaces without obvious two-scale characteristics, a scale-compression filter can divide the auto-correlation spectrum into two parts with different correlation lengths. The Kirchhoff approximation and the small perturbation method are used to obtain the surface field, then a bistatic scattering model, the bi-spectrum model (BSM), is used to derive an explicit expression from the surface field. Examples using the integral equation model (IEM), finite difference of the time domain (FDTD) method, and BSM show that the BSM accuracy is acceptable and its range of validity is similar to IEM. BSM can also be extended to a scattering model for dielectric randomly rough surfaces.
Prestack wavefield approximations
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.
Institute of Scientific and Technical Information of China (English)
LIU Zheng-Feng; WANG Xiao-Hong
2008-01-01
Adopting Yoshizawa's two-scale expansion technique,the fluctuating field is expanded around the isotropic field.The renormalization group method is applied for calculating the covariance of the fluctuating field at the lower order expansion,A nonlinear Reynolds stress model is derived and the turbulent constants inside are evaluated analytically.Compared with the two-scale direct interaction approximation analysis for turbulent shear flows proposed by Yoshizawa,the calculation is much more simple.The analytical model presented here is close to the Speziale model,which is widely applied in the numerical simulations for the complex turbulent flows.
Two-scale Modelling of material degradation and failure
Aliabadi, Ferri M. H.
2016-08-01
It is widely recognized that macroscopic material properties depend on the features of the microstructure. The understanding of the links between microscopic and macroscopic material properties, main topic of Micromechanics, is of relevant technological interest, as it may enable deep understanding of the mechanisms governing materials degradation and failure. Polycrystalline materials are used in many engineering applications. Their microstructure is determined by distribution, size, morphology, anisotropy and orientation of the crystals [1]. At temperature below 0.3-0.5 Tmelting there are no ductile or creep mechanisms and two are the main failure patterns: intergranular, where the damage follows the grain boundaries and transgranular where instead the damage goes through the grain by splitting it into two parts. In this talk a two-scale approach to degradation and failure in polycrystalline materials will be presented. The formulation involves the engineering component level (macro-scale) and the material grain level (micro-scale). The macro-continuum is modelled using two- and three-dimensional boundary element formulation in which the presence of damage is formulated through an initial stress approach to account for the local softening in the neighborhood of points experiencing degradation at the micro-scale. The microscopic degradation is explicitly modelled by associating Representative Volume Elements (RVEs) to relevant points of the macro continuum, for representing the polycrystalline microstructure in the neighbourhood of the selected points. A grainboundary formulation is used to simulate intergranular/transgranular degradation and failure in the microstructure, whose morphology is generated using the Voronoi tessellations. Intergranular/transgranular degradation and failure are modeled through cohesive and frictional contact laws. To couple the two scales, macro-strains are transferred to the RVEs as periodic boundary conditions, while overall macro
Two-scale analysis of solar magnetic helicity
Brandenburg, Axel; Singh, Nishant K
2016-01-01
We develop a two-scale formalism to determine global magnetic helicity spectra in systems where the local magnetic helicity has opposite signs on both sides of the equator, giving rise to cancelation with conventional methods. We verify this approach using first synthetic one-dimensional magnetic field and then two-dimensional slices from a three-dimensional alpha effect-type dynamo-generated magnetic field with forced turbulence of opposite helicity above and below the midplane of the domain. We then apply this formalism to global solar synoptic vector magnetograms. To improve the statistics, data from three consecutive Carrington rotations (2161--2163) are combined into a single map. We find that the spectral magnetic helicity representative of the northern hemisphere is negative at all wavenumbers and peaks at ~0.06 Mm^{-1} (scales around 100 Mm). There is no evidence of bihelical magnetic fields that are found in three-dimensional turbulence simulations of helicity-driven alpha effect-type turbulent dynam...
Approximate Representations and Approximate Homomorphisms
Moore, Cristopher
2010-01-01
Approximate algebraic structures play a defining role in arithmetic combinatorics and have found remarkable applications to basic questions in number theory and pseudorandomness. Here we study approximate representations of finite groups: functions f:G -> U_d such that Pr[f(xy) = f(x) f(y)] is large, or more generally Exp_{x,y} ||f(xy) - f(x)f(y)||^2$ is small, where x and y are uniformly random elements of the group G and U_d denotes the unitary group of degree d. We bound these quantities in terms of the ratio d / d_min where d_min is the dimension of the smallest nontrivial representation of G. As an application, we bound the extent to which a function f : G -> H can be an approximate homomorphism where H is another finite group. We show that if H's representations are significantly smaller than G's, no such f can be much more homomorphic than a random function. We interpret these results as showing that if G is quasirandom, that is, if d_min is large, then G cannot be embedded in a small number of dimensi...
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...
Experimental demonstration of a homogeneous two-scale dynamo
Stieglitz, R.; Muller, U.
2002-06-01
It has been shown theoretically in the past that homogeneous dynamos may occur for various velocity fields. G.O. Roberts investigated spatially periodic velocity fields, which Busse confined to a finite cylindrical domain. Using a mean field approach he derived an approximate condition for the onset of dynamo action. Based on Busse's idea at the Forschungszentrum Karlsruhe a conceptual design for an experimental homogeneous dynamo was developed, and a test facility was set up. The first experiments demonstrated that a permanent dynamo can exist in a cylindrical container filled with liquid sodium in which by means of guide vanes counter rotating and counter current spiral vortices are arranged. The dynamo is self-exciting at sufficiently high flow rates, and the magnetic field saturates at a mean value. The instantaneous magnetic field fluctuates around this mean value by about 5%. As predicted by theory the mode of the observed magnetic field is strongly non-axisymmetric. In a series of experiments a phase and a bifurcation diagramm for dynamo action was derived which depend on the spiral and axial flow rates. Figs 5, Refs 14.
Resonant-state expansion Born Approximation
Doost, M B
2015-01-01
The Born Approximation is a fundamental formula in Physics, it allows the calculation of weak scattering via the Fourier transform of the scattering potential. I extend the Born Approximation by including in the formula the Fourier transform of a truncated basis of the infinite number of appropriately normalised resonant states. This extension of the Born Approximation is named the Resonant-State Expansion Born Approximation or RSE Born Approximation. The resonant-states of the system can be calculated using the recently discovered RSE perturbation theory for electrodynamics and normalised correctly to appear in spectral Green's functions via the flux volume normalisation.
Well-posedness of a two-scale model for liquid phase epitaxy with elasticity
Kutter, Michael; Rohde, Christian; Sändig, Anna-Margarete
2017-07-01
Epitaxy, a special form of crystal growth, is a technically relevant process for the production of thin films and layers. It can generate microstructures of different morphologies, such as steps, spirals or pyramids. These microstructures are influenced by elastic effects in the epitaxial layer. There are different epitaxial techniques, one being liquid phase epitaxy. Thereby, single particles are deposited out of a supersaturated liquid solution on a substrate where they contribute to the growth process. This article studies a two-scale model including elasticity, introduced in Eck et al. (Eur Phys J Special Topics 177:5-21, 2009) and extended in Eck et al. (2006). It consists of a macroscopic Navier-Stokes system and a macroscopic convection-diffusion equation for the transport of matter in the liquid, and a microscopic problem that combines a phase field approximation of a Burton-Cabrera-Frank model for the evolution of the epitaxial layer, a Stokes system for the fluid flow near the layer and an elasticity system for the elastic deformation of the solid film. Suitable conditions couple the single parts of the model. As the main result, existence and uniqueness of a solution are proven in suitable function spaces. Furthermore, an iterative solving procedure is proposed, which reflects, on the one hand, the strategy of the proof of the main result via fixed point arguments and, on the other hand, can be the basis for a numerical algorithm.
Validity of the Eikonal Approximation
Kabat, Daniel
1992-01-01
We summarize results on the reliability of the eikonal approximation in obtaining the high energy behavior of a two particle forward scattering amplitude. Reliability depends on the spin of the exchanged field. For scalar fields the eikonal fails at eighth order in perturbation theory, when it misses the leading behavior of the exchange-type diagrams. In a vector theory the eikonal gets the exchange diagrams correctly, but fails by ignoring certain non-exchange graphs which dominate the asymp...
Institute of Scientific and Technical Information of China (English)
张德悦; 马富明
2004-01-01
In this paper, we consider the electromagnetic scattering from periodic chiral structures. The structure is periodic in one direction and invariant in another direction. The electromagnetic fields in the chiral medium are governed by the Maxwell equations together with the Drude-Born-Fedorov equations. We simplify the problem to a two-dimensional scattering problem and we show that for all but possibly a discrete set of wave numbers, there is a unique quasi-periodic weak solution to the diffraction problem. The diffraction problem can be solved by finite element method. We also establish uniform error estimates for the finite element method and the error estimates when the truncation of the nonlocal transparent boundary operators takes place.
Scattering matrix theory for stochastic scalar fields.
Korotkova, Olga; Wolf, Emil
2007-05-01
We consider scattering of stochastic scalar fields on deterministic as well as on random media, occupying a finite domain. The scattering is characterized by a generalized scattering matrix which transforms the angular correlation function of the incident field into the angular correlation function of the scattered field. Within the accuracy of the first Born approximation this matrix can be expressed in a simple manner in terms of the scattering potential of the scatterer. Apart from determining the angular distribution of the spectral intensity of the scattered field, the scattering matrix makes it possible also to determine the changes in the state of coherence of the field produced on scattering.
Light composite scalar boson from a see-saw mechanism in two-scale TC models
National Research Council Canada - National Science Library
Doff, A; Natale, A.A
2015-01-01
We consider the possibility of a light composite scalar boson arising from mass mixing between a relatively light and heavy scalar singlets in a see-saw mechanism expected to occur in two-scale Technicolor (TC) models...
Two-scale meshes in quasilinear discretized problems of computational mechanics
Jarošová, P.; Vala, J.
2016-06-01
Some problems of continuum mechanics, as the analysis of crack formation in the cohesive zone modelling, require (at least) two-scale numerical approach to finite element (or volume, difference, etc.) computations: i) at the macro-scale for a whole (nearly elastic, partially damaged) body and ii) at the micro-scale near the crack (a new interior surface). The paper presents an always convergent procedure handling overlapping two-scale meshes for such model problems, open to generalizations in many directions.
Watanabe, Ikumu; Terada, Kenjiro; Neto, Eduardo Alberto de Souza; Perić, Djordje
The objective of this contribution is to develop an elastic-plastic-damage constitutive model for crystal grain and to incorporate it with two-scale finite element analyses based on mathematical homogenization method, in order to characterize the macroscopic tensile strength of polycrystalline metals. More specifically, the constitutive model for single crystal is obtained by combining hyperelasticity, a rate-independent single crystal plasticity and a continuum damage model. The evolution equations, stress update algorithm and consistent tangent are derived within the framework of standard elastoplasticity at finite strain. By employing two-scale finite element analysis, the ductile behaviour of polycrystalline metals and corresponding tensile strength are evaluated. The importance of finite element formulation is examined by comparing performance of several finite elements and their convergence behaviour is assessed with mesh refinement. Finally, the grain size effect on yield and tensile strength is analysed in order to illustrate the versatility of the proposed two-scale model.
Resonant-state expansion Born Approximation applied to Schrodinger's Equation
Doost, M B
2015-01-01
The RSE Born Approximation is a new scattering formula in Physics, it allows the calculation of strong scattering via the Fourier transform of the scattering potential and Resonant-states. In this paper I apply the RSE Born Approximation to Schr\\"odinger's Equation. The resonant-states of the system can be calculated using the recently discovered RSE perturbation theory and normalised correctly to appear in spectral Green's functions via the flux volume normalisation.
Diophantine approximation and badly approximable sets
DEFF Research Database (Denmark)
Kristensen, S.; Thorn, R.; Velani, S.
2006-01-01
Let (X,d) be a metric space and (Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Omega. Loosely speaking, these consist of points in Omega which `stay clear' of some given set of points in X. The clas......Let (X,d) be a metric space and (Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Omega. Loosely speaking, these consist of points in Omega which `stay clear' of some given set of points in X....... 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...
A nonlinear kp-εp particle two-scale turbulence model and its application
Institute of Scientific and Technical Information of China (English)
Zhuoxiong Zeng; Zhuozhi Zeng; Yihua Xu
2007-01-01
A particle nonlinear two-scale Kp-εp turbulence model is proposed for simulating the anisotropic turbulent two-phase flow. The particle kinetic energy equation for two-scale fluctuation, particle energy transfer rate equation for large-scale fluctuation, and particle turbulent kinetic energy dissipation rate equation for small-scale fluctuation are deri-ved and closed. This model is used to simulate gas-particle flows in a sudden-expansion chamber. The simulation is com-pared with the experiment and with those obtained by using another two kinds of tow-phase turbulence model, such as the single-scale k-ε two-phase turbulence model and the particle two-scale second-order moment (USM) two-phase turbulence model. It is shown that the present model gives simulation in much better agreement with the experiment than the single-scale k-ε two-phase turbulence model does and is almost as good as the particle two-scale USM turbu-lence model.
Validity of the eikonal approximation
Kabat, D
1992-01-01
We summarize results on the reliability of the eikonal approximation in obtaining the high energy behavior of a two particle forward scattering amplitude. Reliability depends on the spin of the exchanged field. For scalar fields the eikonal fails at eighth order in perturbation theory, when it misses the leading behavior of the exchange-type diagrams. In a vector theory the eikonal gets the exchange diagrams correctly, but fails by ignoring certain non-exchange graphs which dominate the asymptotic behavior of the full amplitude. For spin--2 tensor fields the eikonal captures the leading behavior of each order in perturbation theory, but the sum of eikonal terms is subdominant to graphs neglected by the approximation. We also comment on the eikonal for Yang-Mills vector exchange, where the additional complexities of the non-abelian theory may be absorbed into Regge-type modifications of the gauge boson propagators.
Energy Technology Data Exchange (ETDEWEB)
Kostorz, G. [Eidgenoessische Technische Hochschule, Angewandte Physik, Zurich (Switzerland)
1996-12-31
While Bragg scattering is characteristic for the average structure of crystals, static local deviations from the average lattice lead to diffuse elastic scattering around and between Bragg peaks. This scattering thus contains information on the occupation of lattice sites by different atomic species and on static local displacements, even in a macroscopically homogeneous crystalline sample. The various diffuse scattering effects, including those around the incident beam (small-angle scattering), are introduced and illustrated by typical results obtained for some Ni alloys. (author) 7 figs., 41 refs.
Leike, Reimar H
2016-01-01
In Bayesian statistics probability distributions express beliefs. However, for many problems the beliefs cannot be computed analytically and approximations of beliefs are needed. We seek a ranking function that quantifies how "embarrassing" it is to communicate a given approximation. We show that there is only one ranking under the requirements that (1) the best ranked approximation is the non-approximated belief and (2) that the ranking judges approximations only by their predictions for actual outcomes. We find that this ranking is equivalent to the Kullback-Leibler divergence that is frequently used in the literature. However, there seems to be confusion about the correct order in which its functional arguments, the approximated and non-approximated beliefs, should be used. We hope that our elementary derivation settles the apparent confusion. We show for example that when approximating beliefs with Gaussian distributions the optimal approximation is given by moment matching. This is in contrast to many su...
High frequency and pulse scattering physical acoustics
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
On surface approximation using developable surfaces
DEFF Research Database (Denmark)
Chen, H. Y.; Lee, I. K.; Leopoldseder, s.
1999-01-01
We introduce a method for approximating a given surface by a developable surface. It will be either a G(1) surface consisting of pieces of cones or cylinders of revolution or a G(r) NURBS developable surface. Our algorithm will also deal properly with the problems of reverse engineering and produce...... robust approximation of given scattered data. The presented technique can be applied in computer aided manufacturing, e.g. in shipbuilding. (C) 1999 Academic Press....
On surface approximation using developable surfaces
DEFF Research Database (Denmark)
Chen, H. Y.; Lee, I. K.; Leopoldseder, S.
1998-01-01
We introduce a method for approximating a given surface by a developable surface. It will be either a G_1 surface consisting of pieces of cones or cylinders of revolution or a G_r NURBS developable surface. Our algorithm will also deal properly with the problems of reverse engineering and produce...... robust approximation of given scattered data. The presented technique can be applied in computer aided manufacturing, e.g. in shipbuilding....
Carr, E. J.; Perré, P.; Turner, I. W.
2016-12-01
Numerous problems involving gradient-driven transport processes-e.g., Fourier's and Darcy's law-in heterogeneous materials concern a physical domain that is much larger than the scale at which the coefficients vary spatially. To overcome the prohibitive computational cost associated with such problems, the well-established Distributed Microstructure Model (DMM) provides a two-scale description of the transport process that produces a computationally cheap approximation to the fine-scale solution. This is achieved via the introduction of sparsely distributed micro-cells that together resolve small patches of the fine-scale structure: a macroscopic equation with an effective coefficient describes the global transport and a microscopic equation governs the local transport within each micro-cell. In this paper, we propose a new formulation, the Extended Distributed Microstructure Model (EDMM), where the macroscopic flux is instead defined as the average of the microscopic fluxes within the micro-cells. This avoids the need for any effective parameters and more accurately accounts for a non-equilibrium field in the micro-cells. Another important contribution of the work is the presentation of a new and improved numerical scheme for performing the two-scale computations using control volume, Krylov subspace and parallel computing techniques. Numerical tests are carried out on two challenging test problems: heat conduction in a composite medium and unsaturated water flow in heterogeneous soils. The results indicate that while DMM is more efficient, EDMM is more accurate and is able to capture additional fine-scale features in the solution.
Rašin, Andrija
1994-01-01
We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed.
On Element SDD Approximability
Avron, Haim; Toledo, Sivan
2009-01-01
This short communication shows that in some cases scalar elliptic finite element matrices cannot be approximated well by an SDD matrix. We also give a theoretical analysis of a simple heuristic method for approximating an element by an SDD matrix.
Approximate iterative algorithms
Almudevar, Anthony Louis
2014-01-01
Iterative algorithms often rely on approximate evaluation techniques, which may include statistical estimation, computer simulation or functional approximation. This volume presents methods for the study of approximate iterative algorithms, providing tools for the derivation of error bounds and convergence rates, and for the optimal design of such algorithms. Techniques of functional analysis are used to derive analytical relationships between approximation methods and convergence properties for general classes of algorithms. This work provides the necessary background in functional analysis a
Sulfate attack in sewer pipes: Derivation of a concrete corrosion model via two-scale convergence
Fatima, Tasnim
2010-01-01
We explore the homogenization limit and rigorously derive upscaled equations for a microscopic reaction-diffusion system modeling sulfate corrosion in sewer pipes made of concrete. The system, defined in a periodically-perforated domain, is semi-linear, partially dissipative and weakly coupled via a non-linear ordinary differential equation posed on the solid-water interface at the pore level. Firstly, we show the well-posedness of the microscopic model. We then apply homogenization techniques based on two-scale convergence for an uniformly periodic domain and derive upscaled equations together with explicit formulae for the effective diffusion coefficients and reaction constants. We use a boundary unfolding method to pass to the homogenization limit in the non-linear ordinary differential equation. Finally, besides giving its strong formulation, we also prove that the upscaled two-scale model admits a unique solution.
A two-scale finite element formulation for the dynamic analysis of heterogeneous materials
Energy Technology Data Exchange (ETDEWEB)
Ionita, Axinte [Los Alamos National Laboratory
2008-01-01
In the analysis of heterogeneous materials using a two-scale Finite Element Method (FEM) the usual assumption is that the Representative Volume Element (RVE) of the micro-scale is much smaller than the finite element discretization of the macro-scale. However there are situations in which the RVE becomes comparable with, or even bigger than the finite element. These situations are considered in this article from the perspective of a two-scale FEM dynamic analysis. Using the principle of virtual power, new equations for the fluctuating fields are developed in terms of velocities rather than displacements. To allow more flexibility in the analysis, a scaling deformation tensor is introduced together with a procedure for its determination. Numerical examples using the new approach are presented.
Institute of Scientific and Technical Information of China (English)
J.Z.Cui; X.G.Yu
2006-01-01
In this paper,a two-scale method (TSM) is presented for identifying the mechanics parameters such as stiffness and strength of composite materials with small periodic configuration.Firstly,a formulation is briefly given for two-scale analysis (TSA) of the composite materials.And then a two-scale computation formulation of strains and stresses is developed by displacement solution with orthotropic material coefficients for three kinds of such composites structures,I.e.,the tension column with a square cross section,the bending cantilever with a rectangular cross section and the torsion column with a circle cross section.The strength formulas for the three kinds of structures are derived and the TSM procedure is discussed.Finally the numerical results of stiffness and strength are presented and compared with experimental data.It shows that the TSM method in this paper is feasible and valid for predicting both the stiffness and the strength of the composite materials with periodic configuration.
Energy Technology Data Exchange (ETDEWEB)
Nakamachi, Eiji; Yoshida, Takashi; Yamaguchi, Toshihiko; Morita, Yusuke [Dept. of Biomedical Engineering, Doshisha Univ., Kyotanabe, Kyoto, 610-0394 (Japan); Kuramae, Hiroyuki [Dept. of Technol. Management, Osaka Institute of Technol., Asahiku, Osaka, 535-8585 (Japan); Morimoto, Hideo [Furukawa Electric Co. Ltd., Okano, Nishiku, Yokohama, Kanagawa, 220-0073 (Japan)
2014-10-06
We developed two-scale FE analysis procedure based on the crystallographic homogenization method by considering the hierarchical structure of poly-crystal aluminium alloy metal. It can be characterized as the combination of two-scale structure, such as the microscopic polycrystal structure and the macroscopic elastic plastic continuum. Micro polycrystal structure can be modeled as a three dimensional representative volume element (RVE). RVE is featured as by 3×3×3 eight-nodes solid finite elements, which has 216 crystal orientations. This FE analysis code can predict the deformation, strain and stress evolutions in the wire drawing processes in the macro- scales, and further the crystal texture and hardening evolutions in the micro-scale. In this study, we analyzed the texture evolution in the wire drawing processes by our two-scale FE analysis code under conditions of various drawing angles of dice. We evaluates the texture evolution in the surface and center regions of the wire cross section, and to clarify the effects of processing conditions on the texture evolution.
Nakamachi, Eiji; Yoshida, Takashi; Kuramae, Hiroyuki; Morimoto, Hideo; Yamaguchi, Toshihiko; Morita, Yusuke
2014-10-01
We developed two-scale FE analysis procedure based on the crystallographic homogenization method by considering the hierarchical structure of poly-crystal aluminium alloy metal. It can be characterized as the combination of two-scale structure, such as the microscopic polycrystal structure and the macroscopic elastic plastic continuum. Micro polycrystal structure can be modeled as a three dimensional representative volume element (RVE). RVE is featured as by 3×3×3 eight-nodes solid finite elements, which has 216 crystal orientations. This FE analysis code can predict the deformation, strain and stress evolutions in the wire drawing processes in the macro- scales, and further the crystal texture and hardening evolutions in the micro-scale. In this study, we analyzed the texture evolution in the wire drawing processes by our two-scale FE analysis code under conditions of various drawing angles of dice. We evaluates the texture evolution in the surface and center regions of the wire cross section, and to clarify the effects of processing conditions on the texture evolution.
Approximation of distributed delays
Lu, Hao; Eberard, Damien; Simon, Jean-Pierre
2010-01-01
We address in this paper the approximation problem of distributed delays. Such elements are convolution operators with kernel having bounded support, and appear in the control of time-delay systems. From the rich literature on this topic, we propose a general methodology to achieve such an approximation. For this, we enclose the approximation problem in the graph topology, and work with the norm defined over the convolution Banach algebra. The class of rational approximates is described, and a constructive approximation is proposed. Analysis in time and frequency domains is provided. This methodology is illustrated on the stabilization control problem, for which simulations results show the effectiveness of the proposed methodology.
Diophantine approximation and badly approximable sets
DEFF Research Database (Denmark)
Kristensen, S.; Thorn, R.; Velani, S.
2006-01-01
Let (X,d) be a metric space and (Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Omega. Loosely speaking, these consist of points in Omega which `stay clear' of some given set of points in X. The clas......Let (X,d) be a metric space and (Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Omega. Loosely speaking, these consist of points in Omega which `stay clear' of some given set of points in X...
Sparse approximation with bases
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...
Microscopic distorted wave theory of inelastic scattering
Picklesimer, A.; Tandy, P. C.; Thaler, R. M.
1982-03-01
An exact microscopic distorted wave theory of inelastic scattering is formulated which contains the physical picture usually associated with distorted wave approximations without the usual redundancy. This formulation encompasses the inelastic scattering of two fragments, elementary or composite (both with or without the full complexity of interfragment Pauli symmetries). The fact that these considerations need not be based upon elementary potential interactions is an indication of the generality of the approach and supports its applicability to inelastic meson scattering. The theory also maintains a description of inelastic scattering which is a natural extension of the description of elastic scattering and it provides a general basis for obtaining truncation models with an explicit distorted wave structure. The distorted wave impulse approximation is presented as an example of a particular truncation/approximation encompassed by this theory and the nature of the distorted waves is explicated. NUCLEAR REACTIONS Distorted wave theory, inelastic scattering, multiple scattering, spectator expansion, Pauli exclusion principle, composite particles, unitarity structure.
Approximation techniques for engineers
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.
Achieser, N I
2004-01-01
A pioneer of many modern developments in approximation theory, N. I. Achieser designed this graduate-level text from the standpoint of functional analysis. The first two chapters address approximation problems in linear normalized spaces and the ideas of P. L. Tchebysheff. Chapter III examines the elements of harmonic analysis, and Chapter IV, integral transcendental functions of the exponential type. The final two chapters explore the best harmonic approximation of functions and Wiener's theorem on approximation. Professor Achieser concludes this exemplary text with an extensive section of pr
Magnetotransport of multiple-band nearly antiferromagnetic metals due to hot-spot scattering
Koshelev, A. E.
2016-09-01
Multiple-band electronic structure and proximity to antiferromagnetic (AF) instability are the key properties of iron-based superconductors. We explore the influence of scattering by the AF spin fluctuations on transport of multiple-band metals above the magnetic transition. A salient feature of scattering on the AF fluctuations is that it is strongly enhanced at the Fermi surface locations where the nesting is perfect ("hot spots" or "hot lines"). We review derivation of the collision integral for the Boltzmann equation due to AF-fluctuations scattering. In the paramagnetic state, the enhanced scattering rate near the hot lines leads to anomalous behavior of electronic transport in magnetic field. We explore this behavior by analytically solving the Boltzmann transport equation with approximate transition rates. This approach accounts for return scattering events and is more accurate than the relaxation-time approximation. The magnetic-field dependences are characterized by two very different field scales: the lower scale is set by the hot-spot width and the higher scale is set by the total scattering amplitude. A conventional magnetotransport behavior is limited to magnetic fields below the lower scale. In the wide range in-between these two scales, the longitudinal conductivity has linear dependence on the magnetic field and the Hall conductivity has quadratic dependence. The linear dependence of the diagonal component reflects growth of the Fermi-surface area affected by the hot spots proportional to the magnetic field. We discuss applicability of this theoretical framework for describing of anomalous magnetotransport properties in different iron pnictides and chalcogenides in the paramagnetic state.
Chalupecký, Vladimír
2011-01-01
We propose a semi-discrete finite difference multiscale scheme for a concrete corrosion model consisting of a system of two-scale reaction-diffusion equations coupled with an ode. We prove energy and regularity estimates and use them to get the necessary compactness of the approximation estimates. Finally, we illustrate numerically the behavior of the two-scale finite difference approximation of the weak solution.
Two-scale cost efficiency optimization of 5G wireless backhaul networks
Ge, Xiaohu; Tu, Song; Mao, Guoqiang; Lau, Vincent K. N.; Pan, Linghui
2016-01-01
To cater for the demands of future fifth generation (5G) ultra-dense small cell networks, the wireless backhaul network is an attractive solution for the urban deployment of 5G wireless networks. Optimization of 5G wireless backhaul networks is a key issue. In this paper we propose a two-scale optimization solution to maximize the cost efficiency of 5G wireless backhaul networks. Specifically, the number and positions of gateways are optimized in the long time scale of 5G wireless backhaul ne...
Quasi-potential and Two-Scale Large Deviation Theory for Gillespie Dynamics
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.
Two-scale cost efficiency optimization of 5G wireless backhaul networks
Ge, Xiaohu; Tu, Song; Mao, Guoqiang; Lau, Vincent K. N.; Pan, Linghui
2016-01-01
To cater for the demands of future fifth generation (5G) ultra-dense small cell networks, the wireless backhaul network is an attractive solution for the urban deployment of 5G wireless networks. Optimization of 5G wireless backhaul networks is a key issue. In this paper we propose a two-scale optimization solution to maximize the cost efficiency of 5G wireless backhaul networks. Specifically, the number and positions of gateways are optimized in the long time scale of 5G wireless backhaul ne...
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...
Ordered cones and approximation
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.
Approximate Modified Policy Iteration
Scherrer, Bruno; Ghavamzadeh, Mohammad; Geist, Matthieu
2012-01-01
Modified policy iteration (MPI) is a dynamic programming (DP) algorithm that contains the two celebrated policy and value iteration methods. Despite its generality, MPI has not been thoroughly studied, especially its approximation form which is used when the state and/or action spaces are large or infinite. In this paper, we propose three approximate MPI (AMPI) algorithms that are extensions of the well-known approximate DP algorithms: fitted-value iteration, fitted-Q iteration, and classification-based policy iteration. We provide an error propagation analysis for AMPI that unifies those for approximate policy and value iteration. We also provide a finite-sample analysis for the classification-based implementation of AMPI (CBMPI), which is more general (and somehow contains) than the analysis of the other presented AMPI algorithms. An interesting observation is that the MPI's parameter allows us to control the balance of errors (in value function approximation and in estimating the greedy policy) in the fina...
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.
[The development and validation of two scales on retribution practices: PRG-13 and PRE-21].
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.
The degenerate-internal-states approximation for cold collisions
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.
Approximate calculation of integrals
Krylov, V I
2006-01-01
A systematic introduction to the principal ideas and results of the contemporary theory of approximate integration, this volume approaches its subject from the viewpoint of functional analysis. In addition, it offers a useful reference for practical computations. Its primary focus lies in the problem of approximate integration of functions of a single variable, rather than the more difficult problem of approximate integration of functions of more than one variable.The three-part treatment begins with concepts and theorems encountered in the theory of quadrature. The second part is devoted to t
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.)
Approximating Stationary Statistical Properties
Institute of Scientific and Technical Information of China (English)
Xiaoming WANG
2009-01-01
It is well-known that physical laws for large chaotic dynamical systems are revealed statistically. Many times these statistical properties of the system must be approximated numerically. The main contribution of this manuscript is to provide simple and natural criterions on numerical methods (temporal and spatial discretization) that are able to capture the stationary statistical properties of the underlying dissipative chaotic dynamical systems asymptotically. The result on temporal approximation is a recent finding of the author, and the result on spatial approximation is a new one. Applications to the infinite Prandtl number model for convection and the barotropic quasi-geostrophic model are also discussed.
Modern Electromagnetic Scattering
2013-08-10
Section 4.3) of the cylindrical annulus is properly accounted for, and if the cylindrical void is sufficiently small . We refer to this approximation as...tempered distributions . . . . . . . . . . . . . 59 CHAPTER 4 MEASURING THE VOID: THEORETICAL STUDY OF SCATTERING BY A CYLINDRICAL ANNULUS ...and phase of the far-field pattern in the forward direction for a Teflon cylindrical annulus in vacuum, with an outer radius of 10 cm at 100 GHz, is
Collisions of halo nuclei within a dynamical eikonal approximation.
Baye, D; Capel, P; Goldstein, G
2005-08-19
The dynamical eikonal approximation unifies the semiclassical time-dependent and eikonal methods. It allows calculating differential cross sections for elastic scattering and breakup in a quantal way by taking into account interference effects. Good agreement is obtained with experiment for 11Be breakup on 208Pb. Dynamical effects are weak for elastic scattering.
Energy Technology Data Exchange (ETDEWEB)
Stirling, W.G. [Liverpool Univ., Dep. of Physics, Liverpool (United Kingdom); Perry, S.C. [Keele Univ. (United Kingdom). Dept. of Physics
1996-12-31
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{sub 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.
Directory of Open Access Journals (Sweden)
Malvina Baica
1985-01-01
Full Text Available The author uses a new modification of Jacobi-Perron Algorithm which holds for complex fields of any degree (abbr. ACF, and defines it as Generalized Euclidean Algorithm (abbr. GEA to approximate irrationals.
Approximations in Inspection Planning
DEFF Research Database (Denmark)
Engelund, S.; Sørensen, John Dalsgaard; Faber, M. H.
2000-01-01
Planning of inspections of civil engineering structures may be performed within the framework of Bayesian decision analysis. The effort involved in a full Bayesian decision analysis is relatively large. Therefore, the actual inspection planning is usually performed using a number of approximations....... One of the more important of these approximations is the assumption that all inspections will reveal no defects. Using this approximation the optimal inspection plan may be determined on the basis of conditional probabilities, i.e. the probability of failure given no defects have been found...... by the inspection. In this paper the quality of this approximation is investigated. The inspection planning is formulated both as a full Bayesian decision problem and on the basis of the assumption that the inspection will reveal no defects....
The Karlqvist approximation revisited
Tannous, C
2015-01-01
The Karlqvist approximation signaling the historical beginning of magnetic recording head theory is reviewed and compared to various approaches progressing from Green, Fourier, Conformal mapping that obeys the Sommerfeld edge condition at angular points and leads to exact results.
Approximations in Inspection Planning
DEFF Research Database (Denmark)
Engelund, S.; Sørensen, John Dalsgaard; Faber, M. H.
2000-01-01
Planning of inspections of civil engineering structures may be performed within the framework of Bayesian decision analysis. The effort involved in a full Bayesian decision analysis is relatively large. Therefore, the actual inspection planning is usually performed using a number of approximations....... One of the more important of these approximations is the assumption that all inspections will reveal no defects. Using this approximation the optimal inspection plan may be determined on the basis of conditional probabilities, i.e. the probability of failure given no defects have been found...... by the inspection. In this paper the quality of this approximation is investigated. The inspection planning is formulated both as a full Bayesian decision problem and on the basis of the assumption that the inspection will reveal no defects....
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
Approximation Behooves Calibration
DEFF Research Database (Denmark)
da Silva Ribeiro, André Manuel; Poulsen, Rolf
2013-01-01
Calibration based on an expansion approximation for option prices in the Heston stochastic volatility model gives stable, accurate, and fast results for S&P500-index option data over the period 2005–2009.......Calibration based on an expansion approximation for option prices in the Heston stochastic volatility model gives stable, accurate, and fast results for S&P500-index option data over the period 2005–2009....
Approximate kernel competitive learning.
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.
Directory of Open Access Journals (Sweden)
Maksim Duškin
2015-11-01
Full Text Available Approximation and supposition This article compares exponents of approximation (expressions like Russian около, примерно, приблизительно, более, свыше and the words expressing supposition (for example Russian скорее всего, наверное, возможно. These words are often confused in research, in particular researchers often mention exponents of supposition in case of exponents of approximation. Such approach arouses some objections. The author intends to demonstrate in this article a notional difference between approximation and supposition, therefore the difference between exponents of these two notions. This difference could be described by specifying different attitude of approximation and supposition to the notion of knowledge. Supposition implies speaker’s ignorance of the exact number, while approximation does not mean such ignorance. The article offers examples proving this point of view.
Reviewing deaths in British and US hospitals: a study of two scales for assessing preventability
Manaseki-Holland, Semira; Lilford, Richard J; Bishop, Jonathan R B; Girling, Alan J; Chen, Yen-Fu; Hofer, Timothy P
2017-01-01
Background Standardised mortality ratios do not provide accurate measures of preventable mortality. This has generated interest in using case notes to assess the preventable component of mortality. But, different methods of measurement have not been compared. We compared the reliability of two scales for assessing preventability and the correspondence between them. Methods Medical specialists reviewed case notes of patients who had died in hospital, using two instruments: a five-point Likert scale and a continuous (0–100) scale of preventability. To enhance generalisability, we used two different hospital datasets with different types of acute medical patients across different epochs, and in two jurisdictions (UK and USA). We investigated the reliability of measurement and correspondence of preventability estimates across the two scales. Ordinal mixed effects regression methods were used to analyse the Likert scale and to calibrate it against the continuous scale. We report the estimates of the probability a death could have been prevented, accounting for reviewer inconsistency. Results Correspondence between the two scales was strong; the Likert categories explained most of the variation (76% UK, 73% USA) in the continuous scale. Measurement reliability was low, but similar across the two instruments in each dataset (intraclass correlation: 0.27, UK; 0.23, USA). Adjusting for the inconsistency of reviewer judgements reduced the proportion of cases with high preventability, such that the proportion of all deaths judged probably or definitely preventable on the balance of probability was less than 1%. Conclusions The correspondence is high between a Likert and a continuous scale, although the low reliability of both would suggest careful measurement design would be needed to use either scale. Few to no cases are above the threshold when using a balance of probability approach to determining a preventable death, and in any case, there is little evidence supporting
Unveiling small sphere's scattering behavior
Tzarouchis, Dimitrios C; Sihvola, Ari
2016-01-01
A classical way for exploring the scattering behavior of a small sphere is to approximate Mie coefficients with a Taylor series expansion. This ansatz delivered a plethora of insightful results, mostly for small spheres supporting electric localized plasmonic resonances. However, many scattering aspects are still uncharted, especially for the case of magnetic resonances. Here, an alternative system ansatz is proposed based on the Pad\\'e approximants for the Mie coefficients. The extracted results reveal new aspects, such as the existence of a self-regulating radiative damping mechanism for the first magnetic resonance. Hence, a systematic way of exploring the scattering behavior is introduced, sharpening our understanding about sphere's scattering behavior and its emergent functionalities.
Towards an efficient two-scale approach to model technical textiles
Fillep, Sebastian; Mergheim, Julia; Steinmann, Paul
2017-03-01
The paper proposes and investigates an efficient two-scale approach to describe the material behavior of technical textiles. On the macroscopic scale the considered textile materials are modeled as homogeneous by means of shell elements. The heterogeneous microstructure, which consists e.g. of woven fibers, is explicitly resolved in representative volume elements (RVE). A shell-specific homogenization scheme is applied to connect the macro and the micro scale. The simultaneous solution of the macroscopic and the nonlinear microscopic simulations, e.g. by means of the FE^2-method, is very expensive. Therefore, a different approach is applied here: the macro constitutive response is computed in advance and tabulated for a certain RVE and for different loading scenarios. These homogenized stress and tangent values are then used in a macroscopic simulation without the need to explicitly resort to the microscopic simulations. The efficiency of the approach is analyzed by means of numerical examples.
Impedance Matching for Discrete, Periodic Media and Application to Two-Scale Wave Propagation Models
Thirunavukkarasu, Senganal
This dissertation introduces the idea of an equivalent continuous medium (ECM) that has the same impedance as that of an unbounded discrete periodic medium. Contrary to existing knowledge, we constructively show that it is indeed possible to achieve perfect matching for periodic and discrete media. We present analytical results relating the propagation characteristics of periodic media and the corresponding ECM, leading to the development of numerical methods for wave propagation in these media. In this dissertation, we present the main idea of ECM and apply it, with mixed results, to seemingly different problems requiring effective numerical methods for modeling wave propagation in unbounded media. An immediate application of ECM is in developing absorbing boundary conditions (ABCs) for wave propagation in unbounded discrete media. Using the idea of ECM, and building on class of continuous ABCs called perfectly matched discrete layers (PMDL), we propose a new class of discrete ABCs called discrete PMDL and develop frequency domain formulations that are shown to be superior to continuous ABCs. Another application that is explored in this dissertation is the design of interface conditions for concurrent coupling of two-scale wave propagation models, e.g. Atomistic-to-Continuum (AtC) coupling. We propose a domain-decomposition (DD) approach and develop accurate interface conditions that are critical for the concurrent coupling of the two-scale models. It turns out that time-domain discrete ABCs are key to the the accuracy of these interface conditions. Since discrete PMDL is well-posed and accurate for the model problem, we build on it to propose an efficient and accurate interface condition for two-scale wave propagation models. Although many open problems remain with respect to implementation, we believe that the proposed DD based approach is a good first step towards achieving efficient coupling of two-scale wave propagation models. Time-domain discrete PMDL can
Towards an efficient two-scale approach to model technical textiles
Fillep, Sebastian; Mergheim, Julia; Steinmann, Paul
2016-11-01
The paper proposes and investigates an efficient two-scale approach to describe the material behavior of technical textiles. On the macroscopic scale the considered textile materials are modeled as homogeneous by means of shell elements. The heterogeneous microstructure, which consists e.g. of woven fibers, is explicitly resolved in representative volume elements (RVE). A shell-specific homogenization scheme is applied to connect the macro and the micro scale. The simultaneous solution of the macroscopic and the nonlinear microscopic simulations, e.g. by means of the FE^2 -method, is very expensive. Therefore, a different approach is applied here: the macro constitutive response is computed in advance and tabulated for a certain RVE and for different loading scenarios. These homogenized stress and tangent values are then used in a macroscopic simulation without the need to explicitly resort to the microscopic simulations. The efficiency of the approach is analyzed by means of numerical examples.
A critique and comparison of two scales from fifteen years of studying compulsive buying.
Manolis, Chris; Roberts, James A; Kashyap, Vishal
2008-02-01
Compulsive buying is an important construct in marketing that has far-reaching personal and social implications. The profile of the adult compulsive buyer in the literature is based largely on the 1992 Faber and O'Guinn Compulsive Buying Scale. A second compulsive buying scale by Edwards has also been used but sparingly. Empirical research conducted over that past 15 years with these two scales shows that, although both scales were designed to measure compulsive buying, the two appear to be different operationalizations of the construct. The present review raises several psychometric issues about both scales. Their robustness is crucial to a clear understanding of the antecedents and consequences of compulsive buying. Directions for research are added.
An Efficient Two-Scale Hybrid Embedded Fracture Model for Shale Gas Simulation
Amir, Sahar
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.
Covariant approximation averaging
Shintani, Eigo; Blum, Thomas; Izubuchi, Taku; Jung, Chulwoo; Lehner, Christoph
2014-01-01
We present a new class of statistical error reduction techniques for Monte-Carlo simulations. Using covariant symmetries, we show that correlation functions can be constructed from inexpensive approximations without introducing any systematic bias in the final result. We introduce a new class of covariant approximation averaging techniques, known as all-mode averaging (AMA), in which the approximation takes account of contributions of all eigenmodes through the inverse of the Dirac operator computed from the conjugate gradient method with a relaxed stopping condition. In this paper we compare the performance and computational cost of our new method with traditional methods using correlation functions and masses of the pion, nucleon, and vector meson in $N_f=2+1$ lattice QCD using domain-wall fermions. This comparison indicates that AMA significantly reduces statistical errors in Monte-Carlo calculations over conventional methods for the same cost.
Diophantine approximations on fractals
Einsiedler, Manfred; Shapira, Uri
2009-01-01
We exploit dynamical properties of diagonal actions to derive results in Diophantine approximations. In particular, we prove that the continued fraction expansion of almost any point on the middle third Cantor set (with respect to the natural measure) contains all finite patterns (hence is well approximable). Similarly, we show that for a variety of fractals in [0,1]^2, possessing some symmetry, almost any point is not Dirichlet improvable (hence is well approximable) and has property C (after Cassels). We then settle by similar methods a conjecture of M. Boshernitzan saying that there are no irrational numbers x in the unit interval such that the continued fraction expansions of {nx mod1 : n is a natural number} are uniformly eventually bounded.
Approximate formulas for moderately small eikonal amplitudes
Kisselev, A. V.
2016-08-01
We consider the eikonal approximation for moderately small scattering amplitudes. To find numerical estimates of these approximations, we derive formulas that contain no Bessel functions and consequently no rapidly oscillating integrands. To obtain these formulas, we study improper integrals of the first kind containing products of the Bessel functions J0(z). We generalize the expression with four functions J0(z) and also find expressions for the integrals with the product of five and six Bessel functions. We generalize a known formula for the improper integral with two functions Jυ (az) to the case with noninteger υ and complex a.
Monotone Boolean approximation
Energy Technology Data Exchange (ETDEWEB)
Hulme, B.L.
1982-12-01
This report presents a theory of approximation of arbitrary Boolean functions by simpler, monotone functions. Monotone increasing functions can be expressed without the use of complements. Nonconstant monotone increasing functions are important in their own right since they model a special class of systems known as coherent systems. It is shown here that when Boolean expressions for noncoherent systems become too large to treat exactly, then monotone approximations are easily defined. The algorithms proposed here not only provide simpler formulas but also produce best possible upper and lower monotone bounds for any Boolean function. This theory has practical application for the analysis of noncoherent fault trees and event tree sequences.
Light Scattering by Optically Soft Particles Theory and Applications
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.
On Convex Quadratic Approximation
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
Norton, Andrew H.
1991-01-01
Local spline approximants offer a means for constructing finite difference formulae for numerical solution of PDEs. These formulae seem particularly well suited to situations in which the use of conventional formulae leads to non-linear computational instability of the time integration. This is explained in terms of frequency responses of the FDF.
On Convex Quadratic Approximation
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
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...
Institute of Scientific and Technical Information of China (English)
Lanqing Xu; Hui Li; Yongping Zheng
2009-01-01
Monte Carlo algorithm and Stokes-Mueller formalism are used to simulate the propagation behavior of polarized light in turbid media. The influence of single scattering and multiple scattering on backscattered Mueller matrix in turbid media is discussed. Single and double scattering photons form the major part of backscattered polarization patterns, while multiple scattering photons present more likely as background. Further quantitative analyses show that single scattering approximation and double scattering approxima tion are quite accurate when discussing the polarization patterns near the incident point.
Light scattering by marine heterotrophic bacteria
Ulloa, Osvaldo; Sathyendranath, Shubha; Platt, Trevor; Quinones, Renato A.
1992-01-01
Mie theory is applied to estimate scattering by polydispersions of marine heterotrophic bacteria, and a simple expression is derived for the bacterial scattering coefficient. The error incurred in deriving bacterial optical properties by use of the van de Hulst approximations is computed. The scattering properties of natural bacterial assemblages in three marine environments, Georges Bank, Northeast Channel, and Sargasso Sea, are assessed by applying Mie theory to field data on bacterial size and abundance. Results are used to examine the potential contribution of bacteria to the scattering properties of seawater. The utility of using pigment data to predict the magnitude of scattering by bacteria is discussed.
Topology, calculus and approximation
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...
Prestack traveltime approximations
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.
A Two-Scale Reduced Model for Darcy Flow in Fractured Porous Media
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.
Contributions to the theory of a two-scale homogeneous dynamo experiment.
Rädler, Karl-Heinz; Brandenburg, Axel
2003-02-01
The principle of the two-scale dynamo experiment at the Forschungszentrum Karlsruhe is closely related to that of the Roberts dynamo working with a simple fluid flow which is, with respect to proper Cartesian coordinates x, y, and z, periodic in x and y and independent of z. A modified Roberts dynamo problem is considered with a flow more similar to that in the experimental device. Solutions are calculated numerically, and on this basis an estimate of the excitation condition of the experimental dynamo is given. The modified Roberts dynamo problem is also considered in the framework of the mean-field dynamo theory, in which the crucial induction effect of the fluid motion is an anisotropic alpha effect. Numerical results are given for the dependence of the mean-field coefficients on the fluid flow rates. The excitation condition of the dynamo is also discussed within this framework. The behavior of the dynamo in the nonlinear regime, i.e., with backreaction of the magnetic field on the fluid flow, depends on the effect of the Lorentz force on the flow rates. The quantities determining this effect are calculated numerically. The results for the mean-field coefficients and the quantities describing the backreaction provide corrections to earlier results, which were obtained under simplifying assumptions.
A Two-Scale Discretization Scheme for Mixed Variational Formulation of Eigenvalue Problems
Directory of Open Access Journals (Sweden)
Yidu Yang
2012-01-01
Full Text Available This paper discusses highly efficient discretization schemes for mixed variational formulation of eigenvalue problems. A new finite element two-scale discretization scheme is proposed by combining the mixed finite element method with the shifted-inverse power method for solving matrix eigenvalue problems. With this scheme, the solution of an eigenvalue problem on a fine grid Kh is reduced to the solution of an eigenvalue problem on a much coarser grid KH and the solution of a linear algebraic system on the fine grid Kh. Theoretical analysis shows that the scheme has high efficiency. For instance, when using the Mini element to solve Stokes eigenvalue problem, the resulting solution can maintain an asymptotically optimal accuracy by taking H=O(h4, and when using the Pk+1-Pk element to solve eigenvalue problems of electric field, the calculation results can maintain an asymptotically optimal accuracy by taking H=O(h3. Finally, numerical experiments are presented to support the theoretical analysis.
Numerical fatigue life assessment of cardiovascular stents: A two-scale plasticity-damage model
Santos, H. A. F. A.; Auricchio, F.; Conti, M.
2013-07-01
Cardiovascular disease has become a major global health care problem in the last decades. To tackle this problem, the use of cardiovascular stents has been considered a promising and effective approach. Numerical simulations to evaluate the in vivo behavior of stents are becoming more and more important to assess potential failures. As the material failure of a stent device has been often associated with fatigue issues, numerical approaches for fatigue life assessment of stents have gained special interest in the engineering community. Numerical fatigue life predictions can be used to modify the design and prevent failure without making and testing numerous physical devices, thus preventing from undesired fatigue failures. We present a numerical fatigue life model for the analysis of cardiovascular balloon-expandable stainless steel stents that can hopefully provide useful information either to be used for product improvement or for clinicians to make life-saving decisions. This model incorporates a two-scale continuum damage mechanics model and the so-called Soderberg fatigue failure criterion. We provide numerical results for both Palmaz-Schatz and Cypher stent designs and demonstrate that a good agreement is found between the numerical and the available experimental results.
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.
Two-Scale Modeling Approach to Predict Permeability of Fibrous Media
Directory of Open Access Journals (Sweden)
Sudhakar Jaganathan
2008-06-01
Full Text Available We previously demonstrated how one can develop a 3-D geometry to model the fibrous microstructure of a nonwoven fiberweb and use it to simulate its permeability at fiber level [1-6]. Developing 3-D models of most nonwoven fabrics (bonded fiberwebs, however, is cumbersome, as in the case of hydroentangled fabrics, for instance. In such cases, microscopic techniques are often used to generate 3-D images of the media’s microstructures. Nevertheless, whether the microstructure is modeled or obtained from 3-D imaging, extensive computational resources are required to use them in fluid flow simulations [7]. To circumvent this problem, a two-scale modeling approach is proposed here that allows us to simulate the entire thickness of a commercial fabric/filter on a personal computer. In particular, the microscale permeability of a hydroentangled nonwoven is computed using 3-D reconstructed microstructures obtained from Digital Volumetric Imaging (DVI. The resulting microstructural permeability tensors are then used in a macroscale porous model to simulate the flow through the material’s thickness and the calculation of its overall permeability.
Optimization and approximation
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.
Topics in Metric Approximation
Leeb, William Edward
This thesis develops effective approximations of certain metrics that occur frequently in pure and applied mathematics. We show that distances that often arise in applications, such as the Earth Mover's Distance between two probability measures, can be approximated by easily computed formulas for a wide variety of ground distances. We develop simple and easily computed characterizations both of norms measuring a function's regularity -- such as the Lipschitz norm -- and of their duals. We are particularly concerned with the tensor product of metric spaces, where the natural notion of regularity is not the Lipschitz condition but the mixed Lipschitz condition. A theme that runs throughout this thesis is that snowflake metrics (metrics raised to a power less than 1) are often better-behaved than ordinary metrics. For example, we show that snowflake metrics on finite spaces can be approximated by the average of tree metrics with a distortion bounded by intrinsic geometric characteristics of the space and not the number of points. Many of the metrics for which we characterize the Lipschitz space and its dual are snowflake metrics. We also present applications of the characterization of certain regularity norms to the problem of recovering a matrix that has been corrupted by noise. We are able to achieve an optimal rate of recovery for certain families of matrices by exploiting the relationship between mixed-variable regularity conditions and the decay of a function's coefficients in a certain orthonormal basis.
Scattering problems in elastodynamics
Diatta, Andre; Kadic, Muamer; Wegener, Martin; Guenneau, Sebastien
2016-09-01
In electromagnetism, acoustics, and quantum mechanics, scattering problems can routinely be solved numerically by virtue of perfectly matched layers (PMLs) at simulation domain boundaries. Unfortunately, the same has not been possible for general elastodynamic wave problems in continuum mechanics. In this Rapid Communication, we introduce a corresponding scattered-field formulation for the Navier equation. We derive PMLs based on complex-valued coordinate transformations leading to Cosserat elasticity-tensor distributions not obeying the minor symmetries. These layers are shown to work in two dimensions, for all polarizations, and all directions. By adaptative choice of the decay length, the deep subwavelength PMLs can be used all the way to the quasistatic regime. As demanding examples, we study the effectiveness of cylindrical elastodynamic cloaks of the Cosserat type and approximations thereof.
Scattering problems in elastodynamics
Diatta, Andre; Wegener, Martin; Guenneau, Sebastien
2016-01-01
In electromagnetism, acoustics, and quantum mechanics, scattering problems can routinely be solved numerically by virtue of perfectly matched layers (PMLs) at simulation domain boundaries. Unfortunately, the same has not been possible for general elastodynamic wave problems in continuum mechanics. In this paper, we introduce a corresponding scattered-field formulation for the Navier equation. We derive PMLs based on complex-valued coordinate transformations leading to Cosserat elasticity-tensor distributions not obeying the minor symmetries. These layers are shown to work in two dimensions, for all polarizations, and all directions. By adaptative choice of the decay length, the deep subwavelength PMLs can be used all the way to the quasi-static regime. As demanding examples, we study the effectiveness of cylindrical elastodynamic cloaks of the Cosserat type and approximations thereof.
Microscopic distorted wave theory of inelastic scattering
Energy Technology Data Exchange (ETDEWEB)
Picklesimer, A.; Tandy, P.C.; Thaler, R.M.
1982-03-01
An exact microscopic distorted wave theory of inelastic scattering is formulated which contains the physical picture usually associated with distorted wave approximations without the usual redundancy. This formulation encompasses the inelastic scattering of two fragments, elementary or composit (both with or without the full complexity of interfragment Pauli symmetries). The fact that these considerations need not be based upon elementary potential interactions is an indication of the generality of the approach and supports its applicability to inelastic meson scattering. This theory also maintains a description of inelastic scattering which is a natural extension of the description of elastic scattering and it provides a general basis for obtaining truncation models with an explicit distorted wave structure. This distorted wave impulse approximation is presented as an example of a particular truncation/approximation encompassed by this theory and the nature of the distorted waves is explicated.
Many-knot spline technique for approximation of data
Institute of Scientific and Technical Information of China (English)
齐东旭; 李华山
1999-01-01
A class of new fundamental functions with compact support called many-knot spline is introduced. The two-scale relation for the fundamental functions is investigated, and the higher order accuracy spline approximation scheme is constructed by using the available degrees of freedom which come from additional knots. The technique has been efficiently applied to the problems such as time-frequency analysis, computer aided geometric design, and digital signal processing.
Energy Technology Data Exchange (ETDEWEB)
Chalasani, P.; Saias, I. [Los Alamos National Lab., NM (United States); Jha, S. [Carnegie Mellon Univ., Pittsburgh, PA (United States)
1996-04-08
As increasingly large volumes of sophisticated options (called derivative securities) are traded in world financial markets, determining a fair price for these options has become an important and difficult computational problem. Many valuation codes use the binomial pricing model, in which the stock price is driven by a random walk. In this model, the value of an n-period option on a stock is the expected time-discounted value of the future cash flow on an n-period stock price path. Path-dependent options are particularly difficult to value since the future cash flow depends on the entire stock price path rather than on just the final stock price. Currently such options are approximately priced by Monte carlo methods with error bounds that hold only with high probability and which are reduced by increasing the number of simulation runs. In this paper the authors show that pricing an arbitrary path-dependent option is {number_sign}-P hard. They show that certain types f path-dependent options can be valued exactly in polynomial time. Asian options are path-dependent options that are particularly hard to price, and for these they design deterministic polynomial-time approximate algorithms. They show that the value of a perpetual American put option (which can be computed in constant time) is in many cases a good approximation to the value of an otherwise identical n-period American put option. In contrast to Monte Carlo methods, the algorithms have guaranteed error bounds that are polynormally small (and in some cases exponentially small) in the maturity n. For the error analysis they derive large-deviation results for random walks that may be of independent interest.
Zhang, Lu; Chen, Xingyu; Zhang, Zhenxi; Chen, Wei; Zhao, Hong; Zhao, Xin; Li, Kaixing; Yuan, Li
2016-04-01
Scattering pulse is sensitive to the morphology and components of each single label-free cell. The most direct detection result, label free cell's scattering pulse is studied in this paper as a novel trait to recognize large malignant cells from small normal cells. A set of intrinsic scattering pulse calculation method is figured out, which combines both hydraulic focusing theory and small particle's scattering principle. Based on the scattering detection angle ranges of widely used flow cytometry, the scattering pulses formed by cell scattering energy in forward scattering angle 2°-5° and side scattering angle 80°-110° are discussed. Combining the analysis of cell's illuminating light energy, the peak, area, and full width at half maximum (FWHM) of label free cells' scattering pulses for fine structure cells with diameter 1-20 μm are studied to extract the interrelations of scattering pulse's features and cell's morphology. The theoretical and experimental results show that cell's diameter and FWHM of its scattering pulse agree with approximate linear distribution; the peak and area of scattering pulse do not always increase with cell's diameter becoming larger, but when cell's diameter is less than about 16 μm the monotone increasing relation of scattering pulse peak or area with cell's diameter can be obtained. This relationship between the features of scattering pulse and cell's size is potentially a useful but very simple criterion to distinguishing malignant and normal cells by their sizes and morphologies in label free cells clinical examinations.
Finite elements and approximation
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
Energy Technology Data Exchange (ETDEWEB)
Friedrich, Harald [Technische Univ. Muenchen, Garching (Germany). Physik-Department
2013-08-01
Written by the author of the widely acclaimed textbook. Theoretical Atomic Physics Includes sections on quantum reflection, tunable Feshbach resonances and Efimov states. Useful for advanced students and researchers. This book presents a concise and modern coverage of scattering theory. 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. 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. The level of abstraction is kept as low as at all possible, and deeper questions related to mathematical foundations of scattering theory are passed by. The book should be understandable for anyone with a basic knowledge of nonrelativistic quantum mechanics. It is intended for advanced students and researchers, and it is hoped that it will be useful for theorists and experimentalists alike.
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...
Institute of Scientific and Technical Information of China (English)
Xiao-Hong Wang; Zheng-Feng Liu; Xiao-Xia Lu
2011-01-01
With the two-scale expansion technique proposed by Yoshizawa,the turbulent fluctuating field is expanded around the isotropic field.At a low-order two-scale expansion,applying the mode coupling approximation in the Yakhot-Orszag renormalization group method to analyze the fluctuating field,the Reynolds-average terms in the Reynolds stress transport equation,such as the convective term,the pressure-gradient-velocity correlation term and the dissipation term,are modeled.Two numerical examples:turbulent flow past a backward-facing step and the fully developed flow in a rotating channel,are presented for testing the efficiency of the proposed second-order model.For these two numerical examples,the proposed model performs as well as the Gibson-Launder (GL) model,giving better prediction than the standard k-ε model,especially in the abilities to calculate the secondary flow in the backward-facing step flow and to capture the asymmetric turbulent structure caused by frame rotation.
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.
Hierarchy in chaotic scattering in Hill's problem
Kovács, Z
1997-01-01
Hierarchic properties of chaotic scattering in a model of satellite encounters, studied first by Petit and Henon, are examined by decomposing the dwell time function and comparing scattering trajectories. The analysis reveals an (approximate) ternary organization in the chaotic set of bounded orbits and the presence of a stable island. The results can open the way for a calculation of global quantities characterizing the scattering process by using tools of the thermodynamic formalism.
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.
Roy, Swapnoneel; Thakur, Ashok Kumar
2008-01-01
Genome rearrangements have been modelled by a variety of primitives such as reversals, transpositions, block moves and block interchanges. We consider such a genome rearrangement primitive Strip Exchanges. Given a permutation, the challenge is to sort it by using minimum number of strip exchanges. A strip exchanging move interchanges the positions of two chosen strips so that they merge with other strips. The strip exchange problem is to sort a permutation using minimum number of strip exchanges. We present here the first non-trivial 2-approximation algorithm to this problem. We also observe that sorting by strip-exchanges is fixed-parameter-tractable. Lastly we discuss the application of strip exchanges in a different area Optical Character Recognition (OCR) with an example.
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...... projection of the surface onto this plane, a reference curve is determined by use of methods for thinning of binary images. Finally, the cylinder surface is constructed as follows: the directrix of the cylinder surface is determined by a least squares method minimizing the distance to the points...... in the projection within a tolerance given by the reference curve, and the rulings are lines perpendicular to the projection plane. Application of the method in ship design is given....
S-Approximation: A New Approach to Algebraic Approximation
Directory of Open Access Journals (Sweden)
M. R. Hooshmandasl
2014-01-01
Full Text Available We intend to study a new class of algebraic approximations, called S-approximations, and their properties. We have shown that S-approximations can be used for applied problems which cannot be modeled by inclusion based approximations. Also, in this work, we studied a subclass of S-approximations, called Sℳ-approximations, and showed that this subclass preserves most of the properties of inclusion based approximations but is not necessarily inclusionbased. The paper concludes by studying some basic operations on S-approximations and counting the number of S-min functions.
Lie, Désirée Annabel; Fung, Cha Chi; Trial, Janet; Lohenry, Kevin
2013-01-01
Rationale The validated 19-item Readiness for Interprofessional Learning Scale (RIPLS) is often used for assessing attitudes toward interprofessional education (IPE). The 12-item Interdisciplinary Education Perception Scale (IEPS), also used for this purpose, has not been validated among the professions of medicine, pharmacy, and physician assistants (PAs). The discriminatory ability of the two scales has not been directly compared. Comparison of the two will aid educators in selecting the optimal scale. Objective To compare psychometric properties of the RIPLS and IEPS and to examine the ability of each scale to discriminate mean scores among student subgroups (gender, profession, seniority, and prior IPE exposure). Method We conducted a cross-sectional (Qualtrics©) survey (RIPLS and IEPS) of junior and senior students in medicine (n=360), pharmacy (n=360), and the PA profession (n=106). Descriptive statistics were used to report aggregate mean scores of subgroups. The internal consistency of each scale was assessed using Cronbach's α. Concurrent validity was measured by Pearson's correlation coefficients. Independent-sample t-tests and analysis of variances (ANOVAs) were performed to assess the discriminatory ability of each scale. Cohen's d effect sizes were calculated for all significant pair-wise comparisons. Results Response rate was 82%. Cronbach's α was 0.85 (RIPLS) and 0.91 (IEPS). The RIPLS discriminated scores by gender among junior students only, and scores by IPE exposure among all students. The IEPS distinguished score differences for the three professions among junior students and by prior IPE exposure for all three professions. Neither scale detected differences in mean scores by profession among all students or by level of training among the three professions. Conclusions Neither the RIPLS nor the IEPS has greater discriminatory ability for detecting attitude differences among the student subgroups. Reason for differences may be explained by
Directory of Open Access Journals (Sweden)
Désirée Annabel Lie
2013-12-01
Full Text Available Rationale : The validated 19-item Readiness for Interprofessional Learning Scale (RIPLS is often used for assessing attitudes toward interprofessional education (IPE. The 12-item Interdisciplinary Education Perception Scale (IEPS, also used for this purpose, has not been validated among the professions of medicine, pharmacy, and physician assistants (PAs. The discriminatory ability of the two scales has not been directly compared. Comparison of the two will aid educators in selecting the optimal scale. Objective : To compare psychometric properties of the RIPLS and IEPS and to examine the ability of each scale to discriminate mean scores among student subgroups (gender, profession, seniority, and prior IPE exposure. Method : We conducted a cross-sectional (Qualtrics© survey (RIPLS and IEPS of junior and senior students in medicine (n=360, pharmacy (n=360, and the PA profession (n=106. Descriptive statistics were used to report aggregate mean scores of subgroups. The internal consistency of each scale was assessed using Cronbach's α. Concurrent validity was measured by Pearson's correlation coefficients. Independent-sample t-tests and analysis of variances (ANOVAs were performed to assess the discriminatory ability of each scale. Cohen's d effect sizes were calculated for all significant pair-wise comparisons. Results : Response rate was 82%. Cronbach's α was 0.85 (RIPLS and 0.91 (IEPS. The RIPLS discriminated scores by gender among junior students only, and scores by IPE exposure among all students. The IEPS distinguished score differences for the three professions among junior students and by prior IPE exposure for all three professions. Neither scale detected differences in mean scores by profession among all students or by level of training among the three professions. Conclusions : Neither the RIPLS nor the IEPS has greater discriminatory ability for detecting attitude differences among the student subgroups. Reason for differences may be
Lie, Désirée Annabel; Fung, Cha Chi; Trial, Janet; Lohenry, Kevin
2013-12-02
The validated 19-item Readiness for Interprofessional Learning Scale (RIPLS) is often used for assessing attitudes toward interprofessional education (IPE). The 12-item Interdisciplinary Education Perception Scale (IEPS), also used for this purpose, has not been validated among the professions of medicine, pharmacy, and physician assistants (PAs). The discriminatory ability of the two scales has not been directly compared. Comparison of the two will aid educators in selecting the optimal scale. To compare psychometric properties of the RIPLS and IEPS and to examine the ability of each scale to discriminate mean scores among student subgroups (gender, profession, seniority, and prior IPE exposure). We conducted a cross-sectional (Qualtrics(©)) survey (RIPLS and IEPS) of junior and senior students in medicine (n=360), pharmacy (n=360), and the PA profession (n=106). Descriptive statistics were used to report aggregate mean scores of subgroups. The internal consistency of each scale was assessed using Cronbach's α. Concurrent validity was measured by Pearson's correlation coefficients. Independent-sample t-tests and analysis of variances (ANOVAs) were performed to assess the discriminatory ability of each scale. Cohen's d effect sizes were calculated for all significant pair-wise comparisons. Response rate was 82%. Cronbach's α was 0.85 (RIPLS) and 0.91 (IEPS). The RIPLS discriminated scores by gender among junior students only, and scores by IPE exposure among all students. The IEPS distinguished score differences for the three professions among junior students and by prior IPE exposure for all three professions. Neither scale detected differences in mean scores by profession among all students or by level of training among the three professions. Neither the RIPLS nor the IEPS has greater discriminatory ability for detecting attitude differences among the student subgroups. Reason for differences may be explained by slightly different scale constructs. The RIPLS
Dong, Hao; Nie, Yu-Feng; Cui, Jun-Zhi; Wu, Ya-Tao
2015-09-01
We study the hyperbolic-parabolic equations with rapidly oscillating coefficients. The formal second-order two-scale asymptotic expansion solutions are constructed by the multiscale asymptotic analysis. In addition, we theoretically explain the importance of the second-order two-scale solution by the error analysis in the pointwise sense. The associated explicit convergence rates are also obtained. Then a second-order two-scale numerical method based on the Newmark scheme is presented to solve the equations. Finally, some numerical examples are used to verify the effectiveness and efficiency of the multiscale numerical algorithm we proposed. Project supported by the National Natural Science Foundation of China (Grant No. 11471262), the National Basic Research Program of China (Grant No. 2012CB025904), and the State Key Laboratory of Science and Engineering Computing and the Center for High Performance Computing of Northwestern Polytechnical University, China.
Institute of Scientific and Technical Information of China (English)
LI Youyun; CUI Junzhi
2004-01-01
A two-scale analysis (TSA) method for predicting the heat transfer performance of composite materials with the random distribution of same-scale grains is presented. First the representation of the materials with the random distribution is briefly described. Then the two-scale analysis formulation of heat transfer behavior of the materials with random grain distribution of small periodicity is formally derived by means of construction way for each cell. Finally the numerical result on the heat transfer parameters of composite materials is shown. The numerical result shows that TSA is effective to predict the heat transfer performance of composite materials with random grain distribution.
Superradiant Forward Scattering in Multiple Scattering
Chabe, Julien; Bienaime, Tom; Bachelard, Romain; Piovella, Nicola; Kaiser, Robin
2012-01-01
We report on an interference effect in multiple scattering by resonant scatterers resulting in enhanced forward scattering, violating Ohm's law for photons. The underlying mechanism of this wave effect is superradiance, which we have investigated using cold atoms as a toy model. We present numerical and experimental evidences for this superradiant forward scattering, which is robust against disorder and configuration averaging.
Prestack traveltime approximations
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.
A Quasiclassical Approximation in the Theory of the Landau-Pomeranchuk Effect
Tarasov, A V; Voskresenskaya, O O
2012-01-01
With the use of revised within the quasiclassical approximation the values of parameters of the Moliere multiple scattering theory it is shown that the best agreement of the Migdal theory of the LPM-effect with experiment achieved if to describe the electron-atomic scattering the quasiclassical approximation is used instead of the traditionally used Born one.
Approximate formulas for moderately small eikonal amplitudes
Kisselev, A V
2015-01-01
The eikonal approximation for moderately small scattering amplitudes is considered. With the purpose of using for their numerical estimations, the formulas are derived which contain no Bessel functions, and, hence, no rapidly oscillating integrands. To obtain these formulas, the improper integrals of the first kind which contain products of the Bessel functions J_0(z) are studied. The expression with four functions J_0(z) is generalized. The expressions for the integrals with the product of five and six Bessel functions J_0(z) are also found. The known formula for the improper integral with two functions J_nu(z) is generalized for non-integer nu.
Proximity effect correction concerning forward scattering
Tsunoda, Dai; Shoji, Masahiro; Tsunoe, Hiroyuki
2010-09-01
The Proximity Effect is a critical problem in EB Lithography which is used in Photomask writing. Proximity Effect means that an electron shot by gun scatters by collided with resist molecule or substrate atom causes CD variation depending on pattern density [1]. Scattering by collision with resist molecule is called as "forward scattering", that affects in dozens of nanometer range, and with substrate atom is called as "backward scattering, that affects approximately 10 micrometer in 50keV acceleration voltage respectively. In conventional Proximity Effect Correction (PEC) for mask writing, we don't need to think forward scattering effect. However we should think about forward scattering because of smaller feature size. We have proposed a PEC software product named "PATACON PC-Cluster"[2], which can concern forward scattering and calculate optimum dose modulation. In this communication, we explain the PEC processing throughput when the that takes forward scattering into account. The key technique is to use different processing field size for forward scattering calculation. Additionally, the possibility is shown that effective PEC may be available by connecting forward scattering and backward scattering.
The Scattering of Fast Nucleons from Nuclei
Kerman, A. K.; McManus, H.; Thaler, R. M.
2000-04-01
The formal theory of the scattering of high-energy nucleons by nuclei is developed in terms of the nucleon-nucleon scattering amplitude. The most important approximations necessary to make numerical calculation feasible are then examined. The optical model potential is derived on this basis and compared with the optical model parameters found from experiment. The elastic scattering and polarization of nucleons from light nuclei is predicted and compared with experiment. The effect of nuclear correlations is discussed. The polarization of inelastically scattered nucleons is discussed and predictions compared with experiments. To within the validity of the approximations the experimental data on the scattering of nucleons from nuclei at energies above ˜100 Mev appears to be consistent with the theory.
The scattering of fast nucleons from nuclei
Energy Technology Data Exchange (ETDEWEB)
Kerman, A. K. [Massachusetts Institute of Technology, Cambridge, Massachusetts (United States); McManus, H. [Chalk River Laboratory, Chalk River, Ontario, (Canada); Thaler, R. M. [Los Alamos Scientific Laboratory, Los Alamos, New Mexico (United States)
2000-04-10
The formal theory of the scattering of high-energy nucleons by nuclei is developed in terms of the nucleon nucleon scattering amplitude. The most important approximations necessary to make numerical calculation feasible are then examined. The optical model potential is derived on this basis and compared with the optical model parameters found from experiment. The elastic scattering and polarization of nucleons from light nuclei is predicted and compared with experiment. The effect of nuclear correlations is discussed. The polarization of inelastically scattered nucleons is discussed and predictions compared with experiments. To within the validity of the approximations the experimental data on the scattering of nucleons from nuclei at energies above {approx}100 Mev appears to be consistent with the theory. (c) 2000 Academic Press, Inc.
Operators of Approximations and Approximate Power Set Spaces
Institute of Scientific and Technical Information of China (English)
ZHANG Xian-yong; MO Zhi-wen; SHU Lan
2004-01-01
Boundary inner and outer operators are introduced; and union, intersection, complement operators of approximations are redefined. The approximation operators have a good property of maintaining union, intersection, complement operators, so the rough set theory has been enriched from the operator-oriented and set-oriented views. Approximate power set spaces are defined, and it is proved that the approximation operators are epimorphisms from power set space to approximate power set spaces. Some basic properties of approximate power set space are got by epimorphisms in contrast to power set space.
International Conference Approximation Theory XV
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...
Relativistic Coulomb scattering of spinless bosons
Garcia, M G
2015-01-01
The relativistic scattering of spin-0 bosons by spherically symmetric Coulomb fields is analyzed in detail with an arbitrary mixing of vector and scalar couplings. It is shown that the partial wave series reduces the scattering amplitude to the closed Rutherford formula exactly when the vector and scalar potentials have the same magnitude, and as an approximation for weak fields. The behavior of the scattering amplitude near the conditions that furnish its closed form is also discussed. Strong suppressions of the scattering amplitude when the vector and scalar potentials have the same magnitude are observed either for particles or antiparticles with low incident momentum. We point out that such strong suppressions might be relevant in the analysis of the scattering of fermions near the conditions for the spin and pseudospin symmetries. From the complex poles of the partial scattering amplitude the exact closed form of bound-state solutions for both particles and antiparticles with different scenarios for the ...
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.
Radiative transfer in disc galaxies $-$ V. The accuracy of the KB approximation
Lee, Dukhang; Seon, Kwang-Il; Camps, Peter; Verstocken, Sam; Han, Wonyong
2016-01-01
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 ($i \\gtrsim 85^{\\circ}$) and/or optically thick (central face-on optical depth $\\gtrsim1$) galaxy models, the approximation can give rise to substantial errors, sometimes, up to $\\gtrsim 40\\%$. Moreover, it is also found that the KB approximation is not always physical, sometimes producing infinite inten...
Uranium and radon in private bedrock well water in Maine: geospatial analysis at two scales
Yang, Qiang; Smitherman, Paul; Hess, C.T.; Culbertson, Charles W.; Marvinney, Robert G.; Zheng, Yan
2014-01-01
In greater Augusta of central Maine, 53 out of 1093 (4.8%) private bedrock well water samples from 1534 km2 contained [U] >30 μg/L, the U.S. Environmental Protection Agency’s (EPA) Maximum Contaminant Level (MCL) for drinking water; and 226 out of 786 (29%) samples from 1135 km2 showed [Rn] >4,000 pCi/L (148 Bq/L), the U.S. EPA’s Alternative MCL. Groundwater pH, calcite dissolution and redox condition are factors controlling the distribution of groundwater U but not Rn due to their divergent chemical and hydrological properties. Groundwater U is associated with incompatible elements (S, As, Mo, F, and Cs) in water samples within granitic intrusions. Elevated [U] and [Rn] are located within 5–10 km distance of granitic intrusions but do not show correlations with metamorphism at intermediate scales (100−101 km). This spatial association is confirmed by a high-density sampling (n = 331, 5–40 samples per km2) at local scales (≤10–1 km) and the statewide sampling (n = 5857, 1 sample per 16 km2) at regional scales (102–103 km). Wells located within 5 km of granitic intrusions are at risk of containing high levels of [U] and [Rn]. Approximately 48 800–63 900 and 324 000 people in Maine are estimated at risk of exposure to U (>30 μg/L) and Rn (>4000 pCi/L) in well water, respectively.
Uranium and radon in private bedrock well water in Maine: geospatial analysis at two scales.
Yang, Qiang; Smitherman, Paul; Hess, C T; Culbertson, Charles W; Marvinney, Robert G; Smith, Andrew E; Zheng, Yan
2014-04-15
In greater Augusta of central Maine, 53 out of 1093 (4.8%) private bedrock well water samples from 1534 km(2) contained [U] >30 μg/L, the U.S. Environmental Protection Agency's (EPA) Maximum Contaminant Level (MCL) for drinking water; and 226 out of 786 (29%) samples from 1135 km(2) showed [Rn] >4,000 pCi/L (148 Bq/L), the U.S. EPA's Alternative MCL. Groundwater pH, calcite dissolution and redox condition are factors controlling the distribution of groundwater U but not Rn due to their divergent chemical and hydrological properties. Groundwater U is associated with incompatible elements (S, As, Mo, F, and Cs) in water samples within granitic intrusions. Elevated [U] and [Rn] are located within 5-10 km distance of granitic intrusions but do not show correlations with metamorphism at intermediate scales (10(0)-10(1) km). This spatial association is confirmed by a high-density sampling (n = 331, 5-40 samples per km(2)) at local scales (≤10(-1) km) and the statewide sampling (n = 5857, 1 sample per 16 km(2)) at regional scales (10(2)-10(3) km). Wells located within 5 km of granitic intrusions are at risk of containing high levels of [U] and [Rn]. Approximately 48 800-63 900 and 324 000 people in Maine are estimated at risk of exposure to U (>30 μg/L) and Rn (>4000 pCi/L) in well water, respectively.
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.
Hierarchical low-rank approximation for high dimensional approximation
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.
Helium atom scattering from surfaces
1992-01-01
High resolution helium atom scattering can be applied to study a number of interesting properties of solid surfaces with great sensitivity and accuracy. This book treats in detail experimental and theoretical aspects ofthis method as well as all current applications in surface science. The individual chapters - all written by experts in the field - are devoted to the investigation of surface structure, defect shapes and concentrations, the interaction potential, collective and localized surface vibrations at low energies, phase transitions and surface diffusion. Over the past decade helium atom scattering has gained widespread recognitionwithin the surface science community. Points in its favour are comprehensiveunderstanding of the scattering theory and the availability of well-tested approximation to the rigorous theory. This book will be invaluable to surface scientists wishing to make an informed judgement on the actual and potential capabilities of this technique and its results.
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.
Positron-alkali atom scattering
Mceachran, R. P.; Horbatsch, M.; Stauffer, A. D.; Ward, S. J.
1990-01-01
Positron-alkali atom scattering was recently investigated both theoretically and experimentally in the energy range from a few eV up to 100 eV. On the theoretical side calculations of the integrated elastic and excitation cross sections as well as total cross sections for Li, Na and K were based upon either the close-coupling method or the modified Glauber approximation. These theoretical results are in good agreement with experimental measurements of the total cross section for both Na and K. Resonance structures were also found in the L = 0, 1 and 2 partial waves for positron scattering from the alkalis. The structure of these resonances appears to be quite complex and, as expected, they occur in conjunction with the atomic excitation thresholds. Currently both theoretical and experimental work is in progress on positron-Rb scattering in the same energy range.
On scattered subword complexity
Kása, Zoltán
2011-01-01
Special scattered subwords, in which the gaps are of length from a given set, are defined. The scattered subword complexity, which is the number of such scattered subwords, is computed for rainbow words.
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.
Nonlinear Approximation Using Gaussian Kernels
Hangelbroek, Thomas
2009-01-01
It is well-known that non-linear approximation has an advantage over linear schemes in the sense that it provides comparable approximation rates to those of the linear schemes, but to a larger class of approximands. This was established for spline approximations and for wavelet approximations, and more recently for homogeneous radial basis function (surface spline) approximations. However, no such results are known for the Gaussian function. The crux of the difficulty lies in the necessity to vary the tension parameter in the Gaussian function spatially according to local information about the approximand: error analysis of Gaussian approximation schemes with varying tension are, by and large, an elusive target for approximators. We introduce and analyze in this paper a new algorithm for approximating functions using translates of Gaussian functions with varying tension parameters. Our scheme is sophisticated to a degree that it employs even locally Gaussians with varying tensions, and that it resolves local ...
Forms of Approximate Radiation Transport
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.
Approximation by Multivariate Singular Integrals
Anastassiou, George A
2011-01-01
Approximation by Multivariate Singular Integrals is the first monograph to illustrate the approximation of multivariate singular integrals to the identity-unit operator. The basic approximation properties of the general multivariate singular integral operators is presented quantitatively, particularly special cases such as the multivariate Picard, Gauss-Weierstrass, Poisson-Cauchy and trigonometric singular integral operators are examined thoroughly. This book studies the rate of convergence of these operators to the unit operator as well as the related simultaneous approximation. The last cha
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
Approximations of fractional Brownian motion
Li, Yuqiang; 10.3150/10-BEJ319
2012-01-01
Approximations of fractional Brownian motion using Poisson processes whose parameter sets have the same dimensions as the approximated processes have been studied in the literature. In this paper, a special approximation to the one-parameter fractional Brownian motion is constructed using a two-parameter Poisson process. The proof involves the tightness and identification of finite-dimensional distributions.
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....
Bidirectional optical scattering facility
Federal Laboratory Consortium — Goniometric optical scatter instrument (GOSI)The bidirectional reflectance distribution function (BRDF) quantifies the angular distribution of light scattered from a...
Bidirectional optical scattering facility
Federal Laboratory Consortium — Goniometric optical scatter instrument (GOSI) The bidirectional reflectance distribution function (BRDF) quantifies the angular distribution of light scattered from...
Gluon transport equations with condensate in the small angle approximation
Energy Technology Data Exchange (ETDEWEB)
Blaizot, Jean-Paul [Institut de Physique Théorique (IPhT), CNRS/URA2306, CEA Saclay, F-91191 Gif-sur-Yvette (France); Liao, Jinfeng [Physics Department and Center for Exploration of Energy and Matter, Indiana University, 2401 N Milo B. Sampson Lane, Bloomington, IN 47408 (United States); RIKEN BNL Research Center, Bldg. 510A, Brookhaven National Laboratory, Upton, NY 11973 (United States)
2016-05-15
We derive the set of kinetic equations that control the evolution of gluons in the presence of a condensate. We show that the dominant singularities remain logarithmic when the scattering involves particles in the condensate. This allows us to define a consistent small angle approximation.
International Conference Approximation Theory XIV
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.
Exact constants in approximation theory
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
Coherence effects in scattering order expansion of light by atomic clouds
Rouabah, Mohamed-Taha; Bachelard, Romain; Courteille, Philippe W; Kaiser, Robin; Piovella, Nicola
2014-01-01
We interpret cooperative scattering by a collection of cold atoms as a multiple scattering process. Starting from microscopic equations describing the response of $N$ atoms to a probe light beam, we represent the total scattered field as an infinite series of multiple scattering events. As an application of the method, we obtain analytical expressions of the coherent intensity in the double scattering approximation for Gaussian density profiles. In particular, we quantify the contributions of coherent backward and forward scattering.
Coherence effects in scattering order expansion of light by atomic clouds.
Rouabah, Mohamed-Taha; Samoylova, Marina; Bachelard, Romain; Courteille, Philippe W; Kaiser, Robin; Piovella, Nicola
2014-05-01
We interpret cooperative scattering by a collection of cold atoms as a multiple-scattering process. Starting from microscopic equations describing the response of N atoms to a probe light beam, we represent the total scattered field as an infinite series of multiple-scattering events. As an application of the method, we obtain analytical expressions of the coherent intensity in the double-scattering approximation for Gaussian density profiles. In particular, we quantify the contributions of coherent backward and forward scattering.
On the choice of phase in the CS approximation: Integral equation approach
Snider, R. F.
1986-10-01
As usually presented, the centrifugal sudden approximation examines how each individual angular momentum component of the scattering wave function and scattering matrix element is to be estimated. Here the three-dimensional structure of the scattering wave function is emphasized and any decisions about associating exact and approximate partial waves with correcting phase factors are put off till the implications on the three-dimensional wave function have been made clear. It is found that no correcting phase factor needs to be applied to the CS S matrix when estimating the exact S matrix, while at the same time, the asymptotic behavior of the exact and approximating wave functions has the same form. Direct and operator methods of estimating the transition matrix confirm this conclusion. A suggested modification of how the sudden approximations are to be implemented allows the weak potential limit of the resulting scattering amplitudes to reduce to the Born approximation.
Conference on Abstract Spaces and Approximation
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...
Generalized Quasilinear Approximation: Application to Zonal Jets
Marston, J. B.; Chini, G. P.; Tobias, S. M.
2016-05-01
Quasilinear theory is often utilized to approximate the dynamics of fluids exhibiting significant interactions between mean flows and eddies. We present a generalization of quasilinear theory to include dynamic mode interactions on the large scales. This generalized quasilinear (GQL) approximation is achieved by separating the state variables into large and small zonal scales via a spectral filter rather than by a decomposition into a formal mean and fluctuations. Nonlinear interactions involving only small zonal scales are then removed. The approximation is conservative and allows for scattering of energy between small-scale modes via the large scale (through nonlocal spectral interactions). We evaluate GQL for the paradigmatic problems of the driving of large-scale jets on a spherical surface and on the beta plane and show that it is accurate even for a small number of large-scale modes. As GQL is formally linear in the small zonal scales, it allows for the closure of the system and can be utilized in direct statistical simulation schemes that have proved an attractive alternative to direct numerical simulation for many geophysical and astrophysical problems.
Electromagnetic Fields Restrictions and Approximation
Katsenelenbaum, Boris Z
2003-01-01
The fields scattered by metallic bodies or radiated by some types of antennas are created by the surfaces currents and therefore they are subject to some restrictions. The book is the first one where the properties of these fields are investigated in details. The properties have the important significance for the antenna synthesis, body shape reconstruction and other diffraction problems. The material of the book lies in the meetingpoint of the antenna theory, highfrequency electrodynamics and inverse scattering problems. The author is an internationally renowned investigator in the field of e
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)
BDD Minimization for Approximate Computing
Soeken, Mathias; Grosse, Daniel; Chandrasekharan, Arun; Drechsler, Rolf
2016-01-01
We present Approximate BDD Minimization (ABM) as a problem that has application in approximate computing. Given a BDD representation of a multi-output Boolean function, ABM asks whether there exists another function that has a smaller BDD representation but meets a threshold w.r.t. an error metric. We present operators to derive approximated functions and present algorithms to exactly compute the error metrics directly on the BDD representation. An experimental evaluation demonstrates the app...
Tree wavelet approximations with applications
Institute of Scientific and Technical Information of China (English)
XU Yuesheng; ZOU Qingsong
2005-01-01
We construct a tree wavelet approximation by using a constructive greedy scheme(CGS). We define a function class which contains the functions whose piecewise polynomial approximations generated by the CGS have a prescribed global convergence rate and establish embedding properties of this class. We provide sufficient conditions on a tree index set and on bi-orthogonal wavelet bases which ensure optimal order of convergence for the wavelet approximations encoded on the tree index set using the bi-orthogonal wavelet bases. We then show that if we use the tree index set associated with the partition generated by the CGS to encode a wavelet approximation, it gives optimal order of convergence.
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)
Imaging with Scattered Neutrons
Ballhausen, H.; Abele, H.; Gaehler, R.; Trapp, M.; Van Overberghe, A.
2006-01-01
We describe a novel experimental technique for neutron imaging with scattered neutrons. These scattered neutrons are of interest for condensed matter physics, because they permit to reveal the local distribution of incoherent and coherent scattering within a sample. In contrast to standard attenuation based imaging, scattered neutron imaging distinguishes between the scattering cross section and the total attenuation cross section including absorption. First successful low-noise millimeter-re...
Investigating Static and Dynamic Light Scattering
Sun, Yong
2011-01-01
A new size, static radii $R_{s}$, can be measured accurately using Static Light Scattering (SLS) technique when the Rayleigh-Gans-Debye approximation is valid for dilute homogenous spherical particles in dispersion. The method proposed in this work not only can measures the particle size distribution and average molar mass accurately but also enables us to explore Dynamic Light Scattering (DLS) technique further. Detailed investigation of the normalized time auto-correlation function of the scattered light intensity $g^{2)}(\\tau)$ shows that the measurements of DLS can be expected accurately and the static and hydrodynamic radii of nanoparticles are different. Only at some special conditions, the Z-average hydrodynamic radius can be measured accurately at a given scattering angle. The fact that the values of average hydrodynamic radius measured at different scattering angles are consistent or the values of polydispersity index are small does not mean the particle size distribution is narrow or monodisperse.
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...
Medium energy hadron scattering from nuclei
Energy Technology Data Exchange (ETDEWEB)
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 ..gamma.. unstable rotor, and both prolate and oblate axially symmetric rotors. We give examples of application of this formalism to proton scattering from /sup 154/Sm and /sup 154/Gd. 27 refs., 5 figs., 1 tab.
Diophantine approximation and automorphic spectrum
Ghosh, Anish; Nevo, Amos
2010-01-01
The present paper establishes qunatitative estimates on the rate of diophantine approximation in homogeneous varieties of semisimple algebraic groups. The estimates established generalize and improve previous ones, and are sharp in a number of cases. We show that the rate of diophantine approximation is controlled by the spectrum of the automorphic representation, and is thus subject to the generalised Ramanujan conjectures.
Some results in Diophantine approximation
DEFF Research Database (Denmark)
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...
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...
Uniform approximation by (quantum) polynomials
Drucker, A.; de Wolf, R.
2011-01-01
We show that quantum algorithms can be used to re-prove a classical theorem in approximation theory, Jackson's Theorem, which gives a nearly-optimal quantitative version of Weierstrass's Theorem on uniform approximation of continuous functions by polynomials. We provide two proofs, based respectivel
Global approximation of convex functions
Azagra, D
2011-01-01
We show that for every (not necessarily bounded) open convex subset $U$ of $\\R^n$, every (not necessarily Lipschitz or strongly) convex function $f:U\\to\\R$ can be approximated by real analytic convex functions, uniformly on all of $U$. In doing so we provide a technique which transfers results on uniform approximation on bounded sets to results on uniform approximation on unbounded sets, in such a way that not only convexity and $C^k$ smoothness, but also local Lipschitz constants, minimizers, order, and strict or strong convexity, are preserved. This transfer method is quite general and it can also be used to obtain new results on approximation of convex functions defined on Riemannian manifolds or Banach spaces. We also provide a characterization of the class of convex functions which can be uniformly approximated on $\\R^n$ by strongly convex functions.
Approximate circuits for increased reliability
Energy Technology Data Exchange (ETDEWEB)
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.
Approximate circuits for increased reliability
Energy Technology Data Exchange (ETDEWEB)
Hamlet, Jason R.; Mayo, Jackson R.
2015-12-22
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.
A surface-scattering model satisfying energy conservation and reciprocity
Sasihithlu, Karthik; Hugonin, Jean-Paul; Greffet, Jean-Jacques
2015-01-01
In order for surface scattering models to be accurate they must necessarily satisfy energy conservation and reciprocity principles. Roughness scattering models based on Kirchoff's approximation or perturbation theory do not satisfy these criteria in all frequency ranges. Here we present a surface scattering model based on analysis of scattering from a layer of particles on top of a substrate in the dipole approximation which satisfies both energy conservation and reciprocity and is thus accurate in all frequency ranges. The model takes into account the absorption in the substrate induced by the particles but does not take into account the near-field interactions between the particles.
Soft Gluon Radiation off Heavy Quarks beyond Eikonal Approximation
Directory of Open Access Journals (Sweden)
Trambak Bhattacharyya
2016-01-01
Full Text Available 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.
Eikonal quantum gravity and Planckian scattering
Kabat, D; Kabat, Dan; Ortiz, Miguel
1992-01-01
Various approaches to high energy forward scattering in quantum gravity are compared using the eikonal approximation. The massless limit of the eikonal is shown to be equivalent to other approximations for the same process, specifically the semiclassical calculation due to G. 't Hooft and the topological field theory due to H. and E. Verlinde. This comparison clarifies these previous results, as it is seen that the amplitude arises purely from a linearised gravitational interaction. The interpretation of poles in the scattering amplitude is also clarified.
High Energy Asymptotics of the Scattering Amplitude for the Schrödinger Equation
Indian Academy of Sciences (India)
D Yafaev
2002-02-01
We find an explicit function approximating at high energies the kernel of the scattering matrix with arbitrary accuracy. Moreover, the same function gives all diagonal singularities of the kernel of the scattering matrix in the angular variables.
Scattering of electrons from neon atoms
Dasgupta, A.; Bhatia, A. K.
1984-01-01
Scattering of electrons from neon atoms is investigated by the polarized-orbital method. The perturbed orbitals calculated with use of the Sternheimer approximation lead to the polarizability 2.803 a(0)-cube in fairly good agreement with the experimental value 2.66 a(0)-cube. Phase shifts for various partial waves are calculated in the exchange, exchange-adiabatic, and polarized-orbital approximations. They are compared with the previous results. The calculated elastic differential, total, and momentum-transfer cross sections are compared with the experimental results. The polarized-orbital approximation yields results which show general improvement over the exchange-adiabatic approximation.
Rollout sampling approximate policy iteration
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
Approximate common divisors via lattices
Cohn, Henry
2011-01-01
We analyze the multivariate generalization of Howgrave-Graham's algorithm for the approximate common divisor problem. In the m-variable case with modulus N and approximate common divisor of size N^beta, this improves the size of the error tolerated from N^(beta^2) to N^(beta^((m+1)/m)), under a commonly used heuristic assumption. This gives a more detailed analysis of the hardness assumption underlying the recent fully homomorphic cryptosystem of van Dijk, Gentry, Halevi, and Vaikuntanathan. While these results do not challenge the suggested parameters, a 2^sqrt(n) approximation algorithm for lattice basis reduction in n dimensions could be used to break these parameters. We have implemented our algorithm, and it performs better in practice than the theoretical analysis suggests. Our results fit into a broader context of analogies between cryptanalysis and coding theory. The multivariate approximate common divisor problem is the number-theoretic analogue of noisy multivariate polynomial interpolation, and we ...
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.
Binary nucleation beyond capillarity approximation
Kalikmanov, V.I.
2010-01-01
Large discrepancies between binary classical nucleation theory (BCNT) and experiments result from adsorption effects and inability of BCNT, based on the phenomenological capillarity approximation, to treat small clusters. We propose a model aimed at eliminating both of these deficiencies. Adsorption
Weighted approximation with varying weight
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.
Nonlinear approximation with redundant dictionaries
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, M.; Gribonval, R.
2005-01-01
In this paper we study nonlinear approximation and data representation with redundant function dictionaries. In particular, approximation with redundant wavelet bi-frame systems is studied in detail. Several results for orthonormal wavelets are generalized to the redundant case. In general......, for a wavelet bi-frame system the approximation properties are limited by the number of vanishing moments of the system. In some cases this can be overcome by oversampling, but at a price of replacing the canonical expansion by another linear expansion. Moreover, for special non-oversampled wavelet bi-frames we...... can obtain good approximation properties not restricted by the number of vanishing moments, but again without using the canonical expansion....
Mathematical algorithms for approximate reasoning
Murphy, John H.; Chay, Seung C.; Downs, Mary M.
1988-01-01
Most state of the art expert system environments contain a single and often ad hoc strategy for approximate reasoning. Some environments provide facilities to program the approximate reasoning algorithms. However, the next generation of expert systems should have an environment which contain a choice of several mathematical algorithms for approximate reasoning. To meet the need for validatable and verifiable coding, the expert system environment must no longer depend upon ad hoc reasoning techniques but instead must include mathematically rigorous techniques for approximate reasoning. Popular approximate reasoning techniques are reviewed, including: certainty factors, belief measures, Bayesian probabilities, fuzzy logic, and Shafer-Dempster techniques for reasoning. A group of mathematically rigorous algorithms for approximate reasoning are focused on that could form the basis of a next generation expert system environment. These algorithms are based upon the axioms of set theory and probability theory. To separate these algorithms for approximate reasoning various conditions of mutual exclusivity and independence are imposed upon the assertions. Approximate reasoning algorithms presented include: reasoning with statistically independent assertions, reasoning with mutually exclusive assertions, reasoning with assertions that exhibit minimum overlay within the state space, reasoning with assertions that exhibit maximum overlay within the state space (i.e. fuzzy logic), pessimistic reasoning (i.e. worst case analysis), optimistic reasoning (i.e. best case analysis), and reasoning with assertions with absolutely no knowledge of the possible dependency among the assertions. A robust environment for expert system construction should include the two modes of inference: modus ponens and modus tollens. Modus ponens inference is based upon reasoning towards the conclusion in a statement of logical implication, whereas modus tollens inference is based upon reasoning away
di Francia, Giuliano Toraldo
1973-01-01
The art of deriving information about an object from the radiation it scatters was once limited to visible light. Now due to new techniques, much of the modern physical science research utilizes radiation scattering. (DF)
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...
Twisted inhomogeneous Diophantine approximation and badly approximable sets
Harrap, Stephen
2010-01-01
For any real pair i, j geq 0 with i+j=1 let Bad(i, j) denote the set of (i, j)-badly approximable pairs. That is, Bad(i, j) consists of irrational vectors x:=(x_1, x_2) in R^2 for which there exists a positive constant c(x) such that max {||qx_1||^(-i), ||qx_2||^(-j)} > c(x)/q for all q in N. Building on a result of Kurzweil, a new characterization of the set Bad(i, j) in terms of `well-approximable' vectors in the area of `twisted' inhomogeneous Diophantine approximation is established. In addition, it is shown that Bad^x(i, j), the `twisted' inhomogeneous analogue of Bad(i, j), has full Hausdorff dimension 2 when x is chosen from the set Bad(i, j).
A two-scale second-order moment two-phase turbulence model for simulating dense gas-particle flows
Institute of Scientific and Technical Information of China (English)
Zhuoxiong Zeng; Lixing Zhou; Jian Zhang; Keren Wang
2005-01-01
A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concepts of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision and through a unified treatment of these two kinds of fluctuations. The proposed model is used to simulate gas-particle flows in a channel and in a downer. Simulation results are in agreement with the experimental results reported in references and are near the results obtained using the single-scale second-order moment two-phase turbulence model superposed with a particle collision model (USM-θ model)in most regions.
Institute of Scientific and Technical Information of China (English)
HU Chun-bo; ZENG Zhuo-xiong
2006-01-01
A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concept of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision. The proposed model is used to simulate gas-particle downer reactor flows. The computationsl results of both particle volume fraction and mean velocity are in agreement with the experimental results. After analyzing effects of empirical coefficient on prediction results, we can come to a conclusion that, inside the limit range of empirical coefficient, the predictions do not reveal a large sensitivity to the empirical coefficient in the downer reactor, but a relatively great change of the constants has important effect on the prediction.
Mielenz, Thelma J; Edwards, Michael C; Callahan, Leigh F
2011-07-01
Benefits of physical activity for those with arthritis are clear, yet physical activity is difficult to initiate and maintain. Self-efficacy is a key modifiable psychosocial determinant of physical activity. This study examined two scales for self-efficacy for exercise behavior (SEEB) to identify their strengths and weaknesses using item response theory (IRT) from community-based randomized controlled trials of physical activity programs in adults with arthritis. The 2 SEEB scales included the 9-item scale by Resnick developed with older adults and the 5-item scale by Marcus developed with employed adults. All IRT analyses were conducted using the graded-response model. IRT assumptions were assessed using both exploratory and confirmatory factor analysis. The IRT analyses indicated that these scales are precise and reliable measures for identifying people with arthritis and low SEEB. The Resnick SEEB scale is slightly more precise at lower levels of self-efficacy in older adults with arthritis.
Directory of Open Access Journals (Sweden)
W. M. Macek
2011-05-01
Full Text Available To quantify solar wind turbulence, we consider a generalized two-scale weighted Cantor set with two different scales describing nonuniform distribution of the kinetic energy flux between cascading eddies of various sizes. We examine generalized dimensions and the corresponding multifractal singularity spectrum depending on one probability measure parameter and two rescaling parameters. In particular, we analyse time series of velocities of the slow speed streams of the solar wind measured in situ by Voyager 2 spacecraft in the outer heliosphere during solar maximum at various distances from the Sun: 10, 30, and 65 AU. This allows us to look at the evolution of multifractal intermittent scaling of the solar wind in the distant heliosphere. Namely, it appears that while the degree of multifractality for the solar wind during solar maximum is only weakly correlated with the heliospheric distance, but the multifractal spectrum could substantially be asymmetric in a very distant heliosphere beyond the planetary orbits. Therefore, one could expect that this scaling near the frontiers of the heliosphere should rather be asymmetric. It is worth noting that for the model with two different scaling parameters a better agreement with the solar wind data is obtained, especially for the negative index of the generalized dimensions. Therefore we argue that there is a need to use a two-scale cascade model. Hence we propose this model as a useful tool for analysis of intermittent turbulence in various environments and we hope that our general asymmetric multifractal model could shed more light on the nature of turbulence.
Andersson, N
2000-01-01
This is a chapter on Black-hole Scattering that was commissioned for an Encyclopaedia on Scattering edited by Pike and Sabatier, to be published by Academic Press. The chapter surveys wave propagation in black-hole spacetimes, diffraction effects in wave scattering, resonances, quasinormal modes and related topics.
Evaluation of Influence of Multiple Scattering Effect in Light-Scattering-Based Applications
Institute of Scientific and Technical Information of China (English)
XU Sheng-Hua; SUN Zhi-Wei
2007-01-01
The extinction cross sections of a system containing two particles are calculated by the T-matrix method, and the results are compared with those of two single particles with single-scattering approximation. The necessity of the correction of the refractive indices of water and polystyrene for different incident wavelengths is particularly addressed in the calculation. By this means, the volume fractions allowed for certain accuracy requirements of single-scattering approximation in the light scattering experiment can be evaluated. The volume fractions calculated with corrected refractive indices are compared with those obtained with fixed refractive indices which have been rather commonly used, showing that fixed refractive indices may cause significant error in evaluating multiple scattering effect. The results also give a simple criterion for selecting the incident wavelength and particle size to avoid the 'blind zone' in the turbidity measurement, where the turbidity change is insensitive to aggregation of two particles.
Born approximation in linear-time invariant system
Gumjudpai, Burin
2015-01-01
Linear-time invariant (LTI) oscillation systems such as forced mechanical vibration, series RLC and parallel RLC circuits can be solved by using simplest initial conditions or employing of Green's function of which knowledge of initial condition of the force term is needed. Here we show a mathematical connection of the LTI system and the Helmholtz equation form of the time-independent Schr\\"{o}dinger equation in quantum mechanical scattering problem. We apply Born approximation in quantum mechanics to obtain LTI general solution in form of infinite Born series which can be expressed as a series of one-dimensional Feynman graphs. Conditions corresponding to the approximation are given for the case of harmonic driving force. The Born series of the harmonic forced oscillation case are derived by directly applying the approximation to the LTI system or by transforming the LTI system to Helmholtz equation prior to doing the approximation.
Reinforcement Learning via AIXI Approximation
Veness, Joel; Hutter, Marcus; Silver, David
2010-01-01
This paper introduces a principled approach for the design of a scalable general reinforcement learning agent. This approach is based on a direct approximation of AIXI, a Bayesian optimality notion for general reinforcement learning agents. Previously, it has been unclear whether the theory of AIXI could motivate the design of practical algorithms. We answer this hitherto open question in the affirmative, by providing the first computationally feasible approximation to the AIXI agent. To develop our approximation, we introduce a Monte Carlo Tree Search algorithm along with an agent-specific extension of the Context Tree Weighting algorithm. Empirically, we present a set of encouraging results on a number of stochastic, unknown, and partially observable domains.
Approximate Matching of Hierarchial Data
DEFF Research Database (Denmark)
Augsten, Nikolaus
The goal of this thesis is to design, develop, and evaluate new methods for the approximate matching of hierarchical data represented as labeled trees. In approximate matching scenarios two items should be matched if they are similar. Computing the similarity between labeled trees is hard...... as in addition to the data values also the structure must be considered. A well-known measure for comparing trees is the tree edit distance. It is computationally expensive and leads to a prohibitively high run time. Our solution for the approximate matching of hierarchical data are pq-grams. The pq...... formally proof that the pq-gram index can be incrementally updated based on the log of edit operations without reconstructing intermediate tree versions. The incremental update is independent of the data size and scales to a large number of changes in the data. We introduce windowed pq...
Concept Approximation between Fuzzy Ontologies
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Fuzzy ontologies are efficient tools to handle fuzzy and uncertain knowledge on the semantic web; but there are heterogeneity problems when gaining interoperability among different fuzzy ontologies. This paper uses concept approximation between fuzzy ontologies based on instances to solve the heterogeneity problems. It firstly proposes an instance selection technology based on instance clustering and weighting to unify the fuzzy interpretation of different ontologies and reduce the number of instances to increase the efficiency. Then the paper resolves the problem of computing the approximations of concepts into the problem of computing the least upper approximations of atom concepts. It optimizes the search strategies by extending atom concept sets and defining the least upper bounds of concepts to reduce the searching space of the problem. An efficient algorithm for searching the least upper bounds of concept is given.
Approximating Graphic TSP by Matchings
Mömke, Tobias
2011-01-01
We present a framework for approximating the metric TSP based on a novel use of matchings. Traditionally, matchings have been used to add edges in order to make a given graph Eulerian, whereas our approach also allows for the removal of certain edges leading to a decreased cost. For the TSP on graphic metrics (graph-TSP), the approach yields a 1.461-approximation algorithm with respect to the Held-Karp lower bound. For graph-TSP restricted to a class of graphs that contains degree three bounded and claw-free graphs, we show that the integrality gap of the Held-Karp relaxation matches the conjectured ratio 4/3. The framework allows for generalizations in a natural way and also leads to a 1.586-approximation algorithm for the traveling salesman path problem on graphic metrics where the start and end vertices are prespecified.
Diophantine approximation and Dirichlet series
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...
Approximation methods in probability theory
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.
Approximate Sparse Regularized Hyperspectral Unmixing
Directory of Open Access Journals (Sweden)
Chengzhi Deng
2014-01-01
Full Text Available Sparse regression based unmixing has been recently proposed to estimate the abundance of materials present in hyperspectral image pixel. In this paper, a novel sparse unmixing optimization model based on approximate sparsity, namely, approximate sparse unmixing (ASU, is firstly proposed to perform the unmixing task for hyperspectral remote sensing imagery. And then, a variable splitting and augmented Lagrangian algorithm is introduced to tackle the optimization problem. In ASU, approximate sparsity is used as a regularizer for sparse unmixing, which is sparser than l1 regularizer and much easier to be solved than l0 regularizer. Three simulated and one real hyperspectral images were used to evaluate the performance of the proposed algorithm in comparison to l1 regularizer. Experimental results demonstrate that the proposed algorithm is more effective and accurate for hyperspectral unmixing than state-of-the-art l1 regularizer.
Semiclassical Quantization by Pade Approximant to Periodic Orbit Sums
Main, J; Belkic, D; Taylor, H S; Belkic, Dz.
1999-01-01
Periodic orbit quantization requires an analytic continuation of non-convergent semiclassical trace formulae. We propose a method for semiclassical quantization based upon the Pade approximant to the periodic orbit sums. The Pade approximant allows the re-summation of the typically exponentially divergent periodic orbit terms. The technique does not depend on the existence of a symbolic dynamics and can be applied to both bound and open systems. Numerical results are presented for two different systems with chaotic and regular classical dynamics, viz. the three-disk scattering system and the circle billiard.
Delta-function Approximation SSC Model in 3C 273
Indian Academy of Sciences (India)
S. J. Kang; Y. G. Zheng; Q. Wu
2014-09-01
We obtain an approximate analytical solution using approximate calculation on the traditional one-zone synchrotron self-Compton (SSC) model. In this model, we describe the electron energy distribution by a broken power-law function with a sharp cut-off, and non-thermal photons are produced by both synchrotron and inverse Compton scattering of synchrotron photons. We calculate the radiation energy spectrum of electrons by the function. We apply this model to the multi-wavelength Spectral Energy Distributions (SED) of the 3C 273 in different states, and obtain excellent fits to the observed spectra of this source.
Properties of strongly dipolar Bose gases beyond the Born approximation
Ołdziejewski, Rafał
2016-01-01
Strongly dipolar Bose gases can form liquid droplets stabilized by quantum fluctuations. In theoretical description of this phenomenon, low energy scattering amplitude is utilized as an effective potential. We show that for magnetic atoms corrections with respect to Born approximation arise, and derive modified pseudopotential using realistic interaction model. We discuss the resulting changes in collective mode frequencies and droplet stability diagram. Our results are relevant for recent experiments with erbium and dysprosium atoms.
Transfinite Approximation of Hindman's Theorem
Beiglböck, Mathias
2010-01-01
Hindman's Theorem states that in any finite coloring of the integers, there is an infinite set all of whose finite sums belong to the same color. This is much stronger than the corresponding finite form, stating that in any finite coloring of the integers there are arbitrarily long finite sets with the same property. We extend the finite form of Hindman's Theorem to a "transfinite" version for each countable ordinal, and show that Hindman's Theorem is equivalent to the appropriate transfinite approximation holding for every countable ordinal. We then give a proof of Hindman's Theorem by directly proving these transfinite approximations.
Microscopic optical potentials for $^4$He scattering
Egashira, Kei; Toyokawa, Masakazu; Matsumoto, Takuma; Yahiro, Masanobu
2014-01-01
We present a reliable double-folding (DF) model for $^{4}$He-nucleus scattering, using the Melbourne $g$-matrix nucleon-nucleon interaction that explains nucleon-nucleus scattering with no adjustable parameter. In the DF model, only the target density is taken as the local density in the Melbourne $g$-matrix. For $^{4}$He elastic scattering from $^{58}$Ni and $^{208}$Pb targets in a wide range of incident energies from 20~MeV/nucleon to 200~MeV/nucleon, the DF model with the target-density approximation (TDA) yields much better agreement with the experimental data than the usual DF model with the frozen-density approximation in which the sum of projectile and target densities is taken as the local density. We also discuss the relation between the DF model with the TDA and the conventional folding model in which the nucleon-nucleus potential is folded with the $^{4}$He density.
Correlations in neutrino-nucleus scattering
Van Cuyck, Tom; Jachowicz, Natalie; González-Jiménez, Raul; Martini, Marco; Ryckebusch, Jan; Van Dessel, Nils
2016-01-01
We present a detailed study of charged-current quasielastic neutrino-nucleus scattering and of the influence of correlations on one- and two-nucleon knockout processes. The quasielastic neutrino-nucleus scattering cross sections, including the influence of long-range correlations, are evaluated within a continuum random phase approximation approach. The short-range correlation formalism is implemented in the impulse approximation by shifting the complexity induced by the correlations from the wave functions to the operators. The model is validated by confronting $(e,e^\\prime)$ cross-section predictions with electron scattering data in the kinematic region where the quasielastic channel is expected to dominate. Further, the $^{12}$C$(\
Quasielastic K-nucleus scattering
Pace, A D; Oset, E
1997-01-01
Quasielastic K^+ - nucleus scattering data at q=290, 390 and 480 MeV/c are analyzed in a finite nucleus continuum random phase approximation framework, using a density-dependent particle-hole interaction. The reaction mechanism is consistently treated according to Glauber theory, keeping up to two-step inelastic processes. A good description of the data is achieved, also providing a useful constraint on the strength of the effective particle-hole interaction in the scalar-isoscalar channel at intermediate momentum transfers. We find no evidence for the increase in the effective number of nucleons participating in the reaction which has been reported in the literature.
Moliere multiple scattering theory revisited
Tarasov, Alexander
2012-01-01
We have received the rigorous relations between the screening parameters of the Moliere multiple scattering theory, instead of the approximate one obtained in the original paper by Moliere. We also calculated the relative Coulomb corrections to the first Born screening angle in the range from Z=4 to Z=82, and showed that their maximum values comprise the order of 40 percent. Additionally, we evaluated absolute and relative accuracies of the Moliere theory in determining the screening angle and have concluded that for Z~80 they are about 20, and 34 percents, respectively.
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...
Quantum transport velocity in strongly scattering media
Malfliet, R
1998-01-01
Based on the Kadanoff-Baym equations of quantum transport: theory, an approach is proposed which goes beyond the usual quasiparticle approximation. It allows one to deduct the correct transport velocity for propagation in strongly scattering media, a quantity of great importance for localization phe
Tree wavelet approximations with applications
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
[1]Baraniuk, R. G., DeVore, R. A., Kyriazis, G., Yu, X. M., Near best tree approximation, Adv. Comput. Math.,2002, 16: 357-373.[2]Cohen, A., Dahmen, W., Daubechies, I., DeVore, R., Tree approximation and optimal encoding, Appl. Comput.Harmonic Anal., 2001, 11: 192-226.[3]Dahmen, W., Schneider, R., Xu, Y., Nonlinear functionals of wavelet expansions-adaptive reconstruction and fast evaluation, Numer. Math., 2000, 86: 49-101.[4]DeVore, R. A., Nonlinear approximation, Acta Numer., 1998, 7: 51-150.[5]Davis, G., Mallat, S., Avellaneda, M., Adaptive greedy approximations, Const. Approx., 1997, 13: 57-98.[6]DeVore, R. A., Temlyakov, V. N., Some remarks on greedy algorithms, Adv. Comput. Math., 1996, 5: 173-187.[7]Kashin, B. S., Temlyakov, V. N., Best m-term approximations and the entropy of sets in the space L1, Mat.Zametki (in Russian), 1994, 56: 57-86.[8]Temlyakov, V. N., The best m-term approximation and greedy algorithms, Adv. Comput. Math., 1998, 8:249-265.[9]Temlyakov, V. N., Greedy algorithm and m-term trigonometric approximation, Constr. Approx., 1998, 14:569-587.[10]Hutchinson, J. E., Fractals and self similarity, Indiana. Univ. Math. J., 1981, 30: 713-747.[11]Binev, P., Dahmen, W., DeVore, R. A., Petruchev, P., Approximation classes for adaptive methods, Serdica Math.J., 2002, 28: 1001-1026.[12]Gilbarg, D., Trudinger, N. S., Elliptic Partial Differential Equations of Second Order, Berlin: Springer-Verlag,1983.[13]Ciarlet, P. G., The Finite Element Method for Elliptic Problems, New York: North Holland, 1978.[14]Birman, M. S., Solomiak, M. Z., Piecewise polynomial approximation of functions of the class Wαp, Math. Sb.,1967, 73: 295-317.[15]DeVore, R. A., Lorentz, G. G., Constructive Approximation, New York: Springer-Verlag, 1993.[16]DeVore, R. A., Popov, V., Interpolation of Besov spaces, Trans. Amer. Math. Soc., 1988, 305: 397-414.[17]Devore, R., Jawerth, B., Popov, V., Compression of wavelet decompositions, Amer. J. Math., 1992, 114: 737-785.[18]Storozhenko, E
On the scattering power of radiotherapy protons
Gottschalk, Bernard
2009-01-01
Scattering power (T = d/dx of mean squared multiple Coulomb scattering (MCS) angle), as used in proton transport theory, is properly viewed as a differential description of the Gaussian approximation to MCS theories such as Moliere's. That is, we seek a function T which, when integrated over a finite slab, will recover the Moliere/Fano/Hanson angle for that slab. To be accurate, T must include a single scattering correction, which means mathematically it must be nonlocal, depending on how much MCS has taken place as well as the energy and scattering material at the POI. We review five formulas for T and introduce a sixth, testing each against the Moliere/Fano/Hanson prediction as well as experimental data. We discuss how sensitive some practical problems are to the choice of T. That choice is probably most important for general Monte Carlo codes, which are expected to address a wide variety of problems.
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. Fo...
Through-the-Wall Imaging from Electromagnetic Scattered Field Measurements
2007-03-01
the transmission Greens function. This simplified model is then used in a Lippman- Schwinger integral equation to predict the scattered field associated...model is then used in a Lippman- Schwinger integral equation to predict the scattered field associated with interrogating THz waves. We investigate the...59 B. LIPPMAN- SCHWINGER EQUATION . . . . . . . . . . . . . . 59 C. BORN APPROXIMATION
Quasi-elastic nuclear scattering at high energies
Cucinotta, Francis A.; Townsend, Lawrence W.; Wilson, John W.
1992-01-01
The quasi-elastic scattering of two nuclei is considered in the high-energy optical model. Energy loss and momentum transfer spectra for projectile ions are evaluated in terms of an inelastic multiple-scattering series corresponding to multiple knockout of target nucleons. The leading-order correction to the coherent projectile approximation is evaluated. Calculations are compared with experiments.
Eigenstates of Laser-Assisted Scattering in a Noninertial Frame
Institute of Scientific and Technical Information of China (English)
FENG Zi-Min; LI Shu-Min
2005-01-01
In a rotating noninertial frame, we investigate the eigenstates of the time-dependent problem for electronnucleus scattering assisted by a circularly polarized laser field. Numerical results of probability distribution, quantum potential, and current density are discussed. An approximate expression of scattering cross section for low laser frequency is given.
Multiple scattering and energy loss in semi-inclusive deeply inelastic eA scattering
Guo, Xiaofeng
2007-01-01
We calculate the multiple scattering effect on single hadron production in semi-inclusive lepton-nucleus deeply inelastic scattering. We show that the quantum interference of multiple scattering amplitudes leads to suppression in hadron productions. At the leading power in medium length, the suppression can be approximately expressed in terms of a shift in $z$ of the fragmentation function $D(z)$, and could be therefore interpreted as the collisional energy loss. We compare our calculation with existing experimental data. We also discuss the effect of quark mass on the suppression. Our approach can be extended to other observables in hadronic collisions.
WKB Approximation in Noncommutative Gravity
Directory of Open Access Journals (Sweden)
Maja Buric
2007-12-01
Full Text Available We consider the quasi-commutative approximation to a noncommutative geometry defined as a generalization of the moving frame formalism. The relation which exists between noncommutativity and geometry is used to study the properties of the high-frequency waves on the flat background.
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.
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...
Approximate Reasoning with Fuzzy Booleans
Broek, van den P.M.; Noppen, J.A.R.
2004-01-01
This paper introduces, in analogy to the concept of fuzzy numbers, the concept of fuzzy booleans, and examines approximate reasoning with the compositional rule of inference using fuzzy booleans. It is shown that each set of fuzzy rules is equivalent to a set of fuzzy rules with singleton crisp ante
Ultrafast Approximation for Phylogenetic Bootstrap
Bui Quang Minh, [No Value; Nguyen, Thi; von Haeseler, Arndt
2013-01-01
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
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...
Rational approximation of vertical segments
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.
Approximation on the complex sphere
Alsaud, Huda; Kushpel, Alexander; Levesley, Jeremy
2012-01-01
We develop new elements of harmonic analysis on the complex sphere on the basis of which Bernstein's, Jackson's and Kolmogorov's inequalities are established. We apply these results to get order sharp estimates of $m$-term approximations. The results obtained is a synthesis of new results on classical orthogonal polynomials, harmonic analysis on manifolds and geometric properties of Euclidean spaces.
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...
Pythagorean Approximations and Continued Fractions
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…
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...
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...
Low Rank Approximation in $G_0W_0$ Approximation
Shao, Meiyue; Yang, Chao; Liu, Fang; da Jornada, Felipe H; Deslippe, Jack; Louie, Steven G
2016-01-01
The single particle energies obtained in a Kohn--Sham density functional theory (DFT) calculation are generally known to be poor approximations to electron excitation energies that are measured in transport, tunneling and spectroscopic experiments such as photo-emission spectroscopy. The correction to these energies can be obtained from the poles of a single particle Green's function derived from a many-body perturbation theory. From a computational perspective, the accuracy and efficiency of such an approach depends on how a self energy term that properly accounts for dynamic screening of electrons is approximated. The $G_0W_0$ approximation is a widely used technique in which the self energy is expressed as the convolution of a non-interacting Green's function ($G_0$) and a screened Coulomb interaction ($W_0$) in the frequency domain. The computational cost associated with such a convolution is high due to the high complexity of evaluating $W_0$ at multiple frequencies. In this paper, we discuss how the cos...
Relativistic models for quasielastic electron and neutrino-nucleus scattering
Directory of Open Access Journals (Sweden)
Meucci Andrea
2012-12-01
Full Text Available Relativistic models developed within the framework of the impulse approximation for quasielastic (QE electron scattering and successfully tested in comparison with electron-scattering data have been extended to neutrino-nucleus scattering. Different descriptions of final-state interactions (FSI in the inclusive scattering are compared. In the relativistic Green’s function (RGF model FSI are described consistently with the exclusive scattering using a complex optical potential. In the relativistic mean field (RMF model FSI are described by the same RMF potential which gives the bound states. The results of the models are compared for electron and neutrino scattering and, for neutrino scattering, with the recently measured charged-current QE (CCQE MiniBooNE cross sections.
H-function for three-term scattering indicatrix
Karanjai, S.; Karanjai, M.
1985-07-01
In solving the equation of transfer for a semiinfinite, plane-parallel atmosphere, the emergent intensity is largely obtained in terms of Chandrasekhar's H-function; in cases where the H-function is within an integral sign, a good approximate form is needed to minimize computational effort. The Karanjai and Sen (1971) H-function approximation for isotropic scattering is presently extended to the case of the three-term scattering indicatrix.
Collet, Remo; Hayek, Wolfgang; Asplund, Martin
2011-08-01
We study the effects of different approximations of scattering in 3D radiation-hydrodynamics simulations on the photospheric temperature stratification of metal-poor red giant stars. We find that assuming a Planckian source function and neglecting the contribution of scattering to extinction in optically thin layers provides a good approximation of the effects of coherent scattering on the photospheric temperature balance.
Liu, F.; Borja, R. I.
2009-12-01
Stress concentration induced by the heterogeneity in brittle geomaterials is generally considered as the driving force in the evolution of the microstructure (such as the crack and pore microstructure). Specifically, modeling heterogeneity is key to properly predicting the nucleation, coalescence and propagation of micro-cracks in brittle solids. In this paper, we propose a two-scale model for frictional cracks in fractured brittle media. The major crack in the study domain is modeled at a macro level, while the micro-cracks are modeled at a finer scale. The macro-scale behavior is described by a standard boundary value problem. The finer-scale problem is modeled using the notion of representative elementary volume (REV) consisting of a solid volume with distributed micro-cracks. Periodic boundary condition and small strain formulation are assumed in the finer-scale analysis. The scale bridging mechanism is borrowed from the standard homogenization technique. The proposed model is implemented with the extended finite element method. The macro stress at each Gauss point in the finite element formulation is computed as the volume average of finer-scale stresses in each corresponding REV. The macro tangent operator is computed using a perturbation method. For 3D problems, six independent linear perturbation analyses are carried out for each numerical integration point. Our numerical examples capture the nucleation and coalescence of micro-cracks, which can be used to infer the potential propagation direction of the major crack.
Covariant Impulse Approximation for the study of the internal structure of composite particles
De Sanctis, M; Milanes, D A; Sandoval, C E; Sanctis, Maurizio De; Acero, Mario A.; Milanes, Diego A.; Sandoval, Carlos E.
2004-01-01
We present a brief review on the Impulse Approximation method to study processes of scattering off composite particles. We first construct the model in a non-relativistic fashion that enables us to extend the model to a covariant Impulse Approximation, which is needed for the study of high momentum transfer processes.
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...... complexity can potentially lead to limited power consumption, which translates into longer battery life-time in the handsets. The scope of the thesis is more specifically to investigate approximate (nearoptimal) detection methods that can reduce the computationally complexity significantly compared...... 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...
Hydrogen Beyond the Classic Approximation
Scivetti, I
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
Approximate Privacy: Foundations and Quantification
Feigenbaum, Joan; Schapira, Michael
2009-01-01
Increasing use of computers and networks in business, government, recreation, and almost all aspects of daily life has led to a proliferation of online sensitive data about individuals and organizations. Consequently, concern about the privacy of these data has become a top priority, particularly those data that are created and used in electronic commerce. There have been many formulations of privacy and, unfortunately, many negative results about the feasibility of maintaining privacy of sensitive data in realistic networked environments. We formulate communication-complexity-based definitions, both worst-case and average-case, of a problem's privacy-approximation ratio. We use our definitions to investigate the extent to which approximate privacy is achievable in two standard problems: the second-price Vickrey auction and the millionaires problem of Yao. For both the second-price Vickrey auction and the millionaires problem, we show that not only is perfect privacy impossible or infeasibly costly to achieve...
Approximate Counting of Graphical Realizations.
Erdős, Péter L; Kiss, Sándor Z; Miklós, István; Soukup, Lajos
2015-01-01
In 1999 Kannan, Tetali and Vempala proposed a MCMC method to uniformly sample all possible realizations of a given graphical degree sequence and conjectured its rapidly mixing nature. Recently their conjecture was proved affirmative for regular graphs (by Cooper, Dyer and Greenhill, 2007), for regular directed graphs (by Greenhill, 2011) and for half-regular bipartite graphs (by Miklós, Erdős and Soukup, 2013). Several heuristics on counting the number of possible realizations exist (via sampling processes), and while they work well in practice, so far no approximation guarantees exist for such an approach. This paper is the first to develop a method for counting realizations with provable approximation guarantee. In fact, we solve a slightly more general problem; besides the graphical degree sequence a small set of forbidden edges is also given. We show that for the general problem (which contains the Greenhill problem and the Miklós, Erdős and Soukup problem as special cases) the derived MCMC process is rapidly mixing. Further, we show that this new problem is self-reducible therefore it provides a fully polynomial randomized approximation scheme (a.k.a. FPRAS) for counting of all realizations.
Approximate Counting of Graphical Realizations.
Directory of Open Access Journals (Sweden)
Péter L Erdős
Full Text Available In 1999 Kannan, Tetali and Vempala proposed a MCMC method to uniformly sample all possible realizations of a given graphical degree sequence and conjectured its rapidly mixing nature. Recently their conjecture was proved affirmative for regular graphs (by Cooper, Dyer and Greenhill, 2007, for regular directed graphs (by Greenhill, 2011 and for half-regular bipartite graphs (by Miklós, Erdős and Soukup, 2013. Several heuristics on counting the number of possible realizations exist (via sampling processes, and while they work well in practice, so far no approximation guarantees exist for such an approach. This paper is the first to develop a method for counting realizations with provable approximation guarantee. In fact, we solve a slightly more general problem; besides the graphical degree sequence a small set of forbidden edges is also given. We show that for the general problem (which contains the Greenhill problem and the Miklós, Erdős and Soukup problem as special cases the derived MCMC process is rapidly mixing. Further, we show that this new problem is self-reducible therefore it provides a fully polynomial randomized approximation scheme (a.k.a. FPRAS for counting of all realizations.
Many Faces of Boussinesq Approximations
Vladimirov, Vladimir A
2016-01-01
The \\emph{equations of Boussinesq approximation} (EBA) for an incompressible and inhomogeneous in density fluid are analyzed from a viewpoint of the asymptotic theory. A systematic scaling shows that there is an infinite number of related asymptotic models. We have divided them into three classes: `poor', `reasonable' and `good' Boussinesq approximations. Each model can be characterized by two parameters $q$ and $k$, where $q =1, 2, 3, \\dots$ and $k=0, \\pm 1, \\pm 2,\\dots$. Parameter $q$ is related to the `quality' of approximation, while $k$ gives us an infinite set of possible scales of velocity, time, viscosity, \\emph{etc.} Increasing $q$ improves the quality of a model, but narrows the limits of its applicability. Parameter $k$ allows us to vary the scales of time, velocity and viscosity and gives us the possibility to consider any initial and boundary conditions. In general, we discover and classify a rich variety of possibilities and restrictions, which are hidden behind the routine use of the Boussinesq...
Silveirinha, Mario G
2016-01-01
In time-reversal invariant electronic systems the scattering matrix is anti-symmetric. This property enables an effect, designated here as "scattering anomaly", such that the electron transport does not suffer from back reflections, independent of the specific geometry of the propagation path or the presence of time-reversal invariant defects. In contrast, for a generic time-reversal invariant photonic system the scattering matrix is symmetric and there is no similar anomaly. Here, it is theoretically proven that despite these fundamental differences there is a wide class of photonic platforms - in some cases formed only by time-reversal invariant media - in which the scattering anomaly can occur. It is shown that an optical system invariant under the action of the composition of the time-reversal, parity and duality operators is characterized by an anti-symmetric scattering matrix. Specific examples of photonic platforms wherein the scattering anomaly occurs are given, and it is demonstrated with full wave n...
Multiple scattering effects on spaceborne lidar
Winker, David M.; Poole, Lamont R.
1992-01-01
A semianalytic Monte Carlo code originally developed for oceanographic calculations (Poole et al., 1981) has been modified for use in studying multiple scattering of space-based lidar. The approach is very similar to that described by Kunkel and Weinman (1976). The trajectory of each photon is followed from the transmitter through multiple scattering until the photon is either scattered backward out of the atmosphere, scattered forward into the ground and absorbed, or scattered out the sides of the cloud. The probability that the photon will return directly to the detector is computed and summed over all significant scattering events within the field of view of the detector. Multiple scattering of the lidar pulse causes an apparent increase in the transmittance of the medium. Multiple scattering effects for space-based lidar are more significant than for ground-based lidar due to the much larger beam diameter in the atmosphere. These larger diameters are due not only to the greater range between the lidar and the scattering volume, but also the need to maintain relatively large beam divergences to satisfy eye safety restrictions on the laser irradiance at the Earth's surface. The simulations presented here are for a wavelength of 1064 nm and the Deirmendjian C1 phase function, which yields an extinction coefficient of 17.259/km. We have looked at two cases: a space-based lidar at 296 km observing a C1 cloud 293 km from the lidar and, for comparison purposes, a ground-based lidar looking at a C1 cloud with a base height of either 2 km or 5 km. The C1 size distribution roughly approximates that of stratocumulus or altocumulus clouds (aufm Kampe and Weickmann, 1957).
Radiative transfer in disc galaxies - V. The accuracy of the KB approximation
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.
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.
Scattering by a long-range potential
Hod, Shahar
2013-01-01
The phenomenon of wave tails has attracted much attention over the years from both physicists and mathematicians. However, our understanding of this fascinating phenomenon is not complete yet. In particular, most former studies of the tail phenomenon have focused on scattering potentials which approach zero asymptotically ($x\\to\\infty$) faster than $x^{-2}$. It is well-known that for these (rapidly decaying) scattering potentials the late-time tails are determined by the first Born approximation and are therefore {\\it linear} in the amplitudes of the scattering potentials (there are, however, some exceptional cases in which the first Born approximation vanishes and one has to consider higher orders of the scattering problem). In the present study we analyze in detail the late-time dynamics of the Klein-Gordon wave equation with a ({\\it slowly} decaying) Coulomb-like scattering potential: $V(x\\to\\infty)=\\alpha/x$. In particular, we write down an explicit solution (that is, an exact analytic solution which is n...
Elastic scattering phenomenology
Energy Technology Data Exchange (ETDEWEB)
Mackintosh, R.S. [The Open University, School of Physical Sciences, Milton Keynes (United Kingdom)
2017-04-15
We argue that, in many situations, fits to elastic scattering data that were historically, and frequently still are, considered ''good'', are not justifiably so describable. Information about the dynamics of nucleon-nucleus and nucleus-nucleus scattering is lost when elastic scattering phenomenology is insufficiently ambitious. It is argued that in many situations, an alternative approach is appropriate for the phenomenology of nuclear elastic scattering of nucleons and other light nuclei. The approach affords an appropriate means of evaluating folding models, one that fully exploits available empirical data. It is particularly applicable for nucleons and other light ions. (orig.)
Wave-scattering from a gently curved surface
Bimonte, Giuseppe
2016-01-01
We study wave scattering from a gently curved surface. We show that the recursive relations, implied by shift invariance, among the coefficients of the perturbative series for the scattering amplitude allow to perform an infinite resummation of the perturbative series to all orders in the amplitude of the corrugation. The resummed series provides a derivative expansion of the scattering amplitude in powers of derivatives of the height profile, which is expected to become exact in the limit of quasi-specular scattering. We discuss the relation of our results with the so-called small-slope approximation introduced some time ago by Voronovich.
Scaling in light scattering by sharp conical metal tips
Pors, Anders; Bozhevolnyi, Sergey I
2016-01-01
Using the electrostatic approximation, we analyze electromagnetic fields scattered by sharp conical metal tips, which are illuminated with light polarized along the tip axis. We establish scaling relations for the scattered field amplitude and phase, whose validity is verified with numerical simulations. Analytic expressions for the wavelength, at which the scattered field near the tip changes its direction, and field decay near the tip extremity are obtained, relating these characteristics to the cone angle and metal permittivity. The results obtained have important implications to various tip-enhanced phenomena, ranging from Raman and scattering near-field imaging to photoemission spectroscopy and nano-optical trapping.
A Recursive Born Approach to Nonlinear Inverse Scattering
Kamilov, Ulugbek S; Mansour, Hassan; Boufounos, Petros T
2016-01-01
The Iterative Born Approximation (IBA) is a well-known method for describing waves scattered by semi-transparent objects. In this paper, we present a novel nonlinear inverse scattering method that combines IBA with an edge-preserving total variation (TV) regularizer. The proposed method is obtained by relating iterations of IBA to layers of a feedforward neural network and developing a corresponding error backpropagation algorithm for efficiently estimating the permittivity of the object. Simulations illustrate that, by accounting for multiple scattering, the method successfully recovers the permittivity distribution where the traditional linear inverse scattering fails.
Argente dos Santos, H A F; Auricchio, F; Conti, M
2012-11-01
Cardiovascular disease has become a major global health care problem in the present decade. To tackle this problem, the use of cardiovascular stents has been considered a promising and effective approach. Numerical simulations to evaluate the in vivo behavior of stents are becoming more and more important to assess potential failures. As the material failure of a stent device has been often associated with fatigue issues, as a result of the high number of cyclic loads these devices are subjected to in vivo, numerical approaches for fatigue life assessment of stents has gained special interest in the engineering community. Numerical fatigue predictions can be used to modify the design and prevent failure, without making and testing numerous physical devices, thus preventing from undesired fatigue failures. This work presents a fatigue life numerical method for the analysis of cardiovascular balloon-expandable stainless steel stents. The method is based on a two-scale continuum damage mechanics model in which both plasticity and damage mechanisms are assumed to take place at a scale smaller than the scale of the representative volume element. The fatigue failure criterion is based on the Soderberg relation. The method is applied to the fatigue life assessment of both PalmazShatz and Cypher stent designs. Validation of the method is performed through comparison of the obtained numerical results with some experimental results available for the PalmazShatz stent design. The present study gives also possible directions for future research developments in the framework of the numerical fatigue life assessment of real balloon-expandable stents.
Scattering of thermal phonons by extended defects in dielectric crystals
Energy Technology Data Exchange (ETDEWEB)
Roth, E. P.
1975-01-01
The scattering of thermal phonons by extended defects in dielectric crystals has been observed through measurements of thermal conductivity and ballistic heat pulse propagation. The thermal conductivities of LiF and NaCl conatining 500 low-angle grain boundaries per cm were measured in the range 0.08-5 K. The measurements gave little or no evidence for phonon scattering from the grain boundaries. Measurements of phonon scattering at a 10 deg. grain boundary in silicon using direct generation and detection of ballistically propagating heat pulses were made over an effective phonon temperature range of 2 to 20 K. The grain boundary reflection coefficient was determined to be < 2%. The thermal conductivities of LiF crystals containing 5 x 10/sup 6/ - 3 x 10/sup 7/ dislocations per square cm were measured over the temperature range 0.1 to 10 K. The measurements of the sheared crystal indicated that the slow transverse phonon mode was strongly scattered by a dynamic phonon-dislocation interaction at T approximately < 2 K, while the remaining modes were scattered primarily by the boundaries. The measurements of the bent crystals indicated that, for T approximately < 2 K, the slow transverse and possibly the longitudinal phonons were strongly scattered by a dynamic phonon-dislocation interaction. For T approximately > 2 k, some fraction of the phonons (at least the slow transverse mode) were still strongly scattered, even after long exposure to ..gamma.. irradiation, while the remaining phonons were scattered primarily by the boundaries.
Rollout Sampling Approximate Policy Iteration
Dimitrakakis, Christos
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 supervised learning problem. This paper proposes variants of an improved policy iteration scheme which addresses the core sampling problem in evaluating a policy through simulation as a multi-armed bandit machine. The resulting algorithm offers comparable performance to the previous algorithm achieved, however, with significantly less computational effort. An order of magnitude improvement is demonstrated experimentally in two standard reinforcement learning domains: inverted pendulum and mountain-car.
Approximate Deconvolution Reduced Order Modeling
Xie, Xuping; Wang, Zhu; Iliescu, Traian
2015-01-01
This paper proposes a large eddy simulation reduced order model(LES-ROM) framework for the numerical simulation of realistic flows. In this LES-ROM framework, the proper orthogonal decomposition(POD) is used to define the ROM basis and a POD differential filter is used to define the large ROM structures. An approximate deconvolution(AD) approach is used to solve the ROM closure problem and develop a new AD-ROM. This AD-ROM is tested in the numerical simulation of the one-dimensional Burgers equation with a small diffusion coefficient(10^{-3})
Approximation for Bayesian Ability Estimation.
1987-02-18
posterior pdfs of ande are given by p(-[Y) p(F) F P((y lei’ j)P )d. SiiJ i (4) a r~d p(e Iy) - p(t0) 1 J i P(Yij ei, (5) As shown in Tsutakawa and Lin...inverse A Hessian of the log of (27) with respect to , evaulatedat a Then, under regularity conditions, the marginal posterior pdf of O is...two-way contingency tables. Journal of Educational Statistics, 11, 33-56. Lindley, D.V. (1980). Approximate Bayesian methods. Trabajos Estadistica , 31
Stover, John C.
1991-12-01
Optical scatter is a bothersome source of optical noise, limits resolution and reduces system throughput. However, it is also an extremely sensitive metrology tool. It is employed in a wide variety of applications in the optics industry (where direct scatter measurement is of concern) and is becoming a popular indirect measurement in other industries where its measurement in some form is an indicator of another component property - like roughness, contamination or position. This paper presents a brief review of the current state of this technology as it emerges from university and government laboratories into more general industry use. The bidirectional scatter distribution function (or BSDF) has become the common format for expressing scatter data and is now used almost universally. Measurements made at dozens of laboratories around the country cover the spectrum from the uv to the mid- IR. Data analysis of optical component scatter has progressed to the point where a variety of analysis tools are becoming available for discriminating between the various sources of scatter. Work has progressed on the analysis of rough surface scatter and the application of these techniques to some challenging problems outside the optical industry. Scatter metrology is acquiring standards and formal test procedures. The available scatter data base is rapidly expanding as the number and sophistication of measurement facilities increases. Scatter from contaminants is continuing to be a major area of work as scatterometers appear in vacuum chambers at various laboratories across the country. Another area of research driven by space applications is understanding the non-topographic sources of mid-IR scatter that are associated with Beryllium and other materials. The current flurry of work in this growing area of metrology can be expected to continue for several more years and to further expand to applications in other industries.
Effect of anisotropic scattering on radiative heat transfer in two-dimensional rectangular media
Hao Jin Bo
2003-01-01
Effect of scattering on radiative heat transfer in two-dimensional rectangular media by the finite-volume method has been studied. Compared with the existing solutions, it shows that the result obtained by the finite-volume method is reliable. Furthermore, relative errors caused by the approximation that linear and nonlinear anisotropic scattering media is simplified to isotropic scattering media have been studied.
Plasma Physics Approximations in Ares
Energy Technology Data Exchange (ETDEWEB)
Managan, R. A.
2015-01-08
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, F_{n}( 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.
Rational approximations to fluid properties
Kincaid, J. M.
1990-05-01
The purpose of this report is to summarize some results that were presented at the Spring AIChE meeting in Orlando, Florida (20 March 1990). We report on recent attempts to develop a systematic method, based on the technique of rational approximation, for creating mathematical models of real-fluid equations of state and related properties. Equation-of-state models for real fluids are usually created by selecting a function tilde p(T,rho) that contains a set of parameters (gamma sub i); the (gamma sub i) is chosen such that tilde p(T,rho) provides a good fit to the experimental data. (Here p is the pressure, T the temperature and rho is the density). In most cases, a nonlinear least-squares numerical method is used to determine (gamma sub i). There are several drawbacks to this method: one has essentially to guess what tilde p(T,rho) should be; the critical region is seldom fit very well and nonlinear numerical methods are time consuming and sometimes not very stable. The rational approximation approach we describe may eliminate all of these drawbacks. In particular, it lets the data choose the function tilde p(T,rho) and its numerical implementation involves only linear algorithms.
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.
Inelastic Light Scattering Processes
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.
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
Dodgson's Rule Approximations and Absurdity
McCabe-Dansted, John C
2010-01-01
With the Dodgson rule, cloning the electorate can change the winner, which Young (1977) considers an "absurdity". Removing this absurdity results in a new rule (Fishburn, 1977) for which we can compute the winner in polynomial time (Rothe et al., 2003), unlike the traditional Dodgson rule. We call this rule DC and introduce two new related rules (DR and D&). Dodgson did not explicitly propose the "Dodgson rule" (Tideman, 1987); we argue that DC and DR are better realizations of the principle behind the Dodgson rule than the traditional Dodgson rule. These rules, especially D&, are also effective approximations to the traditional Dodgson's rule. We show that, unlike the rules we have considered previously, the DC, DR and D& scores differ from the Dodgson score by no more than a fixed amount given a fixed number of alternatives, and thus these new rules converge to Dodgson under any reasonable assumption on voter behaviour, including the Impartial Anonymous Culture assumption.
Approximation by double Walsh polynomials
Directory of Open Access Journals (Sweden)
Ferenc Móricz
1992-01-01
Full Text Available We study the rate of approximation by rectangular partial sums, Cesàro means, and de la Vallée Poussin means of double Walsh-Fourier series of a function in a homogeneous Banach space X. In particular, X may be Lp(I2, where 1≦p<∞ and I2=[0,1×[0,1, or CW(I2, the latter being the collection of uniformly W-continuous functions on I2. We extend the results by Watari, Fine, Yano, Jastrebova, Bljumin, Esfahanizadeh and Siddiqi from univariate to multivariate cases. As by-products, we deduce sufficient conditions for convergence in Lp(I2-norm and uniform convergence on I2 as well as characterizations of Lipschitz classes of functions. At the end, we raise three problems.
Interplay of approximate planning strategies.
Huys, Quentin J M; Lally, Níall; Faulkner, Paul; Eshel, Neir; Seifritz, Erich; Gershman, Samuel J; Dayan, Peter; Roiser, Jonathan P
2015-03-10
Humans routinely formulate plans in domains so complex that even the most powerful computers are taxed. To do so, they seem to avail themselves of many strategies and heuristics that efficiently simplify, approximate, and hierarchically decompose hard tasks into simpler subtasks. Theoretical and cognitive research has revealed several such strategies; however, little is known about their establishment, interaction, and efficiency. Here, we use model-based behavioral analysis to provide a detailed examination of the performance of human subjects in a moderately deep planning task. We find that subjects exploit the structure of the domain to establish subgoals in a way that achieves a nearly maximal reduction in the cost of computing values of choices, but then combine partial searches with greedy local steps to solve subtasks, and maladaptively prune the decision trees of subtasks in a reflexive manner upon encountering salient losses. Subjects come idiosyncratically to favor particular sequences of actions to achieve subgoals, creating novel complex actions or "options."
Approximate reduction of dynamical systems
Tabuada, Paulo; Julius, Agung; Pappas, George J
2007-01-01
The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with mechanical systems with symmetry--which, unfortunately, limits the type of systems to which it can be applied. The goal of this paper is to consider a more general form of reduction, termed approximate reduction, in order to extend the class of systems that can be reduced. Using notions related to incremental stability, we give conditions on when a dynamical system can be projected to a lower dimensional space while providing hard bounds on the induced errors, i.e., when it is behaviorally similar to a dynamical system on a lower dimensional space. These concepts are illustrated on a series of examples.
Diophantine approximations and Diophantine equations
Schmidt, Wolfgang M
1991-01-01
"This book by a leading researcher and masterly expositor of the subject studies diophantine approximations to algebraic numbers and their applications to diophantine equations. The methods are classical, and the results stressed can be obtained without much background in algebraic geometry. In particular, Thue equations, norm form equations and S-unit equations, with emphasis on recent explicit bounds on the number of solutions, are included. The book will be useful for graduate students and researchers." (L'Enseignement Mathematique) "The rich Bibliography includes more than hundred references. The book is easy to read, it may be a useful piece of reading not only for experts but for students as well." Acta Scientiarum Mathematicarum
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...... maximization in this setting. With m being the number of alternatives, we exhibit a randomized truthful-in-expectation ordinal mechanism implementing an outcome whose expected social welfare is at least an Omega(m^{-3/4}) fraction of the social welfare of the socially optimal alternative. On the other hand, we...... show that for sufficiently many agents and any truthful-in-expectation ordinal mechanism, there is a valuation profile where the mechanism achieves at most an O(m^{-{2/3}) fraction of the optimal social welfare in expectation. We get tighter bounds for the natural special case of m = 3...
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...... projection of the surface onto this plane, a reference curve is determined by use of methods for thinning of binary images. Finally, the cylinder surface is constructed as follows: the directrix of the cylinder surface is determined by a least squares method minimizing the distance to the points...... in the projection within a tolerance given by the reference curve, and the rulings are lines perpendicular to the projection plane. Application of the method in ship design is given....
Analytical approximations for spiral waves
Energy Technology Data Exchange (ETDEWEB)
Löber, Jakob, E-mail: jakob@physik.tu-berlin.de; Engel, Harald [Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, EW 7-1, 10623 Berlin (Germany)
2013-12-15
We propose a non-perturbative attempt to solve the kinematic equations for spiral waves in excitable media. From the eikonal equation for the wave front we derive an implicit analytical relation between rotation frequency Ω and core radius R{sub 0}. For free, rigidly rotating spiral waves our analytical prediction is in good agreement with numerical solutions of the linear eikonal equation not only for very large but also for intermediate and small values of the core radius. An equivalent Ω(R{sub +}) dependence improves the result by Keener and Tyson for spiral waves pinned to a circular defect of radius R{sub +} with Neumann boundaries at the periphery. Simultaneously, analytical approximations for the shape of free and pinned spirals are given. We discuss the reasons why the ansatz fails to correctly describe the dependence of the rotation frequency on the excitability of the medium.
On quantum and approximate privacy
Klauck, H
2001-01-01
This paper studies privacy in communication complexity. The focus is on quantum versions of the model and on protocols with only approximate privacy against honest players. We show that the privacy loss (the minimum divulged information) in computing a function can be decreased exponentially by using quantum protocols, while the class of privately computable functions (i.e., those with privacy loss 0) is not increased by quantum protocols. Quantum communication combined with small information leakage on the other hand makes certain functions computable (almost) privately which are not computable using quantum communication without leakage or using classical communication with leakage. We also give an example of an exponential reduction of the communication complexity of a function by allowing a privacy loss of o(1) instead of privacy loss 0.
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.
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
IONIS: Approximate atomic photoionization intensities
Heinäsmäki, Sami
2012-02-01
A program to compute relative atomic photoionization cross sections is presented. The code applies the output of the multiconfiguration Dirac-Fock method for atoms in the single active electron scheme, by computing the overlap of the bound electron states in the initial and final states. The contribution from the single-particle ionization matrix elements is assumed to be the same for each final state. This method gives rather accurate relative ionization probabilities provided the single-electron ionization matrix elements do not depend strongly on energy in the region considered. The method is especially suited for open shell atoms where electronic correlation in the ionic states is large. Program summaryProgram title: IONIS Catalogue identifier: AEKK_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKK_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 1149 No. of bytes in distributed program, including test data, etc.: 12 877 Distribution format: tar.gz Programming language: Fortran 95 Computer: Workstations Operating system: GNU/Linux, Unix Classification: 2.2, 2.5 Nature of problem: Photoionization intensities for atoms. Solution method: The code applies the output of the multiconfiguration Dirac-Fock codes Grasp92 [1] or Grasp2K [2], to compute approximate photoionization intensities. The intensity is computed within the one-electron transition approximation and by assuming that the sum of the single-particle ionization probabilities is the same for all final ionic states. Restrictions: The program gives nonzero intensities for those transitions where only one electron is removed from the initial configuration(s). Shake-type many-electron transitions are not computed. The ionized shell must be closed in the initial state. Running time: Few seconds for a
Laser-Assisted Elastic Electron Scattering from Argon
Institute of Scientific and Technical Information of China (English)
HU Qiu-Bo; SUN Jin-Feng
2009-01-01
The second Born approximation (SBA) theory is applied to the study of electron-atom scattering in the presence of a CO2 laser field. The absolute differential cross sections of e-At scattering are calculated with multiphoton exchange in two special scattering geometries G1 (for small-angle scattering) and G2. For geometry G1, compared with the results of two different model potentials for electron elastic scattering by atoms, it is found that electronatom polarization potential plays an important role in laser-assisted electron-atom scattering. Some calculational results in geometries G2 are given. Our results are found to be better than other theoretical results as compared with the experimental data in geometries G1 and G2.
Photon Scattering in 3D Radiative MHD Simulations
Hayek, Wolfgang
2009-09-01
Recent results from 3D time-dependent radiative hydrodynamic simulations of stellar atmospheres are presented, which include the effects of coherent scattering in the radiative transfer treatment. Rayleigh scattering and electron scattering are accounted for in the source function, requiring an iterative solution of the transfer equation. Opacities and scattering coefficients are treated in the multigroup opacity approximation. The impact of scattering on the horizontal mean temperature structure is investigated, which is an important diagnostic for model atmospheres, with implications for line formation and stellar abundance measurements. We find that continuum scattering is not important for the atmosphere of a metal-poor Sun with metailicity [Fe/H] = -3.0, similar to the previously investigated photosphere at solar metallicity.
Approximate analytic solutions to the NPDD: Short exposure approximations
Close, Ciara E.; Sheridan, John T.
2014-04-01
There have been many attempts to accurately describe the photochemical processes that take places in photopolymer materials. As the models have become more accurate, solving them has become more numerically intensive and more 'opaque'. Recent models incorporate the major photochemical reactions taking place as well as the diffusion effects resulting from the photo-polymerisation process, and have accurately described these processes in a number of different materials. It is our aim to develop accessible mathematical expressions which provide physical insights and simple quantitative predictions of practical value to material designers and users. In this paper, starting with the Non-Local Photo-Polymerisation Driven Diffusion (NPDD) model coupled integro-differential equations, we first simplify these equations and validate the accuracy of the resulting approximate model. This new set of governing equations are then used to produce accurate analytic solutions (polynomials) describing the evolution of the monomer and polymer concentrations, and the grating refractive index modulation, in the case of short low intensity sinusoidal exposures. The physical significance of the results and their consequences for holographic data storage (HDS) are then discussed.
Deharak, B. A.; Savich, J. L.; Roberts, H. M.; Brown, E. G.; McGill, M. R.; Kim, B. N.; Weaver, C. M.; Martin, N. L. S.
2016-05-01
We have conducted a series of Monte Carlo simulations of laser assisted free-free scattering experiments. The simulations make use of Kroll-Watson approximation to account for the effects of the laser field on the scattering process. The parameters for these simulations are believed to mimic the experimental conditions of the work reported by Wallbank and Holmes, particularly the target number density. The simulations account for the effects multiple scattering (i.e., the scattering of a single incident electron from multiple target atoms). We present a comparison of the results of these simulations to the experimental results of Wallbank and Holmes. This work was supported by the National Science Foundation under Grants Nos. PHY-0855040 (NLSM) and PHY-1402899 (BAd).
Convergence of the discrete dipole approximation. I. Theoretical analysis
Yurkin, Maxim A; Hoekstra, Alfons G
2006-01-01
We performed a rigorous theoretical convergence analysis of the discrete dipole approximation (DDA). We prove that errors in any measured quantity are bounded by a sum of a linear and quadratic term in the size of a dipole d, when the latter is in the range of DDA applicability. Moreover, the linear term is significantly smaller for cubically than for non-cubically shaped scatterers. Therefore, for small d errors for cubically shaped particles are much smaller than for non-cubically shaped. The relative importance of the linear term decreases with increasing size, hence convergence of DDA for large enough scatterers is quadratic in the common range of d. Extensive numerical simulations were carried out for a wide range of d. Finally we discuss a number of new developments in DDA and their consequences for convergence.
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.
Single-scattering properties of droxtals
Ping, Y; Heymsfield, A J; Hu, Y X; Huang, H L; Tsay, S C; Ackerman, S
2003-01-01
Small ice crystals have been found to occur in high concentrations in polar stratospheric clouds and the upper portion of cirrus clouds, where temperatures are extremely low (often less than -50 deg. C). The scattering properties of these small crystals are important to space-borne remote sensing, especially for the retrieval of cirrus properties using visible and near-infrared channels. Previous research has shown that the commonly used spherical and 'quasi-spherical' approximations for these ice crystals can lead to significant errors in light scattering and radiative transfer calculations. We suggest that droxtals more accurately represent the shape of these small ice crystals. The single-scattering properties of ice droxtals have been computed at visible and infrared wavelengths using the finite-difference time domain method for size parameters smaller than 20. Further study of the optical properties of larger droxtals (size parameter greater than 20) will be carried out using an improved geometric optics...
Medium corrections within a multiple scattering theory
Energy Technology Data Exchange (ETDEWEB)
Chinn, C.R. [Oak Ridge National Lab., TN (United States)]|[Vanderbilt Univ., Nashville, TN (United States); Elster, Ch.; Thaler, R.M.
1993-04-01
A systematic formalism to include the effects of the nuclear medium into a multiple scattering expansion is developed. Although the use of a free nucleon-nucleon (NN) t-matrix accounts in an impulse approximation for the short-range interaction between the projectile and a target nucleon, the influence of the interactions between this target nucleon on the rest of the nucleus is often ignored. In the first order Watson expansion such higher order effects arise from the difference between the free NN propagator and the propagator in the nuclear medium. A formal framework consistent with a multiple scattering expansion has been constructed to include these contributions by using a nuclear mean field potential. The application of this formalism to nucleon scattering from various nuclei employing different local and nonlocal Hartree-Fock mean field potentials will be discussed.
Scattering by a draining bathtub vortex
Dolan, Sam R.; Oliveira, Ednilton S.
2013-06-01
We present an analysis of scattering by a fluid-mechanical “black hole analogue,” known as the draining bathtub vortex: a two-dimensional flow that possesses both a sonic horizon and an ergoregion. We consider the scattering of a plane wave of fixed frequency impinging upon the vortex. At low frequency, we encounter a modified Aharonov-Bohm effect. At high frequencies, we observe regular “orbiting” oscillations in the scattering length, due to interference between contra-orbiting rays. We present approximate formulas for both effects and a selection of numerical results obtained by summing partial-wave series. Finally, we examine interference patterns in the vicinity of the vortex and highlight the prospects for experimental investigation.
Scattering by a draining bathtub vortex
Dolan, Sam R
2013-01-01
We present an analysis of scattering by a fluid-mechanical `black hole analogue', known as the draining bathtub (DBT) vortex: a two-dimensional flow which possesses both a sonic horizon and an ergoregion. We consider the scattering of a plane wave of fixed frequency impinging upon the vortex. At low frequency, we encounter a modified Aharonov-Bohm effect. At high frequencies, we observe regular `orbiting' oscillations in the scattering length, due to interference between contra-orbiting rays. We present approximate formulae for both effects, and a selection of numerical results obtained by summing partial-wave series. Finally, we examine interference patterns in the vicinity of the vortex, and highlight the prospects for experimental investigation.
Discrete Ordinates Approximations to the First- and Second-Order Radiation Transport Equations
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.
Seismic topographic scattering in the context of GW detector site selection
Coughlin, Michael; Harms, Jan
2011-01-01
In this paper, we present a calculation of seismic scattering from irregular surface topography in the Born approximation. Based on US-wide topographic data, we investigate topographic scattering at specific sites to demonstrate its impact on Newtonian-noise estimation and subtraction for future gravitational-wave detectors. We find that topographic scattering at a comparatively flat site in Oregon would not pose any problems, whereas scattering at a second site in Montana leads to significan...
Modeling of electromagnetic scattering by thin cylinders using Pattern Equation Method
Demin, D. B.; Kleev, A. I.; Kyurkchan, A. G.
2017-01-01
To solve the problem related to scattering by a perfectly conducting thin cylinder, approximate approach was developed based on use of Pattern Equation Method (PEM). Explicit formulas were obtained for total scattering cross-section applicable for cylindric scatterers of complex shape. It is shown that calculation accuracy controlled by calculating the balance of power flows for incident and scattered waves (checking the accomplishment of optical theorem) is quite sufficient for practice.
Polonyi, Janos
2011-01-01
The cross section of elastic electron-proton scattering taking place in an electron gas is calculated within the Closed Time Path method. It is found to be the sum of two terms, one being the expression in the vacuum except that it involves dressing due to the electron gas. The other term is due to the scattering particles-electron gas entanglement. This term dominates the usual one when the exchange energy is in the vicinity of the Fermi energy. Furthermore it makes the trajectories of the colliding particles more consistent and the collision more irreversible, rendering the scattering more classical in this regime.
Manipulating scattering features by metamaterials
Directory of Open Access Journals (Sweden)
Lu Cui
2016-01-01
Full Text Available We present a review on manipulations of electromagnetic scattering features by using metamaterials or metasurfaces. Several approaches in controlling the scattered fields of objects are presented, including invisibility cloaks and radar illusions based on transformation optics, carpet cloak using gradient metamaterials, dc cloaks, mantle cloaks based on scattering cancellation, “skin” cloaks using phase compensation, scattering controls with coding/programmable metasurfaces, and scattering reductions by multilayered structures. Finally, the future development of metamaterials on scattering manipulation is predicted.
Manipulating scattering features by metamaterials
Directory of Open Access Journals (Sweden)
Lu Cui
2016-01-01
Full Text Available We present a review on manipulations of electromagnetic scattering features by using metamaterials or metasurfaces. Several approaches in controlling the scattered fields of objects are presented, including invisibility cloaks and radar illusions based on transformation optics, carpet cloak using gradient metamaterials, dc cloaks, mantle cloaks based on scattering cancellation, “skin” cloaks using phase compensation, scattering controls with coding/programmable metasurfaces, and scattering reductions by multilayered structures. Finally, the future development of metamaterials on scattering manipulation is predicted.
Randomized approximate nearest neighbors algorithm.
Jones, Peter Wilcox; Osipov, Andrei; Rokhlin, Vladimir
2011-09-20
We present a randomized algorithm for the approximate nearest neighbor problem in d-dimensional Euclidean space. Given N points {x(j)} in R(d), the algorithm attempts to find k nearest neighbors for each of x(j), where k is a user-specified integer parameter. The algorithm is iterative, and its running time requirements are proportional to T·N·(d·(log d) + k·(d + log k)·(log N)) + N·k(2)·(d + log k), with T the number of iterations performed. The memory requirements of the procedure are of the order N·(d + k). A by-product of the scheme is a data structure, permitting a rapid search for the k nearest neighbors among {x(j)} for an arbitrary point x ∈ R(d). The cost of each such query is proportional to T·(d·(log d) + log(N/k)·k·(d + log k)), and the memory requirements for the requisite data structure are of the order N·(d + k) + T·(d + N). The algorithm utilizes random rotations and a basic divide-and-conquer scheme, followed by a local graph search. We analyze the scheme's behavior for certain types of distributions of {x(j)} and illustrate its performance via several numerical examples.
Scattering of Electromagnetic Waves by Drift Vortex in Plasma
Institute of Scientific and Technical Information of China (English)
WANG Dong; CHEN Yinhua; WANG Ge
2008-01-01
In a quasi-two-dimensional model, the scattering of incident ordinary electromag-netic 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 (kia << 1), it is found that the angle at which the scattering cross-section reaches its maxim depends significantly on the approxi-mation 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 ki<< 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.
High-energy limit of quantum electrodynamics beyond Sudakov approximation
Directory of Open Access Journals (Sweden)
Alexander A. Penin
2015-05-01
Full Text Available We study the high-energy behavior of the scattering amplitudes in quantum electrodynamics beyond the leading order of the small electron mass expansion in the leading logarithmic approximation. In contrast to the Sudakov logarithms, the mass-suppressed double-logarithmic radiative corrections are induced by a soft electron pair exchange and result in enhancement of the power-suppressed contribution, which dominates the amplitudes at extremely high energies. Possible applications of our result to the analysis of the high-energy processes in quantum chromodynamics is also discussed.
High-energy limit of quantum electrodynamics beyond Sudakov approximation
Energy Technology Data Exchange (ETDEWEB)
Penin, Alexander A., E-mail: penin@ualberta.ca [Department of Physics, University of Alberta, Edmonton, Alberta T6G 2J1 (Canada); Institut für Theoretische Teilchenphysik, Karlsruhe Institute of Technology, 76128 Karlsruhe (Germany)
2015-05-18
We study the high-energy behavior of the scattering amplitudes in quantum electrodynamics beyond the leading order of the small electron mass expansion in the leading logarithmic approximation. In contrast to the Sudakov logarithms, the mass-suppressed double-logarithmic radiative corrections are induced by a soft electron pair exchange and result in enhancement of the power-suppressed contribution, which dominates the amplitudes at extremely high energies. Possible applications of our result to the analysis of the high-energy processes in quantum chromodynamics is also discussed.
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.
Dynamically generated open charmed baryons beyond the zero range approximation
Jimenez-Tejero, C E; Vidaña, I
2009-01-01
The interaction of the low lying pseudo-scalar mesons with the ground state baryons in the charm sector is studied within a coupled channel approach using a t-channel vector-exchange driving force. The amplitudes describing the scattering of the pseudo-scalar mesons off the ground-state baryons are obtained by solving the Lippmann--Schwinger equation. We analyze in detail the effects of going beyond the $t=0$ approximation. Our model predicts the dynamical generation of several open charmed baryon resonances in different isospin and strangeness channels, some of which can be clearly identified with recently observed states.
Polyhedral Scattering of Fundamental Monopoles
Battye, R; Rychenkova, P; Sutcliffe, P; Battye, Richard; Gibbons, Gary; Rychenkova, Paulina; Sutcliffe, Paul
2003-01-01
The dynamics of n slowly moving fundamental monopoles in the SU(n+1) BPS Yang-Mills-Higgs theory can be approximated by geodesic motion on the 4n-dimensional hyperkahler Lee-Weinberg-Yi manifold. In this paper we apply a variational method to construct some scaling geodesics on this manifold. These geodesics describe the scattering of n monopoles which lie on the vertices of a bouncing polyhedron; the polyhedron contracts from infinity to a point, representing the spherically symmetric n-monopole, and then expands back out to infinity. For different monopole masses the solutions generalize to form bouncing nested polyhedra. The relevance of these results to the dynamics of well separated SU(2) monopoles is also discussed.
Applied electromagnetic scattering theory
Osipov, Andrey A
2017-01-01
Besides classical applications (radar and stealth, antennas, microwave engineering), scattering and diffraction are enabling phenomena for some emerging research fields (artificial electromagnetic materials or metamaterials, terahertz technologies, electromagnetic aspects of nano-science). This book is a tutorial for advanced students who need to study diffraction theory. The textbook gives fundamental knowledge about scattering and diffraction of electromagnetic waves and provides some working examples of solutions for practical high-frequency scattering and diffraction problems. The book focuses on the most important diffraction effects and mechanisms influencing the scattering process and describes efficient and physically justified simulation methods - physical optics (PO) and the physical theory of diffraction (PTD) - applicable in typical remote sensing scenarios. The material is presented in a comprehensible and logical form, which relates the presented results to the basic principles of electromag...
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...
Dremin, I M
2012-01-01
When colliding, the high energy hadrons can either produce new particles or scatter elastically without change of their quantum num- bers and other particles produced. Namely elastic scattering of hadrons is considered in this review paper. Even though the inelastic processes dominate at high energies, the elastic scattering constitutes the notice- able part of the total cross section ranging between 18 and 25% with some increase at higher energies. The scattering proceeds mostly at small angles and reveals peculiar dependences at larger angles disclos- ing the geometrical structure of the colliding particles and di?erent dynamical mechanisms. The fast decreasing Gaussian peak at small angles is followed by the exponential (Orear) regime with some shoul- ders and dips and then by the power-like decrease. Results of various theoretical approaches are compared with exper- imental data. Phenomenological models pretending to describe this process are reviewed. The unitarity condition requires the exponen- tial re...
Environment scattering in GADRAS.
Energy Technology Data Exchange (ETDEWEB)
Thoreson, Gregory G.; Mitchell, Dean J; Theisen, Lisa Anne; Harding, Lee T.
2013-09-01
Radiation transport calculations were performed to compute the angular tallies for scattered gamma-rays as a function of distance, height, and environment. Greens Functions were then used to encapsulate the results a reusable transformation function. The calculations represent the transport of photons throughout scattering surfaces that surround sources and detectors, such as the ground and walls. Utilization of these calculations in GADRAS (Gamma Detector Response and Analysis Software) enables accurate computation of environmental scattering for a variety of environments and source configurations. This capability, which agrees well with numerous experimental benchmark measurements, is now deployed with GADRAS Version 18.2 as the basis for the computation of scattered radiation.
True and false symmetries in the classification of optical scatterers
Crosta, Giovanni F.; Videen, Gorden
2014-05-01
A plane wave is scattered by a potential of bounded support. Translation, rotation and reflection of the potential, q0 induce transformations of the scattered wave. The latter can be represented by means of Born sequences, where q0 appears under the integral sign: non-local formulas are thus derived, the properties of which are discussed. Next, the symmetries induced by the 1st BORN approximation are addressed. Invariance of the squared modulus of the scattering amplitude holds for translation and reflection. The transformation Tɛ := 13 +Σ3ℓ=1ɛℓAℓ, with {ɛℓ;} real and {Aℓ} the generators of rotations in IR3, is investigated. Conditions on the {ɛ ℓ} are derived, by which the scattering amplitude coming from the first BORN approximation is invariant to Tɛ. As an application, these "false symmetries" are compared to those induced by limited angular resolution of a detector in light scattering experiments. Namely, scattering patterns are made available by the TAOS (Two-dimensional Angle-resolved Optical Scattering) method, which consists of detecting single airborne aerosol particles and collecting the intensity of the light they scatter from a pulsed, monochromatic laser beam. The optics and the detector properties determine the resolution at which a pattern is saved. The implications on the performance of TAOS pattern analysis are briefly discussed.
Park, Kiwan
2012-01-01
Models of large scale (magnetohydrodynamic) dynamos (LSD) which couple large scale field growth to total magnetic helicity evolution best predict the saturation of LSDs seen in simulations. For the simplest so called "{\\alpha}2" LSDs in periodic boxes, the electromotive force driving LSD growth depends on the difference between the time-integrated kinetic and current helicity associated with fluctuations. When the system is helically kinetically forced (KF), the growth of the large scale helical field is accompanied by growth of small scale magnetic (and current) helicity which ultimately quench the LSD. Here, using both simulations and theory, we study the complementary magnetically forced(MF) case in which the system is forced with an electric field that supplies magnetic helicity. For this MF case, the kinetic helicity becomes the back-reactor that saturates the LSD. Simulations of both MF and KF cases can be approximately modeled with the same equations of magnetic helicity evolution, but with complementa...
DEFF Research Database (Denmark)
Gudel, H. U.; Furrer, A.; Kjems, Jørgen
1986-01-01
Insulating compounds containing dimers of transition metal and rare earth ions have been studied by inelastic neutron scattering (INS). Energy splittings can be directly determined, and the corresponding parameters are easily extracted from the experimental data. The intensities of dimer excitati......Insulating compounds containing dimers of transition metal and rare earth ions have been studied by inelastic neutron scattering (INS). Energy splittings can be directly determined, and the corresponding parameters are easily extracted from the experimental data. The intensities of dimer...
Dremin, I. M.
2013-01-01
Colliding high-energy hadrons either produce new particles or scatter elastically with their quantum numbers conserved and no other particles produced. We consider the latter case here. Although inelastic processes dominate at high energies, elastic scattering contributes considerably (18-25%) to the total cross section. Its share first decreases and then increases at higher energies. Small-angle scattering prevails at all energies. Some characteristic features can be seen that provide information on the geometrical structure of the colliding particles and the relevant dynamical mechanisms. The steep Gaussian peak at small angles is followed by the exponential (Orear) regime with some shoulders and dips, and then by a power-law decrease. Results from various theoretical approaches are compared with experimental data. Phenomenological models claiming to describe this process are reviewed. The unitarity condition predicts an exponential fall for the differential cross section with an additional substructure to occur exactly between the low momentum transfer diffraction cone and a power-law, hard parton scattering regime under high momentum transfer. Data on the interference of the Coulomb and nuclear parts of amplitudes at extremely small angles provide the value of the real part of the forward scattering amplitude. The real part of the elastic scattering amplitude and the contribution of inelastic processes to the imaginary part of this amplitude (the so-called overlap function) are also discussed. Problems related to the scaling behavior of the differential cross section are considered. The power-law regime at highest momentum transfer is briefly described.
Metastable neon collisions: anisotropy and scattering length
Mogendorff, V P; Verhaar, B J; Beijerinck, H C W
2003-01-01
In this paper we investigate the effective scattering length $a$ of spin-polarized Ne*. Due to its anisotropic electrostatic interaction, its scattering length is determined by five interaction potentials instead of one, even in the spin-polarized case, a unique property among the Bose condensed species and candidates. Because the interaction potentials of Ne* are not known accurately enough to predict the value of the scattering length, we investigate the behavior of $a$ as a function of the five phase integrals corresponding to the five interaction potentials. We find that the scattering length has five resonances instead of only one and cannot be described by a simple gas-kinetic approach or the DIS approximation. However, the probability for finding a positive or large value of the scattering length is not enhanced compared to the single potential case. The complex behavior of $a$ is studied by comparing a quantum mechanical five-channel numerical calculation to simpler two-channel models. We find that th...
Scattered surface wave energy in the seismic coda
Zeng, Y.
2006-01-01
One of the many important contributions that Aki has made to seismology pertains to the origin of coda waves (Aki, 1969; Aki and Chouet, 1975). In this paper, I revisit Aki's original idea of the role of scattered surface waves in the seismic coda. Based on the radiative transfer theory, I developed a new set of scattered wave energy equations by including scattered surface waves and body wave to surface wave scattering conversions. The work is an extended study of Zeng et al. (1991), Zeng (1993) and Sato (1994a) on multiple isotropic-scattering, and may shed new insight into the seismic coda wave interpretation. The scattering equations are solved numerically by first discretizing the model at regular grids and then solving the linear integral equations iteratively. The results show that scattered wave energy can be well approximated by body-wave to body wave scattering at earlier arrival times and short distances. At long distances from the source, scattered surface waves dominate scattered body waves at surface stations. Since surface waves are 2-D propagating waves, their scattered energies should in theory follow a common decay curve. The observed common decay trends on seismic coda of local earthquake recordings particular at long lapse times suggest that perhaps later seismic codas are dominated by scattered surface waves. When efficient body wave to surface wave conversion mechanisms are present in the shallow crustal layers, such as soft sediment layers, the scattered surface waves dominate the seismic coda at even early arrival times for shallow sources and at later arrival times for deeper events.
Obtaining exact value by approximate computations
Institute of Scientific and Technical Information of China (English)
Jing-zhong ZHANG; Yong FENG
2007-01-01
Numerical approximate computations can solve large and complex problems fast. They have the advantage of high efficiency. However they only give approximate results, whereas we need exact results in some fields. There is a gap between approximate computations and exact results.In this paper, we build a bridge by which exact results can be obtained by numerical approximate computations.
Fuzzy Set Approximations in Fuzzy Formal Contexts
Institute of Scientific and Technical Information of China (English)
Mingwen Shao; Shiqing Fan
2006-01-01
In this paper, a kind of multi-level formal concept is introduced. Based on the proposed multi-level formal concept, we present a pair of rough fuzzy set approximations within fuzzy formal contexts. By the proposed rough fuzzy set approximations, we can approximate a fuzzy set according to different precision level. We discuss the properties of the proposed approximation operators in detail.
Obtaining exact value by approximate computations
Institute of Scientific and Technical Information of China (English)
2007-01-01
Numerical approximate computations can solve large and complex problems fast.They have the advantage of high efficiency.However they only give approximate results,whereas we need exact results in some fields.There is a gap between approximate computations and exact results. In this paper,we build a bridge by which exact results can be obtained by numerical approximate computations.
Anomalies of the Schwinger phase shifts in the static exchange approximation
Energy Technology Data Exchange (ETDEWEB)
Apagyi, B.; Levay, P.; Ladanyi, K.
1988-06-15
The Schwinger variational method is applied to the static exchange approximation of the electron--hydrogen-atom scattering. Spurious singularities are encountered in singlet scattering processes. The position of the poles is investigated by a simple numerical procedure. Anomalous poles appear in narrow regions of the nonlinear scale parameter. Results are presented which illustrate the behavior of the phase shifts around the spurious poles. No Kohn-type anomalies are encountered in the triplet case. As a byproduct, it is discussed that the Schwinger formula may be approximated in a separable form which is relatively simple but not free of anomalies.
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...... with algorithmic constraints: thresholding and Chebychev approximation classes are studied, respectively. We consider embeddings of the Jackson type (direct estimates) of sparsity spaces into the mentioned approximation classes. General direct estimates are based on the geometry of the Banach space, and we prove...
Nonlinear approximation with dictionaries, I: Direct estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
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 with algorithmic constraints: thresholding and Chebychev approximation classes are studied respectively. We consider embeddings of the Jackson type (direct estimates) of sparsity spaces into the mentioned approximation classes. General direct estimates are based on the geometry of the Banach space...
Electronic Flux Density beyond the Born-Oppenheimer Approximation.
Schild, Axel; Agostini, Federica; Gross, E K U
2016-05-19
In the Born-Oppenheimer approximation, the electronic wave function is typically real-valued and hence the electronic flux density (current density) seems to vanish. This is unfortunate for chemistry, because it precludes the possibility to monitor the electronic motion associated with the nuclear motion during chemical rearrangements from a Born-Oppenheimer simulation of the process. We study an electronic flux density obtained from a correction to the electronic wave function. This correction is derived via nuclear velocity perturbation theory applied in the framework of the exact factorization of electrons and nuclei. To compute the correction, only the ground state potential energy surface and the electronic wave function are needed. For a model system, we demonstrate that this electronic flux density approximates the true one very well, for coherent tunneling dynamics as well as for over-the-barrier scattering, and already for mass ratios between electrons and nuclei that are much larger than the true mass ratios.
Superfluid Thomas—Fermi approximation for trapped fermi gases
Hernández, E. S.; Capuzzi, P.; Szybisz, L.
2009-02-01
We present a generalization of fermionic fluiddynamics to the case of two trapped fermion species with a contact interaction. Within a mean field approximation, we derive coupled equations of motion for the particle densities, particle currents, and anomalous pair density. For an inhomogeneous system, the equilibrium situation with vanishing currents is described by a generalized Thomas-Fermi relation that includes the superfluid gap, together with a new nonlocal gap equation that replaces the usual BCS one. These equations are numericaly solved resorting to a local density approximation (LDA). Density and gap profiles are analyzed in terms of the scattering length, revealing that the current frame can exhibit microscopic details of quantum origin that are frequently absent in more macroscopic scenarios.
Superfluid Thomas-Fermi approximation for trapped fermi gases
Energy Technology Data Exchange (ETDEWEB)
Hernandez, E S; Capuzzi, P; Szybisz, L [Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires (Argentina)], E-mail: shernand@df.uba.ar, E-mail: capuzzi@df.uba.ar, E-mail: szybisz@tandar.cnea.gov.ar
2009-02-01
We present a generalization of fermionic fluiddynamics to the case of two trapped fermion species with a contact interaction. Within a mean field approximation, we derive coupled equations of motion for the particle densities, particle currents, and anomalous pair density. For an inhomogeneous system, the equilibrium situation with vanishing currents is described by a generalized Thomas-Fermi relation that includes the superfluid gap, together with a new nonlocal gap equation that replaces the usual BCS one. These equations are numericaly solved resorting to a local density approximation (LDA). Density and gap profiles are analyzed in terms of the scattering length, revealing that the current frame can exhibit microscopic details of quantum origin that are frequently absent in more macroscopic scenarios.
Approximate formulation of redistribution in the Ly-alpha, Ly-beta, H-alpha system
Cooper, J.; Ballagh, R. J.; Hubeny, I.
1989-01-01
Simple approximate formulas are given for the coupled redistribution of Ly-alpha, Ly-beta, and H-alpha, by using well-defined approximations to an essentially exact formulation. These formulas incorporate all the essential physics including Raman scattering, lower state radiative decay, and correlated terms representing emission during a collision which must be retained in order that the emission coefficients are properly behaved in the line wings. Approximate expressions for the appropriate line broadening parameters are collected. Finally, practical expressions for the source functions are given. These are formulated through newly introduced nonimpact redistribution functions, which are shown to be reasonably approximated by existing (ordinary and generalized) redistribution functions.
Energy Technology Data Exchange (ETDEWEB)
Baron, A.Q.R.
1995-04-01
This thesis explores resonant nudear scattering of synchrotron radiation. An introductory chapter describes some useful concepts, such as speedup and coherent enhancement, in the context of some basic physical principles. Methods of producing highly monochromatic synchrotron beams usmg either electronic or nuclear scattering are also discussed. The body of the thesis concentrates on detector development and specular scattering from iynthetic layered materials. A detector employing n-dcrochannel plate electron multipliers is shown to have good ({approximately}50%) effidency for detecting 14.4 key x-rays incident at small ({approximately}0.5 degree) grazing angles onto Au or CsI photocathodes. However, being complicated to use, it was replaced with a large area (>=lan2) avalanche photodiode (APD) detector. The APD`s are simpler to use and have comparable (30--70%) efficiencies at 14.4 key, subnanosecond time resolution, large dynan-dc range (usable at rates up to {approximately}10{sup 8} photons/second) and low (<{approximately}0.01 cts/sec) background rates. Maxwell`s equations are used to derive the specular x-ray reflectivity of layered materials with resonant transitions and complex polarization dependencies. The effects of interfadal roughness are treated with some care, and the distorted wave Born approximation (DWBA) used to describe electronic scattering is generalized to the nuclear case. The implications of the theory are discussed in the context of grazing incidence measurements with emphasis on the kinematic and dynamical aspects of the scattering.
One dimensional scattering of a two body interacting system by an infinite wall
Moro, A M; Gomez-Camacho, J
2010-01-01
The one-dimensional scattering of a two body interacting system by an infinite wall is studied in a quantum-mechanical framework. This problem contains some of the dynamical features present in the collision of atomic, molecular and nuclear systems. The scattering problem is solved exactly, for the case of a harmonic interaction between the fragments. The exact result is used to assess the validity of two different approximations to the scattering process. The adiabatic approximation, which considers that the relative co-ordinate is frozen during the scattering process, is found to be inadequate for this problem. The uncorrelated scattering approximation, which neglects the correlation between the fragments, gives results in accordance with the exact calculations when the scattering energy is high compared to the oscillator parameter.
Shao, Hongbing
Software testing with scientific software systems often suffers from test oracle problem, i.e., lack of test oracles. Amsterdam discrete dipole approximation code (ADDA) is a scientific software system that can be used to simulate light scattering of scatterers of various types. Testing of ADDA suffers from "test oracle problem". In this thesis work, I established a testing framework to test scientific software systems and evaluated this framework using ADDA as a case study. To test ADDA, I first used CMMIE code as the pseudo oracle to test ADDA in simulating light scattering of a homogeneous sphere scatterer. Comparable results were obtained between ADDA and CMMIE code. This validated ADDA for use with homogeneous sphere scatterers. Then I used experimental result obtained for light scattering of a homogeneous sphere to validate use of ADDA with sphere scatterers. ADDA produced light scattering simulation comparable to the experimentally measured result. This further validated the use of ADDA for simulating light scattering of sphere scatterers. Then I used metamorphic testing to generate test cases covering scatterers of various geometries, orientations, homogeneity or non-homogeneity. ADDA was tested under each of these test cases and all tests passed. The use of statistical analysis together with metamorphic testing is discussed as a future direction. In short, using ADDA as a case study, I established a testing framework, including use of pseudo oracles, experimental results and the metamorphic testing techniques to test scientific software systems that suffer from test oracle problems. Each of these techniques is necessary and contributes to the testing of the software under test.
Scattering in the ultrastrong regime: nonlinear optics with one photon
Sánchez-Burillo, Eduardo; Zueco, David; García-Ripoll, Juanjo; Martín-Moreno, Luis
2014-01-01
The scattering of a flying photon by a two-level system ultrastrongly coupled to a one-dimensional photonic waveguide is studied numerically. The photonic medium is modeled as an array of coupled cavities and the whole system is analyzed beyond the rotating wave approximation using Matrix Product States. It is found that the scattering is strongly influenced by the single- and multi-photon dressed bound states present in the system. In the ultrastrong coupling regime a new channel for inelast...
Efficient light propagation for multiple anisotropic volume scattering
Energy Technology Data Exchange (ETDEWEB)
Max, N. [Lawrence Livermore National Lab., CA (United States)]|[California Univ., Davis, CA (United States)
1993-12-01
Realistic rendering of participating media like clouds requires multiple anisotropic light scattering. This paper presents a propagation approximation for light scattered into M direction bins, which reduces the ``ray effect`` problem in the traditional ``discrete ordinates`` method. For a volume of n{sup 3} elements, it takes O(M n{sup 3} log n + M{sup 2} n{sup 3}) time and O(M n{sup 3}) space.
A New Glauber Theory based on Multiple Scattering Theory
Yahiro, Masanobu; Ogata, Kazuyuki; Kawai, Mitsuji
2008-01-01
Glauber theory for nucleus-nucleus scattering at high incident energies is reformulated so as to become applicable also for the scattering at intermediate energies. We test validity of the eikonal and adiabatic approximations used in the formulation, and discuss the relation between the present theory and the conventional Glauber calculations with either the empirical nucleon-nucleon profile function or the modified one including the in-medium effect.
Mott scattering of polarized electrons in a strong laser field
Manaut, B; Attaourti, Y
2004-01-01
We present analytical and numerical results of the relativistic calculation of the transition matrix element $S_{fi}$ and differential cross section for Mott scattering of initially polarized Dirac particles (electrons) in the presence of strong laser field with linear polarization. We use exact Dirac-Volkov wave functions to describe the dressed electrons and the collision process is treated in the first Born approximation. The influence of the laser field on the degree of polarization of the scattered electron is reported.
EM Scattering from Conducting Flat Plates Coated with Thin RAM
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
According to the equivalence principles, high frequency approximation and boundary conditions, a method has been developed to deal with the EM scattering by a rectangular conducting flat plate coated with uniaxial anisotropic radar absorbing material (RAM). The simple and effective method is available to the system of RCS prediction in which the large complex targets modeled by facets and wedges. Numerical results show some properties of EM scattering by conducting plate coated with thin uniaxial anisotropic RAM.
Miller, Erin A; Caggiano, Joseph A; Runkle, Robert C; White, Timothy A; Bevill, Aaron M
2011-03-01
As a complement to passive detection systems, radiographic inspection of cargo is an increasingly important tool for homeland security because it has the potential to detect highly attenuating objects associated with special nuclear material or surrounding shielding, in addition to screening for items such as drugs or contraband. Radiographic detection of such threat objects relies on high image contrast between regions of different density and atomic number (Z). Threat detection is affected by scatter of the interrogating beam in the cargo, the radiographic system itself, and the surrounding environment, which degrades image contrast. Here, we estimate the extent to which scatter plays a role in radiographic imaging of cargo containers. Stochastic transport simulations were performed to determine the details of the radiography equipment and surrounding environment, which are important in reproducing measured data and to investigate scatter magnitudes for typical cargo. We find that scatter plays a stronger role in cargo radiography than in typical medical imaging scenarios, even for low-density cargo, with scatter-to-primary ratios ranging from 0.14 for very low density cargo, to between 0.20 and 0.40 for typical cargo, and higher yet for dense cargo.
Multiscale analysis of the acoustic scattering by many scatterers of impedance type
Challa, Durga Prasad; Sini, Mourad
2016-06-01
We are concerned with the acoustic scattering problem, at a frequency {κ}, by many small obstacles of arbitrary shapes with impedance boundary condition. These scatterers are assumed to be included in a bounded domain {Ω} in {{R}^3} which is embedded in an acoustic background characterized by an eventually locally varying index of refraction. The collection of the scatterers {D_m, m=1,ldots,M} is modeled by four parameters: their number M, their maximum radius a, their minimum distance d and the surface impedances {λ_m, m=1,ldots,M}. We consider the parameters M, d and {λ_m}'s having the following scaling properties: {M:=M(a)=O(a^{-s}), d:=d(a)≈ a^t} and {λ_m:=λ_m(a)=λ_{m,0}a^{-β}}, as {a→ 0}, with non negative constants s, t and {β} and complex numbers {λ_{m, 0}}'s with eventually negative imaginary parts. We derive the asymptotic expansion of the far-fields with explicit error estimate in terms of a, as {a→ 0}. The dominant term is the Foldy-Lax field corresponding to the scattering by the point-like scatterers located at the centers {z_m}'s of the scatterers {D_m}'s with {λ_m \\vert partial D_m\\vert} as the related scattering coefficients. This asymptotic expansion is justified under the following conditions a ≤ a_0, \\vert Re (λ_{m,0})\\vert ≥ λ_-,quad \\vertλ_{m,0}\\vert ≤ λ_+,quad β quad 0 ≤ s ≤2-β,quads/3 ≤ t and the error of the approximation is {C a^{3-2β-s}}, as {a → 0}, where the positive constants {a_0, λ_-,λ_+} and C depend only on the a priori uniform bounds of the Lipschitz characters of the obstacles {D_m}'s and the ones of {M(a)a^s} and {d(a)/a^t}. We do not assume the periodicity in distributing the small scatterers. In addition, the scatterers can be arbitrary close since t can be arbitrary large, i.e., we can handle the mesoscale regime. Finally, for spherical scatterers, we can also allow the limit case {β=1} with a slightly better error of the approximation.
Elastic scattering of gamma rays and X-rays
Energy Technology Data Exchange (ETDEWEB)
Kane, P.P. [Physics Department, Indian Institute of Technology, Powai, Mumbai 400076 (India)]. E-mail: ppkane@vsnl.com
2005-12-15
Studies of elastic gamma ray scattering were pursued independently by the groups of Prof. Ghose and the author for several decades in spite of somewhat meagre support. Several techniques for such studies developed by the two groups and some of the results obtained in the energy range from tens of keV to about 1.5 MeV are described briefly. The theoretical background necessary for understanding these results is also outlined. The results showed the importance of Modified Relativistic Form Factor (MRFF) approximation in the explanation of atomic Rayleigh scattering cross sections in the small angle regime and the necessity for an inclusion of real Delbrueck scattering amplitudes at large scattering angles. Dispersion corrections to form factor amplitudes or the so-called anomalous scattering factors are shown to be needed at photon energies close to electron binding energy thresholds. A few promising future extensions of such studies are indicated at the end.
Scattering from elastic sea beds: first-order theory.
Jackson, D R; Ivakin, A N
1998-01-01
A perturbation model for high-frequency sound scattering from an irregular elastic sea bed is considered. The sea bed is assumed homogeneous on the average and two kinds of irregularities are assumed to cause scattering: roughness of the water-sea bed interface and volume inhomogeneities of the sediment mass density and the speeds of compressional and shear waves. The first-order small perturbation approximation is used to obtain expressions for the scattering amplitude and bistatic scattering strength. The angular dependence of the scattering strength is calculated for sedimentary rock and the influence of shear elasticity is examined by comparison with the case of a fluid bottom. Shear effects are shown to be strong and complicated.
The Generalized Quasilinear Approximation: Application to Zonal Jets
Marston, J B; Tobias, S M
2016-01-01
Quasilinear theory is often utilized to approximate the dynamics of fluids exhibiting significant interactions between mean flows and eddies. In this paper we present a generalization of quasilinear theory to include dynamic mode interactions on the large scales. This generalized quasilinear (GQL) approximation is achieved by separating the state variables into large and small zonal scales via a spectral filter rather than by a decomposition into a formal mean and fluctuations. Nonlinear interactions involving only small zonal scales are then removed. The approximation is conservative and allows for scattering of energy between small-scale modes via the large scale (through non-local spectral interactions). We evaluate GQL for the paradigmatic problems of the driving of large-scale jets on a spherical surface and on the beta-plane and show that it is accurate even for a small number of large-scale modes. As this approximation is formally linear in the small zonal scales it allows for the closure of the system...
APPROXIMATE SAMPLING THEOREM FOR BIVARIATE CONTINUOUS FUNCTION
Institute of Scientific and Technical Information of China (English)
杨守志; 程正兴; 唐远炎
2003-01-01
An approximate solution of the refinement equation was given by its mask, and the approximate sampling theorem for bivariate continuous function was proved by applying the approximate solution. The approximate sampling function defined uniquely by the mask of the refinement equation is the approximate solution of the equation, a piece-wise linear function, and posseses an explicit computation formula. Therefore the mask of the refinement equation is selected according to one' s requirement, so that one may controll the decay speed of the approximate sampling function.
Bernstein-type approximations of smooth functions
Directory of Open Access Journals (Sweden)
Andrea Pallini
2007-10-01
Full Text Available The Bernstein-type approximation for smooth functions is proposed and studied. We propose the Bernstein-type approximation with definitions that directly apply the binomial distribution and the multivariate binomial distribution. The Bernstein-type approximations generalize the corresponding Bernstein polynomials, by considering definitions that depend on a convenient approximation coefficient in linear kernels. In the Bernstein-type approximations, we study the uniform convergence and the degree of approximation. The Bernstein-type estimators of smooth functions of population means are also proposed and studied.
Virtual neutron scattering experiments
DEFF Research Database (Denmark)
Overgaard, Julie Hougaard; Bruun, Jesper; May, Michael
2017-01-01
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....... 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...... on physics and data rather than the overwhelming instrumentation. We argue that this is because they can transfer their virtual experimental experience to the real-life situation. However, we also find that learning is still situated in the sense that only knowledge of particular experiments is transferred...
Virtual neutron scattering experiments
DEFF Research Database (Denmark)
Overgaard, Julie Hougaard; Bruun, Jesper; May, Michael
2016-01-01
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....... 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...... on physics and data rather than the overwhelming instrumentation. We argue that this is because they can transfer their virtual experimental experience to the real-life situation. However, we also find that learning is still situated in the sense that only knowledge of particular experiments is transferred...
Invariant Scattering Convolution Networks
Bruna, Joan
2012-01-01
A wavelet scattering network computes a translation invariant image representation, which is stable to deformations and preserves high frequency information for classification. It cascades wavelet transform convolutions with non-linear modulus and averaging operators. The first network layer outputs SIFT-type descriptors whereas the next layers provide complementary invariant information which improves classification. The mathematical analysis of wavelet scattering networks explains important properties of deep convolution networks for classification. A scattering representation of stationary processes incorporates higher order moments and can thus discriminate textures having the same Fourier power spectrum. State of the art classification results are obtained for handwritten digits and texture discrimination, using a Gaussian kernel SVM and a generative PCA classifier.
Energy Technology Data Exchange (ETDEWEB)
ZALIZNYAK,I.A.; LEE,S.H.
2004-07-30
Much of our understanding of the atomic-scale magnetic structure and the dynamical properties of solids and liquids was gained from neutron-scattering studies. Elastic and inelastic neutron spectroscopy provided physicists with an unprecedented, detailed access to spin structures, magnetic-excitation spectra, soft-modes and critical dynamics at magnetic-phase transitions, which is unrivaled by other experimental techniques. Because the neutron has no electric charge, it is an ideal weakly interacting and highly penetrating probe of matter's inner structure and dynamics. Unlike techniques using photon electric fields or charged particles (e.g., electrons, muons) that significantly modify the local electronic environment, neutron spectroscopy allows determination of a material's intrinsic, unperturbed physical properties. The method is not sensitive to extraneous charges, electric fields, and the imperfection of surface layers. Because the neutron is a highly penetrating and non-destructive probe, neutron spectroscopy can probe the microscopic properties of bulk materials (not just their surface layers) and study samples embedded in complex environments, such as cryostats, magnets, and pressure cells, which are essential for understanding the physical origins of magnetic phenomena. Neutron scattering is arguably the most powerful and versatile experimental tool for studying the microscopic properties of the magnetic materials. The magnitude of the cross-section of the neutron magnetic scattering is similar to the cross-section of nuclear scattering by short-range nuclear forces, and is large enough to provide measurable scattering by the ordered magnetic structures and electron spin fluctuations. In the half-a-century or so that has passed since neutron beams with sufficient intensity for scattering applications became available with the advent of the nuclear reactors, they have became indispensable tools for studying a variety of important areas of modern
Energy Technology Data Exchange (ETDEWEB)
Quaglioni, S; Navratil, P; Roth, R
2009-12-15
The exact treatment of nuclei starting from the constituent nucleons and the fundamental interactions among them has been a long-standing goal in nuclear physics. Above all nuclear scattering and reactions, which require the solution of the many-body quantum-mechanical problem in the continuum, represent an extraordinary theoretical as well as computational challenge for ab initio approaches.We present a new ab initio many-body approach which derives from the combination of the ab initio no-core shell model with the resonating-group method [4]. By complementing a microscopic cluster technique with the use of realistic interactions, and a microscopic and consistent description of the nucleon clusters, this approach is capable of describing simultaneously both bound and scattering states in light nuclei. We will discuss applications to neutron and proton scattering on sand light p-shell nuclei using realistic nucleon-nucleon potentials, and outline the progress toward the treatment of more complex reactions.
$\\Lambda$ Scattering Equations
Gomez, Humberto
2016-01-01
The CHY representation of scattering amplitudes is based on integrals over the moduli space of a punctured sphere. We replace the punctured sphere by a double-cover version. The resulting scattering equations depend on a parameter $\\Lambda$ controlling the opening of a branch cut. The new representation of scattering amplitudes possesses an enhanced redundancy which can be used to fix, modulo branches, the location of four punctures while promoting $\\Lambda$ to a variable. Via residue theorems we show how CHY formulas break up into sums of products of smaller (off-shell) ones times a propagator. This leads to a powerful way of evaluating CHY integrals of generic rational functions, which we call the $\\Lambda$ algorithm.
Energy Technology Data Exchange (ETDEWEB)
ZALIZNYAK,I.A.; LEE,S.H.
2004-07-30
Much of our understanding of the atomic-scale magnetic structure and the dynamical properties of solids and liquids was gained from neutron-scattering studies. Elastic and inelastic neutron spectroscopy provided physicists with an unprecedented, detailed access to spin structures, magnetic-excitation spectra, soft-modes and critical dynamics at magnetic-phase transitions, which is unrivaled by other experimental techniques. Because the neutron has no electric charge, it is an ideal weakly interacting and highly penetrating probe of matter's inner structure and dynamics. Unlike techniques using photon electric fields or charged particles (e.g., electrons, muons) that significantly modify the local electronic environment, neutron spectroscopy allows determination of a material's intrinsic, unperturbed physical properties. The method is not sensitive to extraneous charges, electric fields, and the imperfection of surface layers. Because the neutron is a highly penetrating and non-destructive probe, neutron spectroscopy can probe the microscopic properties of bulk materials (not just their surface layers) and study samples embedded in complex environments, such as cryostats, magnets, and pressure cells, which are essential for understanding the physical origins of magnetic phenomena. Neutron scattering is arguably the most powerful and versatile experimental tool for studying the microscopic properties of the magnetic materials. The magnitude of the cross-section of the neutron magnetic scattering is similar to the cross-section of nuclear scattering by short-range nuclear forces, and is large enough to provide measurable scattering by the ordered magnetic structures and electron spin fluctuations. In the half-a-century or so that has passed since neutron beams with sufficient intensity for scattering applications became available with the advent of the nuclear reactors, they have became indispensable tools for studying a variety of important areas of modern
Momentum-space optical potential SND elastic scattering calculations
Energy Technology Data Exchange (ETDEWEB)
Wolfe, D.H.; Hynes, M.V.; Picklesimer, A.; Tandy, P.C.; Thaler, R.M.
1983-01-01
Initial results are presented for proton-nucleus elastic scattering observables calculated with a newly developed microscopic momentum-space code. This is the first phase of a program to treat elastic and inelastic scattering consistently via an integral equation approach. A number of microscopic features which are often approximated or ignored are quite amenable to exact treatment within this approach, e.g. non-local effects in elastic scattering, and inelastic effects which are non-linear in the NN t-matrix and target densities but nevertheless confined to one participating nucleon. 3 references.
Exploiting Universality in Atoms with Large Scattering Lengths
Energy Technology Data Exchange (ETDEWEB)
Braaten, Eric
2012-05-31
The focus of this research project was atoms with scattering lengths that are large compared to the range of their interactions and which therefore exhibit universal behavior at sufficiently low energies. Recent dramatic advances in cooling atoms and in manipulating their scattering lengths have made this phenomenon of practical importance for controlling ultracold atoms and molecules. This research project was aimed at developing a systematically improvable method for calculating few-body observables for atoms with large scattering lengths starting from the universal results as a first approximation. Significant progress towards this goal was made during the five years of the project.
Scattering and; Delay, Scale, and Sum Migration
Energy Technology Data Exchange (ETDEWEB)
Lehman, S K
2011-07-06
How do we see? What is the mechanism? Consider standing in an open field on a clear sunny day. In the field are a yellow dog and a blue ball. From a wave-based remote sensing point of view the sun is a source of radiation. It is a broadband electromagnetic source which, for the purposes of this introduction, only the visible spectrum is considered (approximately 390 to 750 nanometers or 400 to 769 TeraHertz). The source emits an incident field into the known background environment which, for this example, is free space. The incident field propagates until it strikes an object or target, either the yellow dog or the blue ball. The interaction of the incident field with an object results in a scattered field. The scattered field arises from a mis-match between the background refractive index, considered to be unity, and the scattering object refractive index ('yellow' for the case of the dog, and 'blue' for the ball). This is also known as an impedance mis-match. The scattering objects are referred to as secondary sources of radiation, that radiation being the scattered field which propagates until it is measured by the two receivers known as 'eyes'. The eyes focus the measured scattered field to form images which are processed by the 'wetware' of the brain for detection, identification, and localization. When time series representations of the measured scattered field are available, the image forming focusing process can be mathematically modeled by delayed, scaled, and summed migration. This concept of optical propagation, scattering, and focusing have one-to-one equivalents in the acoustic realm. This document is intended to present the basic concepts of scalar scattering and migration used in wide band wave-based remote sensing and imaging. The terms beamforming and (delayed, scaled, and summed) migration are used interchangeably but are to be distinguished from the narrow band (frequency domain) beamforming to determine
Generalized Levinson theorem: Applications to electron-atom scattering
Rosenberg, Leonard; Spruch, Larry
1996-12-01
A recent formulation provides an absolute definition of the zero-energy phase shift δ for multiparticle single-channel scattering of a particle by a neutral compound target in a given partial wave l. This formulation, along with the minimum principle for the scattering length, leads to a determination of δ that represents a generalization of Levinson's theorem. In its original form that theorem is applicable only to potential scattering of a particle and relates δ/π to the number of bound states of that l. The generalized Levinson theorem relates δ/π for scattering in a state of given angular momentum to the number of composite bound states of that angular momentum plus a calculable number that, for a system described in the Hartree-Fock approximation, is the number of states of that angular momentum excluded by the Pauli principle. Thus, for example, for electron scattering by Na, with its (1s)2(2s)2(2p)63s configuration and with one L=0 singlet composite bound state, δ would be π+2π for s-wave singlet scattering, 0+3π for s-wave triplet scattering, and 0+π for both triplet and singlet p-wave scattering; the Pauli contribution has been listed first. The method is applicable to a number of e+/--atom and nucleon-nucleus scattering processes, but only applications of the former type are described here. We obtain the absolute zero-energy phase shifts for e--H and e--He scattering and, in the Hartree-Fock approximation for the target, for atoms that include the noble gases, the alkali-metal atoms, and, as examples, B, C, N, O, and F, which have one, two, three, four, and five p electrons, respectively, outside of closed shells. In all cases, the applications provide results in agreement with expectations.
Yang, Zhi-Qiang; Liu, Shi-Wei; Sun, Yi
2016-09-01
This paper discusses a statistical second-order two-scale (SSOTS) analysis and computation for a heat conduction problem with a radiation boundary condition in random porous materials. Firstly, the microscopic configuration for the structure with random distribution is briefly characterized. Secondly, the SSOTS formulae for computing the heat transfer problem are derived successively by means of the construction way for each cell. Then, the statistical prediction algorithm based on the proposed two-scale model is described in detail. Finally, some numerical experiments are proposed, which show that the SSOTS method developed in this paper is effective for predicting the heat transfer performance of porous materials and demonstrating its significant applications in actual engineering computation. Project supported by the China Postdoctoral Science Foundation (Grant Nos. 2015M580256 and 2016T90276).
Neutron scattering. Experiment manuals
Energy Technology Data Exchange (ETDEWEB)
Brueckel, Thomas; Heger, Gernot; Richter, Dieter; Roth, Georg; Zorn, Reiner (eds.)
2014-07-01
The following topics are dealt with: The thermal triple-axis spectrometer PUMA, the high-resolution powder diffractometer SPODI, the hot-single-crystal diffractometer HEiDi, the three-axis spectrometer PANDA, the backscattering spectrometer SPHERES, the DNS neutron-polarization analysis, the neutron spin-echo spectrometer J-NSE, small-angle neutron scattering at KWS-1 and KWS-2, a very-small-angle neutron scattering diffractometer with focusing mirror, the reflectometer TREFF, the time-of-flight spectrometer TOFTOF. (HSI)
Inversion assuming weak scattering
DEFF Research Database (Denmark)
Xenaki, Angeliki; Gerstoft, Peter; Mosegaard, Klaus
2013-01-01
The study of weak scattering from inhomogeneous media or interface roughness has long been of interest in sonar applications. In an acoustic backscattering model of a stationary field of volume inhomogeneities, a stochastic description of the field is more useful than a deterministic description...... due to the complex nature of the field. A method based on linear inversion is employed to infer information about the statistical properties of the scattering field from the obtained cross-spectral matrix. A synthetic example based on an active high-frequency sonar demonstrates that the proposed...
Neutron scattering. Experiment manuals
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: The thermal triple axis spectrometer PUMA, the high-resolution powder diffractometer SPODI, the hot single-crystal diffractometer HEiDi for structure analysis with neutrons, the backscattering spectrometer SPHERES, neutron polarization analysis with tht time-of-flight spectrometer DNS, the neutron spin-echo spectrometer J-NSE, small-angle neutron scattering with the KWS-1 and KWS-2 diffractometers, the very-small-angle neutron scattering diffractrometer with focusing mirror KWS-3, the resonance spin-echo spectrometer RESEDA, the reflectometer TREFF, the time-of-flight spectrometer TOFTOF. (HSI)
Resonant-state-expansion Born approximation with a correct eigen-mode normalisation
Doost, M. B.
2016-08-01
The Born approximation (Born 1926 Z. Phys. 38 802) is a fundamental result in physics, it allows the calculation of weak scattering via the Fourier transform of the scattering potential. As was done by previous authors (Ge et al 2014 New J. Phys. 16 113048) the Born approximation is extended by including in the formula the resonant-states (RSs) of the scatterer. However in this study unlike previous studies the included eigen-modes are correctly normalised with dramatic positive consequences for the accuracy of the method. The normalisation of RSs used in the previous RS expansion Born approximation or resonant-state expansion (RSE) Born approximation made in Ge et al (2014 New J. Phys. 16 113048) has been shown to be numerically unstable in Muljarov et al (2014 arXiv:1409.6877) and by analytics here. The RSs of the system can be calculated using my recently discovered RSE perturbation theory for dispersive electrodynamic scatterers (Muljarov et al 2010 Europhys. Lett. 92 50010; Doost et al 2012 Phys. Rev. A 85 023835; Doost et al 2013 Phys. Rev. A 87 043827; Armitage et al 2014 Phys. Rev. A 89; Doost et al 2014 Phys. Rev. A 90 013834) and normalised correctly to appear in spectral Green's functions and hence the RSE Born approximation via the flux-volume normalisation which I recently rigorously derived in Armitage et al (2014 Phys. Rev. A 89), Doost et al (2014 Phys. Rev. A 90 013834), Doost (2016 Phys. Rev. A 93 023835). In the case of effectively one-dimensional systems I find a RSE Born approximation alternative to the scattering matrix method.
Radiative properties of materials with surface scattering or volume scattering: A review
Institute of Scientific and Technical Information of China (English)
Qunzhi ZHU; Hyunjin LEE; Zhuomin M. ZHANG
2009-01-01
Radiative properties of rough surfaces, parti-culate media and porous materials are important in thermal engineering and many other applications. These properties are often needed for calculating heat transfer between surfaces and volume elements in participating media, as well as for accurate radiometric temperature measure-ments. In this paper, recent research on scattering of thermal radiation by rough surfaces, fibrous insulation, soot, aerogel, biological materials, and polytetrafluor-oethylene (PTFE) is reviewed. Both theoretical modeling and experimental investigation are discussed. Rigorous solutions and approximation methods for surface scattering and volume scattering are described. The approach of using measured surface roughness statistics in Monte Carlo simulations to predict radiative properties of rough surfaces is emphasized. The effects of various parameters on the radiative properties of particulate media and porous materials are summarized.
Light scattering by fractal dust aggregates: I. Angular dependence of scattering
Tazaki, Ryo; Okuzumi, Satoshi; Kataoka, Akimasa; Nomura, Hideko
2016-01-01
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 (BPCAs). 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 scatteri...
The gap probability model for canopy thermal infrared emission with non-scattering approximation
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
To describe canopy emitting thermal radiance precisely and physically is one of the key researches in retrieving land surface temperature (LST) over vegetation-covered regions by remote sensing technology.This work is aimed at establishing gap probability models to describe the thermal emission characteristics in continuous plant,including the basic model and the sunlit model.They are suitable respectively in the nighttime and in the daytime.The sunlit model is the basic model plus a sunlit correcting item which takes the hot spot effect into account.The researches on the directional distribution of radiance and its relationship to canopy structural parameters,such as the leaf area index (LAI) and leaf angle distribution (LAD),were focused.The characteristics of directional radiance caused by temperature differences among components in canopy,such as those between leaf and soil,and between sunlit leaf or soil and shadowed leaf or soil,were analyzed.A well fitting between experimental data and the theoretical calculations shows that the models are able to illustrate the canopy thermal emission generally.
The gap probability model for canopy thermal infrared emission with non-scattering approximation
Institute of Scientific and Technical Information of China (English)
牛铮; 柳钦火; 高彦春; 张庆员; 王长耀
2000-01-01
To describe canopy emitting thermal radiance precisely and physically is one of the key researches in retrieving land surface temperature (LSI) over vegetation-covered regions by remote sensing technology. This work is aimed at establishing gap probability models to describe the thermal emission characteristics in continuous plant, including the basic model and the sunlit model. They are suitable respectively in the nighttime and in the daytime. The sunlit model is the basic model plus a sunlit correcting item which takes the hot spot effect into account. The researches on the directional distribution of radiance and its relationship to canopy structural parameters, such as the leaf area index (LAI) and leaf angle distribution (LAD), were focused. The characteristics of directional radiance caused by temperature differences among components in canopy, such as those between leaf and soil, and between sunlit leaf or soil and shadowed leaf or soil, were analyzed. A well fitting between experimental data an
Reintjes, Moritz
2015-01-01
It is an open question whether solutions of the Einstein-Euler equations are smooth enough to admit locally inertial coordinates at points of shock wave interaction, or whether "regularity singularities" can exist at such points. The term regularity singularity was proposed by the authors as a point in spacetime where the gravitational metric tensor is Lipschitz continuous ($C^{0,1}$), but no smoother, in any coordinate system of the $C^{1,1}$ atlas. An existence theory for shock wave solutions in $C^{0,1}$ admitting arbitrary interactions has been proven for the Einstein-Euler equations in spherically symmetric spacetimes, but $C^{1,1}$ is the requisite smoothness required for space-time to be locally flat. Thus the open problem of regularity singularities is the problem as to whether locally inertial coordinate systems exist at shock waves, within the larger $C^{1,1}$ atlas. Our purpose here is to clarify and motivate the open problem of regularity singularities, and to prove that if locally inertial coordi...
1988-03-01
the Hankel function as the argument asymptotically approaches infinity in equation (A-16). In Arfken 1 17 , the asymptotic form of the Hankel function...L, E. Horsely and C. M. Thompson, "The Aging of Cork-Rubber Decoupling Materials," Naval Research Laboratory Report No. 8458, (1981). 117. G. Arfken
Applications of Discrepancy Theory in Multiobjective Approximation
Glaßer, Christian; Witek, Maximilian
2011-01-01
We apply a multi-color extension of the Beck-Fiala theorem to show that the multiobjective maximum traveling salesman problem is randomized 1/2-approximable on directed graphs and randomized 2/3-approximable on undirected graphs. Using the same technique we show that the multiobjective maximum satisfiablilty problem is 1/2-approximable.
Fractal Trigonometric Polynomials for Restricted Range Approximation
Chand, A. K. B.; Navascués, M. A.; Viswanathan, P.; Katiyar, S. K.
2016-05-01
One-sided approximation tackles the problem of approximation of a prescribed function by simple traditional functions such as polynomials or trigonometric functions that lie completely above or below it. In this paper, we use the concept of fractal interpolation function (FIF), precisely of fractal trigonometric polynomials, to construct one-sided uniform approximants for some classes of continuous functions.
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.
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.
Nonlinear approximation with dictionaries, I: Direct estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
$-term approximation with algorithmic constraints: thresholding and Chebychev approximation classes are studied respectively. We consider embeddings of the Jackson type (direct estimates) of sparsity spaces into the mentioned approximation classes. General direct estimates are based on the geometry of the Banach space...
Operator approximant problems arising from quantum theory
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.
Advanced Concepts and Methods of Approximate Reasoning
1989-12-01
and L. Valverde. On mode and implication in approximate reasoning. In M.M. Gupta, A. Kandel, W. Bandler , J.B. Kiszka, editors, Approximate Reasoning and...190, 1981. [43] E. Trillas and L. Valverde. On mode and implication in approximate reasoning. In M.M. Gupta, A. Kandel, W. Bandler , J.B. Kiszka
NONLINEAR APPROXIMATION WITH GENERAL WAVE PACKETS
Institute of Scientific and Technical Information of China (English)
L. Borup; M. Nielsen
2005-01-01
We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete characterization of the approximation spaces is derived.
Approximate Nearest Neighbor Queries among Parallel Segments
DEFF Research Database (Denmark)
Emiris, Ioannis Z.; Malamatos, Theocharis; Tsigaridas, Elias
2010-01-01
We develop a data structure for answering efficiently approximate nearest neighbor queries over a set of parallel segments in three dimensions. We connect this problem to approximate nearest neighbor searching under weight constraints and approximate nearest neighbor searching on historical data...
Nonlinear approximation with general wave packets
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, Morten
2005-01-01
We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete...... characterization of the approximation spaces is derived....
Nonlinear approximation with bi-framelets
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, Morten; Gribonval, Rémi
2005-01-01
We study the approximation in Lebesgue spaces of wavelet bi-frame systems given by translations and dilations of a finite set of generators. A complete characterization of the approximation spaces associated with best m-term approximation of wavelet bi-framelet systems is given...
Approximation properties of fine hyperbolic graphs
Indian Academy of Sciences (India)
Benyin Fu
2016-05-01
In this paper, we propose a definition of approximation property which is called the metric invariant translation approximation property for a countable discrete metric space. Moreover, we use the techniques of Ozawa’s to prove that a fine hyperbolic graph has the metric invariant translation approximation property.
Relativistic description of electron scattering on the deuteron
Hummel, E
1994-01-01
Within a quasipotential framework a relativistic analysis is presented of the deuteron current. Assuming that the singularities from the nucleon propagators are important, a so-called equal time approximation of the current is constructed. This is applied to both elastic and inelastic electron scattering. As dynamical model the relativistic one boson exchange model is used. Reasonable agreement is found with a previous relativistic calculation of the elastic electromagnetic form factors of the deuteron. For the unpolarized inelastic electron scattering effects of final state interactions and relativistic corrections to the structure functions are considered in the impulse approximation. Two specific kinematic situations are studied as examples.
Electron-atom scattering in a circularly polarized laser field
Cionga, Aurelia; Zloh, Gabriela; 10.1103/PhysRevA.61.063417
2013-01-01
We consider electron-atom scattering in a circularly polarized laser field at sufficiently high electron energies, permitting to describe the scattering process by the first order Born approximation. Assuming the radiation field has sufficiently moderate intensities, the laser-dressing of the hydrogen target atom in its ground state will be treated in second order perturbation theory. Within this approximation scheme, it is shown that the nonlinear differential cross sections of free-free transitions do neither depend on the {\\it dynamical phase} $\\phi$ of the radiative process nor on the {\\it helicity} of the circularly polarized laser light. Relations to the corresponding results for linear laser polarization are established.
Directory of Open Access Journals (Sweden)
Robert de Mello Koch
2017-05-01
Full Text Available We study the worldsheet S-matrix of a string attached to a D-brane in AdS5×S5. The D-brane is either a giant graviton or a dual giant graviton. In the gauge theory, the operators we consider belong to the su(2|3 sector of the theory. Magnon excitations of open strings can exhibit both elastic (when magnons in the bulk of the string scatter and inelastic (when magnons at the endpoint of an open string participate scattering. Both of these S-matrices are determined (up to an overall phase by the su(2|22 global symmetry of the theory. In this note we study the S-matrix for inelastic scattering. We show that it exhibits poles corresponding to boundstates of bulk and boundary magnons. A crossing equation is derived for the overall phase. It reproduces the crossing equation for maximal giant gravitons, in the appropriate limit. Finally, scattering in the su(2 sector is computed to two loops. This two loop result, which determines the overall phase to two loops, will be useful when a unique solution to the crossing equation is to be selected.
Koch, Robert de Mello
2016-01-01
We study the worldsheet S-matrix of a string attached to a D-brane in AdS$_5\\times$S$^5$. The D-brane is either a giant graviton or a dual giant graviton. In the gauge theory, the operators we consider belong to the $su(2|3)$ sector of the theory. Magnon excitations of open strings can exhibit both elastic (when magnons in the bulk of the string scatter) and inelastic (when magnons at the endpoint of an open string participate) scattering. Both of these $S$-matrices are determined (up to an overall phase) by the $su(2|2)^2$ global symmetry of the theory. In this note we study the $S$-matrix for inelastic scattering. We show that it exhibits poles corresponding to boundstates of bulk and boundary magnons. A crossing equation is derived for the overall phase. It reproduces the crossing equation for maximal giant gravitons, in the appropriate limit. Finally, scattering in the $su(2)$ sector is computed to two loops. This two loop result, which determines the overall phase to two loops, will be useful when a uniq...
Energy Technology Data Exchange (ETDEWEB)
Friedrich, Harald [Technische Univ. Muenchen, Garching (Germany). Physik-Department
2016-07-01
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 kept as low as at all possible and deeper questions related to the mathematical foundations of scattering theory are passed by. It should be understandable for anyone with a basic knowledge of nonrelativistic quantum mechanics. The book is intended for advanced students and researchers, and it is hoped that it will be useful for theorists and experimentalists alike.
Vaarkamp, J; TenBosch, JJ; Verdonschot, EH; Tranaeus, S
1997-01-01
The instruments clinically available for the diagnosis of approximal caries lesions are inadequate to detect lesions early and quantitatively. The aim of this study was to investigate whether wavelength-dependent light scattering and absorption of carious tissues may be utilized for the quantitative
Vaarkamp, J; TenBosch, JJ; Verdonschot, EH; Tranaeus, S
The instruments clinically available for the diagnosis of approximal caries lesions are inadequate to detect lesions early and quantitatively. The aim of this study was to investigate whether wavelength-dependent light scattering and absorption of carious tissues may be utilized for the quantitative
Modal analysis of the scattering coefficients of an open cavity in a waveguide
Tong, Yuhui
2016-01-01
The characteristics of an acoustic scatterer are often described by scattering coefficients. The understanding of the mechanisms involved in the frequency dependent features of the coefficients has been a challenge task, owing to the complicated coupling between the waves in open space and the modes inside the finite scatterer. In this paper, a frequency-dependent modal description of the scattering coefficient is utilized to study the modal properties of the scatterer. The important role that eigenmodes play in defining the features of the scattering coefficients is revealed via an expansion of the coefficients by the eigenmodes. The results show the local extrema of the scattering coefficients can be attributed to the constructive/destructive interference of resonant and non-resonant modes. In particular, an approximated equation, which is equivalent to the standard Fano formula, is obtained to describe the sharp anti-symmetric Fano characteristics of the scattering coefficients. The special cases where sca...
Hadron scattering in an asymmetric box*
China Lattice QCD Collaboration; Li, Xin; Chen, Ying; Meng, Guo-Zhan; Feng, Xu; Gong, Ming; He, Song; Li, Gang; Liu, Chuan; Liu, Yu-Bin; Ma, Jian-Ping; Meng, Xiang-Fei; Shen, Yan; Zhang, Jian-Bo
2007-06-01
We propose to study hadron-hadron scattering using lattice QCD in an asymmetric box which allows one to access more non-degenerate low-momentum modes for a given volume. The conventional Lüscher's formula applicable in a symmetric box is modified accordingly. To illustrate the feasibility of this approach, pion-pion elastic scattering phase shifts in the I = 2, J = 0 channel are calculated within quenched approximation using improved gauge and Wilson fermion actions on anisotropic lattices in an asymmetric box. After the chiral and continuum extrapolation, we find that our quenched results for the scattering phase shifts in this channel are consistent with the experimental data when the three-momentum of the pion is below 300MeV. Agreement is also found when compared with previous theoretical results from lattice and other means. Moreover, with the usage of asymmetric volume, we are able to compute the scattering phases in the low-momentum range (pion three momentum less than about 350MeV in the center of mass frame) for over a dozen values of the pion three-momenta, much more than using the conventional symmetric box with comparable volume.
Scattering by coupled resonating elements in air
Krynkin, Anton; Chong, Alvin Y B; Taherzadeh, Shahram; Attenborough, Keith
2011-01-01
Scattering by (a) a single composite scatterer consisting of a concentric arrangement of an outer N-slit rigid cylinder and an inner cylinder which is either rigid or in the form of a thin elastic shell and (b) by a finite periodic array of these scatterers in air has been investigated analytically and through laboratory experiments. The composite scatterer forms a system of coupled resonators and gives rise to multiple low frequency resonances. The corresponding analytical model employs polar angle dependent boundary conditions on the surface of the N-slit cylinder. The solution inside the slits assumes plane waves. It is shown also that in the low-frequency range the N-slit rigid cylinder can be replaced by an equivalent fluid layer. Further approximations suggest a simple square root dependence of the resonant frequencies on the number of slits and this is confirmed by data. The observed resonant phenomena are associated with Helmholtz-like behaviour of the resonator for which the radius and width of the o...
Cooperativity in light scattering by cold atoms
Bienaime, Tom; Piovella, Nicola; Kaiser, Robin
2012-01-01
A cloud of cold N two-level atoms driven by a resonant laser beam shows cooperative effects both in the scattered radiation field and in the radiation pressure force acting on the cloud center-of-mass. The induced dipoles synchronize and the scattered light presents superradiant and/or subradiant features. We present a quantum description of the process in terms of a master equation for the atomic density matrix in the scalar, Born-Markov approximations, reduced to the single-excitation limit. From a perturbative approach for weak incident field, we derive from the master equation the effective Hamiltonian, valid in the linear regime. We discuss the validity of the driven timed Dicke ansatz and of a partial wave expansion for different optical thicknesses and we give analytical expressions for the scattered intensity and the radiation pressure force on the center of mass. We also derive an expression for collective suppression of the atomic excitation and the scattered light by these correlated dipoles.
Energy Technology Data Exchange (ETDEWEB)
Noyes, H.P.
1990-01-29
We construct discrete space-time coordinates separated by the Lorentz-invariant intervals h/mc in space and h/mc{sup 2} in time using discrimination (XOR) between pairs of independently generated bit-strings; we prove that if this space is homogeneous and isotropic, it can have only 1, 2 or 3 spacial dimensions once we have related time to a global ordering operator. On this space we construct exact combinatorial expressions for free particle wave functions taking proper account of the interference between indistinguishable alternative paths created by the construction. Because the end-points of the paths are fixed, they specify completed processes; our wave functions are born collapsed''. A convenient way to represent this model is in terms of complex amplitudes whose squares give the probability for a particular set of observable processes to be completed. For distances much greater than h/mc and times much greater than h/mc{sup 2} our wave functions can be approximated by solutions of the free particle Dirac and Klein-Gordon equations. Using a eight-counter paradigm we relate this construction to scattering experiments involving four distinguishable particles, and indicate how this can be used to calculate electromagnetic and weak scattering processes. We derive a non-perturbative formula relating relativistic bound and resonant state energies to mass ratios and coupling constants, equivalent to our earlier derivation of the Bohr relativistic formula for hydrogen. Using the Fermi-Yang model of the pion as a relativistic bound state containing a nucleon-antinucleon pair, we find that (G{sub {pi}N}{sup 2}){sup 2} = (2m{sub N}/m{sub {pi}}){sup 2} {minus} 1. 21 refs., 1 fig.
Small angle neutron scattering
Directory of Open Access Journals (Sweden)
Cousin Fabrice
2015-01-01
Full Text Available Small Angle Neutron Scattering (SANS is a technique that enables to probe the 3-D structure of materials on a typical size range lying from ∼ 1 nm up to ∼ a few 100 nm, the obtained information being statistically averaged on a sample whose volume is ∼ 1 cm3. This very rich technique enables to make a full structural characterization of a given object of nanometric dimensions (radius of gyration, shape, volume or mass, fractal dimension, specific area… through the determination of the form factor as well as the determination of the way objects are organized within in a continuous media, and therefore to describe interactions between them, through the determination of the structure factor. The specific properties of neutrons (possibility of tuning the scattering intensity by using the isotopic substitution, sensitivity to magnetism, negligible absorption, low energy of the incident neutrons make it particularly interesting in the fields of soft matter, biophysics, magnetic materials and metallurgy. In particular, the contrast variation methods allow to extract some informations that cannot be obtained by any other experimental techniques. This course is divided in two parts. The first one is devoted to the description of the principle of SANS: basics (formalism, coherent scattering/incoherent scattering, notion of elementary scatterer, form factor analysis (I(q→0, Guinier regime, intermediate regime, Porod regime, polydisperse system, structure factor analysis (2nd Virial coefficient, integral equations, characterization of aggregates, and contrast variation methods (how to create contrast in an homogeneous system, matching in ternary systems, extrapolation to zero concentration, Zero Averaged Contrast. It is illustrated by some representative examples. The second one describes the experimental aspects of SANS to guide user in its future experiments: description of SANS spectrometer, resolution of the spectrometer, optimization of
Canonical Sets of Best L1-Approximation
Directory of Open Access Journals (Sweden)
Dimiter Dryanov
2012-01-01
Full Text Available In mathematics, the term approximation usually means either interpolation on a point set or approximation with respect to a given distance. There is a concept, which joins the two approaches together, and this is the concept of characterization of the best approximants via interpolation. It turns out that for some large classes of functions the best approximants with respect to a certain distance can be constructed by interpolation on a point set that does not depend on the choice of the function to be approximated. Such point sets are called canonical sets of best approximation. The present paper summarizes results on canonical sets of best L1-approximation with emphasis on multivariate interpolation and best L1-approximation by blending functions. The best L1-approximants are characterized as transfinite interpolants on canonical sets. The notion of a Haar-Chebyshev system in the multivariate case is discussed also. In this context, it is shown that some multivariate interpolation spaces share properties of univariate Haar-Chebyshev systems. We study also the problem of best one-sided multivariate L1-approximation by sums of univariate functions. Explicit constructions of best one-sided L1-approximants give rise to well-known and new inequalities.
Mapping moveout approximations in TI media
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.
An Approximate Approach to Automatic Kernel Selection.
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.
On Gakerkin approximations for the quasigeostrophic equations
Rocha, Cesar B; Grooms, Ian
2015-01-01
We study the representation of approximate solutions of the three-dimensional quasigeostrophic (QG) equations using Galerkin series with standard vertical modes. In particular, we show that standard modes are compatible with nonzero buoyancy at the surfaces and can be used to solve the Eady problem. We extend two existing Galerkin approaches (A and B) and develop a new Galerkin approximation (C). Approximation A, due to Flierl (1978), represents the streamfunction as a truncated Galerkin series and defines the potential vorticity (PV) that satisfies the inversion problem exactly. Approximation B, due to Tulloch and Smith (2009b), represents the PV as a truncated Galerkin series and calculates the streamfunction that satisfies the inversion problem exactly. Approximation C, the true Galerkin approximation for the QG equations, represents both streamfunction and PV as truncated Galerkin series, but does not satisfy the inversion equation exactly. The three approximations are fundamentally different unless the b...
Light scattering reviews 8 radiative transfer and light scattering
Kokhanovsky, Alexander A
2013-01-01
Light scattering review (vol 8) is aimed at the presentation of recent advances in radiative transfer and light scattering optics. The topics to be covered include: scattering of light by irregularly shaped particles suspended in atmosphere (dust, ice crystals), light scattering by particles much larger as compared the wavelength of incident radiation, atmospheric radiative forcing, astrophysical radiative transfer, radiative transfer and optical imaging in biological media, radiative transfer of polarized light, numerical aspects of radiative transfer.
Effect of Scatterering on Coherent Anti-Stokes Raman Scattering (CARS) signals
Ranasinghesagara, Janaka C; Piazza, Vincenzo; Potma, Eric O; Venugopalan, Vasan
2016-01-01
We develop a computational framework to examine the factors responsible for scattering-induced distortions of coherent anti-Stokes Raman scattering (CARS) signals in turbid samples. We use the Huygens-Fresnel Wave-based Electric Field Superposition (HF-WEFS) method combined with the radiating dipole approximation to compute the effects of scattering-induced distortions of focal excitation fields on the far-field CARS signal. We analyze the effect of spherical scatterers, placed in the vicinity of the focal volume, on the CARS signal emitted by different objects (2{\\mu}m diameter solid sphere, 2{\\mu}m diameter myelin cylinder and 2{\\mu}m diameter myelin tube). We find that distortions in the CARS signals arise not only from attenuation of the focal field but also from scattering-induced changes in the spatial phase that modifies the angular distribution of the CARS emission. Our simulations further show that CARS signal attenuation can be minimized by using a high numerical aperture condenser. Moreover, unlike...
Sound wave scattering by a spherical scatterer located near an ice surface
Grigorieva, N. S.; Kupriyanov, M. S.; Mikhailova, D. A.; Ostrovskiy, D. B.
2016-01-01
An echo signal is simulated, which is reflected from a spherical scatterer located near an ice surface. The homogeneous water medium in which the scatterer is located is assumed semi-infinite. For the scattering coefficients of the sphere, asymptotic formulas are obtained by the saddle point method, which can be used for sufficiently large distances between the source emitting a spherical wave and the scatterer. For the occurring branch cut integrals using the steepest descent method, asymptotic expressions are also obtained. Numerical results are obtained for an acoustically rigid sphere and an ice sphere. The density of the ice medium and speed of longitudinal waves in it coincide with the analogous parameters of the ice cover. In a wide frequency range of 8-12 kHz, echo signals are compared that have been calculated for two models of media: a water half-space bordering an ice half-space and an ice-covered homogeneous waveguide with a fluid bottom under the assumption that the source placed in the water layer is directional. It is shown that in a large distance interval between the source and the spherical scatterer, the half-space model sufficiently accurately describes the echo signal while substantially reducing calculation time (by approximately a factor of 10 for the waveguide with a depth of 200 m and a sandy bottom considered in the paper).
Theory of Compton scattering by anisotropic electrons
Poutanen, Juri
2010-01-01
Compton scattering plays an important role in various astrophysical objects such as accreting black holes and neutron stars, pulsars, and relativistic jets, clusters of galaxies as well as the early Universe. In most of the calculations it is assumed that the electrons have isotropic angular distribution in some frame. However, there are situations where the anisotropy may be significant due to the bulk motions, or anisotropic cooling by synchrotron radiation, or anisotropic source of seed soft photons. We develop here an analytical theory of Compton scattering by anisotropic distribution of electrons that can simplify significantly the calculations. Assuming that the electron angular distribution can be represented by a second order polynomial over cosine of some angle (dipole and quadrupole anisotropy), we integrate the exact Klein-Nishina cross-section over the angles. Exact analytical and approximate formulae valid for any photon and electron energies are derived for the redistribution functions describin...
Laser Pulsing in Linear Compton Scattering
Krafft, Geoffrey; Deitrick, Kirsten; Terzic, Balsa; Kelmar, R; Hodges, Todd; Melnitchouk, W; Delayen, Jean
2016-01-01
Previous work on calculating energy spectra from Compton scattering events has either neglected considering the pulsed structure of the incident laser beam, or has calculated these effects in an approximate way subject to criticism. In this paper, this problem has been reconsidered within a linear plane wave model for the incident laser beam. By performing the proper Lorentz transformation of the Klein-Nishina scattering cross section, a spectrum calculation can be created which allows the electron beam energy spread and emittance effects on the spectrum to be accurately calculated, essentially by summing over the emission of each individual electron. Such an approach has the obvious advantage that it is easily integrated with a particle distribution generated by particle tracking, allowing precise calculations of spectra for realistic particle distributions in collision. The method is used to predict the energy spectrum of radiation passing through an aperture for the proposed Old Dominion University inverse...
Electrodynamics of surface-enhanced Raman scattering
Adles, E J; Aspnes, D E
2011-01-01
We examine SERS from two perspectives: as a phenomenon described by the Laplace Equation (the electrostatic or Rayleigh limit) and by the Helmholtz Equation (electrodynamic or Mie limit). We formulate the problem in terms of the scalar potential, which simplifies calculations without introducing approximations. Because scattering is not usually calculated this way, we provide the necessary theoretical justification showing that the scalar-potential description is complete. Additional simplifications result from treating the scatterer as a point charge q instead of a dipole. This allows us to determine the consequences of including the longitudinal (Coulomb) interaction between q and a passive resonator. This interaction suppresses the mathematical singularities that lead to the unphysical resonant infinities in first and second enhancements. It also modifies the effective restoring-force constant of a resonant denominator, which permits us to explore the possibility of dual resonance through a molecular pathw...
Approximating multileg processes: Higgs production via W-fusion
Philippides, K
2003-01-01
Meaningful approximations for multileg processes at tree level are constructed which circumvent the problems of unitarity violation and gauge invariance. In this article we study the LHC: pp to ZZ + 2 jets + X and the Linear Collider: e/sup +/e/sup -/ to ZZ nu /sub e/ nu /sub e/ processes both of which contain the W-fusion scattering process for off-shell Ws. Using the pinch technique the signal and background, which contribute coherently, are separated in a well defined and gauge invariant way thus defining a resonant approximation which behaves well at high energies. The speed of the numerical calculation is greatly reduced compared to the lengthy calculation of the complete set of diagrams while at the same time the approximations describe very well the full result not only close to the resonance but also beyond it, as shown in various differential distributions of the cross section. The problem of regulating the resonant Higgs diagram is treated both with the naive approach of adding a constant width to t...
Electron scattering for exotic nuclei
Indian Academy of Sciences (India)
Toshimi Suda
2014-11-01
A brand-new electron scattering facility, the SCRIT Electron Scattering Facility, will soon start its operation at RIKEN RI Beam Factory, Japan. This is the world’s first electron scattering facility dedicated to the structure studies of short-lived nuclei. The goal of this facility is to determine the charge density distributions of short-lived exotic nuclei by elastic electron scattering. The first collision between electrons and exotic nuclei will be observed in the year 2014.
Coulomb interaction in multiple scattering theory
Ray, L.; Hoffmann, G. W.; Thaler, R. M.
1980-10-01
The treatment of the Coulomb interaction in the multiple scattering theories of Kerman-McManus-Thaler and Watson is examined in detail. By neglecting virtual Coulomb excitations, the lowest order Coulomb term in the Watson optical potential is shown to be a convolution of the point Coulomb interaction with the distributed nuclear charge, while the equivalent Kerman-McManus-Thaler Coulomb potential is obtained from an averaged, single-particle Coulombic T matrix. The Kerman-McManus-Thaler Coulomb potential is expressed as the Watson Coulomb term plus additional Coulomb-nuclear and Coulomb-Coulomb cross terms, and the omission of the extra terms in usual Kerman-McManus-Thaler applications leads to negative infinite total reaction cross section predictions and incorrect pure Coulomb scattering limits. Approximations are presented which eliminate these anomalies. Using the two-potential formula, the full projectile-nucleus T matrix is separated into two terms, one resulting from the distributed nuclear charge and the other being a Coulomb distorted nuclear T matrix. It is shown that the error resulting from the omission of the Kerman-McManus-Thaler Coulomb terms is effectively removed when the pure Coulomb T matrix in Kerman-McManus-Thaler is replaced by the analogous quantity in the Watson approach. Using the various approximations, theoretical angular distributions are obtained for 800 MeV p+208Pb elastic scattering and compared with experimental data. NUCLEAR REACTIONS 208Pb(p, p), E=0.8 GeV, Kerman, McManus, and Thaler, and Watson multiple scattering theories, Coulomb correction terms, high momentum transfer.
Improving biconnectivity approximation via local optimization
Energy Technology Data Exchange (ETDEWEB)
Ka Wong Chong; Tak Wah Lam [Univ. of Hong Kong (Hong Kong)
1996-12-31
The problem of finding the minimum biconnected spanning subgraph of an undirected graph is NP-hard. A lot of effort has been made to find biconnected spanning subgraphs that approximate to the minimum one as close as possible. Recently, new polynomial-time (sequential) approximation algorithms have been devised to improve the approximation factor from 2 to 5/3 , then 3/2, while NC algorithms have also been known to achieve 7/4 + {epsilon}. This paper presents a new technique which can be used to further improve parallel approximation factors to 5/3 + {epsilon}. In the sequential context, the technique reveals an algorithm with a factor of {alpha} + 1/5, where a is the approximation factor of any 2-edge connectivity approximation algorithm.
Frankenstein's Glue: Transition functions for approximate solutions
Yunes, N
2006-01-01
Approximations are commonly employed to find approximate solutions to the Einstein equations. These solutions, however, are usually only valid in some specific spacetime region. A global solution can be constructed by gluing approximate solutions together, but this procedure is difficult because discontinuities can arise, leading to large violations of the Einstein equations. In this paper, we provide an attempt to formalize this gluing scheme by studying transition functions that join approximate solutions together. In particular, we propose certain sufficient conditions on these functions and proof that these conditions guarantee that the joined solution still satisfies the Einstein equations to the same order as the approximate ones. An example is also provided for a binary system of non-spinning black holes, where the approximate solutions are taken to be given by a post-Newtonian expansion and a perturbed Schwarzschild solution. For this specific case, we show that if the transition functions satisfy the...