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Sample records for eikonal approximation

  1. Analysis of corrections to the eikonal approximation

    Science.gov (United States)

    Hebborn, C.; Capel, P.

    2017-11-01

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

  2. Renormalization and scaling behaviour of eikonal perturbation theories. [Eikonal approximation

    Energy Technology Data Exchange (ETDEWEB)

    Din, A M [Chalmers Tekniska Hoegskola, Goeteborg (Sweden). Institutionen foer Teoretisk Fysik; Nielsen, N K [Aarhus Univ. (Denmark)

    1975-01-04

    Some observations on the renormalization and scaling behaviour of the charged-particle propagator in scalar quantum electrodynamics, in the ordinary eikonal approximation as well as in the eikonal perturbation theory, are reported. The conclusions indicate that scaling behaviour is not realized in the simple sense.

  3. The wave equation: From eikonal to anti-eikonal approximation

    Directory of Open Access Journals (Sweden)

    Luis Vázquez

    2016-06-01

    Full Text Available When the refractive index changes very slowly compared to the wave-length we may use the eikonal approximation to the wave equation. In the opposite case, when the refractive index highly variates over the distance of one wave-length, we have what can be termed as the anti-eikonal limit. This situation is addressed in this work. The anti-eikonal limit seems to be a relevant tool in the modelling and design of new optical media. Besides, it describes a basic universal behaviour, independent of the actual values of the refractive index and, thus, of the media, for the components of a wave with wave-length much greater than the characteristic scale of the refractive index.

  4. Role of eikonal approximation in the infrared domain

    Energy Technology Data Exchange (ETDEWEB)

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

    1977-01-31

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

  5. The role of eikonal approximation in the infrared domain

    International Nuclear Information System (INIS)

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

    1977-01-01

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

  6. An Approximate Method for the Acoustic Attenuating VTI Eikonal Equation

    KAUST Repository

    Hao, Q.

    2017-05-26

    We present an approximate method to solve the acoustic eikonal equation for attenuating transversely isotropic media with a vertical symmetry axis (VTI). A perturbation method is used to derive the perturbation formula for complex-valued traveltimes. The application of Shanks transform further enhances the accuracy of approximation. We derive both analytical and numerical solutions to the acoustic eikonal equation. The analytic solution is valid for homogeneous VTI media with moderate anellipticity and strong attenuation and attenuation-anisotropy. The numerical solution is applicable for inhomogeneous attenuating VTI media.

  7. An Approximate Method for the Acoustic Attenuating VTI Eikonal Equation

    KAUST Repository

    Hao, Q.; Alkhalifah, Tariq Ali

    2017-01-01

    We present an approximate method to solve the acoustic eikonal equation for attenuating transversely isotropic media with a vertical symmetry axis (VTI). A perturbation method is used to derive the perturbation formula for complex-valued traveltimes. The application of Shanks transform further enhances the accuracy of approximation. We derive both analytical and numerical solutions to the acoustic eikonal equation. The analytic solution is valid for homogeneous VTI media with moderate anellipticity and strong attenuation and attenuation-anisotropy. The numerical solution is applicable for inhomogeneous attenuating VTI media.

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

    CERN Document Server

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

    1998-01-01

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

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

    International Nuclear Information System (INIS)

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

    1997-01-01

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

  10. Symmetric eikonal expansion

    International Nuclear Information System (INIS)

    Matsuki, Takayuki

    1976-01-01

    Symmetric eikonal expansion for the scattering amplitude is formulated for nonrelativistic and relativistic potential scatterings and also for the quantum field theory. The first approximations coincide with those of Levy and Sucher. The obtained scattering amplitudes are time reversal invariant for all cases and are crossing symmetric for the quantum field theory in each order of approximation. The improved eikonal phase introduced by Levy and Sucher is also derived from the different approximation scheme from the above. (auth.)

  11. Soft Gluon Radiation off Heavy Quarks beyond Eikonal Approximation

    International Nuclear Information System (INIS)

    Mazumder, Surasree; Bhattacharyya, Trambak; Abir, Raktim

    2016-01-01

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

  12. On next-to-eikonal exponentiation

    CERN Document Server

    Laenen, Eric; Stavenga, Gerben; White, Chris D

    2010-01-01

    The eikonal approximation is at the heart of many theoretical and phenomenological studies involving multiple soft gauge boson emissions in high energy physics. We describe our efforts towards the extension of the eikonal approximation for scattering amplitudes to the first subleading power in the soft momentum.

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2009-02-15

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

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

    International Nuclear Information System (INIS)

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

    2009-01-01

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

  15. Eikonal Approximation in AdS/CFT From Shock Waves to Four-Point Functions

    CERN Document Server

    Cornalba, L; Costa, Miguel S; Penedones, Joao; Cornalba, Lorenzo; Costa, M S; Penedones, J; Schiappa, Ricardo

    2007-01-01

    We initiate a program to generalize the standard eikonal approximation to compute amplitudes in Anti-de Sitter spacetimes. Inspired by the shock wave derivation of the eikonal amplitude in flat space, we study the two-point function E ~ _{shock} in the presence of a shock wave in Anti-de Sitter, where O_1 is a scalar primary operator in the dual conformal field theory. At tree level in the gravitational coupling, we relate the shock two-point function E to the discontinuity across a kinematical branch cut of the conformal field theory four-point function A ~ , where O_2 creates the shock geometry in Anti-de Sitter. Finally, we extend the above results by computing E in the presence of shock waves along the horizon of Schwarzschild BTZ black holes. This work gives new tools for the study of Planckian physics in Anti-de Sitter spacetimes.

  16. Factorization of in-medium parton branching beyond the eikonal approximation

    Science.gov (United States)

    Apolinário, Liliana; Armesto, Néstor; Milhano, José Guilherme; Salgado, Carlos A.

    2017-08-01

    The description of the in-medium modifications of partonic showers is at the forefront of current theoretical and experimental efforts in heavy-ion physics. The theory of jet quenching, a commonly used alias for the modifications of the parton branching resulting from the interactions with the QGP, has been significantly developed over the last years. Within a weak coupling approach, several elementary processes that build up the parton shower evolution, such as single gluon emissions, interference effects between successive emissions and corrections to radiative energy loss off massive quarks, have been addressed both at eikonal accuracy and beyond by taking into account the Brownian motion that high-energy particles experience when traversing a hot and dense medium. In this work, by using the setup of single gluon emission from a color correlated quark-antiquark pair in a singlet state (q- q ‾ antenna), we calculate the in-medium gluon radiation spectrum beyond the eikonal approximation. This allows to fully explore the physical interplay between broadening and coherence/decoherence effects. The results show that we are able to factorize broadening effects from the modifications of the radiation process itself. This provides a very strong indication that a probabilistic picture of parton shower evolution holds even in the presence of a QGP, a feature that is of the utmost importance for a successful future generation of Jet quenching Monte Carlos.

  17. Efficient Traveltime Solutions of the TI Acoustic Eikonal Equation

    KAUST Repository

    Waheed, Umair bin

    2014-10-22

    Numerical solutions of the eikonal (Hamilton-Jacobi) equation for transversely isotropic (TI) media are essential for integral imaging and traveltime tomography applications. Such solutions, however, suffer from the inherent higher-order nonlinearity of the TI eikonal equation, which requires solving a quartic polynomial at each computational step. Using perturbation theory, we approximate the first-order discretized form of the TI eikonal equation with a series of simpler equations for the coefficients of a polynomial expansion of the eikonal solution in terms of the anellipticity anisotropy parameter. Such perturbation, applied to the discretized form of the eikonal equation, does not impose any restrictions on the complexity of the perturbed parameter field. Therefore, it provides accurate traveltime solutions even for the anisotropic Marmousi model, with complex distribution of velocity and anellipticity anisotropy parameter. The formulation allows tremendous cost reduction compared to using the exact TI eikonal solver. Furthermore, comparative tests with previously developed approximations illustrate remarkable gain in accuracy of the proposed approximation, without any addition to the computational cost.

  18. Efficient Traveltime Solutions of the TI Acoustic Eikonal Equation

    KAUST Repository

    Waheed, Umair bin; Alkhalifah, Tariq Ali

    2014-01-01

    Numerical solutions of the eikonal (Hamilton-Jacobi) equation for transversely isotropic (TI) media are essential for integral imaging and traveltime tomography applications. Such solutions, however, suffer from the inherent higher-order nonlinearity of the TI eikonal equation, which requires solving a quartic polynomial at each computational step. Using perturbation theory, we approximate the first-order discretized form of the TI eikonal equation with a series of simpler equations for the coefficients of a polynomial expansion of the eikonal solution in terms of the anellipticity anisotropy parameter. Such perturbation, applied to the discretized form of the eikonal equation, does not impose any restrictions on the complexity of the perturbed parameter field. Therefore, it provides accurate traveltime solutions even for the anisotropic Marmousi model, with complex distribution of velocity and anellipticity anisotropy parameter. The formulation allows tremendous cost reduction compared to using the exact TI eikonal solver. Furthermore, comparative tests with previously developed approximations illustrate remarkable gain in accuracy of the proposed approximation, without any addition to the computational cost.

  19. Second-order symmetric eikonal approximation for electron capture at high energies

    Energy Technology Data Exchange (ETDEWEB)

    Deco, G R; Rivarola, R D [Rosario Univ. Nacional (Argentina). Dept. de Fisica

    1985-06-14

    A symmetric eikonal approximation for electron capture in ion-atom collisions at high energies has been developed within the Dodd and Greider (1966, Phys. Rev. 146 675) formalism. Implicit intermediate states are included through the choice of distorted initial and final wavefunctions. Explicit intermediate state are considered by the introduction of a free-particle Green's function G/sup +//sub 0/. The model is applied for the resonant charge exchange in H/sup +/+H(1s) collisions. Also, the characteristic dip of the continuum distorted-wave model is analysed when higher orders are included at 'realistic' high energies.

  20. Fast sweeping method for the factored eikonal equation

    Science.gov (United States)

    Fomel, Sergey; Luo, Songting; Zhao, Hongkai

    2009-09-01

    We develop a fast sweeping method for the factored eikonal equation. By decomposing the solution of a general eikonal equation as the product of two factors: the first factor is the solution to a simple eikonal equation (such as distance) or a previously computed solution to an approximate eikonal equation. The second factor is a necessary modification/correction. Appropriate discretization and a fast sweeping strategy are designed for the equation of the correction part. The key idea is to enforce the causality of the original eikonal equation during the Gauss-Seidel iterations. Using extensive numerical examples we demonstrate that (1) the convergence behavior of the fast sweeping method for the factored eikonal equation is the same as for the original eikonal equation, i.e., the number of iterations for the Gauss-Seidel iterations is independent of the mesh size, (2) the numerical solution from the factored eikonal equation is more accurate than the numerical solution directly computed from the original eikonal equation, especially for point sources.

  1. High-energy behavior of the charge-transfer cross section in the eikonal approximation

    International Nuclear Information System (INIS)

    Dewangan, D.P.

    1982-01-01

    In the now popular version of the eikonal theory of charge transfer, the eikonal wave function does not satisfy the proper boundary conditions and the charge-transfer amplitude is uncertain by an undefined phase factor. The inclusion of the internuclear potential in a consistent way, in the eikonal theory overcomes theses difficulties. However, it also changes the high-energy asymptotic form of proton-hydrogen charge-transfer cross section from sigma/sub eik/ approx.(23/48) sigma/sub BK/ by a small amount to sigma/sub G/approx.(20.109/48)sigma/sub BK/ where sigma/sub BK/ is the Brinkman-Kramers cross section

  2. Energy loss and (de)coherence effects beyond eikonal approximation

    CERN Document Server

    Apolinário, Liliana; Milhano, Guilherme; Salgado, Carlos A.

    2014-01-01

    The parton branching process is known to be modified in the presence of a medium. Colour decoherence processes are known to determine the process of energy loss when the density of the medium is large enough to break the correlations between partons emitted from the same parent. In order to improve existing calculations that consider eikonal trajectories for both the emitter and the hardest emitted parton, we provide in this work, the calculation of all finite energy corrections for the gluon radiation off a quark in a QCD medium that exist in the small angle approximation and for static scattering centres. Using the path integral formalism, all particles are allowed to undergo Brownian motion in the transverse plane and the offspring allowed to carry an arbitrary fraction of the initial energy. The result is a general expression that contains both coherence and decoherence regimes that are controlled by the density of the medium and by the amount of broadening that each parton acquires independently.

  3. Collision kernels in the eikonal approximation for Lennard-Jones interaction potential

    International Nuclear Information System (INIS)

    Zielinska, S.

    1985-03-01

    The velocity changing collisions are conveniently described by collisional kernels. These kernels depend on an interaction potential and there is a necessity for evaluating them for realistic interatomic potentials. Using the collision kernels, we are able to investigate the redistribution of atomic population's caused by the laser light and velocity changing collisions. In this paper we present the method of evaluating the collision kernels in the eikonal approximation. We discuss the influence of the potential parameters Rsub(o)sup(i), epsilonsub(o)sup(i) on kernel width for a given atomic state. It turns out that unlike the collision kernel for the hard sphere model of scattering the Lennard-Jones kernel is not so sensitive to changes of Rsub(o)sup(i) as the previous one. Contrary to the general tendency of approximating collisional kernels by the Gaussian curve, kernels for the Lennard-Jones potential do not exhibit such a behaviour. (author)

  4. Eikonal Approximation in AdS/CFT: Conformal Partial Waves and Finite N Four-Point Functions

    CERN Document Server

    Cornalba, L; Penedones, J; Schiappa, R; Cornalba, Lorenzo; Costa, Miguel S.; Penedones, Joao; Schiappa, Ricardo

    2007-01-01

    We introduce the impact-parameter representation for conformal field theory correlators of the form A ~ . This representation is appropriate in the eikonal kinematical regime, and approximates the conformal partial-wave decomposition in the limit of large spin and dimension of the exchanged primary. Using recent results on the two-point function _{shock} in the presence of a shock wave in Anti-de Sitter, and its relation to the discontinuity of the four-point amplitude A across a kinematical branch-cut, we find the high spin and dimension conformal partial- wave decomposition of all tree-level Anti-de Sitter Witten diagrams. We show that, as in flat space, the eikonal kinematical regime is dominated by the T-channel exchange of the massless particle with highest spin (graviton dominance). We also compute the anomalous dimensions of the high-spin O_1 O_2 composites. Finally, we conjecture a formula re-summing crossed-ladder Witten diagrams to all orders in the gravitational coupling.

  5. Efficient traveltime solutions of the acoustic TI eikonal equation

    KAUST Repository

    Waheed, Umair bin

    2015-02-01

    Numerical solutions of the eikonal (Hamilton-Jacobi) equation for transversely isotropic (TI) media are essential for imaging and traveltime tomography applications. Such solutions, however, suffer from the inherent higher-order nonlinearity of the TI eikonal equation, which requires solving a quartic polynomial for every grid point. Analytical solutions of the quartic polynomial yield numerically unstable formulations. Thus, it requires a numerical root finding algorithm, adding significantly to the computational load. Using perturbation theory we approximate, in a first order discretized form, the TI eikonal equation with a series of simpler equations for the coefficients of a polynomial expansion of the eikonal solution, in terms of the anellipticity anisotropy parameter. Such perturbation, applied to the discretized form of the eikonal equation, does not impose any restrictions on the complexity of the perturbed parameter field. Therefore, it provides accurate traveltime solutions even for models with complex distribution of velocity and anisotropic anellipticity parameter, such as that for the complicated Marmousi model. The formulation allows for large cost reduction compared to using the direct TI eikonal solver. Furthermore, comparative tests with previously developed approximations illustrate remarkable gain in accuracy in the proposed algorithm, without any addition to the computational cost.

  6. Next-to-next-to-eikonal corrections in the CGC

    Energy Technology Data Exchange (ETDEWEB)

    Altinoluk, Tolga; Armesto, Néstor [Departamento de Física de Partículas and IGFAE,Universidade de Santiago de Compostela,E-15706 Santiago de Compostela, Galicia (Spain); Beuf, Guillaume [Department of Physics, Ben-Gurion University of the Negev,Beer Sheva 84105 (Israel); Moscoso, Alexis [Departamento de Física de Partículas and IGFAE,Universidade de Santiago de Compostela,E-15706 Santiago de Compostela, Galicia (Spain)

    2016-01-19

    We extend the study of corrections to the eikonal approximation that was initiated in ref. http://dx.doi.org/10.1007/JHEP07(2014)068 to higher orders. These corrections associated with the finite width of the target are investigated and the gluon propagator in background field is calculated at next-to-next-to-eikonal accuracy. The result is then applied to the single inclusive gluon production cross section at central rapidities and the single transverse spin asymmetry with a transversely polarized target, in pA collisions, in order to analyze these observables beyond the eikonal limit. The next-to-next-to-eikonal corrections to the unpolarized cross section are non-zero and provide the first corrections to the usual k{sub ⊥}-factorized expression. In contrast, the eikonal and next-to-next-to-eikonal contributions to the single transverse spin asymmetry vanish, while the next-to-eikonal ones are non-zero.

  7. Eikonal approximation in AdS/CFT: Conformal partial waves and finite N four-point functions

    International Nuclear Information System (INIS)

    Cornalba, Lorenzo; Costa, Miguel S.; Penedones, Joao; Schiappa, Ricardo

    2007-01-01

    We introduce the impact parameter representation for conformal field theory correlators of the form A∼ 1 O 2 O 1 O 2 >. This representation is appropriate in the eikonal kinematical regime, and approximates the conformal partial wave decomposition in the limit of large spin and dimension of the exchanged primary. Using recent results on the two-point function 1 O 1 > shock in the presence of a shock wave in anti-de Sitter, and its relation to the discontinuity of the four-point amplitude A across a kinematical branch cut, we find the high spin and dimension conformal partial wave decomposition of all tree-level anti-de Sitter Witten diagrams. We show that, as in flat space, the eikonal kinematical regime is dominated by the T-channel exchange of the massless particle with highest spin (graviton dominance). We also compute the anomalous dimensions of the high spin O 1 O 2 composites. Finally, we conjecture a formula re-summing crossed-ladder Witten diagrams to all orders in the gravitational coupling

  8. Group-theoretical approach to relativistic eikonal physics

    Energy Technology Data Exchange (ETDEWEB)

    Leon, J; Quiros, M [Instituto de Enstructura de la Materia, C.S.I.C., Madrid (Spain); Departamento de Matematica, Universidad Complutense, Campus de Alcala (Spain)); Ramirez Mittelbrunn, J [Instituto de Estructura de la Materia, C.S.I.C., Madrid (Spain)

    1977-09-01

    A contraction of the Poincare group is performed leading to the eikonal approximation. Invariants, one-particle states, spinning particles and some interaction problems are studied with the following results: momenta of ultrarelativistic particles behave as lightlike, the little group being E/sub 2/, spin behaves as that of zero-mass particles, helicity being conserved in the presence of interactions. The full eikonal results are rederived for Green's functions, wave functions, etc. The way for computing corrections due to transverse momenta and spin-dependent interactions is outlined. A parallel analysis is made for the infinite-momentum frame, the similarities and differences between this formalism and the eikonal approach being disclosed.

  9. Multitrajectory eikonal cross sections

    International Nuclear Information System (INIS)

    Turner, R.E.

    1983-01-01

    With the use of reference and distorted transition operators, a time-correlation-function representation of the inelastic differential cross section has recently been used to obtain distorted eikonal cross sections. These cross sections involve straight-line and reference classical translational trajectories that are unaffected by any internal-state changes which have occurred during the collision. This distorted eikonal theory is now extended to include effects of internal-state changes on the translational motion. In particular, a different classical trajectory is associated with each pair of internal states. Expressions for these inelastic cross sections are obtained in terms of time-ordered cosine and sine memory functions using the Zwanzig-Feshbach projection-operator method. Explicit formulas are obtained in the time-disordered perturbation approximation

  10. Generalized eikonalization and unitarity

    Energy Technology Data Exchange (ETDEWEB)

    Giffon, M. [Lyon-1 Univ., 69 - Villeurbanne (France). Inst. de Physique Nucleaire; Predazzi, E. [Universita di Torino (Italy); Martynov, E.

    1996-12-31

    In the literature, the notion of eikonalization is often used as synonymous of unitarization or, at least, as implying that unitarity is not violated. This, to the very least, appears to be wishful thinking. We discuss the properties of various types of eikonalization within a unified treatment. Linear trajectories with intercept larger than unity (so popular nowadays) lead to small asymptotic violations of unitarity even after eikonalization. Classes of eikonalizations in which the Odderon could dominate over the Pomeron are given; even so the maximal Odderon is still excluded by eikonalization. (authors). 18 refs.

  11. Generalized eikonalization and unitarity

    International Nuclear Information System (INIS)

    Giffon, M.; Martynov, E.

    1996-01-01

    In the literature, the notion of eikonalization is often used as synonymous of unitarization or, at least, as implying that unitarity is not violated. This, to the very least, appears to be wishful thinking. We discuss the properties of various types of eikonalization within a unified treatment. Linear trajectories with intercept larger than unity (so popular nowadays) lead to small asymptotic violations of unitarity even after eikonalization. Classes of eikonalizations in which the Odderon could dominate over the Pomeron are given; even so the maximal Odderon is still excluded by eikonalization. (authors)

  12. An acoustic eikonal equation for attenuating VTI media

    KAUST Repository

    Hao, Qi

    2016-09-06

    We present an acoustic eikonal equation governing the complex-valued travel time of P-waves in attenuating, transversely isotropic media with a vertical symmetry axis (VTI). This equation is based on the assumption that the Pwave complex-valued travel time is independent of the Swave velocity parameter v in Thomsen\\'s notation and the attenuation coefficient A in the Thomsen-type notation for attenuating VTI media. We combine perturbation theory and Shanks transform to develop practical approximations to the attenuating acoustic eikonal equation, capable of admitting analytical description of the attenuation in homogeneous media. For a horizontal, attenuating VTI layer, we also derive non-hyperbolic approximations for the real and imaginary parts of the complex-valued reflection travel time.

  13. Quantum reflection of fast atoms from insulator surfaces: Eikonal description

    Energy Technology Data Exchange (ETDEWEB)

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

    2009-11-01

    Interference effects recently observed in grazing scattering of swift atoms from insulator surfaces are studied within a distorted-wave method - the surface eikonal approximation. This approach makes use of the eikonal wave function, involving axial channeled trajectories. The theory is applied to helium atoms colliding with a LiF(001) surface along low-index crystallographic directions. The roles played by the projectile polarization and the surface rumpling are investigated, finding that both effects are important for the description of the experimental projectile distributions.

  14. An acoustic eikonal equation for attenuating orthorhombic media

    KAUST Repository

    Hao, Qi

    2017-04-06

    Attenuating orthorhombic models are often used to describe the azimuthal variation of the seismic wave velocity and amplitude in finely layered hydrocarbon reservoirs with vertical fractures. In addition to the P-wave related medium parameters, shear wave parameters are also present in the complex eikonal equation needed to describe the P-wave complex-valued traveltime in an attenuating orthorhombic medium, which increases the complexity of using the P-wave traveltime to invert for the medium parameters in practice. Here, we use the acoustic assumption to derive an acoustic eikonal equation that approximately governs the complex-valued traveltime of P-waves in an attenuating orthorhombic medium. For a homogeneous attenuating orthorhombic media, we solve the eikonal equation using a combination of the perturbation method and Shanks transform. For a horizontal attenuating orthorhombic layer, both the real and imaginary part of the complex-valued reflection traveltime have nonhyperbolic behaviors in terms of the source-receiver offset. Similar to the roles of normal moveout (NMO) velocity and anellipticity, the attenuation NMO velocity and the attenuation anellipticity characterize the variation of the imaginary part of the complex-valued reflection traveltime around zero source-receiver offset.

  15. Local Ray-Based Traveltime Computation Using the Linearized Eikonal Equation

    KAUST Repository

    Almubarak, Mohammed S.

    2013-05-01

    The computation of traveltimes plays a critical role in the conventional implementations of Kirchhoff migration. Finite-difference-based methods are considered one of the most effective approaches for traveltime calculations and are therefore widely used. However, these eikonal solvers are mainly used to obtain early-arrival traveltime. Ray tracing can be used to pick later traveltime branches, besides the early arrivals, which may lead to an improvement in velocity estimation or in seismic imaging. In this thesis, I improved the accuracy of the solution of the linearized eikonal equation by constructing a linear system of equations (LSE) based on finite-difference approximation, which is of second-order accuracy. The ill-conditioned LSE is initially regularized and subsequently solved to calculate the traveltime update. Numerical tests proved that this method is as accurate as the second-order eikonal solver. Later arrivals are picked using ray tracing. These traveltimes are binned to the nearest node on a regular grid and empty nodes are estimated by interpolating the known values. The resulting traveltime field is used as an input to the linearized eikonal algorithm, which improves the accuracy of the interpolated nodes and yields a local ray-based traveltime. This is a preliminary study and further investigation is required to test the efficiency and the convergence of the solutions.

  16. To the problem of spatial focusing of ultracold neutrons by nonuniform magnetic field. Eikonal approximation

    CERN Document Server

    Chen, T

    2002-01-01

    Motion of the ultracold neutrons in the nonuniform magnetic field with a square nonuniformity by two coordinates is considered. The Schroedinger equation is solved with application of the quasi-classical (eikonal) approach. The theoretical possibility of the neutrons spatial focusing with formation of the point focus and also the neutrons bunches is shown

  17. A fast marching algorithm for the factored eikonal equation

    Energy Technology Data Exchange (ETDEWEB)

    Treister, Eran, E-mail: erantreister@gmail.com [Department of Earth and Ocean Sciences, The University of British Columbia, Vancouver, BC (Canada); Haber, Eldad, E-mail: haber@math.ubc.ca [Department of Earth and Ocean Sciences, The University of British Columbia, Vancouver, BC (Canada); Department of Mathematics, The University of British Columbia, Vancouver, BC (Canada)

    2016-11-01

    The eikonal equation is instrumental in many applications in several fields ranging from computer vision to geoscience. This equation can be efficiently solved using the iterative Fast Sweeping (FS) methods and the direct Fast Marching (FM) methods. However, when used for a point source, the original eikonal equation is known to yield inaccurate numerical solutions, because of a singularity at the source. In this case, the factored eikonal equation is often preferred, and is known to yield a more accurate numerical solution. One application that requires the solution of the eikonal equation for point sources is travel time tomography. This inverse problem may be formulated using the eikonal equation as a forward problem. While this problem has been solved using FS in the past, the more recent choice for applying it involves FM methods because of the efficiency in which sensitivities can be obtained using them. However, while several FS methods are available for solving the factored equation, the FM method is available only for the original eikonal equation. In this paper we develop a Fast Marching algorithm for the factored eikonal equation, using both first and second order finite-difference schemes. Our algorithm follows the same lines as the original FM algorithm and requires the same computational effort. In addition, we show how to obtain sensitivities using this FM method and apply travel time tomography, formulated as an inverse factored eikonal equation. Numerical results in two and three dimensions show that our algorithm solves the factored eikonal equation efficiently, and demonstrate the achieved accuracy for computing the travel time. We also demonstrate a recovery of a 2D and 3D heterogeneous medium by travel time tomography using the eikonal equation for forward modeling and inversion by Gauss–Newton.

  18. The eikonal phase of supersymmetric Coulomb partners

    CERN Document Server

    Lassaut, M; Lombard, R J

    1998-01-01

    We investigate the eikonal phase and its systematic corrections for the two supersymmetric Coulomb partners V sub 1 and V sub 2 derived by Amado. Apart from a constant shift of -pi for V sub 1 and -2 pi for V sub 2 , the eikonal phase decay to the eikonal phase of the Coulomb potential as 1/kb. For the potential V sub 2 , which is phase equivalent to the Coulomb potential, this result is only valid at b approx =0 and asymptotically; in the intermediate range, it constitutes a lower limit. (author)

  19. An acoustic eikonal equation for attenuating transversely isotropic media with a vertical symmetry axis

    KAUST Repository

    Hao, Qi

    2016-11-21

    Seismic-wave attenuation is an important component of describing wave propagation. Certain regions, such as gas clouds inside the earth, exert highly localized attenuation. In fact, the anisotropic nature of the earth induces anisotropic attenuation because the quasi P-wave dispersion effect should be profound along the symmetry direction. We have developed a 2D acoustic eikonal equation governing the complex-valued traveltime of quasi P-waves in attenuating, transversely isotropic media with a vertical-symmetry axis (VTI). This equation is derived under the assumption that the complex-valued traveltime of quasi P-waves in attenuating VTI media are independent of the S-wave velocity parameter υS0 in Thomsen\\'s notation and the S-wave attenuation coefficient AS0 in Zhu and Tsvankin\\'s notation. We combine perturbation theory and Shanks transform to develop practical approximations to the acoustic attenuating eikonal equation, capable of admitting an analytical description of the attenuation in homogeneous media. For a horizontal-attenuating VTI layer, we also derive the nonhyperbolic approximations for the real and imaginary parts of the complex-valued reflection traveltime. These equations reveal that (1) the quasi SV-wave velocity and the corresponding quasi SV-wave attenuation coefficient given as part of Thomsen-type notation barely affect the ray velocity and ray attenuation of quasi P-waves in attenuating VTI media; (2) combining the perturbation method and Shanks transform provides an accurate analytic eikonal solution for homogeneous attenuating VTI media; (3) for a horizontal attenuating VTI layer with weak attenuation, the real part of the complex-valued reflection traveltime may still be described by the existing nonhyperbolic approximations developed for nonattenuating VTI media, and the imaginary part of the complex-valued reflection traveltime still has the shape of nonhyperbolic curves. In addition, we have evaluated the possible extension of the

  20. Three particle scattering at high energies in a model with eikonal Hamiltonian

    International Nuclear Information System (INIS)

    Kharchenko, V.F.; Kuzmichev, V.E.

    1980-04-01

    The three particle collision process 3 → 3 with relative motion of each pair of particles described by a model with eikonal Hamiltonian is investigated. No additional restrictions on the motion of the particles (such as the fixed scattering centre approximation) are imposed. A unique, exact analytical solution of the three-particle problem is then shown to exist. An explicit expression for the 3 → 3 amplitude in the general case off the energy shell is obtained as the result of the exact summation of the multiple scattering series. It is shown that this series terminates on the energy shell. A new formula for the mutual cancellation of terms in the multiple scattering series in a model with eikonal Hamiltonian is found. (orig.)

  1. Eikonal approach to the atomic break-up process by polarized electrons

    International Nuclear Information System (INIS)

    Onaga, Tomohide

    1992-01-01

    The cross section asymmetry for ionization of hydrogen atoms by electron impact is analysed in the eikonal approach. A new formulation is given for the evaluation of the exchange amplitude up to higher partial Coulomb waves. It is concluded that the cross section asymmetry gives an important criterion or interesting test of validity of approximation methods with the exchange effect. (author)

  2. Models of multiparticle production of the eikonal type

    International Nuclear Information System (INIS)

    Martinis, M.

    1974-01-01

    A survey of eikonal type models for multiparticle production is given. Empirical rules concerning the nature of multiparticle reactions are outlined. A discussion involving kinematics and cross sections for inclusive processes is presented. The constraints of multiparticle unitarity are considered to be of great importance in eikonal models for multiproduction at high energy. (HFdV)

  3. Prestack traveltime approximations

    KAUST Repository

    Alkhalifah, Tariq Ali

    2011-01-01

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

  4. On the Eikonal equation in the pedestrian flow problem

    Science.gov (United States)

    Felcman, J.; Kubera, P.

    2017-07-01

    We consider the Pedestrian Flow Equations (PFEs) as the coupled system formed by the Eikonal equation and the first order hyperbolic system with the source term. The hyperbolic system consists of the continuity equation and momentum equation of fluid dynamics. Specifying the social and pressure forces in the momentum equation we come to the assumption that each pedestrian is trying to move in a desired direction (e.g. to the exit in the panic situation) with a desired velocity, where his velocity and the direction of movement depend on the density of pedestrians in his neighborhood. In [1] we used the model, where the desired direction of movement is given by the solution of the Eikonal equation (more precisely by the gradient of the solution). Here we avoid the solution of the Eikonal equation, which is the novelty of the paper. Based on the fact that the solution of the Eikonal equation has the meaning of the shortest time to reach the exit, we define explicitly such a function in the framework of the Dijkstra's algorithm for the shortest path in the graph. This is done at the discrete level of the solution. As the graph we use the underlying triangulation, where the norm of each edge is density depending and has the dimension of the time. The numerical examples of the solution of the PFEs with and without the solution of the Eikonal equation are presented.

  5. High-energy string-brane scattering: leading eikonal and beyond

    CERN Document Server

    D'Appollonio, Giuseppe; Russo, Rodolfo; Veneziano, Gabriele

    2010-01-01

    We extend previous techniques for calculations of transplanckian-energy string-string collisions to the high-energy scattering of massless closed strings from a stack of N Dp-branes in Minkowski spacetime. We show that an effective non-trivial metric emerges from the string scattering amplitudes by comparing them against the semiclassical dynamics of high-energy strings in the extremal p-brane background. By changing the energy, impact parameter and effective open string coupling, we are able to explore various interesting regimes and to reproduce classical expectations, including tidal-force excitations, even beyond the leading-eikonal approximation.

  6. The portrait of eikonal instability in Lovelock theories

    Energy Technology Data Exchange (ETDEWEB)

    Konoplya, R.A. [Theoretical Astrophysics, Eberhard-Karls University of Tübingen, Tübingen 72076 (Germany); Zhidenko, A., E-mail: roman.konoplya@gmail.com, E-mail: olexandr.zhydenko@ufabc.edu.br [Centro de Matemática, Computação e Cognição, Universidade Federal do ABC (UFABC), Rua Abolição, CEP: 09210-180, Santo André, SP (Brazil)

    2017-05-01

    Perturbations and eikonal instabilities of black holes and branes in the Einstein-Gauss-Bonnet theory and its Lovelock generalization were considered in the literature for several particular cases, where the asymptotic conditions (flat, dS, AdS), the number of spacetime dimensions D , non-vanishing coupling constants (α{sub 1}, α{sub 2}, α{sub 3} etc.) and other parameters have been chosen in a specific way. Here we give a comprehensive analysis of the eikonal instabilities of black holes and branes for the most general Lovelock theory, not limited by any of the above cases. Although the part of the stability analysis is performed here purely analytically and formulated in terms of the inequalities for the black hole parameters, the most general case is treated numerically and the accurate regions of instabilities are presented. The shared Mathematica® code allows the reader to construct the regions of eikonal instability for any desired values of the parameters.

  7. The portrait of eikonal instability in Lovelock theories

    Science.gov (United States)

    Konoplya, R. A.; Zhidenko, A.

    2017-05-01

    Perturbations and eikonal instabilities of black holes and branes in the Einstein-Gauss-Bonnet theory and its Lovelock generalization were considered in the literature for several particular cases, where the asymptotic conditions (flat, dS, AdS), the number of spacetime dimensions D, non-vanishing coupling constants (α1, α2, α3 etc.) and other parameters have been chosen in a specific way. Here we give a comprehensive analysis of the eikonal instabilities of black holes and branes for the most general Lovelock theory, not limited by any of the above cases. Although the part of the stability analysis is performed here purely analytically and formulated in terms of the inequalities for the black hole parameters, the most general case is treated numerically and the accurate regions of instabilities are presented. The shared Mathematica® code allows the reader to construct the regions of eikonal instability for any desired values of the parameters.

  8. Non-eikonal effects in high-energy scattering IV. Inelastic scattering

    International Nuclear Information System (INIS)

    Gurvitz, S.A.; Kok, L.P.; Rinat, A.S.

    1978-01-01

    Amplitudes of inelastically scattered high-energy projections were calculated. In the scattering on 12 C(Tsub(P)=1 GeV) sizeable non-eikonal corrections in diffraction extrema even for relatively small q 2 are demonstrated. At least part of the anomaly in the 3 - distribution may be due to these non-eikonal effects. (B.G.)

  9. High energy approximations in quantum field theory

    International Nuclear Information System (INIS)

    Orzalesi, C.A.

    1975-01-01

    New theoretical methods in hadron physics based on a high-energy perturbation theory are discussed. The approximated solutions to quantum field theory obtained by this method appear to be sufficiently simple and rich in structure to encourage hadron dynamics studies. Operator eikonal form for field - theoretic Green's functions is derived and discussion is held on how the eikonal perturbation theory is to be renormalized. This method is extended to massive quantum electrodynamics of scalar charged bosons. Possible developments and applications of this theory are given [pt

  10. Eikonals - from a different point of view

    International Nuclear Information System (INIS)

    Fried, H.M.; Gabellini, Y.

    1999-01-01

    We reopen the old, Abelian problem of t-channel, connected, multiparticle contributions to the eikonal function for quark-quark scattering at ultra-high energies, and ask what might be the resulting forms in non-Abelian QCD. Unless an unexpected, non-Abelian cancellation occurs, there can result a damping of the eikonal contribution to the amplitude at arbitrarily large impact parameter, which violates the condition and spirit of the hadrons' other quarks, treated as spectator particles. A possible resolution of this problem can be accomplished by averaging over the quarks' bound-state, hadronic wave functions, if required effects of sea-quark-pairs and other gluonic structures are displayed. (authors)

  11. The leading eikonal operator in string-brane scattering at high energy

    DEFF Research Database (Denmark)

    Giuseppe, D'Appollonio; di Vecchia, Paolo; Russo, Rodolfo

    2015-01-01

    In this paper we present two (a priori independent) derivations of the eikonal operator in string-brane scattering. The rst one is obtained by summing surfaces with any number of boundaries, while in the second one the eikonal operator is derived from the three-string vertex in a suitable light......-cone gauge. This second derivation shows that the bosonic oscillators present in the leading eikonal operator are to be identied with the string bosonic oscillators in a suitable light-cone gauge, while the rst one shows that it exponentiates recovering unitarity. This paper is a review of results obtained...

  12. High energy hadron dynamics based on a Stochastic-field multi-eikonal theory

    International Nuclear Information System (INIS)

    Arnold, R.C.

    1977-06-01

    Multi-eikonal theory, using a stoichastic-field representation for collective long range rapidity correlations, is developed and applied to the calculation of Regge pole parameters, high transverse momentum enhancements, and fluctuation patterns in rapidity densities. If a short-range-order model, such as the one-dimensional planar bootstrap, with only leading t-channel meson poles, is utilized as input to the multi-eikonal method, the pole spectrum is modified in three ways; promotion and renormalization of leading trajectories (suggesting an effective pomeron above unity at intermediate energies), and a proliferation of dynamical secondary trajectories, reminiscent of dual models. When transverse dimensions are included, the collective effects produce a growth with energy of large-P/sub tau/ inclusive cross-sections. Typical-event rapidity distributions, at energies of a few TeV, can be estimated by suitable approximations; the fluctuations give rise to ''domain'' patterns, which have the appearance of clusters separated by rapidity gaps. The relations between this approach to strong-interaction dynamics and a possible unification of weak, electromagnetic, and strong interactions are outlined

  13. Exact and approximate multiple diffraction calculations

    International Nuclear Information System (INIS)

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

    1976-08-01

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

  14. The leading eikonal operator in string-brane scattering at high energy

    CERN Document Server

    D'Appollonio, Giuseppe; Russo, Rodolfo; Veneziano, Gabriele

    2013-01-01

    In this paper we present two (a priori independent) derivations of the eikonal operator in string-brane scattering. The first one is obtained by summing surfaces with any number of boundaries, while in the second one the eikonal operator is derived from the three-string vertex in a suitable light-cone gauge. This second derivation shows that the bosonic oscillators present in the leading eikonal operator are to be identified with the string bosonic oscillators in a suitable light-cone gauge, while the first one shows that it exponentiates recovering unitarity. This paper is a review of results obtained in two previous publications of the same authors.

  15. Fast sweeping algorithm for accurate solution of the TTI eikonal equation using factorization

    KAUST Repository

    bin Waheed, Umair; Alkhalifah, Tariq Ali

    2017-01-01

    computational domain. We address the source-singularity problem for tilted transversely isotropic (TTI) eikonal solvers using factorization. We solve a sequence of factored tilted elliptically anisotropic (TEA) eikonal equations iteratively, each time

  16. Eikonal phase shift analyses of carbon-carbon scattering

    International Nuclear Information System (INIS)

    Townsend, L.W.; Bidasaria, H.B.; Wilson, J.W.

    1983-01-01

    A high-energy double-folding optical potential approximation to the exact nucleus-nucleus multiple-scattering series is used to determine eikonal phase shifts for carbon-carbon scattering at 204.2, 242.7, and 288.6 MeV. The double-folding potentials are obtained by folding the energy-dependent free nucleon-nucleon interaction with densities for the projectile and target obtained by unfolding the finite nucleon charge density from harmonic-well carbon charge distributions. The charge parameters for the latter are taken from the results of electron scattering experiments. Predictions for total, reaction, and elastic differential cross sections, using standard partial wave analysis for the scattering of identical particles, are made and compared with recent experimental results. Excellent agreement is obtained although there are no arbitrarily adjusted parameters in the theory

  17. An iterative fast sweeping based eikonal solver for tilted orthorhombic media

    KAUST Repository

    Waheed, Umair bin

    2014-08-01

    Computing first-arrival traveltimes of quasi-P waves in the presence of anisotropy is important for high-end near-surface modeling, microseismic-source localization, and fractured-reservoir characterization, and requires solving an anisotropic eikonal equation. Anisotropy deviating from elliptical anisotropy introduces higher-order nonlinearity into the eikonal equation, which makes solving the eikonal equation a challenge. We address this challenge by iteratively solving a sequence of simpler tilted elliptically anisotropic eikonal equations. At each iteration, the source function is updated to capture the effects of the higher order nonlinear terms. We use Aitken extrapolation to speed up the convergence rate of the iterative algorithm. The result is an algorithm for first-arrival traveltime computations in tilted anisotropic media. We demonstrate our method on tilted transversely isotropic media and tilted orthorhombic media. Our numerical tests demonstrate that the proposed method can match the first arrivals obtained by wavefield extrapolation, even for strong anisotropy and complex structures. Therefore, for the cases where oneor two-point ray tracing fails, our method may be a potential substitute for computing traveltimes. Our approach can be extended to anisotropic media with lower symmetries, such as monoclinic or even triclinic media.

  18. An iterative fast sweeping based eikonal solver for tilted orthorhombic media

    KAUST Repository

    Waheed, Umair bin; Yarman, Can Evren; Flagg, Garret

    2014-01-01

    Computing first-arrival traveltimes of quasi-P waves in the presence of anisotropy is important for high-end near-surface modeling, microseismic-source localization, and fractured-reservoir characterization, and requires solving an anisotropic eikonal equation. Anisotropy deviating from elliptical anisotropy introduces higher-order nonlinearity into the eikonal equation, which makes solving the eikonal equation a challenge. We address this challenge by iteratively solving a sequence of simpler tilted elliptically anisotropic eikonal equations. At each iteration, the source function is updated to capture the effects of the higher order nonlinear terms. We use Aitken extrapolation to speed up the convergence rate of the iterative algorithm. The result is an algorithm for first-arrival traveltime computations in tilted anisotropic media. We demonstrate our method on tilted transversely isotropic media and tilted orthorhombic media. Our numerical tests demonstrate that the proposed method can match the first arrivals obtained by wavefield extrapolation, even for strong anisotropy and complex structures. Therefore, for the cases where oneor two-point ray tracing fails, our method may be a potential substitute for computing traveltimes. Our approach can be extended to anisotropic media with lower symmetries, such as monoclinic or even triclinic media.

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

    International Nuclear Information System (INIS)

    Bogdanov, I.V.

    1985-01-01

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

  20. Post-prior discrepancies in the continuum distorted wave-eikonal initial state approximation for ion-helium ionization

    Energy Technology Data Exchange (ETDEWEB)

    Ciappina, M F [CONICET and Departamento de Fisica, Universidad Nacional del Sur, 8000 Bahia Blanca (Argentina); Cravero, W R [CONICET and Departamento de Fisica, Universidad Nacional del Sur, 8000 Bahia Blanca (Argentina); Garibotti, C R [CONICET and Division Colisiones Atomicas, Centro Atomico Bariloche, 8400 Bariloche (Argentina)

    2003-09-28

    We have explored post-prior discrepancies within continuum distorted wave-eikonal initial state theory for ion-atom ionization. Although there are no post-prior discrepancies when electron-target initial and final states are exact solutions of the respective Hamiltonians, discrepancies do arise for multielectronic targets, when a hydrogenic continuum with effective charge is used for the final electron-residual target wavefunction. We have found that the prior version calculations give better results than the post version, particularly for highly charged projectiles. We have explored the reasons for this behaviour and found that the prior version shows less sensitivity to the choice of the final state. The fact that the perturbation potentials operate upon the initial state suggests that the selection of the initial bound state is relatively more important than the final continuum state for the prior version.

  1. Factorized distorted wave approximation for the (e,2e) reaction on atoms : noncoplanar symmetric

    International Nuclear Information System (INIS)

    Dixon, A.J.; McCarthy, I.E.; Noble, C.J.; Weigold, E.

    1977-02-01

    Angular and energy correlations for electrons produced in the ionization of neon and xenon by electrons with energies between 400eV and 2.5 keV have been measured using symmetric noncoplanar kinematics. The reaction yields information about the atomic orbitals and their correlations when analysed with the distorted-wave off-shell impulse approximation. In the past either plane waves or various eikonal approximations have been used for the distorted waves, and in the cases where the eikonal parameters are approximately related to the elastic scattering the spectroscopic sum rule has been approximately verified. In the present work calculations have also been carried out using partial-wave-expanded optical model wave functions which describe the elastic scattering in detail. (Author)

  2. Fast sweeping algorithm for accurate solution of the TTI eikonal equation using factorization

    KAUST Repository

    bin Waheed, Umair

    2017-06-10

    Traveltime computation is essential for many seismic data processing applications and velocity analysis tools. High-resolution seismic imaging requires eikonal solvers to account for anisotropy whenever it significantly affects the seismic wave kinematics. Moreover, computation of auxiliary quantities, such as amplitude and take-off angle, rely on highly accurate traveltime solutions. However, the finite-difference based eikonal solution for a point-source initial condition has an upwind source-singularity at the source position, since the wavefront curvature is large near the source point. Therefore, all finite-difference solvers, even the high-order ones, show inaccuracies since the errors due to source-singularity spread from the source point to the whole computational domain. We address the source-singularity problem for tilted transversely isotropic (TTI) eikonal solvers using factorization. We solve a sequence of factored tilted elliptically anisotropic (TEA) eikonal equations iteratively, each time by updating the right hand side function. At each iteration, we factor the unknown TEA traveltime into two factors. One of the factors is specified analytically, such that the other factor is smooth in the source neighborhood. Therefore, through the iterative procedure we obtain accurate solution to the TTI eikonal equation. Numerical tests show significant improvement in accuracy due to factorization. The idea can be easily extended to compute accurate traveltimes for models with lower anisotropic symmetries, such as orthorhombic, monoclinic or even triclinic media.

  3. A second order discontinuous Galerkin fast sweeping method for Eikonal equations

    Science.gov (United States)

    Li, Fengyan; Shu, Chi-Wang; Zhang, Yong-Tao; Zhao, Hongkai

    2008-09-01

    In this paper, we construct a second order fast sweeping method with a discontinuous Galerkin (DG) local solver for computing viscosity solutions of a class of static Hamilton-Jacobi equations, namely the Eikonal equations. Our piecewise linear DG local solver is built on a DG method developed recently [Y. Cheng, C.-W. Shu, A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations, Journal of Computational Physics 223 (2007) 398-415] for the time-dependent Hamilton-Jacobi equations. The causality property of Eikonal equations is incorporated into the design of this solver. The resulting local nonlinear system in the Gauss-Seidel iterations is a simple quadratic system and can be solved explicitly. The compactness of the DG method and the fast sweeping strategy lead to fast convergence of the new scheme for Eikonal equations. Extensive numerical examples verify efficiency, convergence and second order accuracy of the proposed method.

  4. Prestack first-break traveltime tomography using the double-square-root eikonal equation

    KAUST Repository

    Li, Siwei

    2012-09-01

    Traveltime tomography with shot-based eikonal equation fixes shot positions then relies on inversion to resolve any contradicting information between independent shots and achieve a possible cost-function minimum. On the other hand, the double-square-root (DSR) eikonal equation that describes the whole survey, while providing the same first-arrival travel-times, allows not only the receivers but also the shots to change position and therefore leads to faster convergence in tomo-graphic inversion. The DSR eikonal equation can be solved by a version of the fast-marching method (FMM) with special treatment for its singularity at horizontally traveling waves. For inversion, we use an upwind finite-difference scheme and the adjoint-state method to avoid explicit calculation of Fréchet derivatives. The proposed method generalizes to the 3D case straightforwardly.

  5. Prestack traveltime approximations

    KAUST Repository

    Alkhalifah, Tariq Ali

    2012-05-01

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

  6. An acoustic eikonal equation for attenuating orthorhombic media

    KAUST Repository

    Hao, Qi; Alkhalifah, Tariq Ali

    2017-01-01

    solve the eikonal equation using a combination of the perturbation method and Shanks transform. For a horizontal attenuating orthorhombic layer, both the real and imaginary part of the complex-valued reflection traveltime have nonhyperbolic behaviors

  7. An acoustic eikonal equation for attenuating VTI media

    KAUST Repository

    Hao, Qi; Alkhalifah, Tariq Ali

    2016-01-01

    We present an acoustic eikonal equation governing the complex-valued travel time of P-waves in attenuating, transversely isotropic media with a vertical symmetry axis (VTI). This equation is based on the assumption that the Pwave complex

  8. Eikonal representation of N-body Coulomb scattering amplitudes

    International Nuclear Information System (INIS)

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

    1983-01-01

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

  9. Variational formulation of covariant eikonal theory for vector waves

    International Nuclear Information System (INIS)

    Kaufman, A.N.; Ye, H.; Hui, Y.

    1986-10-01

    The eikonal theory of wave propagation is developed by means of a Lorentz-covariant variational principle, involving functions defined on the natural eight-dimensional phase space of rays. The wave field is a four-vector representing the electromagnetic potential, while the medium is represented by an anisotropic, dispersive nonuniform dielectric tensor D/sup μν/(k,x). The eikonal expansion yields, to lowest order, the Hamiltonian ray equations, which define the Lagrangian manifold k(x), and the wave-action conservation law, which determines the wave-amplitude transport along the rays. The first-order contribution to the variational principle yields a concise expression for the transport of the polarization phase. The symmetry between k-space and x-space allows for a simple implementation of the Maslov transform, which avoids the difficulties of caustic singularities

  10. An iterative, fast-sweeping-based eikonal solver for 3D tilted anisotropic media

    KAUST Repository

    Waheed, Umair bin; Yarman, Can Evren; Flagg, Garret

    2015-01-01

    Computation of first-arrival traveltimes for quasi-P waves in the presence of anisotropy is important for high-end near-surface modeling, microseismic-source localization, and fractured-reservoir characterization - and it requires solving an anisotropic eikonal equation. Anisotropy deviating from elliptical anisotropy introduces higher order nonlinearity into the eikonal equation, which makes solving the eikonal equation a challenge. We addressed this challenge by iteratively solving a sequence of simpler tilted elliptically anisotropic eikonal equations. At each iteration, the source function was updated to capture the effects of the higher order nonlinear terms. We used Aitken's extrapolation to speed up convergence rate of the iterative algorithm. The result is an algorithm for computing first-arrival traveltimes in tilted anisotropic media. We evaluated the applicability and usefulness of our method on tilted transversely isotropic media and tilted orthorhombic media. Our numerical tests determined that the proposed method matches the first arrivals obtained by wavefield extrapolation, even for strongly anisotropic and highly complex subsurface structures. Thus, for the cases where two-point ray tracing fails, our method can be a potential substitute for computing traveltimes. The approach presented here can be easily extended to compute first-arrival traveltimes for anisotropic media with lower symmetries, such as monoclinic or even the triclinic media.

  11. An iterative, fast-sweeping-based eikonal solver for 3D tilted anisotropic media

    KAUST Repository

    Waheed, Umair bin

    2015-03-30

    Computation of first-arrival traveltimes for quasi-P waves in the presence of anisotropy is important for high-end near-surface modeling, microseismic-source localization, and fractured-reservoir characterization - and it requires solving an anisotropic eikonal equation. Anisotropy deviating from elliptical anisotropy introduces higher order nonlinearity into the eikonal equation, which makes solving the eikonal equation a challenge. We addressed this challenge by iteratively solving a sequence of simpler tilted elliptically anisotropic eikonal equations. At each iteration, the source function was updated to capture the effects of the higher order nonlinear terms. We used Aitken\\'s extrapolation to speed up convergence rate of the iterative algorithm. The result is an algorithm for computing first-arrival traveltimes in tilted anisotropic media. We evaluated the applicability and usefulness of our method on tilted transversely isotropic media and tilted orthorhombic media. Our numerical tests determined that the proposed method matches the first arrivals obtained by wavefield extrapolation, even for strongly anisotropic and highly complex subsurface structures. Thus, for the cases where two-point ray tracing fails, our method can be a potential substitute for computing traveltimes. The approach presented here can be easily extended to compute first-arrival traveltimes for anisotropic media with lower symmetries, such as monoclinic or even the triclinic media.

  12. Eikonal Tomography of the Southern California Plate Boundary Region

    Science.gov (United States)

    Qiu, H.; Ben-Zion, Y.; Zigone, D.; Lin, F. C.

    2016-12-01

    We use eikonal tomography to derive directionally-dependent phase velocities of surface waves for the plate boundary region in southern CA sensitive to the approximate depth range 1-20 km. Seismic noise data recorded by 346 stations in the area provide a spatial coverage with 5-25 km typical station spacing and period range of 1-20 s. Noise cross-correlations are calculated for vertical component data recorded in year 2014. Rayleigh wave group and phase travel times between 2 and 13 sec period are derived for each station pair using frequency-time analysis. For each common station, all available phase travel time measurements with sufficient signal to noise ratio and envelope peak amplitude are used to construct a travel time map for a virtual source at the common station location. By solving the eikonal equation, both phase velocity and propagation direction are evaluated at each location for each virtual source. Isotropic phase velocities and 2-psi azimuthal anisotropy and their uncertainties are determined statistically using measurements from different virtual sources. Following the method of Barmin et al. (2001), group velocities are also inverted using all the group travel times that pass quality criteria. The obtained group and phase dispersions of Rayleigh waves are then inverted on a 6 x 6 km2 grid for local 1D piecewise shear wave velocity structures using the procedure of Herrmann (2013). The results agree well with previous observations of Zigone et al. (2015) in the overlapping area. Clear velocity contrasts and low velocity zones are seen for the San Andreas, San Jacinto, Elsinore and Garlock faults. We also find 2-psi azimuthal anisotropy with fast directions parallel to geometrically-simple fault sections. Details and updated results will be presented in the meeting.

  13. Non-eikonal corrections for the scattering of spin-one particles

    Energy Technology Data Exchange (ETDEWEB)

    Gaber, M.W.; Wilkin, C. [Department of Physics and Astronomy, University College London, WC1E 6BT, London (United Kingdom); Al-Khalili, J.S. [Department of Physics, University of Surrey, GU2 7XH, Guildford, Surrey (United Kingdom)

    2004-08-01

    The Wallace Fourier-Bessel expansion of the scattering amplitude is generalised to the case of the scattering of a spin-one particle from a potential with a single tensor coupling as well as central and spin-orbit terms. A generating function for the eikonal-phase (quantum) corrections is evaluated in closed form. For medium-energy deuteron-nucleus scattering, the first-order correction is dominant and is shown to be significant in the interpretation of analysing power measurements. This conclusion is supported by a numerical comparison of the eikonal observables, evaluated with and without corrections, with those obtained from a numerical resolution of the Schroedinger equation for d-{sup 58}Ni scattering at incident deuteron energies of 400 and 700 MeV. (orig.)

  14. Geometrical scaling vs factorizable eikonal models

    CERN Document Server

    Kiang, D

    1975-01-01

    Among various theoretical explanations or interpretations for the experimental data on the differential cross-sections of elastic proton-proton scattering at CERN ISR, the following two seem to be most remarkable: A) the excellent agreement of the Chou-Yang model prediction of d sigma /dt with data at square root s=53 GeV, B) the general manifestation of geometrical scaling (GS). The paper confronts GS with eikonal models with factorizable opaqueness, with special emphasis on the Chou-Yang model. (12 refs).

  15. Application of perturbation theory to a P-wave eikonal equation in orthorhombic media

    KAUST Repository

    Stovas, Alexey

    2016-10-12

    The P-wave eikonal equation for orthorhombic (ORT) anisotropic media is a highly nonlinear partial differential equation requiring the solution of a sixth-order polynomial to obtain traveltimes, resulting in complex and time-consuming numerical solutions. To alleviate this complexity, we approximate the solution of this equation by applying a multiparametric perturbation approach. We also investigated the sensitivity of traveltime surfaces inORT mediawith respect to three anelliptic parameters. As a result, a simple and accurate P-wave traveltime approximation valid for ORT media was derived. Two different possible anelliptic parameterizations were compared. One of the parameterizations includes anelliptic parameters defined at zero offset: η1, η2, and ηxy. Another parameterization includes anelliptic parameters defined for all symmetry planes: η1, η2, and η3. The azimuthal behavior of sensitivity coefficients with different parameterizations was used to analyze the crosstalk between anelliptic parameters. © 2016 Society of Exploration Geophysicists.

  16. Local Ray-Based Traveltime Computation Using the Linearized Eikonal Equation

    KAUST Repository

    Almubarak, Mohammed S.

    2013-01-01

    used. However, these eikonal solvers are mainly used to obtain early-arrival traveltime. Ray tracing can be used to pick later traveltime branches, besides the early arrivals, which may lead to an improvement in velocity estimation or in seismic imaging

  17. Are eikonal quasinormal modes linked to the unstable circular null geodesics?

    Directory of Open Access Journals (Sweden)

    R.A. Konoplya

    2017-08-01

    Full Text Available In Cardoso et al. [6] it was claimed that quasinormal modes which any stationary, spherically symmetric and asymptotically flat black hole emits in the eikonal regime are determined by the parameters of the circular null geodesic: the real and imaginary parts of the quasinormal mode are multiples of the frequency and instability timescale of the circular null geodesics respectively. We shall consider asymptotically flat black hole in the Einstein–Lovelock theory, find analytical expressions for gravitational quasinormal modes in the eikonal regime and analyze the null geodesics. Comparison of the both phenomena shows that the expected link between the null geodesics and quasinormal modes is violated in the Einstein–Lovelock theory. Nevertheless, the correspondence exists for a number of other cases and here we formulate its actual limits.

  18. Are eikonal quasinormal modes linked to the unstable circular null geodesics?

    Science.gov (United States)

    Konoplya, R. A.; Stuchlík, Z.

    2017-08-01

    In Cardoso et al. [6] it was claimed that quasinormal modes which any stationary, spherically symmetric and asymptotically flat black hole emits in the eikonal regime are determined by the parameters of the circular null geodesic: the real and imaginary parts of the quasinormal mode are multiples of the frequency and instability timescale of the circular null geodesics respectively. We shall consider asymptotically flat black hole in the Einstein-Lovelock theory, find analytical expressions for gravitational quasinormal modes in the eikonal regime and analyze the null geodesics. Comparison of the both phenomena shows that the expected link between the null geodesics and quasinormal modes is violated in the Einstein-Lovelock theory. Nevertheless, the correspondence exists for a number of other cases and here we formulate its actual limits.

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

    International Nuclear Information System (INIS)

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

    1984-01-01

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

  20. Distorted eikonal cross sections: A time-dependent view

    International Nuclear Information System (INIS)

    Turner, R.E.

    1982-01-01

    For Hamiltonians with two potentials, differential cross sections are written as time-correlation functions of reference and distorted transition operators. Distorted eikonal differential cross sections are defined in terms of straight-line and reference classical trajectories. Both elastic and inelastic results are obtained. Expressions for the inelastic cross sections are presented in terms of time-ordered cosine and sine memory functions through the use of the Zwanzig-Feshbach projection-operator method

  1. Eikonal multiple scattering model within the framework of Feynman's positron theory

    International Nuclear Information System (INIS)

    Tekou, A.

    1986-07-01

    The Bethe Salpeter equation for nucleon-nucleon, nucleon-nucleus and nucleus-nucleus scattering is eikonalized. Multiple scattering series is obtained. Contributions of three body interations are included. The model presented below may be used to investigate atomic collisions. (author)

  2. Medium-induced gluon radiation beyond the eikonal approximation

    CERN Document Server

    Apolinário, Liliana; Milhano, Guilherme; Salgado, Carlos A

    2014-01-01

    In this work we improve existing calculations of radiative energy loss by computing corrections that implement energy-momentum conservation, previously only implemented a posteriori, in a rigorous way. Using the path-integral formalism, we compute in-medium splittings allowing transverse motion of all particles in the emission process, thus relaxing the assumption that only the softest particle is permitted such movement. This work constitutes the extension of the computation carried out for x$\\rightarrow$1 in Phys. Lett. B718 (2012) 160-168, to all values of x, the momentum fraction of the energy of the parent parton carried by the emitted gluon. In order to accomplish a general description of the whole in-medium showering process, in this work we allow for arbitrary formation times for the emitted gluon. We provide general expressions and their realisation in the path integral formalism within the harmonic oscillator approximation.

  3. Unitary eikonal formalism for multiproduction of isovector mesons at high energy

    CERN Document Server

    Redei, L B

    1973-01-01

    Unitary eikonal models for multiproduction of isovector mesons are discussed in general terms. A closed analytic expression is derived for the partial production cross sections and for the meson multiplicity moments. A simple class of models is discussed in more detail. (11 refs).

  4. The eikonal equation, envelopes and contact transformations

    International Nuclear Information System (INIS)

    Frittelli, Simonetta; Kamran, Niky; Newman, Ezra T

    2003-01-01

    We begin with an arbitrary but given conformal Lorentzian metric on an open neighbourhood, U, of a four-dimensional manifold (spacetime) and study families of solutions of the eikonal equation. In particular, the families that are of interest to us are the complete solutions. Their level surfaces form a two-parameter (points of S 2 ) family of foliations of U. We show that, from such a complete solution, it is possible to derive a pair of second-order PDEs defined solely on the parameter space S 2 , i.e., they have no reference to the spacetime points. We then show that if one uses the classical envelope method for the construction of new complete solutions from any given complete solution, then the new pair of PDEs (found from the new complete solution) is related to the old pair by contact transformations in the second jet bundle over S 2 . Further, we demonstrate that the pair of second-order PDEs obtained in this manner from any complete solution lies in a subclass of all pairs of second-order PDEs defined by the vanishing of a certain function obtained from the pair and is referred to as the generalized-Wuenschmann invariant. For completeness we briefly discuss the analogous issues associated with the eikonal equation in three dimensions. Finally we point out that conformally invariant geometric structures from the Lorentzian manifold have natural counterparts in the second jet bundle over S 2 on which the pair of PDEs lives

  5. Eikonal Scattering in the sdg Interacting Boson Model:. Analytical Results in the SUsdg(3) Limit and Their Generalizations

    Science.gov (United States)

    Kota, V. K. B.

    General expression for the representation matrix elements in the SUsdg(3) limit of the sdg interacting boson model (sdgIBM) is derived that determine the scattering amplitude in the eikonal approximation for medium energy proton-nucleus scattering when the target nucleus is deformed and it is described by the SUsdg(3) limit. The SUsdg(3) result is generalized to two important situations: (i) when the target nucleus ground band states are described as states arising out of angular momentum projection from a general single Kπ = 0+ intrinsic state in sdg space; (ii) for rotational bands built on one-phonon excitations in sdgIBM.

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

    International Nuclear Information System (INIS)

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

    1975-01-01

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

  7. Prestack first-break traveltime tomography using the double-square-root eikonal equation

    KAUST Repository

    Li, Siwei; Fomel, Sergey; Vladimirsky, Alexander

    2012-01-01

    -square-root (DSR) eikonal equation that describes the whole survey, while providing the same first-arrival travel-times, allows not only the receivers but also the shots to change position and therefore leads to faster convergence in tomo-graphic inversion. The DSR

  8. A model expansion criterion for treating surface topography in ray path calculations using the eikonal equation

    International Nuclear Information System (INIS)

    Ma, Ting; Zhang, Zhongjie

    2014-01-01

    Irregular surface topography has revolutionized how seismic traveltime is calculated and the data are processed. There are two main schemes for dealing with an irregular surface in the seismic first-arrival traveltime calculation: (1) expanding the model and (2) flattening the surface irregularities. In the first scheme, a notional infill medium is added above the surface to expand the physical space into a regular space, as required by the eikonal equation solver. Here, we evaluate the chosen propagation velocity in the infill medium through ray path tracking with the eikonal equation-solved traveltime field, and observe that the ray paths will be physically unrealistic for some values of this propagation velocity. The choice of a suitable propagation velocity in the infill medium is crucial for seismic processing of irregular topography. Our model expansion criterion for dealing with surface topography in the calculation of traveltime and ray paths using the eikonal equation highlights the importance of both the propagation velocity of the infill physical medium and the topography gradient. (paper)

  9. Application of perturbation theory to a P-wave eikonal equation in orthorhombic media

    KAUST Repository

    Stovas, Alexey; Masmoudi, Nabil; Alkhalifah, Tariq Ali

    2016-01-01

    The P-wave eikonal equation for orthorhombic (ORT) anisotropic media is a highly nonlinear partial differential equation requiring the solution of a sixth-order polynomial to obtain traveltimes, resulting in complex and time-consuming numerical

  10. Diffractive dissociation and eikonalization in high energy pp and p bar p collisions

    International Nuclear Information System (INIS)

    Gotsman, E.; Levin, E.M.; Maor, U.

    1994-01-01

    We show that eikonal corrections imposed on diffraction dissociation processes calculated in the triple Regge limit produce a radical change in the energy dependence of the predicted cross section. The induced correction is shown to be in general agreement with the recent Fermilab Tevatron experimental data

  11. An efficient eikonal solver for tilted transversely isotropic and tilted orthorhombic media

    KAUST Repository

    Waheed, Umair bin

    2014-01-01

    Computing first-arrival traveltimes in the presence of anisotropy is important for high-end near surface modeling, microseismic source localization, and fractured reservoir characterization. Anisotropy deviating from elliptical anisotropy introduces higher-order nonlinearity into the eikonal equation, which makes solving the equation a challenging task. We address this challenge by iteratively solving a sequence of simpler tilted elliptically anisotropic eikonal equations. At each iteration, the source function is updated to capture the effects due to the higher order nonlinear terms in the anisotropy. We use Aitken extrapolation to speed up the convergence rate of the iterative algorithm. The result is an efficient algorithm for firstarrival traveltime computations in tilted anisotropic media. We demonstrate the proposed method for the tilted transversely isotropic media and the tilted orthorhombic media. Numerical tests show that the proposed method is feasible and produces results that are comparable to wavefield extrapolation, even for strongly anisotropic and complex structures. Therefore, for the cases where one or two-point ray tracing fails, our method may be a potential substitute for computing traveltimes.

  12. An eikonal-based formulation for traveltime perturbation with respect to the source location

    KAUST Repository

    Alkhalifah, Tariq

    2010-11-01

    Traveltime calculations amount to solving the nonlinear eikonal equation for a given source location. The relationship between the eikonal solution and its perturbations is analyzed with respect to the source location and a partial differential equation is developed that relates the traveltime field for one source location to that for a nearby source. This linear first-order equation in one form depends on lateral changes in velocity and in another form is independent of the velocity field and relies on second-order derivatives of the original traveltime field. For stable finite-difference calculations, this requires the velocity field to be smooth in a sense similar to ray-tracing requirements. Our formulation for traveltime perturbation has several potential applications, such that as traveltime calculation by source-location perturbation, velocity-independent interpolation including datuming, and velocity estimation. Additionally, higher-order expansions provide parameters necessary for Gaussian-beam computations. © 2010 Society of Exploration Geophysicists.

  13. An eikonal-based formulation for traveltime perturbation with respect to the source location

    KAUST Repository

    Alkhalifah, Tariq; Fomel, Sergey

    2010-01-01

    Traveltime calculations amount to solving the nonlinear eikonal equation for a given source location. The relationship between the eikonal solution and its perturbations is analyzed with respect to the source location and a partial differential equation is developed that relates the traveltime field for one source location to that for a nearby source. This linear first-order equation in one form depends on lateral changes in velocity and in another form is independent of the velocity field and relies on second-order derivatives of the original traveltime field. For stable finite-difference calculations, this requires the velocity field to be smooth in a sense similar to ray-tracing requirements. Our formulation for traveltime perturbation has several potential applications, such that as traveltime calculation by source-location perturbation, velocity-independent interpolation including datuming, and velocity estimation. Additionally, higher-order expansions provide parameters necessary for Gaussian-beam computations. © 2010 Society of Exploration Geophysicists.

  14. Modelling of the Woods-Saxon eikonal function for nuclear elastic scattering; Modelirovanie ehjkonal`noj funktsii uprugogo rasseyaniya v pole potentsiala Vudsa-Saksona

    Energy Technology Data Exchange (ETDEWEB)

    Luk` yanov, V K; Permyakov, V P; Chubov, Yu V

    1999-12-31

    The eikonal phase is needed for the analytical calculations for the nuclear scattering in the high energy approximation (E>>U, kR>>1). In this paper we obtain its model expression for scattering on Woods-Saxon potential which with a good accuracy reproduces its behaviour in complex plane which is found numerically. In the case one evaluates explicitly the scattering amplitude using saddle-point method makes the physics more understandable. The numerical amplitudes and cross sections of nucleus-nucleus scattering are compared with exact calculations. (author) 9 refs., 7 figs. Submitted to Izvestiya Akademii Nauk. Rossijskaya Akademiya Nauk. Seriya Fizicheskaya

  15. Eikonal-Based Inversion of GPR Data from the Vaucluse Karst Aquifer

    Science.gov (United States)

    Yedlin, M. J.; van Vorst, D.; Guglielmi, Y.; Cappa, F.; Gaffet, S.

    2009-12-01

    In this paper, we present an easy-to-implement eikonal-based travel time inversion algorithm and apply it to borehole GPR measurement data obtained from a karst aquifer located in the Vaucluse in Provence. The boreholes are situated with a fault zone deep inside the aquifer, in the Laboratoire Souterrain à Bas Bruit (LSBB). The measurements were made using 250 MHz MALA RAMAC borehole GPR antennas. The inversion formulation is unique in its application of a fast-sweeping eikonal solver (Zhao [1]) to the minimization of an objective functional that is composed of a travel time misfit and a model-based regularization [2]. The solver is robust in the presence of large velocity contrasts, efficient, easy to implement, and does not require the use of a sorting algorithm. The computation of sensitivities, which are required for the inversion process, is achieved by tracing rays backward from receiver to source following the gradient of the travel time field [2]. A user wishing to implement this algorithm can opt to avoid the ray tracing step and simply perturb the model to obtain the required sensitivities. Despite the obvious computational inefficiency of such an approach, it is acceptable for 2D problems. The relationship between travel time and the velocity profile is non-linear, requiring an iterative approach to be used. At each iteration, a set of matrix equations is solved to determine the model update. As the inversion continues, the weighting of the regularization parameter is adjusted until an appropriate data misfit is obtained. The inversion results, shown in the attached image, are consistent with previously obtained geological structure. Future work will look at improving inversion resolution and incorporating other measurement methodologies, with the goal of providing useful data for groundwater analysis. References: [1] H. Zhao, “A fast sweeping method for Eikonal equations,” Mathematics of Computation, vol. 74, no. 250, pp. 603-627, 2004. [2] D

  16. Factorized distorted wave approximation for the (e,2e) reaction on atoms : coplanar symmetric

    International Nuclear Information System (INIS)

    Fuss, I.; McCarthy, I.E.; Noble, C.J.; Weigold, E.

    1977-02-01

    The coplanar symmetric (e,2e) cross section has been studied in the intermediate energy region for the valence states of the inert gases He, Ar and Ne. Experimental measurements at 200, 400, 800, and 1200eV for He, and at 400, 800 and 1200eV for Ne and Ar, are compared with calculations based on the factorized half-off-shell distorted-wave impulse approximation. Calculations are carried out using partial wave expanded optical model wave functions which describe elastic scattering for the distorted waves, the eikonal approximation, and the plane wave approximation. (Author)

  17. Black-hole quasinormal resonances: Wave analysis versus a geometric-optics approximation

    International Nuclear Information System (INIS)

    Hod, Shahar

    2009-01-01

    It has long been known that null unstable geodesics are related to the characteristic modes of black holes--the so-called quasinormal resonances. The basic idea is to interpret the free oscillations of a black hole in the eikonal limit in terms of null particles trapped at the unstable circular orbit and slowly leaking out. The real part of the complex quasinormal resonances is related to the angular velocity at the unstable null geodesic. The imaginary part of the resonances is related to the instability time scale (or the inverse Lyapunov exponent) of the orbit. While this geometric-optics description of the black-hole quasinormal resonances in terms of perturbed null rays is very appealing and intuitive, it is still highly important to verify the validity of this approach by directly analyzing the Teukolsky wave equation which governs the dynamics of perturbation waves in the black-hole spacetime. This is the main goal of the present paper. We first use the geometric-optics technique of perturbing a bundle of unstable null rays to calculate the resonances of near-extremal Kerr black holes in the eikonal approximation. We then directly solve the Teukolsky wave equation (supplemented by the appropriate physical boundary conditions) and show that the resultant quasinormal spectrum obtained directly from the wave analysis is in accord with the spectrum obtained from the geometric-optics approximation of perturbed null rays.

  18. Deuteron D-wave and the non-eikonal effects in tensor asymmetries in elastic proton-deuteron scattering

    International Nuclear Information System (INIS)

    Alberi, G.; Bleszynski, M.; California Univ., Los Angeles; Santos, S.; Jaroszewicz, T.

    1980-01-01

    It is shown that the tensor asymmetries in the elastic proton-deuteron scattering at medium energies are very sensitive to the non-eikonal corrections to the Glauber model. This sensitivity originates from the fact that, in double scattering, the non-eikonal corrections affect in a different way the contributions coming from the S- and D-wave parts of the deuteron wave function. This leads to considerable change of the tensor asymmetries not only in the region of the interference between single and double scatterings, but also in the region of dominance of the double scattering. It is suggested that these effects should be taken into account in any careful analysis of the proton-deuteron polarization data, which has as a goal the extraction of the NN amplitudes. (author)

  19. A Color Mutation Hadronic Soft Interaction Model -- Eikonal Formalism and Branching Evolution

    OpenAIRE

    Cao, Zhen

    1998-01-01

    ECOMB is established as a hadronic multiparticle production generator by soft interaction. It incorporates the eikonal formalism, parton model, color mutation, branching, resonance production and decay. A partonic cluster, being color-neutral initially, splits into smaller color-neutral clusters successively due to the color mutation of the quarks. The process stops at hadronic resonance, $q\\bar q$ pair, formation. The model contains self-similar dynamics and exhibits scaling behavior in the ...

  20. High-energy properties of a class of unitary eikonal models for multiproduction

    CERN Document Server

    Redei, L B

    1974-01-01

    The high-energy properties of a simple class of unitary, crossing- symmetric eikonal models of multiproduction are discussed on the basis of the general closed expression given for the S-matrix elements in a previous publication. In particular, the high-energy behaviour of the multiplicity moments is discussed and it is shown that the KNO scaling relation emerges in a very natural fashion in this class of models. (8 refs).

  1. Traveltime approximations for inhomogeneous HTI media

    KAUST Repository

    Alkhalifah, Tariq Ali

    2011-01-01

    Traveltimes information is convenient for parameter estimation especially if the medium is described by an anisotropic set of parameters. This is especially true if we could relate traveltimes analytically to these medium parameters, which is generally hard to do in inhomogeneous media. As a result, I develop traveltimes approximations for horizontaly transversely isotropic (HTI) media as simplified and even linear functions of the anisotropic parameters. This is accomplished by perturbing the solution of the HTI eikonal equation with respect to η and the azimuthal symmetry direction (usually used to describe the fracture direction) from a generally inhomogeneous elliptically anisotropic background medium. The resulting approximations can provide accurate analytical description of the traveltime in a homogenous background compared to other published moveout equations out there. These equations will allow us to readily extend the inhomogenous background elliptical anisotropic model to an HTI with a variable, but smoothly varying, η and horizontal symmetry direction values. © 2011 Society of Exploration Geophysicists.

  2. Eikonal instability of Gauss-Bonnet-(anti-)-de Sitter black holes

    Science.gov (United States)

    Konoplya, R. A.; Zhidenko, A.

    2017-05-01

    Here we have shown that asymptotically anti-de Sitter (AdS) black holes in the Einstein-Gauss-Bonnet (GB) theory are unstable under linear perturbations of space-time in some region of parameters. This (eikonal) instability develops at high multipole numbers. We found the exact parametric regions of the eikonal instability and extended this consideration to asymptotically flat and de Sitter cases. The approach to the threshold of instability is driven by purely imaginary quasinormal modes, which are similar to those found recently in Grozdanov, Kaplis, and Starinets, [J. High Energy Phys. 07 (2016) 151, 10.1007/JHEP07(2016)151] for the higher curvature corrected black hole with the planar horizon. The found instability may indicate limits of holographic applicability of the GB-AdS backgrounds. Recently, through the analysis of critical behavior in AdS space-time in the presence of the Gauss-Bonnet term, it was shown [Deppe et al, Phys. Rev. Lett. 114, 071102 (2015), 10.1103/PhysRevLett.114.071102], that, if the total energy content of the AdS space-time is small, then no black holes can be formed with mass less than some critical value. A similar mass gap was also found when considering collapse of mass shells in asymptotically flat Gauss-Bonnet theories [Frolov, Phys. Rev. Lett. 115, 051102 (2015), 10.1103/PhysRevLett.115.051102]. The found instability of all sufficiently small Einstein-Gauss-Bonnet-AdS, dS and asymptotically flat black holes may explain the existing mass gaps in their formation.

  3. Corrections to the leading eikonal amplitude for high-energy scattering and quasipotential approach

    International Nuclear Information System (INIS)

    Nguyen Suan Hani; Nguyen Duy Hung

    2003-12-01

    Asymptotic behaviour of the scattering amplitude for two scalar particle at high energy and fixed momentum transfers is reconsidered in quantum field theory. In the framework of the quasipotential approach and the modified perturbation theory a systematic scheme of finding the leading eikonal scattering amplitudes and its corrections is developed and constructed. The connection between the solutions obtained by quasipotential and functional approaches is also discussed. (author)

  4. Eikonal form of the dynamic polarization potential and its application to the scattering of exotic nuclei

    Energy Technology Data Exchange (ETDEWEB)

    Canto, L F; Donangelo, R [Universidade Federal do Rio de Janeiro, RJ (Brazil). Inst. de Fisica; Hussein, M S [Sao Paulo Univ. (Brazil). Inst. de Fisica

    1991-07-01

    The eikonal theory of the dynamic polarization potential (DDP) is developed. Application to the scattering of loosely bound exotic nuclei is made. In particular, the effect of our DPP on the scattering of {sup 11}Li+{sup 12}C at 85 AxMeV is discussed. (orig.).

  5. Approximate Global Convergence and Quasi-Reversibility for a Coefficient Inverse Problem with Backscattering Data

    Science.gov (United States)

    2011-04-01

    L1u. Assume that geodesic lines, generated by the eikonal equation corresponding to the function c (x) are regular, i.e. any two points in R3 can be...source x0 is located far from Ω, then similarly with (107) ∆l (x, x0) ≈ 0 in Ω. The function l (x, x0) satisfies the eikonal equation [38] |∇xl (x, x0...called “inverse kinematic problem” which aims to recover the function c (x) from the eikonal equation assuming that the function l (x, x0) is known for

  6. Numerical modeling of Gaussian beam propagation and diffraction in inhomogeneous media based on the complex eikonal equation

    Science.gov (United States)

    Huang, Xingguo; Sun, Hui

    2018-05-01

    Gaussian beam is an important complex geometrical optical technology for modeling seismic wave propagation and diffraction in the subsurface with complex geological structure. Current methods for Gaussian beam modeling rely on the dynamic ray tracing and the evanescent wave tracking. However, the dynamic ray tracing method is based on the paraxial ray approximation and the evanescent wave tracking method cannot describe strongly evanescent fields. This leads to inaccuracy of the computed wave fields in the region with a strong inhomogeneous medium. To address this problem, we compute Gaussian beam wave fields using the complex phase by directly solving the complex eikonal equation. In this method, the fast marching method, which is widely used for phase calculation, is combined with Gauss-Newton optimization algorithm to obtain the complex phase at the regular grid points. The main theoretical challenge in combination of this method with Gaussian beam modeling is to address the irregular boundary near the curved central ray. To cope with this challenge, we present the non-uniform finite difference operator and a modified fast marching method. The numerical results confirm the proposed approach.

  7. Modeling a 400 Hz Signal Transmission Through the South China Sea Basin

    Science.gov (United States)

    2009-03-01

    TRACING ..........................8 1. General Ray Theory and the Eikonal Approximation .....................8 2. Hamiltonian Ray Tracing...HAMILTONIAN RAY TRACING 1. General Ray Theory and the Eikonal Approximation In general, modeling acoustic propagation through the ocean necessitates... eikonal and represents the phase component of the solution. Since solutions of constant phase represent wave fronts, and rays travel in a direction

  8. High Frequency Acoustic Propagation using Level Set Methods

    Science.gov (United States)

    2007-01-01

    solution of the high frequency approximation to the wave equation. Traditional solutions to the Eikonal equation in high frequency acoustics are...the Eikonal equation derived from the high frequency approximation to the wave equation, ucuH ∇±=∇ )(),( xx , with the nonnegative function c(x...For simplicity, we only consider the case ucuH ∇+=∇ )(),( xx . Two difficulties must be addressed when solving the Eikonal equation in a fixed

  9. Numerical Boundary Conditions for Specular Reflection in a Level-Sets-Based Wavefront Propagation Method

    Science.gov (United States)

    2012-12-01

    acoustics One begins with Eikonal equation for the acoustic phase function S(t,x) as derived from the geometric acoustics (high frequency) approximation to...zb(x) is smooth and reasonably approximated as piecewise linear. The time domain ray (characteristic) equations for the Eikonal equation are ẋ(t)= c...travel time is affected, which is more physically relevant than global error in φ since it provides the phase information for the Eikonal equation (2.1

  10. Theory of magnetohydrodynamic waves: The WKB approximation revisited

    International Nuclear Information System (INIS)

    Barnes, A.

    1992-01-01

    Past treatments of the eikonal or WKB theory of the propagation of magnetohydrodynamics waves have assumed a strictly isentropic background. IF in fact there is a gradient in the background entropy, then in second order in the WKB ordering, adiabatic fluctuations (in the Lagrangian sense) are not strictly isentropic in the Eulerian sense. This means that in the second order of the WKB expansion, which determines the variation of wave amplitude along rays, the violation of isentropy must be accounted for. The present paper revisits the derivation of the WKB approximation for small-amplitude magnetohydrodynamic waves, allowing for possible spatial variation of the background entropy. The equation of variation of wave amplitude is rederived; it is a bilinear equation which, it turns out, can be recast in the action conservation form. It is shown that this action conservation equation is in fact equivalent to the action conservation law obtained from Lagrangian treatments

  11. Pure radiation in space-time models that admit integration of the eikonal equation by the separation of variables method

    Science.gov (United States)

    Osetrin, Evgeny; Osetrin, Konstantin

    2017-11-01

    We consider space-time models with pure radiation, which admit integration of the eikonal equation by the method of separation of variables. For all types of these models, the equations of the energy-momentum conservation law are integrated. The resulting form of metric, energy density, and wave vectors of radiation as functions of metric for all types of spaces under consideration is presented. The solutions obtained can be used for any metric theories of gravitation.

  12. An accurate discontinuous Galerkin method for solving point-source Eikonal equation in 2-D heterogeneous anisotropic media

    Science.gov (United States)

    Le Bouteiller, P.; Benjemaa, M.; Métivier, L.; Virieux, J.

    2018-03-01

    Accurate numerical computation of wave traveltimes in heterogeneous media is of major interest for a large range of applications in seismics, such as phase identification, data windowing, traveltime tomography and seismic imaging. A high level of precision is needed for traveltimes and their derivatives in applications which require quantities such as amplitude or take-off angle. Even more challenging is the anisotropic case, where the general Eikonal equation is a quartic in the derivatives of traveltimes. Despite their efficiency on Cartesian meshes, finite-difference solvers are inappropriate when dealing with unstructured meshes and irregular topographies. Moreover, reaching high orders of accuracy generally requires wide stencils and high additional computational load. To go beyond these limitations, we propose a discontinuous-finite-element-based strategy which has the following advantages: (1) the Hamiltonian formalism is general enough for handling the full anisotropic Eikonal equations; (2) the scheme is suitable for any desired high-order formulation or mixing of orders (p-adaptivity); (3) the solver is explicit whatever Hamiltonian is used (no need to find the roots of the quartic); (4) the use of unstructured meshes provides the flexibility for handling complex boundary geometries such as topographies (h-adaptivity) and radiation boundary conditions for mimicking an infinite medium. The point-source factorization principles are extended to this discontinuous Galerkin formulation. Extensive tests in smooth analytical media demonstrate the high accuracy of the method. Simulations in strongly heterogeneous media illustrate the solver robustness to realistic Earth-sciences-oriented applications.

  13. Strong Coupling of Single Emitters to Surface Plasmons

    Science.gov (United States)

    2007-07-01

    however, we can make an eikonal approximation,39 assuming that the plas- mons are emitted completely into the end of the tip z=0 and that the propagative...restricts the re- gimes of validity to ki w, ki d1. An additional set of as- sumptions is made in using the eikonal approximation to arrive at Eq. 49

  14. Maxwell, Yang-Mills, Weyl and eikonal fields defined by any null shear-free congruence

    Science.gov (United States)

    Kassandrov, Vladimir V.; Rizcallah, Joseph A.

    We show that (specifically scaled) equations of shear-free null geodesic congruences on the Minkowski space-time possess intrinsic self-dual, restricted gauge and algebraic structures. The complex eikonal, Weyl 2-spinor, SL(2, ℂ) Yang-Mills and complex Maxwell fields, the latter produced by integer-valued electric charges (“elementary” for the Kerr-like congruences), can all be explicitly associated with any shear-free null geodesic congruence. Using twistor variables, we derive the general solution of the equations of the shear-free null geodesic congruence (as a modification of the Kerr theorem) and analyze the corresponding “particle-like” field distributions, with bounded singularities of the associated physical fields. These can be obtained in a straightforward algebraic way and exhibit nontrivial collective dynamics simulating physical interactions.

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

    CERN Document Server

    Lukyanov, V K; Lukyanov, K V

    2004-01-01

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

  16. Seismic tomography analysis using finite differential calculation of the eikonal equation and reciplocal principle; Eikonal equation no sabunkaiho to sohan genri wo riyoshita danseiha tomography kaiseki

    Energy Technology Data Exchange (ETDEWEB)

    Fujimoto, M; Ashida, Y; Watanabe, T; Sassa, K [Kyoto University, Kyoto (Japan)

    1996-10-01

    This paper describes the seismic tomography analysis of underground structures using finite differential calculation (FDC) and a reciprocal principle which points out that a propagation path is constant even if a source and receiver are exchanged with each other. Tomography analysis generally determines a ray length across each underground cell structure by ray tracing method to modify each cell slowness (inverse of velocity). Travel time field was determined by FDC of eikonal equation among ray tracing methods, and a wave propagation path was determined by reciprocity of elastic wave to carry out inversion. In conventional methods, since a wave length is assumed to be infinitesimal by ray theory, false modified slowness structures frequently appears depending on the density of a ray. Wave propagates in a certain width, and is affected by environment. The slowness was thus modified on the basis of the wave propagation path with a certain width by using not ray-tracing but reciprocity. By this modification, false structures were hardly found under a fine grid, and several propagation paths could be considered. 6 refs., 9 figs.

  17. Light Scattering by Optically Soft Particles Theory and Applications

    CERN Document Server

    Sharma, Subodh K

    2006-01-01

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

  18. System Design, Algorithm Development, and Verification for Optoacoustic Molecular Imaging of Protease Expression in Breast Cancer

    Science.gov (United States)

    2009-05-01

    Green’s function in the acoustically inhomogeneous medium can be written as: G(r, r′, ω) = g0(r, r′) exp(iωτ(r, r′)), (6) where τ is known as the eikonal ...function. The GA approximation gives us the eikonal equation in the limit λ→ 0: [5rτ(r, r′)] = c−2(r), (7) The eikonal equation implies: τ(r, r′) = r...concludes that to first-order in perturbation, this trajectory can chosen to be the path along the reference ray that satisfies the eikonal equation

  19. First and second-order corrections to the eikonal phase shifts for the interactions of two deformed nuclei

    International Nuclear Information System (INIS)

    Metawei, Z.

    2000-01-01

    We present the first and second - order corrections to the eikonal phase shifts for the interactions of two deformed nuclei. The elastic scattering differential cross-section has been calculated for both the interactions of I2 C- 12 C system (at energies 1016, 1449 and 2400 MeV) and 16 O- 12 C system (at energy 1503 MeV). The calculated results corrections seems to improve the agreement with the experimental data.The deflection function, the S-matrix,the near-side and the far-side decompositions of the scattering amplitude has been calculated using the same corrections

  20. Charles I et la voix silencieuse de Eikon Basilike : le silence comme moyen d'expression

    OpenAIRE

    Chaise-Brun, Vanessa

    2017-01-01

    La parole de Charles I, de son vivant, reste, malgré ses efforts, une parole vide et non entendue. Le bruit, qu’il s’agisse des cris de la foule ou bien les querelles engendrées par ses opposants, étouffe sa parole. Son discours est un cri face à la foule et à ses opposants, mais un cri impuissant. Pourtant, peut-on affirmer que la parole de Charles I est inexistante ? Eikon Basilike est une parole écrite, un silence qui crie l’innocence du roi. « Faire silence » ne signifie pas se taire mais...

  1. Hybridized Multiscale Discontinuous Galerkin Methods for Multiphysics

    Science.gov (United States)

    2015-09-14

    local approximation spaces of the hybridizable discontinuous Galerkin methods with precomputed phases which are solutions of the eikonal equation in...geometrical optics. Second, we propose a systematic procedure for computing multiple solutions of the eikonal equation. Third, we utilize the eigenvalue

  2. Eikonal calculation of electron-capture cross sections in collisions of H atoms with fast projectiles

    International Nuclear Information System (INIS)

    Ho, T.S.; Lieber, M.; Chan, F.T.

    1981-01-01

    We have employed the eikonal method to calculate the cross section for the capture of an electron into an arbitrary nl subshell in collisions between hydrogen atoms and fast projectiles. the projectiles were protons, C 6+ , O 8+ , and Fe 24+ . The energy ranges considered were 20--100 keV in the proton case, and 40--200 keV per nucleon in the other cases. These projectiles were selected because of their importance in fusion plasmas. For the highly charged case of Fe 24+ we found that our formulas, while exact, involved a high degree of cancellation and produced unreliable numerical results, so that a numerical integration of the penultimate formula was substituted. In the proton case agreement with recent experimental data is excellent

  3. Design and Fabrication of a Radio Frequency GRIN Lens Using 3D Printing Technology

    Science.gov (United States)

    2013-04-01

    of focusing a uniform plane wave to a point outside the lens. We begin with the Eikonal limit approach, to provide a first estimate for the...wavelength, lenses that operate at RF wavelengths are physically only a few times larger than the wavelength. Therefore, approximations such as Eikonal ...challenges the Eikonal limit. A near-field solution has to be considered for more exact results. We compare the focal length calculated by this

  4. Sound Propagation around Underwater Seamounts

    Science.gov (United States)

    2009-02-01

    eikonal and first order transport equations; this is a high-frequency approximation method. These methods will be discussed futher in Section 2.4. A...2.9 and 2.10 can be substituted back into the Helmholtz equation. Separating terms of the same order Lw gives the following eikonal equation, of O(w 2...n= 1,2,... Ray trajectories can be computed by solving the eikonal equation, and ray amplitude can be computed with the first transport equation. 6

  5. Traveltime approximations for transversely isotropic media with an inhomogeneous background

    KAUST Repository

    Alkhalifah, Tariq

    2011-05-01

    A transversely isotropic (TI) model with a tilted symmetry axis is regarded as one of the most effective approximations to the Earth subsurface, especially for imaging purposes. However, we commonly utilize this model by setting the axis of symmetry normal to the reflector. This assumption may be accurate in many places, but deviations from this assumption will cause errors in the wavefield description. Using perturbation theory and Taylor\\'s series, I expand the solutions of the eikonal equation for 2D TI media with respect to the independent parameter θ, the angle the tilt of the axis of symmetry makes with the vertical, in a generally inhomogeneous TI background with a vertical axis of symmetry. I do an additional expansion in terms of the independent (anellipticity) parameter in a generally inhomogeneous elliptically anisotropic background medium. These new TI traveltime solutions are given by expansions in and θ with coefficients extracted from solving linear first-order partial differential equations. Pade approximations are used to enhance the accuracy of the representation by predicting the behavior of the higher-order terms of the expansion. A simplification of the expansion for homogenous media provides nonhyperbolic moveout descriptions of the traveltime for TI models that are more accurate than other recently derived approximations. In addition, for 3D media, I develop traveltime approximations using Taylor\\'s series type of expansions in the azimuth of the axis of symmetry. The coefficients of all these expansions can also provide us with the medium sensitivity gradients (Jacobian) for nonlinear tomographic-based inversion for the tilt in the symmetry axis. © 2011 Society of Exploration Geophysicists.

  6. Traveltime approximations for transversely isotropic media with an inhomogeneous background

    KAUST Repository

    Alkhalifah, Tariq

    2011-01-01

    A transversely isotropic (TI) model with a tilted symmetry axis is regarded as one of the most effective approximations to the Earth subsurface, especially for imaging purposes. However, we commonly utilize this model by setting the axis of symmetry normal to the reflector. This assumption may be accurate in many places, but deviations from this assumption will cause errors in the wavefield description. Using perturbation theory and Taylor's series, I expand the solutions of the eikonal equation for 2D TI media with respect to the independent parameter θ, the angle the tilt of the axis of symmetry makes with the vertical, in a generally inhomogeneous TI background with a vertical axis of symmetry. I do an additional expansion in terms of the independent (anellipticity) parameter in a generally inhomogeneous elliptically anisotropic background medium. These new TI traveltime solutions are given by expansions in and θ with coefficients extracted from solving linear first-order partial differential equations. Pade approximations are used to enhance the accuracy of the representation by predicting the behavior of the higher-order terms of the expansion. A simplification of the expansion for homogenous media provides nonhyperbolic moveout descriptions of the traveltime for TI models that are more accurate than other recently derived approximations. In addition, for 3D media, I develop traveltime approximations using Taylor's series type of expansions in the azimuth of the axis of symmetry. The coefficients of all these expansions can also provide us with the medium sensitivity gradients (Jacobian) for nonlinear tomographic-based inversion for the tilt in the symmetry axis. © 2011 Society of Exploration Geophysicists.

  7. Maximal Sensitive Dependence and the Optimal Path to Epidemic Extinction

    Science.gov (United States)

    2010-01-01

    1996; Elgart and Kamenev, 2004). Instead, in this article, we will employ an eikonal approximation to recast the problem in terms of an effective...a control strategy on the extinction rate can be determined by its effect on the optimal path (Dykman et al., 2008). Through the use of the eikonal ...the solution of Eqs. (6a)–(6b) in the eikonal form (Elgart and Kamenev, 2004; Doering et al., 2005; Kubo et al., 1973; Wentzell, 1976; Gang, 1987

  8. Analysis of longitudinal momentum distribution of 10Be in 9Be(11Be, 10Be)X reaction

    International Nuclear Information System (INIS)

    Singh, Monika; Kharab, Rajesh; Singh, Ram Mehar

    2013-01-01

    We have analyzed the longitudinal momentum distribution of 10 Be fragment coming from one neutron stripping from 11 Be on 9 Be target at 60AMeV beam energy within the framework of zero and first order eikonal approximation. It has been found that the inclusion of first order correction term in the eikonal approximation results in a substantial improvement in the matching between the predicted and experimental results especially in tail region of the spectrum. (author)

  9. On next-to-eikonal corrections to threshold resummation for the Drell-Yan and DIS cross sections

    International Nuclear Information System (INIS)

    Laenen, Eric; Magnea, Lorenzo; Stavenga, Gerben

    2008-01-01

    We study corrections suppressed by one power of the soft gluon energy to the resummation of threshold logarithms for the Drell-Yan cross section and for Deep Inelastic structure functions. While no general factorization theorem is known for these next-to-eikonal (NE) corrections, it is conjectured that at least a subset will exponentiate, along with the logarithms arising at leading power. Here we develop some general tools to study NE logarithms, and we construct an ansatz for threshold resummation that includes various sources of NE corrections, implementing in this context the improved collinear evolution recently proposed by Dokshitzer, Marchesini and Salam (DMS). We compare our ansatz to existing exact results at two and three loops, finding evidence for the exponentiation of leading NE logarithms and confirming the predictivity of DMS evolution

  10. Traveltime approximations and parameter estimation for orthorhombic media

    KAUST Repository

    Masmoudi, Nabil

    2016-05-30

    Building anisotropy models is necessary for seismic modeling and imaging. However, anisotropy estimation is challenging due to the trade-off between inhomogeneity and anisotropy. Luckily, we can estimate the anisotropy parameters Building anisotropy models is necessary for seismic modeling and imaging. However, anisotropy estimation is challenging due to the trade-off between inhomogeneity and anisotropy. Luckily, we can estimate the anisotropy parameters if we relate them analytically to traveltimes. Using perturbation theory, we have developed traveltime approximations for orthorhombic media as explicit functions of the anellipticity parameters η1, η2, and Δχ in inhomogeneous background media. The parameter Δχ is related to Tsvankin-Thomsen notation and ensures easier computation of traveltimes in the background model. Specifically, our expansion assumes an inhomogeneous ellipsoidal anisotropic background model, which can be obtained from well information and stacking velocity analysis. We have used the Shanks transform to enhance the accuracy of the formulas. A homogeneous medium simplification of the traveltime expansion provided a nonhyperbolic moveout description of the traveltime that was more accurate than other derived approximations. Moreover, the formulation provides a computationally efficient tool to solve the eikonal equation of an orthorhombic medium, without any constraints on the background model complexity. Although, the expansion is based on the factorized representation of the perturbation parameters, smooth variations of these parameters (represented as effective values) provides reasonable results. Thus, this formulation provides a mechanism to estimate the three effective parameters η1, η2, and Δχ. We have derived Dix-type formulas for orthorhombic medium to convert the effective parameters to their interval values.

  11. Resonance spectrum of near-extremal Kerr black holes in the eikonal limit

    International Nuclear Information System (INIS)

    Hod, Shahar

    2012-01-01

    The fundamental resonances of rapidly rotating Kerr black holes in the eikonal limit are derived analytically. We show that there exists a critical value, μ c =√((15-√(193))/2 ), for the dimensionless ratio μ≡m/l between the azimuthal harmonic index m and the spheroidal harmonic index l of the perturbation mode, above which the perturbations become long lived. In particular, it is proved that above μ c the imaginary parts of the quasinormal frequencies scale like the black-hole temperature: ω I (n;μ>μ c )=2πT BH (n+1/2 ). This implies that for perturbations modes in the interval μ c I of the black hole becomes extremely long as the extremal limit T BH →0 is approached. A generalization of the results to the case of scalar quasinormal resonances of near-extremal Kerr-Newman black holes is also provided. In particular, we prove that only black holes that rotate fast enough (with MΩ≥2/5 , where M and Ω are the black-hole mass and angular velocity, respectively) possess this family of remarkably long-lived perturbation modes.

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

    International Nuclear Information System (INIS)

    Andriyanov, A.A.

    1975-01-01

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

  13. A highly scalable massively parallel fast marching method for the Eikonal equation

    Science.gov (United States)

    Yang, Jianming; Stern, Frederick

    2017-03-01

    The fast marching method is a widely used numerical method for solving the Eikonal equation arising from a variety of scientific and engineering fields. It is long deemed inherently sequential and an efficient parallel algorithm applicable to large-scale practical applications is not available in the literature. In this study, we present a highly scalable massively parallel implementation of the fast marching method using a domain decomposition approach. Central to this algorithm is a novel restarted narrow band approach that coordinates the frequency of communications and the amount of computations extra to a sequential run for achieving an unprecedented parallel performance. Within each restart, the narrow band fast marching method is executed; simple synchronous local exchanges and global reductions are adopted for communicating updated data in the overlapping regions between neighboring subdomains and getting the latest front status, respectively. The independence of front characteristics is exploited through special data structures and augmented status tags to extract the masked parallelism within the fast marching method. The efficiency, flexibility, and applicability of the parallel algorithm are demonstrated through several examples. These problems are extensively tested on six grids with up to 1 billion points using different numbers of processes ranging from 1 to 65536. Remarkable parallel speedups are achieved using tens of thousands of processes. Detailed pseudo-codes for both the sequential and parallel algorithms are provided to illustrate the simplicity of the parallel implementation and its similarity to the sequential narrow band fast marching algorithm.

  14. The refraction and reflection laws from a complete integral of the eikonal equation and Huygens’ principle

    International Nuclear Information System (INIS)

    Castro-Ramos, Jorge; Juárez-Reyes, Salvador Alejandro; Ortega-Vidals, Paula; Silva-Ortigoza, Gilberto; Suárez-Xique, Román; Marcelino-Aranda, Mariana; Silva-Ortigoza, Ramón

    2015-01-01

    In this work we assume that we have two given optical media with constant refraction indexes, which are separated by an arbitrary refracting surface. In one of the optical media we place a point light source at an arbitrary position. The aim of this work is to use a particular complete integral of the eikonal equation and Huygens’ principle to obtain the refraction and reflection laws. We remark that this complete integral associates a new point light source with each light ray that arrives at the refracting surface. This means that by using only this complete integral it is not possible to determine the direction of propagation of the refracted light rays; the direction of propagation is obtained by imposing two extra conditions on the complete integral which are equivalent to Huygens’ principle (in two dimensions, only one condition is needed). Finally, we establish the connection between the complete integral used here and that derived by using the k-function procedure introduced by Stavroudis, which works with plane wavefronts instead of spherical ones. (paper)

  15. Progress report for a research program in theoretical high-energy physics

    International Nuclear Information System (INIS)

    Feldman, D.; Fried, H.M.; Guralnik, G.S.; Kang, K.; Tan, C.I.

    1977-01-01

    Last year's research program dealt with a variety of topics including hadron dynamics (Pomeron interaction in the eikonal approximation, estimates of all eikonal pionization graphs, study of the critical behavior in Reggeon field theory, status of Regge pole models in KN scattering); phenomenology of renormalizable gauge theory (tests of flavor mixing, dimuon events, SU(3) gauge model with unmixed quarks, lepton models, CP violation, neutrino magnetic moment); spectral sum rules (axial-vector masses, mixing angles); application of the self-consistent field approximation to relativistic quantum field theory; topics in gravitation and cosmology; as well as other studies involving elementary particle interactions. A list of publications is included

  16. Direct processes in ion-atom collisions at intermediate and high energies

    International Nuclear Information System (INIS)

    Rodriguez Chariarse, V.D.

    1990-01-01

    This thesis deals with direct processes induced by Zp charge ion impact on one or two electron atoms and ions at intermediate energies. At a first step, a one-dimensional collision model is used in order to prove the different theoretical methods available to study collisions at such energy range, such as: perturbative and related variational principles, and distorted wave methods. The best description of both, symmetric and asymmetric collision type, is achieved by the distorted wave methods, particularly the ones using the exact impulsive wave function. As a next step, the appropriate formulations of the wave functions employed in the one-dimensional model to describe the real 3-dimensional Coulomb interaction case are examined by using the Eikonal and impulse hypothesis. In this way, the VPS and Eikonal wave functions are reviewed, and furtherly, the Eikonal form of the extended impulse wave function is derived. The Eikonal impulse approximation (EIA) is introduced. This is a distorted wave method using the Eikonal and extended impulse wave functions. The choice of the EIA prior version, i.e., the one using extended impulse wave function in the final channel for excitation is widely discussed and justified. (Author) [es

  17. Transplanckian collisions in TeV scale gravity

    CERN Document Server

    Rattazzi, Riccardo

    2004-01-01

    Collisions at transplanckian energies offer model independent tests of TeV scale gravity. One spectacular signal is given by black-hole production, though a full calculation of the corresponding cross- section is not yet available. Another signal is given by gravitational elastic scattering, which may be less spectacular but which can be nicely computed in the forward region using the eikonal approximation. In this talk I discuss the distinctive signatures of eikonalized scattering at future accelerators.

  18. Break-up reactions: theoretical aspects

    International Nuclear Information System (INIS)

    Baye, D.

    2007-01-01

    Breakup reactions are one of the main tools for the study of exotic nuclei. In particular, Coulomb breakup is expected to provide information on spectroscopic properties of halo nuclei and on astrophysical S factors for radiative-capture reactions. The simplest studies are based on perturbation theory and especially on its first order. However the validity of the first-order approximation may be limited for extended systems such as halo nuclei and its conditions are not always satisfied in existing experiments. More elaborate reaction models are available: resolution of the semi-classical time-dependent Schroedinger equation, eikonal and dynamical eikonal approximations, method of coupled discretized-continuum channels (CDCC). These methods are reviewed and summarized. Their interest and limitations are discussed. The Be 11 and B 8 breakups are treated as examples of the various approximations. (author)

  19. Diffraction of a Gaussian beam in a three-dimensional smoothly inhomogeneous medium: an eikonal-based complex geometrical-optics approach.

    Science.gov (United States)

    Berczynski, Pawel; Bliokh, Konstantin Yu; Kravtsov, Yuri A; Stateczny, Andrzej

    2006-06-01

    We present an ab initio account of the paraxial complex geometrical optics (CGO) in application to scalar Gaussian beam propagation and diffraction in a 3D smoothly inhomogeneous medium. The paraxial CGO deals with quadratic expansion of the complex eikonal and reduces the wave problem to the solution of ordinary differential equations of the Riccati type. This substantially simplifies the description of Gaussian beam diffraction as compared with full-wave or parabolic (quasi-optics) equations. For a Gaussian beam propagating in a homogeneous medium or along the symmetry axis in a lenslike medium, the CGO equations possess analytical solutions; otherwise, they can be readily solved numerically. As a nontrivial example we consider Gaussian beam propagation and diffraction along a helical ray in an axially symmetric waveguide medium. It is shown that the major axis of the beam's elliptical cross section grows unboundedly; it is oriented predominantly in the azimuthal (binormal) direction and does not obey the parallel-transport law.

  20. Consequences of the factorization hypothesis in nucleon-nucleon, $\\gamma p and \\gamma \\gamma$ scattering

    CERN Document Server

    Block, Martin M

    2002-01-01

    Using an eikonal structure for the scattering amplitude, factorization theorems for nucleon-nucleon, gamma p and gamma gamma scattering at high energies have been derived, using only some very general assumptions. Using a QCD-inspired eikonal analysis of nucleon-nucleon scattering, we present here experimental confirmation for factorization of cross sections, nuclear slope parameters B and rho -values (ratio of real to imaginary portion of forward scattering amplitudes), showing that: 1) the three factorization theorems of Block and Kaidalov [2000] hold, 2) the additive quark model holds to approximately=1%, and 3) vector dominance holds to better than approximately=4%. Predictions for the total cross section, elastic cross section and other forward scattering parameters at the LHC (14 TeV) are given. (12 refs).

  1. Three-dimensional inverse problem of geometrical optics: a mathematical comparison between Fermat's principle and the eikonal equation.

    Science.gov (United States)

    Borghero, Francesco; Demontis, Francesco

    2016-09-01

    In the framework of geometrical optics, we consider the following inverse problem: given a two-parameter family of curves (congruence) (i.e., f(x,y,z)=c1,g(x,y,z)=c2), construct the refractive-index distribution function n=n(x,y,z) of a 3D continuous transparent inhomogeneous isotropic medium, allowing for the creation of the given congruence as a family of monochromatic light rays. We solve this problem by following two different procedures: 1. By applying Fermat's principle, we establish a system of two first-order linear nonhomogeneous PDEs in the unique unknown function n=n(x,y,z) relating the assigned congruence of rays with all possible refractive-index profiles compatible with this family. Moreover, we furnish analytical proof that the family of rays must be a normal congruence. 2. By applying the eikonal equation, we establish a second system of two first-order linear homogeneous PDEs whose solutions give the equation S(x,y,z)=const. of the geometric wavefronts and, consequently, all pertinent refractive-index distribution functions n=n(x,y,z). Finally, we make a comparison between the two procedures described above, discussing appropriate examples having exact solutions.

  2. Theoretical studies in nuclear reaction and nuclear structure. Final report, January 1, 1975--June 30, 1976

    International Nuclear Information System (INIS)

    Banerjee, M.K.; Griffin, J.J.

    1977-07-01

    Progress in theoretical research is reported under the following readings: (1) few nuclear reactions, Eikonal approximations, and optical models; (2) pion reactions; (3) nuclear structure by reaction studies; (4) nuclear dynamics

  3. The proton structure function F sub 2 sup p (x, Q sup 2) at small x in the framework of extended Regge-Eikonal approach

    CERN Document Server

    Petrov, V A

    2001-01-01

    The behaviour of the proton structure function F sub 2 sup p (x, Q sup 2) in the region of small x is described in the framework of the generalized off-shell extention of the Regge-eikonal approach which automatically takes into account off-shell unitarity. A good quality is achieved of description of the experimental data for x < 10 sup - sup 2 and it is argued that the data on F sub 2 sup p (x, Q sup 2) measured at HERA can be fairly well described with classical universal Regge trajectories. No extra, hard trajectories of high intercept are needed for that. The x, Q sup 2 slopes and the effective intercept are discussed as functions of x and Q sup 2

  4. A new traveltime approximation for TI media

    KAUST Repository

    Stovas, Alexey; Alkhalifah, Tariq Ali

    2012-01-01

    In a transversely isotropic (TI) medium, the trade-off between inhomogeneity and anisotropy can dramatically reduce our capability to estimate anisotropy parameters. By expanding the TI eikonal equation in power series in terms of the aneliptic parameter η, we derive an efficient tool to estimate (scan) for η in a generally inhomogeneous, elliptically anisotropic background medium. For a homogeneous-tilted transversely isotropic medium, we obtain an analytic nonhyperbolic moveout equation that is accurate for large offsets. In the common case where we do not have well information and it is necessary to resolve the vertical velocity, the background medium can be assumed isotropic, and the traveltime equations becomes simpler. In all cases, the accuracy of this new TI traveltime equation exceeds previously published formulations and demonstrates how η is better resolved at small offsets when the tilt is large.

  5. A new traveltime approximation for TI media

    KAUST Repository

    Stovas, Alexey

    2012-07-01

    In a transversely isotropic (TI) medium, the trade-off between inhomogeneity and anisotropy can dramatically reduce our capability to estimate anisotropy parameters. By expanding the TI eikonal equation in power series in terms of the aneliptic parameter η, we derive an efficient tool to estimate (scan) for η in a generally inhomogeneous, elliptically anisotropic background medium. For a homogeneous-tilted transversely isotropic medium, we obtain an analytic nonhyperbolic moveout equation that is accurate for large offsets. In the common case where we do not have well information and it is necessary to resolve the vertical velocity, the background medium can be assumed isotropic, and the traveltime equations becomes simpler. In all cases, the accuracy of this new TI traveltime equation exceeds previously published formulations and demonstrates how η is better resolved at small offsets when the tilt is large.

  6. First-arrival traveltime computation for quasi-P waves in 2D transversely isotropic media using Fermat’s principle-based fast marching

    Science.gov (United States)

    Hu, Jiangtao; Cao, Junxing; Wang, Huazhong; Wang, Xingjian; Jiang, Xudong

    2017-12-01

    First-arrival traveltime computation for quasi-P waves in transversely isotropic (TI) media is the key component of tomography and depth migration. It is appealing to use the fast marching method in isotropic media as it efficiently computes traveltime along an expanding wavefront. It uses the finite difference method to solve the eikonal equation. However, applying the fast marching method in anisotropic media faces challenges because the anisotropy introduces additional nonlinearity in the eikonal equation and solving this nonlinear eikonal equation with the finite difference method is challenging. To address this problem, we present a Fermat’s principle-based fast marching method to compute traveltime in two-dimensional TI media. This method is applicable in both vertical and tilted TI (VTI and TTI) media. It computes traveltime along an expanding wavefront using Fermat’s principle instead of the eikonal equation. Thus, it does not suffer from the nonlinearity of the eikonal equation in TI media. To compute traveltime using Fermat’s principle, the explicit expression of group velocity in TI media is required to describe the ray propagation. The moveout approximation is adopted to obtain the explicit expression of group velocity. Numerical examples on both VTI and TTI models show that the traveltime contour obtained by the proposed method matches well with the wavefront from the wave equation. This shows that the proposed method could be used in depth migration and tomography.

  7. Efficient computation of electrograms and ECGs in human whole heart simulations using a reaction-eikonal model.

    Science.gov (United States)

    Neic, Aurel; Campos, Fernando O; Prassl, Anton J; Niederer, Steven A; Bishop, Martin J; Vigmond, Edward J; Plank, Gernot

    2017-10-01

    Anatomically accurate and biophysically detailed bidomain models of the human heart have proven a powerful tool for gaining quantitative insight into the links between electrical sources in the myocardium and the concomitant current flow in the surrounding medium as they represent their relationship mechanistically based on first principles. Such models are increasingly considered as a clinical research tool with the perspective of being used, ultimately, as a complementary diagnostic modality. An important prerequisite in many clinical modeling applications is the ability of models to faithfully replicate potential maps and electrograms recorded from a given patient. However, while the personalization of electrophysiology models based on the gold standard bidomain formulation is in principle feasible, the associated computational expenses are significant, rendering their use incompatible with clinical time frames. In this study we report on the development of a novel computationally efficient reaction-eikonal (R-E) model for modeling extracellular potential maps and electrograms. Using a biventricular human electrophysiology model, which incorporates a topologically realistic His-Purkinje system (HPS), we demonstrate by comparing against a high-resolution reaction-diffusion (R-D) bidomain model that the R-E model predicts extracellular potential fields, electrograms as well as ECGs at the body surface with high fidelity and offers vast computational savings greater than three orders of magnitude. Due to their efficiency R-E models are ideally suitable for forward simulations in clinical modeling studies which attempt to personalize electrophysiological model features.

  8. QED radiative corrections to impact factors

    International Nuclear Information System (INIS)

    Kuraev, E.A.; Lipatov, L.N.; Shishkina, T.V.

    2001-01-01

    We consider radiative corrections to the electron and photon impact factors. The generalized eikonal representation for the e + e - scattering amplitude at high energies and fixed momentum transfers is violated by nonplanar diagrams. An additional contribution to the two-loop approximation appears from the Bethe-Heitler mechanism of fermion pair production with the identity of the fermions in the final state taken into account. The violation of the generalized eikonal representation is also related to the charge parity conservation in QED. A one-loop correction to the photon impact factor for small virtualities of the exchanged photon is obtained using the known results for the cross section of the e + e - production during photon-nuclei interactions

  9. Pramana – Journal of Physics | Indian Academy of Sciences

    Indian Academy of Sciences (India)

    Progress in all-order breakup reaction theories. R Chatterjee. Low and Medium Energy Nuclear Reactions Volume 75 Issue 1 July 2010 pp 127-136 ... Abstract. Progress in breakup reaction theories, like the distorted wave Born approximation, the continuum discretized coupled channels method and the dynamical eikonal ...

  10. Effects of external field on elastic electron-ion collision in a plasma

    International Nuclear Information System (INIS)

    Na, Sang-Chul; Jung, Young-Dae

    2008-01-01

    The field effects on elastic electron-ion collision are investigated in a plasma with the presence of the external field. The eikonal method and effective interaction potential including the far-field term caused by the external field is employed to obtain the eikonal phase shift and eikonal cross section as functions of the field strength, external frequency, impact parameter, collision energy, thermal energy and Debye length. The result shows that the effect of the external field on the eikonal cross section is given by the second-order eikonal phase. In addition, the external field effects suppress the eikonal cross section as well as eikonal phase for the elastic electron-ion collision. The eikonal phase and cross section are found to be increased with an increase of the frequency of the external field. It is also shown that the eikonal cross section increases with an increase of the thermal energy and Debye length.

  11. Diophantine approximation and badly approximable sets

    DEFF Research Database (Denmark)

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

    2006-01-01

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

  12. High Frequency Asymptotic Methods for Traveltimes and Anisotropy Parameter Estimation in Azimuthally Varying Media

    KAUST Repository

    Masmoudi, Nabil

    2014-05-01

    Traveltimes are conventionally evaluated by solving the zero-order approximation of the Wentzel, Kramers and Brillouin (WKB) expansion of the wave equation. This high frequency approximation is good enough for most imaging applications and provides us with a traveltime equation called the eikonal equation. The eikonal equation is a non-linear partial differential equation which can be solved by any of the familiar numerical methods. Among the most popular of these methods is the method of characteristics which yields the ray tracing equations and the finite difference approaches. In the first part of the Master Thesis, we use the ray tracing method to solve the eikonal equation to get P-waves traveltimes for orthorhombic models with arbitrary orientation of symmetry planes. We start with a ray tracing procedure specified in curvilinear coordinate system valid for anisotropy of arbitrary symmetry. The coordinate system is constructed so that the coordinate lines are perpendicular to the symmetry planes of an orthorohombic medium. Advantages of this approach are the conservation of orthorhombic symmetry throughout the model and reduction of the number of parameters specifying the model. We combine this procedure with first-order ray tracing and dynamic ray tracing equations for P waves propagating in smooth, inhomogeneous, weakly anisotropic media. The first-order ray tracing and dynamic ray tracing equations are derived from the exact ones by replacing the exact P-wave eigenvalue of the Christoffel matrix by its first-order approximation. In the second part of the Master Thesis, we compute traveltimes using the fast marching method and we develop an approach to estimate the anisotropy parameters. The idea is to relate them analytically to traveltimes which is challenging in inhomogeneous media. Using perturbation theory, we develop traveltime approximations for transversely isotropic media with horizontal symmetry axis (HTI) as explicit functions of the

  13. The method of regions and next-to-soft corrections in Drell-Yan production

    NARCIS (Netherlands)

    Bonocore, D.; Laenen, E.; Magnea, L.; Vernazza, L.; White, C. D.

    2015-01-01

    We perform a case study of the behaviour of gluon radiation beyond the soft approximation, using as an example the Drell-Yan production cross section at NNLO. We draw a careful distinction between the eikonal expansion, which is in powers of the soft gluon energies, and the expansion in powers of

  14. Diffraction Traveltime Approximation to Estimate Anisotropy Parameters in Complex TI Media

    KAUST Repository

    Waheed, Umair bin

    2013-05-01

    Diffracted waves carry valuable information that can help improve our velocity modeling capability for better imaging of the subsurface. They are especially useful for anisotropic media as they inherently possess a wide range of dips necessary to resolve the angular dependence of velocity. We develop a scheme for diffraction traveltime computations based on perturbation theory for transverse isotropic media with tilted axis of symmetry (TTI). The formulation has advantages on two fronts: firstly it alleviates the computational complexity associated with solving the TTI eikonal equation and secondly it provides a mechanism to scan for the best fit anellipticity parameter without the need for repetitive modeling of traveltimes. The accuracy of such an expansion is further enhanced by the use of Shanks transform. We establish the effectiveness of the proposed formulation with tests on a homogeneous TTI model and the BP TTI model.

  15. Effective anisotropy through traveltime and amplitude matching

    KAUST Repository

    Wang, Hui

    2014-08-05

    Introducing anisotropy to seismic wave propagation reveals more realistic physics of our Earth\\'s subsurface as compared to the isotropic assumption. However wavefield modeling, the engine of seismic inverse problems, in anisotropic media still suffers from computational burdens, in particular with complex anisotropy such as transversely isotropic (TI) and Orthorhombic anisotropy. We develop effective isotropic velocity and density models to package the effects of anisotropy such that the wave propagation behavior using these effective models approximate those of the original anisotropic model. We build these effective models through the high frequency asymptotic approximation based on the eikonal and transport equations. We match the geometrical behavior of the wave-fields, given by traveltimes, from the anisotropic and isotropic eikonal equations. This matching yields the effective isotropic velocity that approximates the kinematics of the anisotropic wavefield. Equivalently, we calculate the effective densities by equating the anisotropic and isotropic transport equations. The effective velocities and densities are then fed into the isotropic acoustic variable density wave equation to obtain cheaper anisotropic wavefields. We justify our approach by testing it on an elliptical anisotropic model. The numerical results demonstrate a good matching of both traveltime and amplitude between anisotropic and effective isotropic wavefields.

  16. LPM-Effect in Monte Carlo Models of Radiative Energy Loss

    CERN Document Server

    Zapp, Korinna C; Wiedemann, Urs Achim

    2009-01-01

    Extending the use of Monte Carlo (MC) event generators to jets in nuclear collisions requires a probabilistic implementation of the non-abelian LPM effect. We demonstrate that a local, probabilistic MC implementation based on the concept of formation times can account fully for the LPM-effect. The main features of the analytically known eikonal and collinear approximation can be reproduced, but we show how going beyond this approximation can lead to qualitatively different results.

  17. Influence of initial state distortion in ion-atom collisions

    Energy Technology Data Exchange (ETDEWEB)

    Ciappina, M F [CONICET and Departamento de FIsica, Universidad Nacional del Sur, 8000 BahIa Blanca (Argentina); Cravero, W R [CONICET and Departamento de FIsica, Universidad Nacional del Sur, 8000 BahIa Blanca (Argentina); Garibotti, C R [CONICET and Division Colisiones Atomicas, Centro Atomico Bariloche, 8400 Bariloche (Argentina)

    2004-05-28

    We have studied the influence of initial state distortion in a single ionization by ion impact. We have taken a continuum distorted wave type distortion and by taking up to the first order in its asymptotic series expansion we build an eikonal-spherical distortion. In this way the influence of each term in the transition amplitude can be stated. This approximation can be considered an intermediate one between the eikonal initial state and the continuum distorted wave approaches for initial state distortion. We have computed doubly differential cross sections for helium ionization by protons and highly charged ions at high and intermediate impact energy. We have also discussed the contribution of the different terms in electron energy spectra, specially in the vicinity of ECC peak. Very good agreement is found with the available experimental data.

  18. Influence of initial state distortion in ion-atom collisions

    International Nuclear Information System (INIS)

    Ciappina, M F; Cravero, W R; Garibotti, C R

    2004-01-01

    We have studied the influence of initial state distortion in a single ionization by ion impact. We have taken a continuum distorted wave type distortion and by taking up to the first order in its asymptotic series expansion we build an eikonal-spherical distortion. In this way the influence of each term in the transition amplitude can be stated. This approximation can be considered an intermediate one between the eikonal initial state and the continuum distorted wave approaches for initial state distortion. We have computed doubly differential cross sections for helium ionization by protons and highly charged ions at high and intermediate impact energy. We have also discussed the contribution of the different terms in electron energy spectra, specially in the vicinity of ECC peak. Very good agreement is found with the available experimental data

  19. Dynamics and Stability of Acoustic Wavefronts in the Ocean

    Science.gov (United States)

    2014-09-30

    method employed in (Godin, 2003, 2007, 2009), where a novel perturbation technique has been developed to solve the eikonal equation and calculate...numerical solution of the eikonal equation lies in the eikonal (and acoustic travel time) being a multi-valued function of position. A number of...computational approaches to solve the eikonal equation without ray tracing had been developed in mathematical and seismological communities (Vidale, 1990

  20. Medium-induced gluon radiation and colour decoherence beyond the soft approximation

    CERN Document Server

    Apolinário, Liliana; Milhano, José Guilherme; Salgado, Carlos A

    2015-01-01

    We derive the in-medium gluon radiation spectrum off a quark within the path integral formalism at finite energies, including all next-to-eikonal corrections in the propagators of quarks and gluons. Results are computed for finite formation times, including interference with vacuum amplitudes. Rewriting the medium averages in a convenient manner we present the spectrum in terms of dipole cross sections and a colour decoherence parameter with the same physical origin as that found in previous studies of the antenna radiation. This factorisation allows us to present a simple physical picture of the medium-induced radiation for any value of the formation time, of interest for a probabilistic implementation of the modified parton shower. Interestingly -- and unexpectedly -- we also find a modification of the contribution from the hard vertex which cannot be factorized, at finite formation time, as the vacuum Altarelli-Parisi splitting function. Known results are recovered for the particular cases of soft radiatio...

  1. Field theoretical approach to proton-nucleus reactions. I - One step inelastic scattering

    International Nuclear Information System (INIS)

    Eiras, A.; Kodama, T.; Nemes, M.C.

    1988-01-01

    In this work we obtain a closed form expression to the double differential cross section for one step proton-nucleus reaction within a field theoretical framework. Energy and momentum conservation as well as nuclear structure effects are consistently taken into account within the field theoretical eikonal approximation. In our formulation the kinematics of such reaction is not dominated by the free nucleon-nucleon cross section but a new factor which we call relativistic differential cross section in a Born Approximation. (author) [pt

  2. Hierarchical low-rank approximation for high dimensional approximation

    KAUST Repository

    Nouy, Anthony

    2016-01-07

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

  3. Hierarchical low-rank approximation for high dimensional approximation

    KAUST Repository

    Nouy, Anthony

    2016-01-01

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

  4. Software for simulation of a computed tomography imaging spectrometer using optical design software

    Science.gov (United States)

    Spuhler, Peter T.; Willer, Mark R.; Volin, Curtis E.; Descour, Michael R.; Dereniak, Eustace L.

    2000-11-01

    Our Imaging Spectrometer Simulation Software known under the name Eikon should improve and speed up the design of a Computed Tomography Imaging Spectrometer (CTIS). Eikon uses existing raytracing software to simulate a virtual instrument. Eikon enables designers to virtually run through the design, calibration and data acquisition, saving significant cost and time when designing an instrument. We anticipate that Eikon simulations will improve future designs of CTIS by allowing engineers to explore more instrument options.

  5. Diffraction traveltime approximation for TI media with an inhomogeneous background

    KAUST Repository

    Waheed, Umair bin; Alkhalifah, Tariq Ali; Stovas, A.

    2013-01-01

    Diffractions in seismic data contain valuable information that can help improve our modeling capability for better imaging of the subsurface. They are especially useful for anisotropic media because they inherently possess a wide range of dips necessary to resolve the angular dependence of velocity. We develop a scheme for diffraction traveltime computations based on perturbation of the anellipticity anisotropy parameter for transversely isotropic media with tilted axis of symmetry (TTI). The expansion, therefore, uses an elliptically anisotropic medium with tilt as the background model. This formulation has advantages on two fronts: first, it alleviates the computational complexity associated with solving the TTI eikonal equation, and second, it provides a mechanism to scan for the best-fitting anellipticity parameter η without the need for repetitive modeling of traveltimes, because the traveltime coefficients of the expansion are independent of the perturbed parameter η. The accuracy of such an expansion is further enhanced by the use of Shanks transform. We established the effectiveness of the proposed formulation with tests on a homogeneous TTI model and complex media such as the Marmousi and BP models.

  6. Diffraction traveltime approximation for TI media with an inhomogeneous background

    KAUST Repository

    Waheed, Umair bin

    2013-09-01

    Diffractions in seismic data contain valuable information that can help improve our modeling capability for better imaging of the subsurface. They are especially useful for anisotropic media because they inherently possess a wide range of dips necessary to resolve the angular dependence of velocity. We develop a scheme for diffraction traveltime computations based on perturbation of the anellipticity anisotropy parameter for transversely isotropic media with tilted axis of symmetry (TTI). The expansion, therefore, uses an elliptically anisotropic medium with tilt as the background model. This formulation has advantages on two fronts: first, it alleviates the computational complexity associated with solving the TTI eikonal equation, and second, it provides a mechanism to scan for the best-fitting anellipticity parameter η without the need for repetitive modeling of traveltimes, because the traveltime coefficients of the expansion are independent of the perturbed parameter η. The accuracy of such an expansion is further enhanced by the use of Shanks transform. We established the effectiveness of the proposed formulation with tests on a homogeneous TTI model and complex media such as the Marmousi and BP models.

  7. Nonlinear Localized Dissipative Structures for Long-Time Solution of Wave Equation

    Science.gov (United States)

    2009-07-01

    are described in this chapter. These details are required to compute interference. WC can be used to generate constant arrival time ( Eikonal phase...complicated using Eikonal schemes. Some recent developments in Eikonal methods [2] can treat multiple arrival times but, these methods require extra

  8. Statistical Field Estimation and Scale Estimation for Complex Coastal Regions and Archipelagos

    Science.gov (United States)

    2009-05-01

    state boundary value problem, known as the Eikonal equation, can be formulated to evalu- ate the arrival time function T(x). The Eikonal equation...representing the time T(x) 34 for the “frontal interface” to reach the position x from its initial position is given by: F |∇T | = 1 (3.7) The Eikonal ...equation simply states that the gradient of the arrival time function is inversely proportional to the speed of the front. To solve the Eikonal equation

  9. High-energy expansion for nuclear multiple scattering

    International Nuclear Information System (INIS)

    Wallace, S.J.

    1975-01-01

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

  10. Optical theorem, depolarization and vector tomography

    International Nuclear Information System (INIS)

    Toperverg, B.P.

    2003-01-01

    A law of the total flux conservation is formulated in the form of the optical theorem. It is employed to explicitly derive equations for the description of the neutron polarization within the range of the direct beam defined by its angular divergence. General considerations are illustrated by calculations using the Born and Eikonal approximations. Results are briefly discussed as applied to Larmor-Fourier tomography

  11. K-Vacancy Production in the Collision of Highly Charged Relativistic Ions With Heavy Atoms

    OpenAIRE

    KHABIBULLAEV, P. K.

    2014-01-01

    A general expression for the cross section of the inelastic collision of relativistic highly charged ion with heavy (relativistic) atoms is obtained using the generalized eikonal approximation. In the ultrarelativistic limit, the obtained formula coincides with a known exact one. As an application of the obtained result, probability and cross section of the K-vacany production in the U92+ - U91+ collision are calculated.

  12. Scaling relations in elastic scattering cross sections between multiply charged ions and hydrogen

    International Nuclear Information System (INIS)

    Rodriguez, V.D.

    1991-01-01

    Differential elastic scattering cross sections of bare ions from hydrogen are calculated using the eikonal approximation. The results satisfy a scaling relation involving the scattering angle, the ion charge and a factor related to the ion mass. A semiclassical explanation in terms of a distant collision hypothesis for small scattering angle is proposed. A unified picture of related scaling rules found in direct processes is discussed. (author)

  13. CDW-EIS model for single-electron capture in ion-atom collisions involving multielectronic targets

    International Nuclear Information System (INIS)

    Abufager, P N; MartInez, A E; Rivarola, R D; Fainstein, P D

    2004-01-01

    A generalization of the continuum distorted wave eikonal initial state (CDW-EIS) approximation, for the description of single-electron capture in ion-atom collisions involving multielectronic targets is presented. This approximation is developed within the framework of the independent electron model taking particular care of the representation of the bound and continuum target states. Total cross sections for single-electron capture from the K-shell of He, Ne and Ar noble gases by impact of bare ions are calculated. Present results are compared to previous CDW-EIS ones and to experimental data

  14. Modeling of High-Frequency Acoustic Propagation in Shallow Water

    Science.gov (United States)

    2007-06-01

    is a product of a phase function, called the eikonal equation, and an amplitude function, called the transport equation. To solve the eikonal ... eikonal equation in the ray coordinate system. Expanding Equation (2.6), 2 1 c =∇⋅∇ ττ , (2.14) so that substituting the value of τ∇ from

  15. Field theoretical approach to proton-nucleus reactions: II-Multiple-step excitation process

    International Nuclear Information System (INIS)

    Eiras, A.; Kodama, T.; Nemes, M.

    1989-01-01

    A field theoretical formulation to multiple step excitation process in proton-nucleus collision within the context of a relativistic eikonal approach is presented. A closed form expression for the double differential cross section can be obtained whose structure is very simple and makes the physics transparent. Glauber's formulation of the same process is obtained as a limit of ours and the necessary approximations are studied and discussed. (author) [pt

  16. Relativistic time delays in the Dirac approach to nucleon-nucleus scattering

    International Nuclear Information System (INIS)

    Suzuki, T.

    1993-01-01

    In connection with a characteristic feature of the effective optical potential in the Dirac approach two types of time delays are considered in the relativistic eikonal approximation. One is obtained from the scattering amplitude and the other given by the wave packet motion in the interaction region. These time delays turn out to differ in sign at intermediate energies, in contrast to the agreement between corresponding nonrelativistic time delays. (orig.)

  17. Turbulent effective absorptivity and refractivity

    International Nuclear Information System (INIS)

    Rax, J.M.

    1984-09-01

    The problem of wave propagation in a turbulent magnetized plasma is investigated. Considering small scale, low frequency density fluctuations we solve the Maxwell equations and show that the eikonal approximation remains valid with an effective refractivity and an effective absorptivity taking into account the energy diffusion due to the turbulent motion. Then the result is applied to the problem of lower hybrid waves scattering by drift waves density fluctuations in tokamaks

  18. Interaction of the precessional wave with free-boundary Alfven surface waves in tandem mirrors

    International Nuclear Information System (INIS)

    Berk, H.L.; Kaiser, T.B.

    1984-04-01

    We consider a symmetric tandem mirror plugging a long central cell, with plugs stabilized by a hot component plasma. The system is taken to have a flat pressure profile with a steep edge gradient. We then consider the interaction of the precessional mode with Alfven waves generated in the central cell. This analysis is non-eikonal and is valid when mΔ/r < 1 (m is the azimuthal mode number. r the plasma radius and Δ the radial gradient scale length) for long-wavelength radial modes. We find that without FLR effects the precessional mode is always destabilized by the excitation of the Alfven waves for m greater than or equal to 2. For m=1, it is possible to achieve stabilization with conducting walls. A discussion is given of how FLR affects stabilization of the m greater than or equal to 2 long-wavelength modes and of finite-Larmor-radius stabilization of modes described in the eikonal approximation

  19. Dynamic effects in fragmentation reactions

    International Nuclear Information System (INIS)

    Bertsch, G. F.; Esbensen, H.

    2002-01-01

    Fragmentation reactions offer a useful tool to study the spectroscopy of halo nuclei, but the large extent of the halo wave function makes the reaction theory more difficult. The simple reaction models based on the eikonal approximation for the nuclear interaction or first-order perturbation theory for the Coulomb interaction have systematic errors that they investigate here, comparing to the predictions of complete dynamical calculations. They find that stripping probabilities are underpredicted by the eikonal model, leading to extracted spectroscopy strengths that are two large. In contrast, the Coulomb excitation is overpredicted by the simple theory. They attribute this to a screening effect, as is well known in the Barkas effect on stopping powers. The errors decrease with beam energy as E(sub beam)(sup -1), and are not significant at beam energies above 50 MeV/u. At lower beam energies, the effects should be taken into account when extracting quantitative spectroscopic strengths

  20. Self-similar factor approximants

    International Nuclear Information System (INIS)

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

    2003-01-01

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

  1. Modeling the Effects of Transbasin Nonlinear Internal Waves Through the South China Sea Basin

    Science.gov (United States)

    2013-06-01

    reference sound speed, f is the acoustic frequency, and is the eikonal when multiplied by k0 gives the phase component of the solution. Equation 2.2...is substituted into Equation 2.1 to yield the eikonal and transport equations in Equation 2.3. The eikonal yields the ray equations and the ray...2π f c0 W r ( ) c0 c r ( ) ⎛ ⎝⎜ ⎞ ⎠⎟ 6 Eikonal Equation: ∇W r( ) 2 = n2 r( ) Transport Equation: 2∇A r( ) ⋅∇W r( ) + A r( )∇2W r

  2. Modulated Pade approximant

    International Nuclear Information System (INIS)

    Ginsburg, C.A.

    1980-01-01

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

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

    Science.gov (United States)

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

    2018-06-01

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

  4. Globally Optimal Path Planning with Anisotropic Running Costs

    Science.gov (United States)

    2013-03-01

    Eikonal equation and has numerous applications, for exam- ple, in path planning, computational geometry, computer vision, and image enhancement...Sethian 1999b]. Numerical methods for solving the Eikonal equation include Tsitsiklis’ control-theoretic algorithm [Tsitsiklis 1995], Fast Marching Methods...methods for Eikonal equations on triangular meshes, SIAM J. Numer. Anal. 45(1), 83—107. Rowe, M. P., Sidhu, H. S. & Mercer, G. N. (2009) Military

  5. 2-Dimensional B-Spline Algorithms with Applications to Ray Tracing in Media of Spatially-Varying Refractive Index

    Science.gov (United States)

    2007-08-01

    In the approach, photon trajectories are computed using a solution of the Eikonal equation (ray-tracing methods) rather than linear trajectories. The...coupling the radiative transport solution into heat transfer and damage models. 15. SUBJECT TERMS: B-Splines, Ray-Tracing, Eikonal Equation...multi-layer biological tissue model. In the approach, photon trajectories are computed using a solution of the Eikonal equation (ray-tracing methods

  6. Two-body tensor interactions in the nuclear matter response function

    International Nuclear Information System (INIS)

    Besprosvany, J.

    1997-01-01

    The inclusive scattering response of nuclear matter is studied in the regime of large momentum transfer q, and around the quasielastic peak. We review interaction corrections to free propagation as embodied in the impulse approximation. Calculations of the two-body and many-body corrections within an eikonal approach are presented. These use an approximated two-body density matrix which takes account of spin and isospin degrees of freedom. Both calculations give similar and sizable corrections at q = 550 MeV and reproduce data extrapolated from finite nuclei; this indicates the relevance of two-body tensor contributions in this regime. (Author)

  7. Real Time Location of Targets in Cluttered Environments

    Science.gov (United States)

    2014-03-13

    be removed in future versions with perturbation terms. This new method is termed the “Generalized Eikonal Method” (GEM). The solution at any...refractions in realistic media, the wave paths, or Eikonal phase will be multi-valued in some regions of space, which represent multiple passes of the...In general, because of the reflections and refractions in realistic media, the wave paths, or Eikonal phase will be multi-valued in some regions of

  8. Implementation of a Pseudo-Bending Seismic Travel-Time Calculator in a Distributed Parallel Computing Environment

    Science.gov (United States)

    2008-09-01

    algorithms that have been proposed to accomplish it fall into three broad categories. Eikonal solvers (e.g., Vidale, 1988, 1990; Podvin and Lecomte, 1991...difference eikonal solvers, the FMM algorithm works by following a wavefront as it moves across a volume of grid points, updating the travel times in...the grid according to the eikonal differential equation, using a second-order finite-difference scheme. We chose to use FMM for our comparison because

  9. Approximate symmetries of Hamiltonians

    Science.gov (United States)

    Chubb, Christopher T.; Flammia, Steven T.

    2017-08-01

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

  10. Development of Vector Parabolic Equation Technique for Propagation in Urban and Tunnel Environments

    Science.gov (United States)

    2010-09-01

    that of the former is geared towards determining the transport amplitude, having found the eikonal by some other means. Among the principal...FOR MODELING RADIO TRANSMISSION LOSS 1761 We can then use the following asymptotic ansatz (10) where (11) and is the tunnel width [26]. The eikonal is a...equation and equating terms of the same order of , we can define the eikonal and find the vector PE [4] for the straight waveguide (12) where is the

  11. Distorted wave calculations for double electron transfer

    International Nuclear Information System (INIS)

    Martinez, A.E.; Rivarola, R.D.; Gayet, R.; Hanssen, J.

    1992-01-01

    The resonant double electron capture by alpha particles in helium targets is studied, at intermediate and high collision energies, using the Continuum Distorted Wave - Eikonal Initial State (CDW-EIS) model. Differential and total cross sections for capture into the He (1 s 2 ) final state are calculated in the framework of an Independent Electron Approximation (IEA). Theoretical results are compared with the experimental data available at present for capture into any final state of helium. (author)

  12. Relativistic scattering theory of two charged spinless particles

    International Nuclear Information System (INIS)

    Alt, E.O.; Hannemann

    1985-01-01

    In the framework of a relativistic quantum mechanics, the authors calculate for two spinless particles with Coulomb interaction exactly the partial-wave S-matrix and the full scattering amplitude. From the former they can extract the exact binding energies which, when expanded in powers of α, reproduce in the hydrogenic case the fourth-order result of a previous study. In the weak field limit, the latter coincides with the amplitude derived by another study from QED in eikonal approximation

  13. On Soft Limits of Large-Scale Structure Correlation Functions

    OpenAIRE

    Ben-Dayan, Ido; Konstandin, Thomas; Porto, Rafael A.; Sagunski, Laura

    2014-01-01

    We study soft limits of correlation functions for the density and velocity fields in the theory of structure formation. First, we re-derive the (resummed) consistency conditions at unequal times using the eikonal approximation. These are solely based on symmetry arguments and are therefore universal. Then, we explore the existence of equal-time relations in the soft limit which, on the other hand, depend on the interplay between soft and hard modes. We scrutinize two approaches in the literat...

  14. Geometric approximation algorithms

    CERN Document Server

    Har-Peled, Sariel

    2011-01-01

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

  15. Sparse approximation with bases

    CERN Document Server

    2015-01-01

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

  16. Neutron-optical effects at very cold neutrons scattering on the spherical particles of different sizes

    International Nuclear Information System (INIS)

    Grinev, V.G.; Kudinova, O.I.; Novokshonova, L.A.; Kuznetsov, S.P.; Udovenko, A.I.; Shelagin, A.V.

    2006-01-01

    Very cold neutrons (VCN) with the wavelength λ > 4.0 ran are convenient tool for investigating the super molecular structures of different nature. Using a Born approximation (BA) to the analysis of dependencies on the wavelength of the VCN scattering cross sections, it is possible to obtain information about average sizes (R) and concentrations of the scattering particles with R∼ λ. However, with an increasing the sizes of scatterers the conditions for BA applicability can be disrupted. In this work we investigated the possibilities of BA, eikonal and geometric-optical approximations for the analysis of VCN scattering on the spherical particles with R ≥ λ

  17. Inversion of the total cross sections for electron-molecule and electron-atom scattering

    International Nuclear Information System (INIS)

    Lun, D.R.; Amos, K.; Allen, L.J.

    1994-01-01

    Inverse scattering theory has been applied to construct the interaction potentials from total cross sections as a function of energy for electrons scattered off of atoms and molecules. The underlying potentials are assumed to be real and energy independent and are evaluated using the Eikonal approximation and with real phase shifts determined from the total cross sections. The inversion potentials have been determined using either a high energy limit approximation or by using a fixed energy inversion method at select energies. These procedures have been used to analyse e - - CH 4 , e - - SiH 4 , e - -Kr and e - -Xe scattering data in particular. 14 refs., 1 tabs., 3 figs

  18. Dynamic Programming Algorithms for Planning and Robotics in Continuous Domains and the Hamilton-Jacobi Equation

    Science.gov (United States)

    2008-09-22

    function essentially binary • Value function measures cost to go – Solution of Eikonal equation – Gradient determines optimal control typical laser...of nodes – Dijkstra’s algorithm is essentially unchanged • Continuous space – Static HJ PDE no longer reduces to the Eikonal equation – Gradient of ϑ...bounded: ||·||1 • If action is bounded in ||·||p, then value function is solution of “ Eikonal ” equation ||ϑ(x)||p* = c(x) in the dual norm p* – p = 1

  19. Approximating distributions from moments

    Science.gov (United States)

    Pawula, R. F.

    1987-11-01

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

  20. Semiclassical treatment of inelastic collisions between electrons and highly ionized atoms

    International Nuclear Information System (INIS)

    Frasier, S.M.

    1984-01-01

    The thesis is concerned with the calculation of excitation cross sections of ions by electron impact at intermediate energies in the limit of Z >> N/sub b/, where Z is the atomic number and N/sub b/ is the number of bound electrons. A semiclassical procedure is developed for calculating total cross sections using analytic bound states and averaged free electron wave functions derived in the second eikonal approximation. The analytic bound states are derived assuming a screened Coulomb potential and using orbital energies obtained from Hartree-Fock calculations. The functional form of the bound states reduces naturally to the hydrogen atom functions in the limit Z → infinity. The free electron functions used are semiclassical solutions to the free electron Schroedinger equation with a screened Coulomb potential. An exact solution is obtained in the second eikonal approximation, including all classical path contributions. This solution is averaged to extract the focusing and acceleration effects resulting from the long range Coulomb potential of the ion. The results are presented in the form of Born-like cross section formulae and demonstrate the appropriate correction of the Born cross section which arises from the acceleration and focusing of the free electrons by the long range Coulomb potential. Comparison is made with the Coulomb-Born results; the results agree to within 10% in most cases

  1. General Rytov approximation.

    Science.gov (United States)

    Potvin, Guy

    2015-10-01

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

  2. Self-consistent coupling of atomic orbitals to a moving charge

    International Nuclear Information System (INIS)

    Da Costa, H.F.M.; Micha, D.A.

    1994-01-01

    The authors describe the time evolution of hydrogenic orbitals perturbed by a moving charge. Starting with the equation for an atom interacting with a charge, the authors use an eikonal representation of the total wave-function, followed by an eikonal approximation, to derive coupled differential equations for the temporal change of the orbitals and the charge's trajectory. The orbitals are represented by functions with complex exponents changing with time, describing electronic density and flux changes. For each orbital, they solve a set of six coupled differential equations; two of them are derived with a time-dependent variational procedure for the real and imaginary parts of the exponents, and the other four are the Hamilton equations of the positions and momenta of the moving charge. The molecular potentials are derived from the exact expressions for the electronic energies. Results of calculations for 1s and 2s orbitals show large variation of the real exponent parts over time, with respect to asymptotic values, and that imaginary parts remain small

  3. Single electron capture in ion-atom collisions involving multielectronic targets

    International Nuclear Information System (INIS)

    Abufager, P.N.; Martinez, A.E.; Rivarola, R.D.; Fainstein, P.D.

    2005-01-01

    The generalized continuum distorted wave-eikonal initial state (GCDW-EIS) approximation is employed to study single electron capture by impact of protons on Ne and Ar targets. We analyze the contributions to the total cross sections coming from the different target shells. Present results are compared with theoretical calculations obtained using the previous CDW-EIS formulation and to experimental data in order to show the importance of the description of the bound and continuum target states in the entry and exit channels, respectively

  4. Effectiveness of projectile screening in single and multiple ionization of Ne by B{sup 2+}

    Energy Technology Data Exchange (ETDEWEB)

    Wolff, W.; Luna, H.; Santos, A. C. F.; Montenegro, E. C. [Instituto de Fisica, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, 21945-970 RJ (Brazil); DuBois, R. D. [Department of Physics, Missouri University of Science and Technology, Rolla, Missouri 65409 (United States); Montanari, C. C.; Miraglia, J. E. [Instituto de Astronomia y Fisica del Espacio, Casilla de Correo 67, Sucursal 28, C1428EGA, Buenos Aires (Argentina)

    2011-10-15

    Pure multiple ionization cross sections of Ne by B{sup 2+} projectiles have been measured in the energy range of 0.75 to 4.0 MeV and calculated using the continuum distorted wave-eikonal initial state approximation. The experiment and calculations show that the ionization cross sections by B{sup 2+}, principally for the production of highly charged recoils, is strongly enhanced when compared to the bare projectile with the same charge state, He{sup 2+}, at the same velocities.

  5. Approximation techniques for engineers

    CERN Document Server

    Komzsik, Louis

    2006-01-01

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

  6. International Conference Approximation Theory XV

    CERN Document Server

    Schumaker, Larry

    2017-01-01

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

  7. Statistical Field Estimation for Complex Coastal Regions and Archipelagos (PREPRINT)

    Science.gov (United States)

    2011-04-09

    φi−1,j ∆x ; D+xφi,j = φi+1,j − φi,j ∆x (10) The above numerical technique of the Level Set Method can be used to solve the Eikonal Equation as...described next. If the scalar speed function of the front F is non-negative, then the steady state boundary value problem, known as the Eikonal equation, can...be formulated to evaluate the arrival time function T(x). The Eikonal equation representing the time T(x) for the “frontal interface” to reach the

  8. On the geometric nature of high energy nucleus-nucleus reaction cross sections

    International Nuclear Information System (INIS)

    Townsend, L.W.; Wilson, J.W.; Bidasaria, H.B.

    1982-01-01

    Within the context of a high energy double-folding optical potential approximation to the exact nucleus-nucleus multiple-scattering series, eikonal scattering theory is used to investigate the validity of geometric reaction cross sections in relativistic heavy ion collisions. The potential used includes a finite range interaction and nuclear single-particle densities extracted from nuclear charge distributions by unfolding the proton charge distribution. Pauli correlation effects are also included in an approximate way. The sensitivity of the predictions to be assumed interaction, Pauli correlation approximation, and nuclear density distributions is investigated. These results are in agreement with early predictions concerning the geometric nature of relativistic heavy ion collisions and in disagreement with a recent analysis, utilizing the zero range approximation, which suggested otherwise. Reasons for the lack of agreement between the analyses are also presented. Finally, approximate applicability for geometric reaction cross sections are determined

  9. Angular distribution in proton-hydrogen charge-transfer collisions

    International Nuclear Information System (INIS)

    Glembocki, O.; Halpern, A.M.

    1977-01-01

    Theoretical angular distributions for p-H charge transfer to the 1s state for energies of 1 keV and above have been examined and compared for three approximation schemes: the plane-wave Born approximation of Jackson and Schiff (JS), the Coulomb projected Born approximation of Geltman (G), and the distorted-wave eikonal approximation of one of the authors (D). The sharp dip in the forward distribution characteristic of JS is found to exist in G and D as well. As expected, G and D give identical results for all but the lowest energies. In the cases of G and D the dip, which is located close to that of JS, disappears and then reappears as the energy rises. Analytic high-energy limits for the angular dependence in both the JS and G cases have been found and are discussed

  10. Path integral approach to eikonal and next-to-eikonal exponentiation

    NARCIS (Netherlands)

    Laenen, E.; Stavenga, G.; White, C.D.

    2009-01-01

    We approach the issue of exponentiation of soft gauge boson corrections to scattering amplitudes from a path integral point of view. We show that if one represents the amplitude as a first quantized path integral in a mixed coordinate-momentum space representation, a charged particle interacting

  11. Ordered cones and approximation

    CERN Document Server

    Keimel, Klaus

    1992-01-01

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

  12. Single electron capture differential cross section in H+ + He collisions at intermediate and high collision energies

    International Nuclear Information System (INIS)

    Abufager, P N; Fainstein, P D; MartInez, A E; Rivarola, R D

    2005-01-01

    The generalized continuum distorted wave-eikonal initial state (CDW-EIS II) approximation is employed to study differential cross sections (DCS) for single electron capture in H + + He collisions at intermediate and high energies. Present results are compared with theoretical calculations obtained using the previous CDW-EIS formulation in order to show the importance of the description of the bound and continuum target states in the entrance and exit channels, respectively. Both DCS are also shown together with other theoretical results and with experimental data

  13. Fast atom diffraction for grazing scattering of Ne atoms from a LiF(0 0 1) surface

    International Nuclear Information System (INIS)

    Gravielle, M.S.; Schueller, A.; Winter, H.; Miraglia, J.E.

    2011-01-01

    Angular distributions of fast Ne atoms after grazing collisions with a LiF(0 0 1) surface under axial surface channeling conditions are experimentally and theoretically studied. We use the surface eikonal approximation to describe the quantum interference of scattered projectiles, while the atom-surface interaction is represented by means of a pairwise additive potential, including the polarization of the projectile atom. Experimental data serve as a benchmark to investigate the performance of the proposed potential model, analyzing the role played by the projectile polarization.

  14. Fast atom diffraction for grazing scattering of Ne atoms from a LiF(0 0 1) surface

    Energy Technology Data Exchange (ETDEWEB)

    Gravielle, M.S., E-mail: msilvia@iafe.uba.ar [Instituto de Astronomia y Fisica del Espacio (CONICET-UBA), Casilla de correo 67, sucursal 28 C1428EGA, Buenos Aires (Argentina); Departamento de Fisica, Fac. de Ciencias Exactas y Naturales, Universidad de Buenos Aires (Argentina); Schueller, A.; Winter, H. [Institut fuer Physik, Humboldt Universitaet zu Berlin, Newtonstrasse 15, D-12489 Berlin-Adlershof (Germany); Miraglia, J.E. [Instituto de Astronomia y Fisica del Espacio (CONICET-UBA), Casilla de correo 67, sucursal 28 C1428EGA, Buenos Aires (Argentina); Departamento de Fisica, Fac. de Ciencias Exactas y Naturales, Universidad de Buenos Aires (Argentina)

    2011-06-01

    Angular distributions of fast Ne atoms after grazing collisions with a LiF(0 0 1) surface under axial surface channeling conditions are experimentally and theoretically studied. We use the surface eikonal approximation to describe the quantum interference of scattered projectiles, while the atom-surface interaction is represented by means of a pairwise additive potential, including the polarization of the projectile atom. Experimental data serve as a benchmark to investigate the performance of the proposed potential model, analyzing the role played by the projectile polarization.

  15. Ejected electron energy distribution in the ionization of atomic hydrogen by C6+ impact

    International Nuclear Information System (INIS)

    Dey, Ritu; Roy, A.C.

    2006-01-01

    We report doubly differential cross section (DDCS) for C 6+ impact ionization of atomic hydrogen at the incident energy of 2.5 MeV/amu. The calculation is based on the eikonal approximation (EA) method. A comparison is made of the present DDCS with the results of other theoretical methods and experiment. It is found that the multiple scattering effect has a significant influence on the energy distributions of the ejected electrons. The cross sections predicted by the present EA also show reasonably good agreement with experiment

  16. Energy-Dependent microscopic optical potential for p+{sup 9}Be elastic scattering

    Energy Technology Data Exchange (ETDEWEB)

    Maridi, H. M., E-mail: h.maridi@gmail.com [Physics Department, Faculty of Science, Cairo University, Giza 12613 (Egypt); Physics Department, Faculty of Applied Science, Taiz University, Taiz (Yemen); Farag, M. Y. H., E-mail: yehiafarag@cu.edu.eg; Esmael, E. H. [Physics Department, Faculty of Applied Science, Taiz University, Taiz (Yemen)

    2016-06-10

    The p+{sup 9}Be elastic scattering at an energy range up to 200 MeV/nucleon is analyzed using the single-folding model. The density- and isospin-dependent M3Y-Paris nucleon-nucleon (NN) interaction is used for the real part and the NN-scattering amplitude of the high-energy approximation for the imaginary one. The analysis reveals that the cross-section data are reproduced well at energies up to 100 MeV/nucleon by use of the partial-wave expansion. For higher energies, the eikonal approximation give results better than the partial-wave expansion calculations. The volume integrals of the optical-potential parts have systematic energy dependencies, and they are parameterized in empirical formulas.

  17. CONTRIBUTIONS TO RATIONAL APPROXIMATION,

    Science.gov (United States)

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

  18. A Review of Methods for Moving Boundary Problems

    Science.gov (United States)

    2009-07-01

    the bound- ary value problem for the eikonal equation: ‖∇u‖ = 1 for x ∈ Ω (29) u = 0 for x ∈ Γ (30) ERDC/CHL TR-09-10 8 where ‖ ‖ is the Euclidean norm...Solutions of the eikonal equation can in turn be characterized as steady state solutions of the initial value prob- lem ut + sgn(u0)(‖∇u‖ − 1) = 0...LS using the eikonal equation and use the NCI equation for the LS dynam- ics. The complete system of equations in weak form is ∫ Ω (‖∇u‖ − 1)wdV = 0

  19. Exact constants in approximation theory

    CERN Document Server

    Korneichuk, N

    1991-01-01

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

  20. Mean Curvature, Threshold Dynamics, and Phase Field Theory on Finite Graphs

    Science.gov (United States)

    2013-06-28

    3380. [DEL12a] Xavier Desquesnes, Abderrahim Elmoataz, and Olivier Lézoray, Eikonal equation adapta- tion on weighted graphs: Fast geometric diffusion...Abderrahim Elmoataz, Olivier Lézoray, and Vinh-Thong Ta, Efficient algorithms for image and high dimensional data processing using eikonal equation on

  1. Emergence of the Green’s Functions from Noise and Passive Acoustic Remote Sensing of Ocean Dynamics

    Science.gov (United States)

    2009-09-30

    have quantified errors in the eikonal estimates retrieved from the noise cross-correlation function. These errors stem from non-uniformity of the...random sources distribution or, in other words, from the noise field not being perfectly diffuse (Godin, 2009g). Our results refer to the eikonal

  2. Optimal random perturbations for stochastic approximation using a simultaneous perturbation gradient approximation

    DEFF Research Database (Denmark)

    Sadegh, Payman; Spall, J. C.

    1998-01-01

    simultaneous perturbation approximation to the gradient based on loss function measurements. SPSA is based on picking a simultaneous perturbation (random) vector in a Monte Carlo fashion as part of generating the approximation to the gradient. This paper derives the optimal distribution for the Monte Carlo...

  3. The Heidelberg pomeron

    Energy Technology Data Exchange (ETDEWEB)

    Pirner, H.J. [Heidelberg Univ., Institute of Theoretical Physics (Germany)

    2005-07-01

    In this work we develop a model combining perturbative and non-perturbative QCD to compute high-energy reactions of hadrons and photons with special emphasis on saturation effects that manifest the S-matrix unitarity. Aiming at a unified description of hadron-hadron, photon-hadron and photon-photon reactions involving real or virtual photons as well, we follow the functional integral approach to high-energy scattering in the eikonal approximation, in which the S-matrix element factorizes into the universal correlation of 2 light-like Wegner-Wilson loops S{sub DD} and reaction-specific light-cone wave functions. The light-like Wegner-Wilson loops describe color-dipoles given by the quark and anti-quark in the meson or photon and in a simplified picture by a quark and diquark in the baryon. Consequently, hadrons and photons are described as color-dipoles with size and orientation determined by appropriate light-cone wave functions. Thus, the loop-loop correlation function S{sub DD} is the basis for our unified description. We compute the T-matrix in a functional integral approach developed for parton-parton scattering in the eikonal approximation. There is a good agreement between the computed total cross-sections and the experimental data collected from accelerators and cosmic rays for pp, pp-bar, {pi}{sup {+-}}p, K{sup {+-}}p, {gamma}p and {gamma}{gamma} scattering. The prediction for the total pp cross-section at LHC ({radical}s = 14 TeV) is {sigma}(tot){sub pp} = 114,2 mb.

  4. Approximate kernel competitive learning.

    Science.gov (United States)

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

    2015-03-01

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

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

    African Journals Online (AJOL)

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

  6. International Conference Approximation Theory XIV

    CERN Document Server

    Schumaker, Larry

    2014-01-01

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

  7. Forms of Approximate Radiation Transport

    CERN Document Server

    Brunner, G

    2002-01-01

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

  8. Approximate and renormgroup symmetries

    International Nuclear Information System (INIS)

    Ibragimov, Nail H.; Kovalev, Vladimir F.

    2009-01-01

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

  9. An acoustic eikonal equation for attenuating transversely isotropic media with a vertical symmetry axis

    KAUST Repository

    Hao, Qi; Alkhalifah, Tariq Ali

    2016-01-01

    in homogeneous media. For a horizontal-attenuating VTI layer, we also derive the nonhyperbolic approximations for the real and imaginary parts of the complex-valued reflection traveltime. These equations reveal that (1) the quasi SV-wave velocity

  10. Water versus DNA A new deal for proton transport modeling in biological matter

    International Nuclear Information System (INIS)

    Champion, C; Quinto, M A; Monti, J M; Galassi, M E; Fojón, O A; Hanssen, J; Rivarola, R D; Week, P F

    2015-01-01

    Water vapor is a common surrogate of DNA for modeling the proton-induced ionizing processes in living tissue exposed to radiations. The present study aims at scrutinizing the validity of this approximation and then revealing new insights into proton-induced energy transfers by a comparative analysis between water and realistic biological medium. In this context, self-consistent quantum mechanical modeling of the ionization and electron capture processes is reported within the continuum distorted wave-eikonal initial state framework for both isolated water molecules and DNA components impacted by proton beams. (paper)

  11. TeV gravity at neutrino telescopes

    CERN Document Server

    Illana, J I; Meloni, D

    2005-01-01

    Cosmogenic neutrinos reach the Earth with energies around 10^9 GeV, and their interactions with matter will be measured in upcoming experiments (Auger, IceCube). Models with extra dimensions and the fundamental scale at the TeV could imply signals in these experiments. In particular, the production of microscopic black holes by cosmogenic neutrinos has been extensively studied in the literature. Here we make a complete analysis of gravity-mediated interactions at larger distances, where they can be calculated in the eikonal approximation. In these processes a neutrino of energy E_\

  12. Effective Elliptic Models for Efficient Wavefield Extrapolation in Anisotropic Media

    KAUST Repository

    Waheed, Umair bin

    2014-05-01

    Wavefield extrapolation operator for elliptically anisotropic media offers significant cost reduction compared to that of transversely isotropic media (TI), especially when the medium exhibits tilt in the symmetry axis (TTI). However, elliptical anisotropy does not provide accurate focusing for TI media. Therefore, we develop effective elliptically anisotropic models that correctly capture the kinematic behavior of the TTI wavefield. Specifically, we use an iterative elliptically anisotropic eikonal solver that provides the accurate traveltimes for a TI model. The resultant coefficients of the elliptical eikonal provide the effective models. These effective models allow us to use the cheaper wavefield extrapolation operator for elliptic media to obtain approximate wavefield solutions for TTI media. Despite the fact that the effective elliptic models are obtained by kinematic matching using high-frequency asymptotic, the resulting wavefield contains most of the critical wavefield components, including the frequency dependency and caustics, if present, with reasonable accuracy. The methodology developed here offers a much better cost versus accuracy tradeoff for wavefield computations in TTI media, considering the cost prohibitive nature of the problem. We demonstrate the applicability of the proposed approach on the BP TTI model.

  13. Effective Elliptic Models for Efficient Wavefield Extrapolation in Anisotropic Media

    KAUST Repository

    Waheed, Umair bin; Alkhalifah, Tariq Ali

    2014-01-01

    Wavefield extrapolation operator for elliptically anisotropic media offers significant cost reduction compared to that of transversely isotropic media (TI), especially when the medium exhibits tilt in the symmetry axis (TTI). However, elliptical anisotropy does not provide accurate focusing for TI media. Therefore, we develop effective elliptically anisotropic models that correctly capture the kinematic behavior of the TTI wavefield. Specifically, we use an iterative elliptically anisotropic eikonal solver that provides the accurate traveltimes for a TI model. The resultant coefficients of the elliptical eikonal provide the effective models. These effective models allow us to use the cheaper wavefield extrapolation operator for elliptic media to obtain approximate wavefield solutions for TTI media. Despite the fact that the effective elliptic models are obtained by kinematic matching using high-frequency asymptotic, the resulting wavefield contains most of the critical wavefield components, including the frequency dependency and caustics, if present, with reasonable accuracy. The methodology developed here offers a much better cost versus accuracy tradeoff for wavefield computations in TTI media, considering the cost prohibitive nature of the problem. We demonstrate the applicability of the proposed approach on the BP TTI model.

  14. Approximations of Fuzzy Systems

    Directory of Open Access Journals (Sweden)

    Vinai K. Singh

    2013-03-01

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

  15. 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.)

  16. Cosmological applications of Padé approximant

    International Nuclear Information System (INIS)

    Wei, Hao; Yan, Xiao-Peng; Zhou, Ya-Nan

    2014-01-01

    As is well known, in mathematics, any function could be approximated by the Padé approximant. The Padé approximant is the best approximation of a function by a rational function of given order. In fact, the Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. In the present work, we consider the Padé approximant in two issues. First, we obtain the analytical approximation of the luminosity distance for the flat XCDM model, and find that the relative error is fairly small. Second, we propose several parameterizations for the equation-of-state parameter (EoS) of dark energy based on the Padé approximant. They are well motivated from the mathematical and physical points of view. We confront these EoS parameterizations with the latest observational data, and find that they can work well. In these practices, we show that the Padé approximant could be an useful tool in cosmology, and it deserves further investigation

  17. Cosmological applications of Padé approximant

    Science.gov (United States)

    Wei, Hao; Yan, Xiao-Peng; Zhou, Ya-Nan

    2014-01-01

    As is well known, in mathematics, any function could be approximated by the Padé approximant. The Padé approximant is the best approximation of a function by a rational function of given order. In fact, the Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. In the present work, we consider the Padé approximant in two issues. First, we obtain the analytical approximation of the luminosity distance for the flat XCDM model, and find that the relative error is fairly small. Second, we propose several parameterizations for the equation-of-state parameter (EoS) of dark energy based on the Padé approximant. They are well motivated from the mathematical and physical points of view. We confront these EoS parameterizations with the latest observational data, and find that they can work well. In these practices, we show that the Padé approximant could be an useful tool in cosmology, and it deserves further investigation.

  18. Prestack wavefield approximations

    KAUST Repository

    Alkhalifah, Tariq

    2013-01-01

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

  19. Prestack wavefield approximations

    KAUST Repository

    Alkhalifah, Tariq

    2013-09-01

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

  20. The Temporal Morphology of Infrasound Propagation

    Science.gov (United States)

    2010-01-01

    of an acoustic wavefront through space and time. The sp equations are an expression of the Eikonal ray-tracing equations (LIGHTHILL, 1978; GOSSARD and...wind fields. It can be shown that this is also equivalent to integrating the Eikonal ray equations in differential form with a negative time step. A

  1. Considerations of the Use of 3-D Geophysical Models to Predict Test Ban Monitoring Observables

    Science.gov (United States)

    2007-09-01

    predict first P arrival times. Since this is a 3-D model, the travel times are predicted with a 3-D finite-difference code solving the eikonal equations...for the eikonal wave equation should provide more accurate predictions of travel-time from 3D models. These techniques and others are being

  2. Free-Surface Flow and Fluid-Object Interaction Modeling With Emphasis on Ship Hydrodynamics

    Science.gov (United States)

    2012-01-01

    0 on Cawt (21) in a weak sense. Equation (20) is the Eikonal partial differential equation subject to the interior constraint given by Eq. (21). To...tion, respectively. The formulation given by Eq. (22) is the SUPG method [30] applied to the Eikonal equation. At the steady state, the above problem

  3. 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...

  4. Approximate number and approximate time discrimination each correlate with school math abilities in young children.

    Science.gov (United States)

    Odic, Darko; Lisboa, Juan Valle; Eisinger, Robert; Olivera, Magdalena Gonzalez; Maiche, Alejandro; Halberda, Justin

    2016-01-01

    What is the relationship between our intuitive sense of number (e.g., when estimating how many marbles are in a jar), and our intuitive sense of other quantities, including time (e.g., when estimating how long it has been since we last ate breakfast)? Recent work in cognitive, developmental, comparative psychology, and computational neuroscience has suggested that our representations of approximate number, time, and spatial extent are fundamentally linked and constitute a "generalized magnitude system". But, the shared behavioral and neural signatures between number, time, and space may alternatively be due to similar encoding and decision-making processes, rather than due to shared domain-general representations. In this study, we investigate the relationship between approximate number and time in a large sample of 6-8 year-old children in Uruguay by examining how individual differences in the precision of number and time estimation correlate with school mathematics performance. Over four testing days, each child completed an approximate number discrimination task, an approximate time discrimination task, a digit span task, and a large battery of symbolic math tests. We replicate previous reports showing that symbolic math abilities correlate with approximate number precision and extend those findings by showing that math abilities also correlate with approximate time precision. But, contrary to approximate number and time sharing common representations, we find that each of these dimensions uniquely correlates with formal math: approximate number correlates more strongly with formal math compared to time and continues to correlate with math even when precision in time and individual differences in working memory are controlled for. These results suggest that there are important differences in the mental representations of approximate number and approximate time and further clarify the relationship between quantity representations and mathematics. Copyright

  5. Approximation and Computation

    CERN Document Server

    Gautschi, Walter; Rassias, Themistocles M

    2011-01-01

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

  6. Constrained Optimization via Stochastic approximation with a simultaneous perturbation gradient approximation

    DEFF Research Database (Denmark)

    Sadegh, Payman

    1997-01-01

    This paper deals with a projection algorithm for stochastic approximation using simultaneous perturbation gradient approximation for optimization under inequality constraints where no direct gradient of the loss function is available and the inequality constraints are given as explicit functions...... of the optimization parameters. It is shown that, under application of the projection algorithm, the parameter iterate converges almost surely to a Kuhn-Tucker point, The procedure is illustrated by a numerical example, (C) 1997 Elsevier Science Ltd....

  7. Some results in Diophantine approximation

    DEFF Research Database (Denmark)

    Pedersen, Steffen Højris

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

  8. Bounded-Degree Approximations of Stochastic Networks

    Energy Technology Data Exchange (ETDEWEB)

    Quinn, Christopher J.; Pinar, Ali; Kiyavash, Negar

    2017-06-01

    We propose algorithms to approximate directed information graphs. Directed information graphs are probabilistic graphical models that depict causal dependencies between stochastic processes in a network. The proposed algorithms identify optimal and near-optimal approximations in terms of Kullback-Leibler divergence. The user-chosen sparsity trades off the quality of the approximation against visual conciseness and computational tractability. One class of approximations contains graphs with speci ed in-degrees. Another class additionally requires that the graph is connected. For both classes, we propose algorithms to identify the optimal approximations and also near-optimal approximations, using a novel relaxation of submodularity. We also propose algorithms to identify the r-best approximations among these classes, enabling robust decision making.

  9. Evidence of two-channel distortion effects in positronium formation reactions

    International Nuclear Information System (INIS)

    Macri, P A; Miraglia, J E; Hanssen, J; Fojon, O A; Rivarola, R D

    2004-01-01

    The formation of ground-state positronium in collisions of positrons on hydrogen-like atoms is considered. In previous theoretical works, two-centre distorted wavefunctions were employed to approximate either the initial or the final channel. Here we report results obtained by means of the eikonal final state continuum distorted wave approximation for which asymptotically correct distorted wavefunctions are used for both the initial and final states of the scattering system. Comparison of the present theoretical total cross sections with experimental data reveals that distortion effects become important in both channels as the impact energy decreases. This work also shows that distorted-wave theories may be extended from their usual domain of high impact energies to lower ones. (letter to the editor)

  10. Evidence of two-channel distortion effects in positronium formation reactions

    Energy Technology Data Exchange (ETDEWEB)

    Macri, P A [Instituto de AstronomIa y FIsica del Espacio, Consejo Nacional de Investigaciones CientIficas y Tecnicas-Universidad de Buenos Aires, Casilla de Correo 67, Suc. 28, 1428 Buenos Aires (Argentina); Miraglia, J E [Instituto de AstronomIa y FIsica del Espacio, Consejo Nacional de Investigaciones CientIficas y Tecnicas-Universidad de Buenos Aires, Casilla de Correo 67, Suc. 28, 1428 Buenos Aires (Argentina); Hanssen, J [Laboratoire de Physique Moleculaire et des Collisions, Institute de Physique Rue Arago, Tecnopole 2000, Metz (France); Fojon, O A [Instituto de FIsica de Rosario, Consejo Nacional de Investigaciones CientIficas y Tecnicas-Universidad Nacional de Rosario, Av. Pellegrini 250, 2000 Rosario (Argentina); Rivarola, R D [Instituto de FIsica de Rosario, Consejo Nacional de Investigaciones CientIficas y Tecnicas-Universidad Nacional de Rosario, Av. Pellegrini 250, 2000 Rosario (Argentina)

    2004-03-28

    The formation of ground-state positronium in collisions of positrons on hydrogen-like atoms is considered. In previous theoretical works, two-centre distorted wavefunctions were employed to approximate either the initial or the final channel. Here we report results obtained by means of the eikonal final state continuum distorted wave approximation for which asymptotically correct distorted wavefunctions are used for both the initial and final states of the scattering system. Comparison of the present theoretical total cross sections with experimental data reveals that distortion effects become important in both channels as the impact energy decreases. This work also shows that distorted-wave theories may be extended from their usual domain of high impact energies to lower ones. (letter to the editor)

  11. Approximation by planar elastic curves

    DEFF Research Database (Denmark)

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

    2016-01-01

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

  12. Limitations of shallow nets approximation.

    Science.gov (United States)

    Lin, Shao-Bo

    2017-10-01

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

  13. High-energy scattering of particles with anomalous magnetic moments in the quantum field theory. πN scattering and Coulomb interference

    International Nuclear Information System (INIS)

    Nguen Suan Khan; Pervushin, V.N.

    1975-01-01

    An eikonal representation has been obtained for the amplitude of the πN-scattering in the asymptotic form into account the anomalous nucleon magnetic moment leads to the introduction of the additive term in to the eikonal phase which is responsible for the spin flip in the scattering process. The Coulomb interference is considered

  14. Approximate circuits for increased reliability

    Science.gov (United States)

    Hamlet, Jason R.; Mayo, Jackson R.

    2015-08-18

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

  15. Mapping moveout approximations in TI media

    KAUST Repository

    Stovas, Alexey; Alkhalifah, Tariq Ali

    2013-01-01

    Moveout approximations play a very important role in seismic modeling, inversion, and scanning for parameters in complex media. We developed a scheme to map one-way moveout approximations for transversely isotropic media with a vertical axis of symmetry (VTI), which is widely available, to the tilted case (TTI) by introducing the effective tilt angle. As a result, we obtained highly accurate TTI moveout equations analogous with their VTI counterparts. Our analysis showed that the most accurate approximation is obtained from the mapping of generalized approximation. The new moveout approximations allow for, as the examples demonstrate, accurate description of moveout in the TTI case even for vertical heterogeneity. The proposed moveout approximations can be easily used for inversion in a layered TTI medium because the parameters of these approximations explicitly depend on corresponding effective parameters in a layered VTI medium.

  16. Analytical approximation of neutron physics data

    International Nuclear Information System (INIS)

    Badikov, S.A.; Vinogradov, V.A.; Gaj, E.V.; Rabotnov, N.S.

    1984-01-01

    The method for experimental neutron-physical data analytical approximation by rational functions based on the Pade approximation is suggested. It is shown that the existence of the Pade approximation specific properties in polar zones is an extremely favourable analytical property essentially extending the convergence range and increasing its rate as compared with polynomial approximation. The Pade approximation is the particularly natural instrument for resonance curve processing as the resonances conform to the complex poles of the approximant. But even in a general case analytical representation of the data in this form is convenient and compact. Thus representation of the data on the neutron threshold reaction cross sections (BOSPOR constant library) in the form of rational functions lead to approximately twenty fold reduction of the storaged numerical information as compared with the by-point calculation at the same accWracy

  17. Mapping moveout approximations in TI media

    KAUST Repository

    Stovas, Alexey

    2013-11-21

    Moveout approximations play a very important role in seismic modeling, inversion, and scanning for parameters in complex media. We developed a scheme to map one-way moveout approximations for transversely isotropic media with a vertical axis of symmetry (VTI), which is widely available, to the tilted case (TTI) by introducing the effective tilt angle. As a result, we obtained highly accurate TTI moveout equations analogous with their VTI counterparts. Our analysis showed that the most accurate approximation is obtained from the mapping of generalized approximation. The new moveout approximations allow for, as the examples demonstrate, accurate description of moveout in the TTI case even for vertical heterogeneity. The proposed moveout approximations can be easily used for inversion in a layered TTI medium because the parameters of these approximations explicitly depend on corresponding effective parameters in a layered VTI medium.

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

    International Nuclear Information System (INIS)

    Cohenca, J.M.

    1970-01-01

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

  19. 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.

  20. Risk approximation in decision making: approximative numeric abilities predict advantageous decisions under objective risk.

    Science.gov (United States)

    Mueller, Silke M; Schiebener, Johannes; Delazer, Margarete; Brand, Matthias

    2018-01-22

    Many decision situations in everyday life involve mathematical considerations. In decisions under objective risk, i.e., when explicit numeric information is available, executive functions and abilities to handle exact numbers and ratios are predictors of objectively advantageous choices. Although still debated, exact numeric abilities, e.g., normative calculation skills, are assumed to be related to approximate number processing skills. The current study investigates the effects of approximative numeric abilities on decision making under objective risk. Participants (N = 153) performed a paradigm measuring number-comparison, quantity-estimation, risk-estimation, and decision-making skills on the basis of rapid dot comparisons. Additionally, a risky decision-making task with exact numeric information was administered, as well as tasks measuring executive functions and exact numeric abilities, e.g., mental calculation and ratio processing skills, were conducted. Approximative numeric abilities significantly predicted advantageous decision making, even beyond the effects of executive functions and exact numeric skills. Especially being able to make accurate risk estimations seemed to contribute to superior choices. We recommend approximation skills and approximate number processing to be subject of future investigations on decision making under risk.

  1. Nonlinear approximation with dictionaries I. Direct estimates

    DEFF Research Database (Denmark)

    Gribonval, Rémi; Nielsen, Morten

    2004-01-01

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

  2. Spline approximation, Part 1: Basic methodology

    Science.gov (United States)

    Ezhov, Nikolaj; Neitzel, Frank; Petrovic, Svetozar

    2018-04-01

    In engineering geodesy point clouds derived from terrestrial laser scanning or from photogrammetric approaches are almost never used as final results. For further processing and analysis a curve or surface approximation with a continuous mathematical function is required. In this paper the approximation of 2D curves by means of splines is treated. Splines offer quite flexible and elegant solutions for interpolation or approximation of "irregularly" distributed data. Depending on the problem they can be expressed as a function or as a set of equations that depend on some parameter. Many different types of splines can be used for spline approximation and all of them have certain advantages and disadvantages depending on the approximation problem. In a series of three articles spline approximation is presented from a geodetic point of view. In this paper (Part 1) the basic methodology of spline approximation is demonstrated using splines constructed from ordinary polynomials and splines constructed from truncated polynomials. In the forthcoming Part 2 the notion of B-spline will be explained in a unique way, namely by using the concept of convex combinations. The numerical stability of all spline approximation approaches as well as the utilization of splines for deformation detection will be investigated on numerical examples in Part 3.

  3. Integration of an Acoustic Modem onto a Wave Glider Unmanned Surface Vehicle

    Science.gov (United States)

    2012-06-01

    of the wave and ωτ represents the phase of the wave. After some amount of math and taking the limit as ω →∞ , we arrive at a form of the eikonal ...the phase front. (5.5) 22 0A Aτ τ∇ ⋅∇ + ∇ = The transport equation and the eikonal equation can be solved by using multiple methods to give

  4. Comparison of halo of 11Be, 15C, and 19C

    Science.gov (United States)

    Kharab, R.; Kumar, R.; Singh, P.; Sharma, H. C.

    2007-12-01

    We have compared the halo of 11Be, 15C, and 19C nuclei by analyzing the one-neutron stripping reaction data on the Be target at 60-, 54-, and 57-MeV/ A beam energies, respectively, within the framework of the eikonal approximation approach. The determination of effective range through the comparison of the total cross section data and prediction has revealed that the halo of 19C is the well developed, while that of 15C is the least and that of 11Be lies in between these two. The longitudinal momentum distribution data also strengthen these observations.

  5. Single ionization of Ne, Ar and Kr by proton impact: Single differential distributions in energy and angle

    Energy Technology Data Exchange (ETDEWEB)

    Otranto, S [CONICET and Dto. de Fisica, Universidad Nacional del Sur, 8000 BahIa Blanca (Argentina); Miraglia, J E [Instituto de AstronomIa y Fisica del Espacio, CONICET and Universidad de Buenos Aires C1428EGA (Argentina); Olson, R E, E-mail: sotranto@uns.edu.a [Physics Department, Missouri University of Science and Technology, Rolla MO 65409 (United States)

    2009-11-01

    In this work we present a theoretical study of singly differential cross sections in energy and angle for the single ionization of neon, argon and krypton by proton impact. Theoretical results obtained by means of the Continuum Distorted Wave-Eikonal initial state (CDW-EIS) model are compared to those provided by the First Born Approximation (FBA) and the classical trajectory Monte Carlo (CTMC) method as well as to experimental data from several laboratories. We note in particular for argon, that the CDW-EIS model does not reproduce the experimental data as accurately as expected, while the CTMC instead is in very good agreement.

  6. Explaining jet quenching with perturbative QCD alone

    CERN Document Server

    Zapp, Korinna C; Wiedemann, Urs A

    2011-01-01

    We present a new formulation of jet quenching in perturbative QCD beyond the eikonal approximation. Multiple scattering in the medium is modelled through infra-red-continued (2 -> 2) scattering matrix elements in QCD and the parton shower describing further emissions. The interplay between these processes is arranged in terms of a formation time constraint such that coherent emissions can be treated consistently. Emerging partons are hadronised by the Lund string model, tuned to describe LEP data in conjunction with the parton shower. Based on this picture we obtain a good description of the nuclear modification factor R_AA at RHIC and LHC.

  7. The efficiency of Flory approximation

    International Nuclear Information System (INIS)

    Obukhov, S.P.

    1984-01-01

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

  8. The role of projectile interactions in triply differential cross sections for excitation-ionization of helium

    Energy Technology Data Exchange (ETDEWEB)

    Dey, R., E-mail: ritud@ipp.mpg.d [Max-Planck Institut fuer Plasmaphysik, Boltzmannstr. 2, D-85748 Garching (Germany); Roy, A.C. [School of Mathematical Sciences, Ramakrishna Mission Vivekananda University, Belur Math 711 202, West Bengal (India)

    2011-02-01

    We report triply differential cross section (TDCS) for the simultaneous excitation-ionization of helium by electron impact for both coplanar and non-coplanar geometry. In the coplanar case, calculations have been performed for an incident energy of 500 eV and low ejection energies (3 and 10 eV), whereas in the noncoplanar case we have considered impact energies in the range 1240-4260 eV for a symmetric geometry. The present calculation is based on the eikonal approximation due to Glauber. We have incorporated the effect of post-collision interaction in the Glauber approximation. A comparison is made of the present calculations with the results of other theoretical methods and recent experiments. The Glauber results are in reasonably good agreement with the experiment for small scattering angles.

  9. Computations of Wall Distances Based on Differential Equations

    Science.gov (United States)

    Tucker, Paul G.; Rumsey, Chris L.; Spalart, Philippe R.; Bartels, Robert E.; Biedron, Robert T.

    2004-01-01

    The use of differential equations such as Eikonal, Hamilton-Jacobi and Poisson for the economical calculation of the nearest wall distance d, which is needed by some turbulence models, is explored. Modifications that could palliate some turbulence-modeling anomalies are also discussed. Economy is of especial value for deforming/adaptive grid problems. For these, ideally, d is repeatedly computed. It is shown that the Eikonal and Hamilton-Jacobi equations can be easy to implement when written in implicit (or iterated) advection and advection-diffusion equation analogous forms, respectively. These, like the Poisson Laplacian term, are commonly occurring in CFD solvers, allowing the re-use of efficient algorithms and code components. The use of the NASA CFL3D CFD program to solve the implicit Eikonal and Hamilton-Jacobi equations is explored. The re-formulated d equations are easy to implement, and are found to have robust convergence. For accurate Eikonal solutions, upwind metric differences are required. The Poisson approach is also found effective, and easiest to implement. Modified distances are not found to affect global outputs such as lift and drag significantly, at least in common situations such as airfoil flows.

  10. Weighted approximation with varying weight

    CERN Document Server

    Totik, Vilmos

    1994-01-01

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

  11. Bent approximations to synchrotron radiation optics

    International Nuclear Information System (INIS)

    Heald, S.

    1981-01-01

    Ideal optical elements can be approximated by bending flats or cylinders. This paper considers the applications of these approximate optics to synchrotron radiation. Analytic and raytracing studies are used to compare their optical performance with the corresponding ideal elements. It is found that for many applications the performance is adequate, with the additional advantages of lower cost and greater flexibility. Particular emphasis is placed on obtaining the practical limitations on the use of the approximate elements in typical beamline configurations. Also considered are the possibilities for approximating very long length mirrors using segmented mirrors

  12. INTOR cost approximation

    International Nuclear Information System (INIS)

    Knobloch, A.F.

    1980-01-01

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

  13. Modeling of Hurricane Impacts

    Science.gov (United States)

    2007-09-01

    terms on the RHS). The wave number k is obtained from the eikonal equations (e.g. Dingemans, 1993): ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ∂ ∂ − ∂ ∂ −= ∂ ∂ + ∂ ∂ y k x k c xt...components and ω represents the absolute radial frequency. The RHS of the eikonal equations ensures the irrotationality of wave number vector field (pers

  14. A unified approach to the Darwin approximation

    International Nuclear Information System (INIS)

    Krause, Todd B.; Apte, A.; Morrison, P. J.

    2007-01-01

    There are two basic approaches to the Darwin approximation. The first involves solving the Maxwell equations in Coulomb gauge and then approximating the vector potential to remove retardation effects. The second approach approximates the Coulomb gauge equations themselves, then solves these exactly for the vector potential. There is no a priori reason that these should result in the same approximation. Here, the equivalence of these two approaches is investigated and a unified framework is provided in which to view the Darwin approximation. Darwin's original treatment is variational in nature, but subsequent applications of his ideas in the context of Vlasov's theory are not. We present here action principles for the Darwin approximation in the Vlasov context, and this serves as a consistency check on the use of the approximation in this setting

  15. An Approximate Approach to Automatic Kernel Selection.

    Science.gov (United States)

    Ding, Lizhong; Liao, Shizhong

    2016-02-02

    Kernel selection is a fundamental problem of kernel-based learning algorithms. In this paper, we propose an approximate approach to automatic kernel selection for regression from the perspective of kernel matrix approximation. We first introduce multilevel circulant matrices into automatic kernel selection, and develop two approximate kernel selection algorithms by exploiting the computational virtues of multilevel circulant matrices. The complexity of the proposed algorithms is quasi-linear in the number of data points. Then, we prove an approximation error bound to measure the effect of the approximation in kernel matrices by multilevel circulant matrices on the hypothesis and further show that the approximate hypothesis produced with multilevel circulant matrices converges to the accurate hypothesis produced with kernel matrices. Experimental evaluations on benchmark datasets demonstrate the effectiveness of approximate kernel selection.

  16. Approximate error conjugation gradient minimization methods

    Science.gov (United States)

    Kallman, Jeffrey S

    2013-05-21

    In one embodiment, a method includes selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, calculating an approximate error using the subset of rays, and calculating a minimum in a conjugate gradient direction based on the approximate error. In another embodiment, a system includes a processor for executing logic, logic for selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, logic for calculating an approximate error using the subset of rays, and logic for calculating a minimum in a conjugate gradient direction based on the approximate error. In other embodiments, computer program products, methods, and systems are described capable of using approximate error in constrained conjugate gradient minimization problems.

  17. Paraxial WKB solution of a scalar wave equation

    International Nuclear Information System (INIS)

    Pereverzev, G.V.

    1993-04-01

    An asymptotic method of solving a scalar wave equation in inhomogeneous media is developed. This method is an extension of the WKB method to the multidimensional case. It reduces a general wave equation to a set of ordinary differential equations similar to that of the eikonal approach and includes the latter as a particular case. However, the WKB method makes use of another kind of asymptotic expansion and, unlike the eikonal approach, describes the wave properties, i.e. diffraction and interference. At the same time, the three-dimensional WKB method is more simple for numerical treatment because the number of equations is less than in the eikonal approach. The method developed may be used for a calculation of wave fields in problems of RF heating, current drive and plasma diagnostics with microwave beams. (orig.)

  18. Self-similar continued root approximants

    International Nuclear Information System (INIS)

    Gluzman, S.; Yukalov, V.I.

    2012-01-01

    A novel method of summing asymptotic series is advanced. Such series repeatedly arise when employing perturbation theory in powers of a small parameter for complicated problems of condensed matter physics, statistical physics, and various applied problems. The method is based on the self-similar approximation theory involving self-similar root approximants. The constructed self-similar continued roots extrapolate asymptotic series to finite values of the expansion parameter. The self-similar continued roots contain, as a particular case, continued fractions and Padé approximants. A theorem on the convergence of the self-similar continued roots is proved. The method is illustrated by several examples from condensed-matter physics.

  19.  Higher Order Improvements for Approximate Estimators

    DEFF Research Database (Denmark)

    Kristensen, Dennis; Salanié, Bernard

    Many modern estimation methods in econometrics approximate an objective function, through simulation or discretization for instance. The resulting "approximate" estimator is often biased; and it always incurs an efficiency loss. We here propose three methods to improve the properties of such appr......Many modern estimation methods in econometrics approximate an objective function, through simulation or discretization for instance. The resulting "approximate" estimator is often biased; and it always incurs an efficiency loss. We here propose three methods to improve the properties...... of such approximate estimators at a low computational cost. The first two methods correct the objective function so as to remove the leading term of the bias due to the approximation. One variant provides an analytical bias adjustment, but it only works for estimators based on stochastic approximators......, such as simulation-based estimators. Our second bias correction is based on ideas from the resampling literature; it eliminates the leading bias term for non-stochastic as well as stochastic approximators. Finally, we propose an iterative procedure where we use Newton-Raphson (NR) iterations based on a much finer...

  20. On Covering Approximation Subspaces

    Directory of Open Access Journals (Sweden)

    Xun Ge

    2009-06-01

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

  1. Approximation methods in probability theory

    CERN Document Server

    Čekanavičius, Vydas

    2016-01-01

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

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

    Energy Technology Data Exchange (ETDEWEB)

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

    1976-05-08

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

  3. Spherical Approximation on Unit Sphere

    Directory of Open Access Journals (Sweden)

    Eman Samir Bhaya

    2018-01-01

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

  4. Ancilla-approximable quantum state transformations

    International Nuclear Information System (INIS)

    Blass, Andreas; Gurevich, Yuri

    2015-01-01

    We consider the transformations of quantum states obtainable by a process of the following sort. Combine the given input state with a specially prepared initial state of an auxiliary system. Apply a unitary transformation to the combined system. Measure the state of the auxiliary subsystem. If (and only if) it is in a specified final state, consider the process successful, and take the resulting state of the original (principal) system as the result of the process. We review known information about exact realization of transformations by such a process. Then we present results about approximate realization of finite partial transformations. We not only consider primarily the issue of approximation to within a specified positive ε, but also address the question of arbitrarily close approximation

  5. Ancilla-approximable quantum state transformations

    Energy Technology Data Exchange (ETDEWEB)

    Blass, Andreas [Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109 (United States); Gurevich, Yuri [Microsoft Research, Redmond, Washington 98052 (United States)

    2015-04-15

    We consider the transformations of quantum states obtainable by a process of the following sort. Combine the given input state with a specially prepared initial state of an auxiliary system. Apply a unitary transformation to the combined system. Measure the state of the auxiliary subsystem. If (and only if) it is in a specified final state, consider the process successful, and take the resulting state of the original (principal) system as the result of the process. We review known information about exact realization of transformations by such a process. Then we present results about approximate realization of finite partial transformations. We not only consider primarily the issue of approximation to within a specified positive ε, but also address the question of arbitrarily close approximation.

  6. Recognition of computerized facial approximations by familiar assessors.

    Science.gov (United States)

    Richard, Adam H; Monson, Keith L

    2017-11-01

    Studies testing the effectiveness of facial approximations typically involve groups of participants who are unfamiliar with the approximated individual(s). This limitation requires the use of photograph arrays including a picture of the subject for comparison to the facial approximation. While this practice is often necessary due to the difficulty in obtaining a group of assessors who are familiar with the approximated subject, it may not accurately simulate the thought process of the target audience (friends and family members) in comparing a mental image of the approximated subject to the facial approximation. As part of a larger process to evaluate the effectiveness and best implementation of the ReFace facial approximation software program, the rare opportunity arose to conduct a recognition study using assessors who were personally acquainted with the subjects of the approximations. ReFace facial approximations were generated based on preexisting medical scans, and co-workers of the scan donors were tested on whether they could accurately pick out the approximation of their colleague from arrays of facial approximations. Results from the study demonstrated an overall poor recognition performance (i.e., where a single choice within a pool is not enforced) for individuals who were familiar with the approximated subjects. Out of 220 recognition tests only 10.5% resulted in the assessor selecting the correct approximation (or correctly choosing not to make a selection when the array consisted only of foils), an outcome that was not significantly different from the 9% random chance rate. When allowed to select multiple approximations the assessors felt resembled the target individual, the overall sensitivity for ReFace approximations was 16.0% and the overall specificity was 81.8%. These results differ markedly from the results of a previous study using assessors who were unfamiliar with the approximated subjects. Some possible explanations for this disparity in

  7. Approximating The DCM

    DEFF Research Database (Denmark)

    Madsen, Rasmus Elsborg

    2005-01-01

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

  8. An approximation for kanban controlled assembly systems

    NARCIS (Netherlands)

    Topan, E.; Avsar, Z.M.

    2011-01-01

    An approximation is proposed to evaluate the steady-state performance of kanban controlled two-stage assembly systems. The development of the approximation is as follows. The considered continuous-time Markov chain is aggregated keeping the model exact, and this aggregate model is approximated

  9. Low Rank Approximation Algorithms, Implementation, Applications

    CERN Document Server

    Markovsky, Ivan

    2012-01-01

    Matrix low-rank approximation is intimately related to data modelling; a problem that arises frequently in many different fields. Low Rank Approximation: Algorithms, Implementation, Applications is a comprehensive exposition of the theory, algorithms, and applications of structured low-rank approximation. Local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. A major part of the text is devoted to application of the theory. Applications described include: system and control theory: approximate realization, model reduction, output error, and errors-in-variables identification; signal processing: harmonic retrieval, sum-of-damped exponentials, finite impulse response modeling, and array processing; machine learning: multidimensional scaling and recommender system; computer vision: algebraic curve fitting and fundamental matrix estimation; bioinformatics for microarray data analysis; chemometrics for multivariate calibration; ...

  10. Shearlets and Optimally Sparse Approximations

    DEFF Research Database (Denmark)

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

    2012-01-01

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

  11. Photoproduction within the two-component Dual Parton Model: amplitudes and cross sections

    International Nuclear Information System (INIS)

    Engel, R.; Siegen Univ.

    1995-01-01

    In the framework of the Dual Parton Model an approximation scheme to describe high energy photoproduction processes is presented. Based on the distinction between direct, resolved soft, and resolved hard interaction processes we construct effective impact parameter amplitudes. In order to treat low mass diffraction within the eikonal formalism in a consistent way a phenomenological ansatz is proposed. The free parameters of the model are determined by fits to high energy hadro- and photoproduction cross sections. We calculate the partial photoproduction cross sections and discuss predictions of the model at HERA energies. Using hadro- and photoproduction data together, the uncertainties of the model predictions are strongly reduced. (orig.)

  12. Electron-hydrogen collisions with dressed target and Volkov projectile states in a laser field

    International Nuclear Information System (INIS)

    Smith, P.H.G.; Flannery, M.R.

    1992-01-01

    Cross sections for the 1S-2S and 1S-2P O transitions in laser-assisted e - -H(1S) collisions are calculated in both the multi-channel eikonal treatment and the Born wave approximation, as a function of impact energy and laser field intensity. The laser considered is a monotonic, plane-polarized CO 2 laser (photon energy = 0.117 eV) with the polarization direction parallel to the initial projectile velocity. The first part of this paper confines the laser perturbation to the bound electrons of the atom. The second part extends the laser perturbation to the projectile electron, and the familiar Volkov dressed states are used. (author)

  13. Influence of the halo upon angular distributions for elastic scattering and breakup

    International Nuclear Information System (INIS)

    Capel, P.; Hussein, M.S.; Baye, D.

    2010-01-01

    The angular distributions for elastic scattering and breakup of halo nuclei are analysed using a near-side/far-side decomposition within the framework of the dynamical eikonal approximation. This analysis is performed for 11 Be impinging on Pb at 69 MeV/nucleon. These distributions exhibit very similar features. In particular they are both near-side dominated, as expected from Coulomb-dominated reactions. The general shape of these distributions is sensitive mostly to the projectile-target interactions, but is also affected by the extension of the halo. This suggests the elastic scattering not to be affected by a loss of flux towards the breakup channel.

  14. Soft and hard pomerons

    International Nuclear Information System (INIS)

    Maor, Uri; Tel Aviv Univ.

    1995-09-01

    The role of s-channel unitarity screening corrections, calculated in the eikonal approximation, is investigated for soft Pomeron exchange responsible for elastic and diffractive hadron scattering in the high energy limit. We examine the differences between our results and those obtained from the supercritical Pomeron-Regge model with no such corrections. It is shown that screening saturation is attained at different scales for different channels. We then proceed to discuss the new HERA data on hard (PQCD) Pomeron diffractive channels and discuss the relationship between the soft and hard Pomerons and the relevance of our analysis to this problem. (author). 18 refs, 9 figs, 1 tab

  15. Projectile charge dependence of the ionisation spectra for H sup + and sup 3 He sup 2+ ions on He and Ne atoms

    Energy Technology Data Exchange (ETDEWEB)

    Bernardi, G.; Garibotti, C.R.; Suarez, S. (Comision Nacional de Energia Atomica, San Carlos de Bariloche (Argentina). Centro Atomico Bariloche Consejo Nacional de Investigaciones Cientificas y Tecnicas, Buenos Aires (Argentina)); Fainstein, P. (Comision Nacional de Energia Atomica, San Carlos de Bariloche (Argentina). Centro Atomico Bariloche)

    1990-05-14

    The spectra of electrons emitted in the collisions of H{sup +} and {sup 3}He{sup 2+} on He at 50 and 100 keV, and on Ne gas at 100 keV were studied. For fixed angle the double differential cross section is analysed as a function of the velocity variable, which has a maximum about halfway between the soft electron and the electron capture to continuum peaks. The experimental results show that the position of this maximum does not depend on the projectile charge. Calculations using the continuum-distorted-wave-eikonal-initial-state approximation are in qualitative agreement with our measurements. (author).

  16. Multilevel weighted least squares polynomial approximation

    KAUST Repository

    Haji-Ali, Abdul-Lateef

    2017-06-30

    Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required to achieve quasi-optimal approximation in a given polynomial subspace scales, up to a logarithmic factor, linearly in the dimension of this space. However, in many applications, the computation of samples includes a numerical discretization error. Thus, obtaining polynomial approximations with a single level method can become prohibitively expensive, as it requires a sufficiently large number of samples, each computed with a sufficiently small discretization error. As a solution to this problem, we propose a multilevel method that utilizes samples computed with different accuracies and is able to match the accuracy of single-level approximations with reduced computational cost. We derive complexity bounds under certain assumptions about polynomial approximability and sample work. Furthermore, we propose an adaptive algorithm for situations where such assumptions cannot be verified a priori. Finally, we provide an efficient algorithm for the sampling from optimal distributions and an analysis of computationally favorable alternative distributions. Numerical experiments underscore the practical applicability of our method.

  17. Improved Dutch Roll Approximation for Hypersonic Vehicle

    Directory of Open Access Journals (Sweden)

    Liang-Liang Yin

    2014-06-01

    Full Text Available An improved dutch roll approximation for hypersonic vehicle is presented. From the new approximations, the dutch roll frequency is shown to be a function of the stability axis yaw stability and the dutch roll damping is mainly effected by the roll damping ratio. In additional, an important parameter called roll-to-yaw ratio is obtained to describe the dutch roll mode. Solution shows that large-roll-to-yaw ratio is the generate character of hypersonic vehicle, which results the large error for the practical approximation. Predictions from the literal approximations derived in this paper are compared with actual numerical values for s example hypersonic vehicle, results show the approximations work well and the error is below 10 %.

  18. Regression with Sparse Approximations of Data

    DEFF Research Database (Denmark)

    Noorzad, Pardis; Sturm, Bob L.

    2012-01-01

    We propose sparse approximation weighted regression (SPARROW), a method for local estimation of the regression function that uses sparse approximation with a dictionary of measurements. SPARROW estimates the regression function at a point with a linear combination of a few regressands selected...... by a sparse approximation of the point in terms of the regressors. We show SPARROW can be considered a variant of \\(k\\)-nearest neighbors regression (\\(k\\)-NNR), and more generally, local polynomial kernel regression. Unlike \\(k\\)-NNR, however, SPARROW can adapt the number of regressors to use based...

  19. Rational approximation of vertical segments

    Science.gov (United States)

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

    2007-08-01

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

  20. On Nash-Equilibria of Approximation-Stable Games

    Science.gov (United States)

    Awasthi, Pranjal; Balcan, Maria-Florina; Blum, Avrim; Sheffet, Or; Vempala, Santosh

    One reason for wanting to compute an (approximate) Nash equilibrium of a game is to predict how players will play. However, if the game has multiple equilibria that are far apart, or ɛ-equilibria that are far in variation distance from the true Nash equilibrium strategies, then this prediction may not be possible even in principle. Motivated by this consideration, in this paper we define the notion of games that are approximation stable, meaning that all ɛ-approximate equilibria are contained inside a small ball of radius Δ around a true equilibrium, and investigate a number of their properties. Many natural small games such as matching pennies and rock-paper-scissors are indeed approximation stable. We show furthermore there exist 2-player n-by-n approximation-stable games in which the Nash equilibrium and all approximate equilibria have support Ω(log n). On the other hand, we show all (ɛ,Δ) approximation-stable games must have an ɛ-equilibrium of support O(Δ^{2-o(1)}/ɛ2{log n}), yielding an immediate n^{O(Δ^{2-o(1)}/ɛ^2log n)}-time algorithm, improving over the bound of [11] for games satisfying this condition. We in addition give a polynomial-time algorithm for the case that Δ and ɛ are sufficiently close together. We also consider an inverse property, namely that all non-approximate equilibria are far from some true equilibrium, and give an efficient algorithm for games satisfying that condition.

  1. Legendre-tau approximations for functional differential equations

    Science.gov (United States)

    Ito, K.; Teglas, R.

    1986-01-01

    The numerical approximation of solutions to linear retarded functional differential equations are considered using the so-called Legendre-tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time-differentiation. The approximate solution is then represented as a truncated Legendre series with time-varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximation is made.

  2. Approximate maximum parsimony and ancestral maximum likelihood.

    Science.gov (United States)

    Alon, Noga; Chor, Benny; Pardi, Fabio; Rapoport, Anat

    2010-01-01

    We explore the maximum parsimony (MP) and ancestral maximum likelihood (AML) criteria in phylogenetic tree reconstruction. Both problems are NP-hard, so we seek approximate solutions. We formulate the two problems as Steiner tree problems under appropriate distances. The gist of our approach is the succinct characterization of Steiner trees for a small number of leaves for the two distances. This enables the use of known Steiner tree approximation algorithms. The approach leads to a 16/9 approximation ratio for AML and asymptotically to a 1.55 approximation ratio for MP.

  3. Local density approximations for relativistic exchange energies

    International Nuclear Information System (INIS)

    MacDonald, A.H.

    1986-01-01

    The use of local density approximations to approximate exchange interactions in relativistic electron systems is reviewed. Particular attention is paid to the physical content of these exchange energies by discussing results for the uniform relativistic electron gas from a new point of view. Work on applying these local density approximations in atoms and solids is reviewed and it is concluded that good accuracy is usually possible provided self-interaction corrections are applied. The local density approximations necessary for spin-polarized relativistic systems are discussed and some new results are presented

  4. 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.

  5. Saddlepoint approximation methods in financial engineering

    CERN Document Server

    Kwok, Yue Kuen

    2018-01-01

    This book summarizes recent advances in applying saddlepoint approximation methods to financial engineering. It addresses pricing exotic financial derivatives and calculating risk contributions to Value-at-Risk and Expected Shortfall in credit portfolios under various default correlation models. These standard problems involve the computation of tail probabilities and tail expectations of the corresponding underlying state variables.  The text offers in a single source most of the saddlepoint approximation results in financial engineering, with different sets of ready-to-use approximation formulas. Much of this material may otherwise only be found in original research publications. The exposition and style are made rigorous by providing formal proofs of most of the results. Starting with a presentation of the derivation of a variety of saddlepoint approximation formulas in different contexts, this book will help new researchers to learn the fine technicalities of the topic. It will also be valuable to quanti...

  6. Approximating centrality in evolving graphs: toward sublinearity

    Science.gov (United States)

    Priest, Benjamin W.; Cybenko, George

    2017-05-01

    The identification of important nodes is a ubiquitous problem in the analysis of social networks. Centrality indices (such as degree centrality, closeness centrality, betweenness centrality, PageRank, and others) are used across many domains to accomplish this task. However, the computation of such indices is expensive on large graphs. Moreover, evolving graphs are becoming increasingly important in many applications. It is therefore desirable to develop on-line algorithms that can approximate centrality measures using memory sublinear in the size of the graph. We discuss the challenges facing the semi-streaming computation of many centrality indices. In particular, we apply recent advances in the streaming and sketching literature to provide a preliminary streaming approximation algorithm for degree centrality utilizing CountSketch and a multi-pass semi-streaming approximation algorithm for closeness centrality leveraging a spanner obtained through iteratively sketching the vertex-edge adjacency matrix. We also discuss possible ways forward for approximating betweenness centrality, as well as spectral measures of centrality. We provide a preliminary result using sketched low-rank approximations to approximate the output of the HITS algorithm.

  7. Non linear shock wave propagation in heterogeneous fluids: a numerical approach beyond the parabolic approximation with application to sonic boom.

    Science.gov (United States)

    Dagrau, Franck; Coulouvrat, François; Marchiano, Régis; Héron, Nicolas

    2008-06-01

    Dassault Aviation as a civil aircraft manufacturer is studying the feasibility of a supersonic business jet with the target of an "acceptable" sonic boom at the ground level, and in particular in case of focusing. A sonic boom computational process has been performed, that takes into account meteorological effects and aircraft manoeuvres. Turn manoeuvres and aircraft acceleration create zones of convergence of rays (caustics) which are the place of sound amplification. Therefore two elements have to be evaluated: firstly the geometrical position of the caustics, and secondly the noise level in the neighbourhood of the caustics. The modelling of the sonic boom propagation is based essentially on the assumptions of geometrical acoustics. Ray tracing is obtained according to Fermat's principle as paths that minimise the propagation time between the source (the aircraft) and the receiver. Wave amplitude and time waveform result from the solution of the inviscid Burgers' equation written along each individual ray. The "age variable" measuring the cumulative nonlinear effects is linked to the ray tube area. Caustics are located as the place where the ray tube area vanishes. Since geometrical acoustics does not take into account diffraction effects, it breaks down in the neighbourhood of caustics where it would predict unphysical infinite pressure amplitude. The aim of this study is to describe an original method for computing the focused noise level. The approach involves three main steps that can be summarised as follows. The propagation equation is solved by a forward marching procedure split into three successive steps: linear propagation in a homogeneous medium, linear perturbation due to the weak heterogeneity of the medium, and non-linear effects. The first step is solved using an "exact" angular spectrum algorithm. Parabolic approximation is applied only for the weak perturbation due to the heterogeneities. Finally, non linear effects are performed by solving the

  8. 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.

  9. Approximation properties of fine hyperbolic graphs

    Indian Academy of Sciences (India)

    2016-08-26

    Aug 26, 2016 ... 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 ... Department of Applied Mathematics, Shanghai Finance University, Shanghai 201209, People's Republic of China ...

  10. Efficient automata constructions and approximate automata

    NARCIS (Netherlands)

    Watson, B.W.; Kourie, D.G.; Ngassam, E.K.; Strauss, T.; Cleophas, L.G.W.A.

    2008-01-01

    In this paper, we present data structures and algorithms for efficiently constructing approximate automata. An approximate automaton for a regular language L is one which accepts at least L. Such automata can be used in a variety of practical applications, including network security pattern

  11. Efficient automata constructions and approximate automata

    NARCIS (Netherlands)

    Watson, B.W.; Kourie, D.G.; Ngassam, E.K.; Strauss, T.; Cleophas, L.G.W.A.; Holub, J.; Zdárek, J.

    2006-01-01

    In this paper, we present data structures and algorithms for efficiently constructing approximate automata. An approximate automaton for a regular language L is one which accepts at least L. Such automata can be used in a variety of practical applications, including network security pattern

  12. Approximation of the semi-infinite interval

    Directory of Open Access Journals (Sweden)

    A. McD. Mercer

    1980-01-01

    Full Text Available The approximation of a function f∈C[a,b] by Bernstein polynomials is well-known. It is based on the binomial distribution. O. Szasz has shown that there are analogous approximations on the interval [0,∞ based on the Poisson distribution. Recently R. Mohapatra has generalized Szasz' result to the case in which the approximating function is αe−ux∑k=N∞(uxkα+β−1Γ(kα+βf(kαuThe present note shows that these results are special cases of a Tauberian theorem for certain infinite series having positive coefficients.

  13. Rational approximations for tomographic reconstructions

    International Nuclear Information System (INIS)

    Reynolds, Matthew; Beylkin, Gregory; Monzón, Lucas

    2013-01-01

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

  14. 'LTE-diffusion approximation' for arc calculations

    International Nuclear Information System (INIS)

    Lowke, J J; Tanaka, M

    2006-01-01

    This paper proposes the use of the 'LTE-diffusion approximation' for predicting the properties of electric arcs. Under this approximation, local thermodynamic equilibrium (LTE) is assumed, with a particular mesh size near the electrodes chosen to be equal to the 'diffusion length', based on D e /W, where D e is the electron diffusion coefficient and W is the electron drift velocity. This approximation overcomes the problem that the equilibrium electrical conductivity in the arc near the electrodes is almost zero, which makes accurate calculations using LTE impossible in the limit of small mesh size, as then voltages would tend towards infinity. Use of the LTE-diffusion approximation for a 200 A arc with a thermionic cathode gives predictions of total arc voltage, electrode temperatures, arc temperatures and radial profiles of heat flux density and current density at the anode that are in approximate agreement with more accurate calculations which include an account of the diffusion of electric charges to the electrodes, and also with experimental results. Calculations, which include diffusion of charges, agree with experimental results of current and heat flux density as a function of radius if the Milne boundary condition is used at the anode surface rather than imposing zero charge density at the anode

  15. FULL ELECTROMAGNETIC FEL SIMULATION VIA THE LORENTZ-BOOSTED FRAME TRANSFORMATION

    International Nuclear Information System (INIS)

    Fawley, William; Vay, Jean-Luc

    2010-01-01

    Numerical electromagnetic simulation of some systems containing charged particles with highly relativistic directed motion can by speeded up by orders of magnitude by choice of the proper Lorentz-boosted frame. A particularly good application for calculation in a boosted frame isthat of short wavelength free-electron lasers (FELs) where a high energy electron beam with small fractional energy spread interacts with a static magnetic undulator. In the optimal boost frame (i.e., the ponderomotive rest frame), the red-shifted FEL radiation and blue-shifted undulator field have identical wavelengths and the number of required longitudinal grid cells and time-steps for fully electromagnetic simulation (relative to the laboratory frame) decrease by factors of gamma 2 each. In theory, boosted frame EM codes permit direct study of FEL problems for which the eikonal approximation for propagation of the radiation field and wiggler-period-averaging for the particle-field interaction may be suspect. We have adapted the WARP code to apply this method to several electromagnetic FEL problems including spontaneous emission, strong exponential gain in a seeded, single pass amplifier configuration, and emission from e-beams in undulators with multiple harmonic components. WARP has a standard relativistic macroparticle mover and a fully 3-D electromagnetic field solver. We discuss our boosted frame results and compare with those obtained using the 'standard' eikonal FEL simulation approach.

  16. 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...

  17. Approximations for stop-loss reinsurance premiums

    NARCIS (Netherlands)

    Reijnen, Rajko; Albers, Willem/Wim; Kallenberg, W.C.M.

    2005-01-01

    Various approximations of stop-loss reinsurance premiums are described in literature. For a wide variety of claim size distributions and retention levels, such approximations are compared in this paper to each other, as well as to a quantitative criterion. For the aggregate claims two models are

  18. 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.

  19. Approximation for the adjoint neutron spectrum

    International Nuclear Information System (INIS)

    Suster, Luis Carlos; Martinez, Aquilino Senra; Silva, Fernando Carvalho da

    2002-01-01

    The proposal of this work is the determination of an analytical approximation which is capable to reproduce the adjoint neutron flux for the energy range of the narrow resonances (NR). In a previous work we developed a method for the calculation of the adjoint spectrum which was calculated from the adjoint neutron balance equations, that were obtained by the collision probabilities method, this method involved a considerable quantity of numerical calculation. In the analytical method some approximations were done, like the multiplication of the escape probability in the fuel by the adjoint flux in the moderator, and after these approximations, taking into account the case of the narrow resonances, were substituted in the adjoint neutron balance equation for the fuel, resulting in an analytical approximation for the adjoint flux. The results obtained in this work were compared to the results generated with the reference method, which demonstrated a good and precise results for the adjoint neutron flux for the narrow resonances. (author)

  20. Operator approximant problems arising from quantum theory

    CERN Document Server

    Maher, Philip J

    2017-01-01

    This book offers an account of a number of aspects of operator theory, mainly developed since the 1980s, whose problems have their roots in quantum theory. The research presented is in non-commutative operator approximation theory or, to use Halmos' terminology, in operator approximants. Focusing on the concept of approximants, this self-contained book is suitable for graduate courses.

  1. Non-Linear Approximation of Bayesian Update

    KAUST Repository

    Litvinenko, Alexander

    2016-01-01

    We develop a non-linear approximation of expensive Bayesian formula. This non-linear approximation is applied directly to Polynomial Chaos Coefficients. In this way, we avoid Monte Carlo sampling and sampling error. We can show that the famous Kalman Update formula is a particular case of this update.

  2. Quirks of Stirling's Approximation

    Science.gov (United States)

    Macrae, Roderick M.; Allgeier, Benjamin M.

    2013-01-01

    Stirling's approximation to ln "n"! is typically introduced to physical chemistry students as a step in the derivation of the statistical expression for the entropy. However, naive application of this approximation leads to incorrect conclusions. In this article, the problem is first illustrated using a familiar "toy…

  3. Non-Linear Approximation of Bayesian Update

    KAUST Repository

    Litvinenko, Alexander

    2016-06-23

    We develop a non-linear approximation of expensive Bayesian formula. This non-linear approximation is applied directly to Polynomial Chaos Coefficients. In this way, we avoid Monte Carlo sampling and sampling error. We can show that the famous Kalman Update formula is a particular case of this update.

  4. Approximations to camera sensor noise

    Science.gov (United States)

    Jin, Xiaodan; Hirakawa, Keigo

    2013-02-01

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

  5. Diophantine approximation and Dirichlet series

    CERN Document Server

    Queffélec, Hervé

    2013-01-01

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

  6. APPROXIMATIONS TO PERFORMANCE MEASURES IN QUEUING SYSTEMS

    Directory of Open Access Journals (Sweden)

    Kambo, N. S.

    2012-11-01

    Full Text Available Approximations to various performance measures in queuing systems have received considerable attention because these measures have wide applicability. In this paper we propose two methods to approximate the queuing characteristics of a GI/M/1 system. The first method is non-parametric in nature, using only the first three moments of the arrival distribution. The second method treads the known path of approximating the arrival distribution by a mixture of two exponential distributions by matching the first three moments. Numerical examples and optimal analysis of performance measures of GI/M/1 queues are provided to illustrate the efficacy of the methods, and are compared with benchmark approximations.

  7. Stochastic approximation Monte Carlo importance sampling for approximating exact conditional probabilities

    KAUST Repository

    Cheon, Sooyoung

    2013-02-16

    Importance sampling and Markov chain Monte Carlo methods have been used in exact inference for contingency tables for a long time, however, their performances are not always very satisfactory. In this paper, we propose a stochastic approximation Monte Carlo importance sampling (SAMCIS) method for tackling this problem. SAMCIS is a combination of adaptive Markov chain Monte Carlo and importance sampling, which employs the stochastic approximation Monte Carlo algorithm (Liang et al., J. Am. Stat. Assoc., 102(477):305-320, 2007) to draw samples from an enlarged reference set with a known Markov basis. Compared to the existing importance sampling and Markov chain Monte Carlo methods, SAMCIS has a few advantages, such as fast convergence, ergodicity, and the ability to achieve a desired proportion of valid tables. The numerical results indicate that SAMCIS can outperform the existing importance sampling and Markov chain Monte Carlo methods: It can produce much more accurate estimates in much shorter CPU time than the existing methods, especially for the tables with high degrees of freedom. © 2013 Springer Science+Business Media New York.

  8. Stochastic approximation Monte Carlo importance sampling for approximating exact conditional probabilities

    KAUST Repository

    Cheon, Sooyoung; Liang, Faming; Chen, Yuguo; Yu, Kai

    2013-01-01

    Importance sampling and Markov chain Monte Carlo methods have been used in exact inference for contingency tables for a long time, however, their performances are not always very satisfactory. In this paper, we propose a stochastic approximation Monte Carlo importance sampling (SAMCIS) method for tackling this problem. SAMCIS is a combination of adaptive Markov chain Monte Carlo and importance sampling, which employs the stochastic approximation Monte Carlo algorithm (Liang et al., J. Am. Stat. Assoc., 102(477):305-320, 2007) to draw samples from an enlarged reference set with a known Markov basis. Compared to the existing importance sampling and Markov chain Monte Carlo methods, SAMCIS has a few advantages, such as fast convergence, ergodicity, and the ability to achieve a desired proportion of valid tables. The numerical results indicate that SAMCIS can outperform the existing importance sampling and Markov chain Monte Carlo methods: It can produce much more accurate estimates in much shorter CPU time than the existing methods, especially for the tables with high degrees of freedom. © 2013 Springer Science+Business Media New York.

  9. Approximate Bayesian evaluations of measurement uncertainty

    Science.gov (United States)

    Possolo, Antonio; Bodnar, Olha

    2018-04-01

    The Guide to the Expression of Uncertainty in Measurement (GUM) includes formulas that produce an estimate of a scalar output quantity that is a function of several input quantities, and an approximate evaluation of the associated standard uncertainty. This contribution presents approximate, Bayesian counterparts of those formulas for the case where the output quantity is a parameter of the joint probability distribution of the input quantities, also taking into account any information about the value of the output quantity available prior to measurement expressed in the form of a probability distribution on the set of possible values for the measurand. The approximate Bayesian estimates and uncertainty evaluations that we present have a long history and illustrious pedigree, and provide sufficiently accurate approximations in many applications, yet are very easy to implement in practice. Differently from exact Bayesian estimates, which involve either (analytical or numerical) integrations, or Markov Chain Monte Carlo sampling, the approximations that we describe involve only numerical optimization and simple algebra. Therefore, they make Bayesian methods widely accessible to metrologists. We illustrate the application of the proposed techniques in several instances of measurement: isotopic ratio of silver in a commercial silver nitrate; odds of cryptosporidiosis in AIDS patients; height of a manometer column; mass fraction of chromium in a reference material; and potential-difference in a Zener voltage standard.

  10. Improved radiative corrections for (e,e'p) experiments: Beyond the peaking approximation and implications of the soft-photon approximation

    International Nuclear Information System (INIS)

    Weissbach, F.; Hencken, K.; Rohe, D.; Sick, I.; Trautmann, D.

    2006-01-01

    Analyzing (e,e ' p) experimental data involves corrections for radiative effects which change the interaction kinematics and which have to be carefully considered in order to obtain the desired accuracy. Missing momentum and energy due to bremsstrahlung have so far often been incorporated into the simulations and the experimental analyses using the peaking approximation. It assumes that all bremsstrahlung is emitted in the direction of the radiating particle. In this article we introduce a full angular Monte Carlo simulation method which overcomes this approximation. As a test, the angular distribution of the bremsstrahlung photons is reconstructed from H(e,e ' p) data. Its width is found to be underestimated by the peaking approximation and described much better by the approach developed in this work. The impact of the soft-photon approximation on the photon angular distribution is found to be minor as compared to the impact of the peaking approximation. (orig.)

  11. Trajectory averaging for stochastic approximation MCMC algorithms

    KAUST Repository

    Liang, Faming

    2010-10-01

    The subject of stochastic approximation was founded by Robbins and Monro [Ann. Math. Statist. 22 (1951) 400-407]. After five decades of continual development, it has developed into an important area in systems control and optimization, and it has also served as a prototype for the development of adaptive algorithms for on-line estimation and control of stochastic systems. Recently, it has been used in statistics with Markov chain Monte Carlo for solving maximum likelihood estimation problems and for general simulation and optimizations. In this paper, we first show that the trajectory averaging estimator is asymptotically efficient for the stochastic approximation MCMC (SAMCMC) algorithm under mild conditions, and then apply this result to the stochastic approximation Monte Carlo algorithm [Liang, Liu and Carroll J. Amer. Statist. Assoc. 102 (2007) 305-320]. The application of the trajectory averaging estimator to other stochastic approximationMCMC algorithms, for example, a stochastic approximation MLE algorithm for missing data problems, is also considered in the paper. © Institute of Mathematical Statistics, 2010.

  12. Toward a consistent random phase approximation based on the relativistic Hartree approximation

    International Nuclear Information System (INIS)

    Price, C.E.; Rost, E.; Shepard, J.R.; McNeil, J.A.

    1992-01-01

    We examine the random phase approximation (RPA) based on a relativistic Hartree approximation description for nuclear ground states. This model includes contributions from the negative energy sea at the one-loop level. We emphasize consistency between the treatment of the ground state and the RPA. This consistency is important in the description of low-lying collective levels but less important for the longitudinal (e,e') quasielastic response. We also study the effect of imposing a three-momentum cutoff on negative energy sea contributions. A cutoff of twice the nucleon mass improves agreement with observed spin-orbit splittings in nuclei compared to the standard infinite cutoff results, an effect traceable to the fact that imposing the cutoff reduces m * /m. Consistency is much more important than the cutoff in the description of low-lying collective levels. The cutoff model also provides excellent agreement with quasielastic (e,e') data

  13. Seismic wave extrapolation using lowrank symbol approximation

    KAUST Repository

    Fomel, Sergey

    2012-04-30

    We consider the problem of constructing a wave extrapolation operator in a variable and possibly anisotropic medium. Our construction involves Fourier transforms in space combined with the help of a lowrank approximation of the space-wavenumber wave-propagator matrix. A lowrank approximation implies selecting a small set of representative spatial locations and a small set of representative wavenumbers. We present a mathematical derivation of this method, a description of the lowrank approximation algorithm and numerical examples that confirm the validity of the proposed approach. Wave extrapolation using lowrank approximation can be applied to seismic imaging by reverse-time migration in 3D heterogeneous isotropic or anisotropic media. © 2012 European Association of Geoscientists & Engineers.

  14. Approximation algorithms for guarding holey polygons ...

    African Journals Online (AJOL)

    Guarding edges of polygons is a version of art gallery problem.The goal is finding the minimum number of guards to cover the edges of a polygon. This problem is NP-hard, and to our knowledge there are approximation algorithms just for simple polygons. In this paper we present two approximation algorithms for guarding ...

  15. Approximation properties of fine hyperbolic graphs

    Indian Academy of Sciences (India)

    2010 Mathematics Subject Classification. 46L07. 1. Introduction. Given a countable discrete group G, some nice approximation properties for the reduced. C∗-algebras C∗ r (G) can give us the approximation properties of G. For example, Lance. [7] proved that the nuclearity of C∗ r (G) is equivalent to the amenability of G; ...

  16. Approximate number word knowledge before the cardinal principle.

    Science.gov (United States)

    Gunderson, Elizabeth A; Spaepen, Elizabet; Levine, Susan C

    2015-02-01

    Approximate number word knowledge-understanding the relation between the count words and the approximate magnitudes of sets-is a critical piece of knowledge that predicts later math achievement. However, researchers disagree about when children first show evidence of approximate number word knowledge-before, or only after, they have learned the cardinal principle. In two studies, children who had not yet learned the cardinal principle (subset-knowers) produced sets in response to number words (verbal comprehension task) and produced number words in response to set sizes (verbal production task). As evidence of approximate number word knowledge, we examined whether children's numerical responses increased with increasing numerosity of the stimulus. In Study 1, subset-knowers (ages 3.0-4.2 years) showed approximate number word knowledge above their knower-level on both tasks, but this effect did not extend to numbers above 4. In Study 2, we collected data from a broader age range of subset-knowers (ages 3.1-5.6 years). In this sample, children showed approximate number word knowledge on the verbal production task even when only examining set sizes above 4. Across studies, children's age predicted approximate number word knowledge (above 4) on the verbal production task when controlling for their knower-level, study (1 or 2), and parents' education, none of which predicted approximation ability. Thus, children can develop approximate knowledge of number words up to 10 before learning the cardinal principle. Furthermore, approximate number word knowledge increases with age and might not be closely related to the development of exact number word knowledge. Copyright © 2014 Elsevier Inc. All rights reserved.

  17. 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.

  18. Pawlak algebra and approximate structure on fuzzy lattice.

    Science.gov (United States)

    Zhuang, Ying; Liu, Wenqi; Wu, Chin-Chia; Li, Jinhai

    2014-01-01

    The aim of this paper is to investigate the general approximation structure, weak approximation operators, and Pawlak algebra in the framework of fuzzy lattice, lattice topology, and auxiliary ordering. First, we prove that the weak approximation operator space forms a complete distributive lattice. Then we study the properties of transitive closure of approximation operators and apply them to rough set theory. We also investigate molecule Pawlak algebra and obtain some related properties.

  19. ENERGY RELAXATION OF HELIUM ATOMS IN ASTROPHYSICAL GASES

    International Nuclear Information System (INIS)

    Lewkow, N. R.; Kharchenko, V.; Zhang, P.

    2012-01-01

    We report accurate parameters describing energy relaxation of He atoms in atomic gases, important for astrophysics and atmospheric science. Collisional energy exchange between helium atoms and atomic constituents of the interstellar gas, heliosphere, and upper planetary atmosphere has been investigated. Energy transfer rates, number of collisions required for thermalization, energy distributions of recoil atoms, and other major parameters of energy relaxation for fast He atoms in thermal H, He, and O gases have been computed in a broad interval of energies from 10 meV to 10 keV. This energy interval is important for astrophysical applications involving the energy deposition of energetic atoms and ions into atmospheres of planets and exoplanets, atmospheric evolution, and analysis of non-equilibrium processes in the interstellar gas and heliosphere. Angular- and energy-dependent cross sections, required for an accurate description of the momentum-energy transfer, are obtained using ab initio interaction potentials and quantum mechanical calculations for scattering processes. Calculation methods used include partial wave analysis for collisional energies below 2 keV and the eikonal approximation at energies higher than 100 eV, keeping a significant energy region of overlap, 0.1-2 keV, between these two methods for their mutual verification. The partial wave method and the eikonal approximation excellently match results obtained with each other as well as experimental data, providing reliable cross sections in the astrophysically important interval of energies from 10 meV to 10 keV. Analytical formulae, interpolating obtained energy- and angular-dependent cross sections, are presented to simplify potential applications of the reported database. Thermalization of fast He atoms in the interstellar gas and energy relaxation of hot He and O atoms in the upper atmosphere of Mars are considered as illustrative examples of potential applications of the new database.

  20. Dynamical cluster approximation plus semiclassical approximation study for a Mott insulator and d-wave pairing

    Science.gov (United States)

    Kim, SungKun; Lee, Hunpyo

    2017-06-01

    Via a dynamical cluster approximation with N c = 4 in combination with a semiclassical approximation (DCA+SCA), we study the doped two-dimensional Hubbard model. We obtain a plaquette antiferromagnetic (AF) Mott insulator, a plaquette AF ordered metal, a pseudogap (or d-wave superconductor) and a paramagnetic metal by tuning the doping concentration. These features are similar to the behaviors observed in copper-oxide superconductors and are in qualitative agreement with the results calculated by the cluster dynamical mean field theory with the continuous-time quantum Monte Carlo (CDMFT+CTQMC) approach. The results of our DCA+SCA differ from those of the CDMFT+CTQMC approach in that the d-wave superconducting order parameters are shown even in the high doped region, unlike the results of the CDMFT+CTQMC approach. We think that the strong plaquette AF orderings in the dynamical cluster approximation (DCA) with N c = 4 suppress superconducting states with increasing doping up to strongly doped region, because frozen dynamical fluctuations in a semiclassical approximation (SCA) approach are unable to destroy those orderings. Our calculation with short-range spatial fluctuations is initial research, because the SCA can manage long-range spatial fluctuations in feasible computational times beyond the CDMFT+CTQMC tool. We believe that our future DCA+SCA calculations should supply information on the fully momentum-resolved physical properties, which could be compared with the results measured by angle-resolved photoemission spectroscopy experiments.

  1. Nuclear Cross Sections for Space Radiation Applications

    Science.gov (United States)

    Werneth, C. M.; Maung, K. M.; Ford, W. P.; Norbury, J. W.; Vera, M. D.

    2015-01-01

    The eikonal, partial wave (PW) Lippmann-Schwinger, and three-dimensional Lippmann-Schwinger (LS3D) methods are compared for nuclear reactions that are relevant for space radiation applications. Numerical convergence of the eikonal method is readily achieved when exact formulas of the optical potential are used for light nuclei (A = 16) and the momentum-space optical potential is used for heavier nuclei. The PW solution method is known to be numerically unstable for systems that require a large number of partial waves, and, as a result, the LS3D method is employed. The effect of relativistic kinematics is studied with the PW and LS3D methods and is compared to eikonal results. It is recommended that the LS3D method be used for high energy nucleon-nucleus reactions and nucleus-nucleus reactions at all energies because of its rapid numerical convergence and stability for both non-relativistic and relativistic kinematics.

  2. Methods of Fourier analysis and approximation theory

    CERN Document Server

    Tikhonov, Sergey

    2016-01-01

    Different facets of interplay between harmonic analysis and approximation theory are covered in this volume. The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first event took place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August 2013, at the section “Approximation Theory and Fourier Analysis”. The second event was the conference on Fourier Analysis and Approximation Theory in the Centre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013, organized by the editors of this volume. All articles selected to be part of this collection were carefully reviewed.

  3. Optimization and approximation

    CERN Document Server

    Pedregal, Pablo

    2017-01-01

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

  4. Uniform analytic approximation of Wigner rotation matrices

    Science.gov (United States)

    Hoffmann, Scott E.

    2018-02-01

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

  5. Multilevel Monte Carlo in Approximate Bayesian Computation

    KAUST Repository

    Jasra, Ajay

    2017-02-13

    In the following article we consider approximate Bayesian computation (ABC) inference. We introduce a method for numerically approximating ABC posteriors using the multilevel Monte Carlo (MLMC). A sequential Monte Carlo version of the approach is developed and it is shown under some assumptions that for a given level of mean square error, this method for ABC has a lower cost than i.i.d. sampling from the most accurate ABC approximation. Several numerical examples are given.

  6. Approximation Properties of Certain Summation Integral Type Operators

    Directory of Open Access Journals (Sweden)

    Patel P.

    2015-03-01

    Full Text Available In the present paper, we study approximation properties of a family of linear positive operators and establish direct results, asymptotic formula, rate of convergence, weighted approximation theorem, inverse theorem and better approximation for this family of linear positive operators.

  7. Semiclassical initial value approximation for Green's function.

    Science.gov (United States)

    Kay, Kenneth G

    2010-06-28

    A semiclassical initial value approximation is obtained for the energy-dependent Green's function. For a system with f degrees of freedom the Green's function expression has the form of a (2f-1)-dimensional integral over points on the energy surface and an integral over time along classical trajectories initiated from these points. This approximation is derived by requiring an integral ansatz for Green's function to reduce to Gutzwiller's semiclassical formula when the integrations are performed by the stationary phase method. A simpler approximation is also derived involving only an (f-1)-dimensional integral over momentum variables on a Poincare surface and an integral over time. The relationship between the present expressions and an earlier initial value approximation for energy eigenfunctions is explored. Numerical tests for two-dimensional systems indicate that good accuracy can be obtained from the initial value Green's function for calculations of autocorrelation spectra and time-independent wave functions. The relative advantages of initial value approximations for the energy-dependent Green's function and the time-dependent propagator are discussed.

  8. The adiabatic approximation in multichannel scattering

    International Nuclear Information System (INIS)

    Schulte, A.M.

    1978-01-01

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

  9. Minimal entropy approximation for cellular automata

    International Nuclear Information System (INIS)

    Fukś, Henryk

    2014-01-01

    We present a method for the construction of approximate orbits of measures under the action of cellular automata which is complementary to the local structure theory. The local structure theory is based on the idea of Bayesian extension, that is, construction of a probability measure consistent with given block probabilities and maximizing entropy. If instead of maximizing entropy one minimizes it, one can develop another method for the construction of approximate orbits, at the heart of which is the iteration of finite-dimensional maps, called minimal entropy maps. We present numerical evidence that the minimal entropy approximation sometimes outperforms the local structure theory in characterizing the properties of cellular automata. The density response curve for elementary CA rule 26 is used to illustrate this claim. (paper)

  10. Function approximation using combined unsupervised and supervised learning.

    Science.gov (United States)

    Andras, Peter

    2014-03-01

    Function approximation is one of the core tasks that are solved using neural networks in the context of many engineering problems. However, good approximation results need good sampling of the data space, which usually requires exponentially increasing volume of data as the dimensionality of the data increases. At the same time, often the high-dimensional data is arranged around a much lower dimensional manifold. Here we propose the breaking of the function approximation task for high-dimensional data into two steps: (1) the mapping of the high-dimensional data onto a lower dimensional space corresponding to the manifold on which the data resides and (2) the approximation of the function using the mapped lower dimensional data. We use over-complete self-organizing maps (SOMs) for the mapping through unsupervised learning, and single hidden layer neural networks for the function approximation through supervised learning. We also extend the two-step procedure by considering support vector machines and Bayesian SOMs for the determination of the best parameters for the nonlinear neurons in the hidden layer of the neural networks used for the function approximation. We compare the approximation performance of the proposed neural networks using a set of functions and show that indeed the neural networks using combined unsupervised and supervised learning outperform in most cases the neural networks that learn the function approximation using the original high-dimensional data.

  11. Hardness and Approximation for Network Flow Interdiction

    OpenAIRE

    Chestnut, Stephen R.; Zenklusen, Rico

    2015-01-01

    In the Network Flow Interdiction problem an adversary attacks a network in order to minimize the maximum s-t-flow. Very little is known about the approximatibility of this problem despite decades of interest in it. We present the first approximation hardness, showing that Network Flow Interdiction and several of its variants cannot be much easier to approximate than Densest k-Subgraph. In particular, any $n^{o(1)}$-approximation algorithm for Network Flow Interdiction would imply an $n^{o(1)}...

  12. Approximate reasoning in physical systems

    International Nuclear Information System (INIS)

    Mutihac, R.

    1991-01-01

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

  13. Face Recognition using Approximate Arithmetic

    DEFF Research Database (Denmark)

    Marso, Karol

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

  14. Double differential distributions of electron emission in ion-atom and electron-atom collisions using an electron spectrometer

    International Nuclear Information System (INIS)

    Misra, Deepankar; Thulasiram, K.V.; Fernandes, W.; Kelkar, Aditya H.; Kadhane, U.; Kumar, Ajay; Singh, Yeshpal; Gulyas, L.; Tribedi, Lokesh C.

    2009-01-01

    We study electron emission from atoms and molecules in collisions with fast electrons and heavy ions (C 6+ ). The soft collision electrons (SE), two center electron emission (TCEE), the binary encounter (BE) events and the KLL Auger lines along with the elastically scattered peaks (in electron collisions) are studied using a hemispherical electrostatic electron analyzer. The details of the measurements along with description of the spectrometer and data acquisition system are given. The angular distributions of the low energy (few eV) electrons in soft collisions and the binary encounter electrons at keV energies are compared with quantum mechanical models based on the first Born (B1) and the continuum distorted wave-Eikonal initial state approximation (CDW-EIS).

  15. Soft hadronic production by ECCO in the geometrical branching model

    International Nuclear Information System (INIS)

    Pan, J.; Hwa, R.C.

    1993-01-01

    Soft production of hadrons in hadronic collisions is described in the geometrical branching model and implemented by the eikonal cascade code (ECCO). It is shown that the major global features of multiparticle production can be reproduced by one essential characterization of the dynamics of branching, namely, a scaling law for the mass distribution of daughter clusters. Without further adjustment of any parameters, the event generator can produce local features of multiplicity fluctuations in agreement with the NA22 intermittency data. The scaling exponent ν is determined to be 1.522 at √s =22 GeV, independent of the dimensionality of the intermittency analysis. It is shown that ν is approximately independent of the collision energy

  16. Unitary screening corrections in high energy hadron reactions

    Energy Technology Data Exchange (ETDEWEB)

    Maor, U

    1994-10-01

    The role of s-channel unitarity screening corrections, calculated in the eikonal approximation, is investigated for elastic and diffractive hadron-hadron and photon-hadron scattering in the energy limit. We examine the differences between our results and those obtained from the supercritical Pomeron-Reggeon model with no such corrections. It is argued that the saturation of cross sections is attained at different scales for different channels. In particular, we point out that whereas the saturation scale for elastic scattering apparently above the Tevatron energy range, the appropriate diffraction scale is considerably lower and can be assessed with presently available data. A review of the relevant data and its implications is presented. (author). 12 refs, 3 figs, 2 tabs.

  17. Next-to-soft corrections to high energy scattering in QCD and gravity

    Energy Technology Data Exchange (ETDEWEB)

    Luna, A.; Melville, S. [SUPA, School of Physics and Astronomy, University of Glasgow,Glasgow G12 8QQ, Scotland (United Kingdom); Naculich, S.G. [Department of Physics, Bowdoin College,Brunswick, ME 04011 (United States); White, C.D. [Centre for Research in String Theory, School of Physics and Astronomy,Queen Mary University of London,327 Mile End Road, London E1 4NS (United Kingdom)

    2017-01-12

    We examine the Regge (high energy) limit of 4-point scattering in both QCD and gravity, using recently developed techniques to systematically compute all corrections up to next-to-leading power in the exchanged momentum i.e. beyond the eikonal approximation. We consider the situation of two scalar particles of arbitrary mass, thus generalising previous calculations in the literature. In QCD, our calculation describes power-suppressed corrections to the Reggeisation of the gluon. In gravity, we confirm a previous conjecture that next-to-soft corrections correspond to two independent deflection angles for the incoming particles. Our calculations in QCD and gravity are consistent with the well-known double copy relating amplitudes in the two theories.

  18. Spatially varying index of refraction: An open ended undergraduate topic

    International Nuclear Information System (INIS)

    Krueger, D.A.

    1980-01-01

    There are many commonplace examples of waves moving along a curved path in an inhomogeneous media. There are reports of a simple lecture demonstration of light bending in a sugar solution being used to motivate students in physics, geophysics, and acoustics courses. For those students who wish to pursue this topic we discuss many avenues of additional research. With relatively simple equipment one can measure the index of refraction n (y,t) and its first and second spatial derivatives as well as the time dependence. The analysis can be approached from a generalization of Snell's law, the equations for the eikonal, Fermat's principle, and the classical approximation and analogies with trajectories of particles

  19. Total and inelastic cross-sections at LHC at CM energy of 7 TeV and beyond

    CERN Document Server

    Achilli, Andrea; Grau, Agnes; Pancheri, Giulia; Shekhovtsova, Olga; Srivastava, Yogendra N

    2011-01-01

    We discuss expectations for the total and inelastic cross-sections at LHC CM energies $\\sqrt{s}\\ =\\ 7\\ TeV$ {and $ 14\\ TeV$} obtained in an eikonal minijet model augmented by soft gluon $k_t$-resummation, which we describe in some detail. We present a band of predictions which encompass recent LHC data and suggest that the inelastic cross-section described by two channel eikonal models include only uncorrelated processes. We show that this interpretation of the model is supported by the LHC data.

  20. Stochastic quantization and mean field approximation

    International Nuclear Information System (INIS)

    Jengo, R.; Parga, N.

    1983-09-01

    In the context of the stochastic quantization we propose factorized approximate solutions for the Fokker-Planck equation for the XY and Zsub(N) spin systems in D dimensions. The resulting differential equation for a factor can be solved and it is found to give in the limit of t→infinity the mean field or, in the more general case, the Bethe-Peierls approximation. (author)

  1. Approximative solutions of stochastic optimization problem

    Czech Academy of Sciences Publication Activity Database

    Lachout, Petr

    2010-01-01

    Roč. 46, č. 3 (2010), s. 513-523 ISSN 0023-5954 R&D Projects: GA ČR GA201/08/0539 Institutional research plan: CEZ:AV0Z10750506 Keywords : Stochastic optimization problem * sensitivity * approximative solution Subject RIV: BA - General Mathematics Impact factor: 0.461, year: 2010 http://library.utia.cas.cz/separaty/2010/SI/lachout-approximative solutions of stochastic optimization problem.pdf

  2. Trajectory averaging for stochastic approximation MCMC algorithms

    KAUST Repository

    Liang, Faming

    2010-01-01

    to the stochastic approximation Monte Carlo algorithm [Liang, Liu and Carroll J. Amer. Statist. Assoc. 102 (2007) 305-320]. The application of the trajectory averaging estimator to other stochastic approximationMCMC algorithms, for example, a stochastic

  3. Reduction of Linear Programming to Linear Approximation

    OpenAIRE

    Vaserstein, Leonid N.

    2006-01-01

    It is well known that every Chebyshev linear approximation problem can be reduced to a linear program. In this paper we show that conversely every linear program can be reduced to a Chebyshev linear approximation problem.

  4. Thin-wall approximation in vacuum decay: A lemma

    Science.gov (United States)

    Brown, Adam R.

    2018-05-01

    The "thin-wall approximation" gives a simple estimate of the decay rate of an unstable quantum field. Unfortunately, the approximation is uncontrolled. In this paper I show that there are actually two different thin-wall approximations and that they bracket the true decay rate: I prove that one is an upper bound and the other a lower bound. In the thin-wall limit, the two approximations converge. In the presence of gravity, a generalization of this lemma provides a simple sufficient condition for nonperturbative vacuum instability.

  5. The dynamics of the quasielastic 16O(e,e'p) reaction at Q2 = 0.8 (GeV/c)2

    International Nuclear Information System (INIS)

    Fissum, Kevin

    2004-01-01

    The physics program in Hall A at Jefferson Lab commenced in the summer of 1997 with a detailed investigation of the 16O(e,e'p) reaction in quasielastic, constant (q,w) kinematics at Q 2 ∼ 0.8 (GeV/c) 2 , q ∼ 1 GeV/c, and w ∼ 445 MeV. Use of a self-calibrating, self-normalizing, thin-film waterfall target enabled a systematically rigorous measurement. Differential cross-section data for proton knockout were obtained for 0 < Emiss < 120 MeV and 0 < pmiss < 350 MeV/c. These results have been used to extract the ALT asymmetry and the RL, RT, RLT, and RL+TT effective response functions. Detailed comparisons of the data with Relativistic Distorted-Wave Impulse Approximation, Relativistic Optical-Model Eikonal Approximation, and Relativistic Multiple-Scattering Glauber Approximation calculations are made. The kinematic consistency of the 1p-shell normalization factors extracted from these data with respect to all available 16O(e,e'p) data is examined. The Q2-dependence of the normalization factors is also discussed

  6. CDW-EIS calculations for multiple ionization of Ne, Ar, Kr and Xe by the impact of H{sup +} and He{sup +}, including post-collisional electron emission

    Energy Technology Data Exchange (ETDEWEB)

    Montanari, C C; Miraglia, J E [Instituto de AstronomIa y FIsica del Espacio, casilla de correo 67, sucursal 28, C1428EGA, Buenos Aires (Argentina); Montenegro, E C, E-mail: mclaudia@iafe.uba.a [Instituto de FIsica, Universidade Federal de Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro 21945-970, RJ (Brazil)

    2010-08-28

    We present theoretical single to quintuple ionization cross sections for Ne, Ar, Kr and Xe bombarded by H{sup +} and He{sup +}. Post-collisional contributions due to Auger-like processes are taken into account using recent photoionization data. The present continuum distorted wave-eikonal initial state (CDW-EIS) and first Born approximation results are compared with the experimental data available in the energy range of 50-10 000 keV amu{sup -1} for H{sup +} on Ne and Ar, and 50-1000 keV amu{sup -1} for the other cases. In general, the combination of the CDW-EIS with the post-collisional branching ratios describes well the multiple ionization data above 300 keV amu{sup -1}, showing a clear tendency to coalesce with the first Born approximation at high energies. The surprising result of this work is the good performance of the first Born approximation which describes rather well the experimental data of double and triple ionization, even in the intermediate energy range (50-300 keV amu{sup -1}), where direct ionization is the dominant contribution.

  7. Smooth function approximation using neural networks.

    Science.gov (United States)

    Ferrari, Silvia; Stengel, Robert F

    2005-01-01

    An algebraic approach for representing multidimensional nonlinear functions by feedforward neural networks is presented. In this paper, the approach is implemented for the approximation of smooth batch data containing the function's input, output, and possibly, gradient information. The training set is associated to the network adjustable parameters by nonlinear weight equations. The cascade structure of these equations reveals that they can be treated as sets of linear systems. Hence, the training process and the network approximation properties can be investigated via linear algebra. Four algorithms are developed to achieve exact or approximate matching of input-output and/or gradient-based training sets. Their application to the design of forward and feedback neurocontrollers shows that algebraic training is characterized by faster execution speeds and better generalization properties than contemporary optimization techniques.

  8. An improved saddlepoint approximation.

    Science.gov (United States)

    Gillespie, Colin S; Renshaw, Eric

    2007-08-01

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

  9. Topology, calculus and approximation

    CERN Document Server

    Komornik, Vilmos

    2017-01-01

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

  10. Comparison of four support-vector based function approximators

    NARCIS (Netherlands)

    de Kruif, B.J.; de Vries, Theodorus J.A.

    2004-01-01

    One of the uses of the support vector machine (SVM), as introduced in V.N. Vapnik (2000), is as a function approximator. The SVM and approximators based on it, approximate a relation in data by applying interpolation between so-called support vectors, being a limited number of samples that have been

  11. Coefficients Calculation in Pascal Approximation for Passive Filter Design

    Directory of Open Access Journals (Sweden)

    George B. Kasapoglu

    2018-02-01

    Full Text Available The recently modified Pascal function is further exploited in this paper in the design of passive analog filters. The Pascal approximation has non-equiripple magnitude, in contrast of the most well-known approximations, such as the Chebyshev approximation. A novelty of this work is the introduction of a precise method that calculates the coefficients of the Pascal function. Two examples are presented for the passive design to illustrate the advantages and the disadvantages of the Pascal approximation. Moreover, the values of the passive elements can be taken from tables, which are created to define the normalized values of these elements for the Pascal approximation, as Zverev had done for the Chebyshev, Elliptic, and other approximations. Although Pascal approximation can be implemented to both passive and active filter designs, a passive filter design is addressed in this paper, and the benefits and shortcomings of Pascal approximation are presented and discussed.

  12. Recursive B-spline approximation using the Kalman filter

    Directory of Open Access Journals (Sweden)

    Jens Jauch

    2017-02-01

    Full Text Available This paper proposes a novel recursive B-spline approximation (RBA algorithm which approximates an unbounded number of data points with a B-spline function and achieves lower computational effort compared with previous algorithms. Conventional recursive algorithms based on the Kalman filter (KF restrict the approximation to a bounded and predefined interval. Conversely RBA includes a novel shift operation that enables to shift estimated B-spline coefficients in the state vector of a KF. This allows to adapt the interval in which the B-spline function can approximate data points during run-time.

  13. Approximate Computing Techniques for Iterative Graph Algorithms

    Energy Technology Data Exchange (ETDEWEB)

    Panyala, Ajay R.; Subasi, Omer; Halappanavar, Mahantesh; Kalyanaraman, Anantharaman; Chavarria Miranda, Daniel G.; Krishnamoorthy, Sriram

    2017-12-18

    Approximate computing enables processing of large-scale graphs by trading off quality for performance. Approximate computing techniques have become critical not only due to the emergence of parallel architectures but also the availability of large scale datasets enabling data-driven discovery. Using two prototypical graph algorithms, PageRank and community detection, we present several approximate computing heuristics to scale the performance with minimal loss of accuracy. We present several heuristics including loop perforation, data caching, incomplete graph coloring and synchronization, and evaluate their efficiency. We demonstrate performance improvements of up to 83% for PageRank and up to 450x for community detection, with low impact of accuracy for both the algorithms. We expect the proposed approximate techniques will enable scalable graph analytics on data of importance to several applications in science and their subsequent adoption to scale similar graph algorithms.

  14. Conditional Density Approximations with Mixtures of Polynomials

    DEFF Research Database (Denmark)

    Varando, Gherardo; López-Cruz, Pedro L.; Nielsen, Thomas Dyhre

    2015-01-01

    Mixtures of polynomials (MoPs) are a non-parametric density estimation technique especially designed for hybrid Bayesian networks with continuous and discrete variables. Algorithms to learn one- and multi-dimensional (marginal) MoPs from data have recently been proposed. In this paper we introduce...... two methods for learning MoP approximations of conditional densities from data. Both approaches are based on learning MoP approximations of the joint density and the marginal density of the conditioning variables, but they differ as to how the MoP approximation of the quotient of the two densities...

  15. Mathematical analysis, approximation theory and their applications

    CERN Document Server

    Gupta, Vijay

    2016-01-01

    Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.

  16. On Love's approximation for fluid-filled elastic tubes

    International Nuclear Information System (INIS)

    Caroli, E.; Mainardi, F.

    1980-01-01

    A simple procedure is set up to introduce Love's approximation for wave propagation in thin-walled fluid-filled elastic tubes. The dispersion relation for linear waves and the radial profile for fluid pressure are determined in this approximation. It is shown that the Love approximation is valid in the low-frequency regime. (author)

  17. WKB approximation in atomic physics

    International Nuclear Information System (INIS)

    Karnakov, Boris Mikhailovich

    2013-01-01

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

  18. SFU-driven transparent approximation acceleration on GPUs

    NARCIS (Netherlands)

    Li, A.; Song, S.L.; Wijtvliet, M.; Kumar, A.; Corporaal, H.

    2016-01-01

    Approximate computing, the technique that sacrifices certain amount of accuracy in exchange for substantial performance boost or power reduction, is one of the most promising solutions to enable power control and performance scaling towards exascale. Although most existing approximation designs

  19. Approximate Networking for Universal Internet Access

    Directory of Open Access Journals (Sweden)

    Junaid Qadir

    2017-12-01

    Full Text Available Despite the best efforts of networking researchers and practitioners, an ideal Internet experience is inaccessible to an overwhelming majority of people the world over, mainly due to the lack of cost-efficient ways of provisioning high-performance, global Internet. In this paper, we argue that instead of an exclusive focus on a utopian goal of universally accessible “ideal networking” (in which we have a high throughput and quality of service as well as low latency and congestion, we should consider providing “approximate networking” through the adoption of context-appropriate trade-offs. In this regard, we propose to leverage the advances in the emerging trend of “approximate computing” that rely on relaxing the bounds of precise/exact computing to provide new opportunities for improving the area, power, and performance efficiency of systems by orders of magnitude by embracing output errors in resilient applications. Furthermore, we propose to extend the dimensions of approximate computing towards various knobs available at network layers. Approximate networking can be used to provision “Global Access to the Internet for All” (GAIA in a pragmatically tiered fashion, in which different users around the world are provided a different context-appropriate (but still contextually functional Internet experience.

  20. Variational Gaussian approximation for Poisson data

    Science.gov (United States)

    Arridge, Simon R.; Ito, Kazufumi; Jin, Bangti; Zhang, Chen

    2018-02-01

    The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback-Leibler divergence from the posterior distribution to the approximation, or equivalently maximizing the lower bound for the model evidence. We derive an explicit expression for the lower bound, and show the existence and uniqueness of the optimal Gaussian approximation. The lower bound functional can be viewed as a variant of classical Tikhonov regularization that penalizes also the covariance. Then we develop an efficient alternating direction maximization algorithm for solving the optimization problem, and analyze its convergence. We discuss strategies for reducing the computational complexity via low rank structure of the forward operator and the sparsity of the covariance. Further, as an application of the lower bound, we discuss hierarchical Bayesian modeling for selecting the hyperparameter in the prior distribution, and propose a monotonically convergent algorithm for determining the hyperparameter. We present extensive numerical experiments to illustrate the Gaussian approximation and the algorithms.

  1. Approximation in two-stage stochastic integer programming

    NARCIS (Netherlands)

    W. Romeijnders; L. Stougie (Leen); M. van der Vlerk

    2014-01-01

    htmlabstractApproximation algorithms are the prevalent solution methods in the field of stochastic programming. Problems in this field are very hard to solve. Indeed, most of the research in this field has concentrated on designing solution methods that approximate the optimal solution value.

  2. Approximation in two-stage stochastic integer programming

    NARCIS (Netherlands)

    Romeijnders, W.; Stougie, L.; van der Vlerk, M.H.

    2014-01-01

    Approximation algorithms are the prevalent solution methods in the field of stochastic programming. Problems in this field are very hard to solve. Indeed, most of the research in this field has concentrated on designing solution methods that approximate the optimal solution value. However,

  3. Magnus approximation in the adiabatic picture

    International Nuclear Information System (INIS)

    Klarsfeld, S.; Oteo, J.A.

    1991-01-01

    A simple approximate nonperturbative method is described for treating time-dependent problems that works well in the intermediate regime far from both the sudden and the adiabatic limits. The method consists of applying the Magnus expansion after transforming to the adiabatic basis defined by the eigenstates of the instantaneous Hamiltonian. A few exactly soluble examples are considered in order to assess the domain of validity of the approximation. (author) 32 refs., 4 figs

  4. Space-efficient path-reporting approximate distance oracles

    DEFF Research Database (Denmark)

    Elkin, Michael; Neiman, Ofer; Wulff-Nilsen, Christian

    2016-01-01

    We consider approximate path-reporting distance oracles, distance labeling and labeled routing with extremely low space requirements, for general undirected graphs. For distance oracles, we show how to break the nlog⁡n space bound of Thorup and Zwick if approximate paths rather than distances need...

  5. Aspects of three field approximations: Darwin, frozen, EMPULSE

    International Nuclear Information System (INIS)

    Boyd, J.K.; Lee, E.P.; Yu, S.S.

    1985-01-01

    The traditional approach used to study high energy beam propagation relies on the frozen field approximation. A minor modification of the frozen field approximation yields the set of equations applied to the analysis of the hose instability. These models are constrasted with the Darwin field approximation. A statement is made of the Darwin model equations relevant to the analysis of the hose instability

  6. On Convex Quadratic Approximation

    NARCIS (Netherlands)

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

    2000-01-01

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

  7. All-Norm Approximation Algorithms

    NARCIS (Netherlands)

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

    2002-01-01

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

  8. 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...

  9. Approximate Noether symmetries and collineations for regular perturbative Lagrangians

    Science.gov (United States)

    Paliathanasis, Andronikos; Jamal, Sameerah

    2018-01-01

    Regular perturbative Lagrangians that admit approximate Noether symmetries and approximate conservation laws are studied. Specifically, we investigate the connection between approximate Noether symmetries and collineations of the underlying manifold. In particular we determine the generic Noether symmetry conditions for the approximate point symmetries and we find that for a class of perturbed Lagrangians, Noether symmetries are related to the elements of the Homothetic algebra of the metric which is defined by the unperturbed Lagrangian. Moreover, we discuss how exact symmetries become approximate symmetries. Finally, some applications are presented.

  10. Square well approximation to the optical potential

    International Nuclear Information System (INIS)

    Jain, A.K.; Gupta, M.C.; Marwadi, P.R.

    1976-01-01

    Approximations for obtaining T-matrix elements for a sum of several potentials in terms of T-matrices for individual potentials are studied. Based on model calculations for S-wave for a sum of two separable non-local potentials of Yukawa type form factors and a sum of two delta function potentials, it is shown that the T-matrix for a sum of several potentials can be approximated satisfactorily over all the energy regions by the sum of T-matrices for individual potentials. Based on this, an approximate method for finding T-matrix for any local potential by approximating it by a sum of suitable number of square wells is presented. This provides an interesting way to calculate the T-matrix for any arbitary potential in terms of Bessel functions to a good degree of accuracy. The method is applied to the Saxon-Wood potentials and good agreement with exact results is found. (author)

  11. Uncertainty relations for approximation and estimation

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Jaeha, E-mail: jlee@post.kek.jp [Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan); Tsutsui, Izumi, E-mail: izumi.tsutsui@kek.jp [Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan); Theory Center, Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba, Ibaraki 305-0801 (Japan)

    2016-05-27

    We present a versatile inequality of uncertainty relations which are useful when one approximates an observable and/or estimates a physical parameter based on the measurement of another observable. It is shown that the optimal choice for proxy functions used for the approximation is given by Aharonov's weak value, which also determines the classical Fisher information in parameter estimation, turning our inequality into the genuine Cramér–Rao inequality. Since the standard form of the uncertainty relation arises as a special case of our inequality, and since the parameter estimation is available as well, our inequality can treat both the position–momentum and the time–energy relations in one framework albeit handled differently. - Highlights: • Several inequalities interpreted as uncertainty relations for approximation/estimation are derived from a single ‘versatile inequality’. • The ‘versatile inequality’ sets a limit on the approximation of an observable and/or the estimation of a parameter by another observable. • The ‘versatile inequality’ turns into an elaboration of the Robertson–Kennard (Schrödinger) inequality and the Cramér–Rao inequality. • Both the position–momentum and the time–energy relation are treated in one framework. • In every case, Aharonov's weak value arises as a key geometrical ingredient, deciding the optimal choice for the proxy functions.

  12. Uncertainty relations for approximation and estimation

    International Nuclear Information System (INIS)

    Lee, Jaeha; Tsutsui, Izumi

    2016-01-01

    We present a versatile inequality of uncertainty relations which are useful when one approximates an observable and/or estimates a physical parameter based on the measurement of another observable. It is shown that the optimal choice for proxy functions used for the approximation is given by Aharonov's weak value, which also determines the classical Fisher information in parameter estimation, turning our inequality into the genuine Cramér–Rao inequality. Since the standard form of the uncertainty relation arises as a special case of our inequality, and since the parameter estimation is available as well, our inequality can treat both the position–momentum and the time–energy relations in one framework albeit handled differently. - Highlights: • Several inequalities interpreted as uncertainty relations for approximation/estimation are derived from a single ‘versatile inequality’. • The ‘versatile inequality’ sets a limit on the approximation of an observable and/or the estimation of a parameter by another observable. • The ‘versatile inequality’ turns into an elaboration of the Robertson–Kennard (Schrödinger) inequality and the Cramér–Rao inequality. • Both the position–momentum and the time–energy relation are treated in one framework. • In every case, Aharonov's weak value arises as a key geometrical ingredient, deciding the optimal choice for the proxy functions.

  13. Diophantine approximation

    CERN Document Server

    Schmidt, Wolfgang M

    1980-01-01

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

  14. Approximate Inference and Deep Generative Models

    CERN Multimedia

    CERN. Geneva

    2018-01-01

    Advances in deep generative models are at the forefront of deep learning research because of the promise they offer for allowing data-efficient learning, and for model-based reinforcement learning. In this talk I'll review a few standard methods for approximate inference and introduce modern approximations which allow for efficient large-scale training of a wide variety of generative models. Finally, I'll demonstrate several important application of these models to density estimation, missing data imputation, data compression and planning.

  15. Approximation of the inverse G-frame operator

    Indian Academy of Sciences (India)

    ... projection method for -frames which works for all conditional -Riesz frames. We also derive a method for approximation of the inverse -frame operator which is efficient for all -frames. We show how the inverse of -frame operator can be approximated as close as we like using finite-dimensional linear algebra.

  16. Optical approximation in the theory of geometric impedance

    International Nuclear Information System (INIS)

    Stupakov, G.; Bane, K.L.F.; Zagorodnov, I.

    2007-02-01

    In this paper we introduce an optical approximation into the theory of impedance calculation, one valid in the limit of high frequencies. This approximation neglects diffraction effects in the radiation process, and is conceptually equivalent to the approximation of geometric optics in electromagnetic theory. Using this approximation, we derive equations for the longitudinal impedance for arbitrary offsets, with respect to a reference orbit, of source and test particles. With the help of the Panofsky-Wenzel theorem we also obtain expressions for the transverse impedance (also for arbitrary offsets). We further simplify these expressions for the case of the small offsets that are typical for practical applications. Our final expressions for the impedance, in the general case, involve two dimensional integrals over various cross-sections of the transition. We further demonstrate, for several known axisymmetric examples, how our method is applied to the calculation of impedances. Finally, we discuss the accuracy of the optical approximation and its relation to the diffraction regime in the theory of impedance. (orig.)

  17. APPROXIMATION OF FREE-FORM CURVE – AIRFOIL SHAPE

    Directory of Open Access Journals (Sweden)

    CHONG PERK LIN

    2013-12-01

    Full Text Available Approximation of free-form shape is essential in numerous engineering applications, particularly in automotive and aircraft industries. Commercial CAD software for the approximation of free-form shape is based almost exclusively on parametric polynomial and rational parametric polynomial. The parametric curve is defined by vector function of one independent variable R(u = (x(u, y(u, z(u, where 0≤u≤1. Bézier representation is one of the parametric functions, which is widely used in the approximating of free-form shape. Given a string of points with the assumption of sufficiently dense to characterise airfoil shape, it is desirable to approximate the shape with Bézier representation. The expectation is that the representation function is close to the shape within an acceptable working tolerance. In this paper, the aim is to explore the use of manual and automated methods for approximating section curve of airfoil with Bézier representation.

  18. Conference on Abstract Spaces and Approximation

    CERN Document Server

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

    1969-01-01

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

  19. Kullback-Leibler divergence and the Pareto-Exponential approximation.

    Science.gov (United States)

    Weinberg, G V

    2016-01-01

    Recent radar research interests in the Pareto distribution as a model for X-band maritime surveillance radar clutter returns have resulted in analysis of the asymptotic behaviour of this clutter model. In particular, it is of interest to understand when the Pareto distribution is well approximated by an Exponential distribution. The justification for this is that under the latter clutter model assumption, simpler radar detection schemes can be applied. An information theory approach is introduced to investigate the Pareto-Exponential approximation. By analysing the Kullback-Leibler divergence between the two distributions it is possible to not only assess when the approximation is valid, but to determine, for a given Pareto model, the optimal Exponential approximation.

  20. Diagonal Pade approximations for initial value problems

    International Nuclear Information System (INIS)

    Reusch, M.F.; Ratzan, L.; Pomphrey, N.; Park, W.

    1987-06-01

    Diagonal Pade approximations to the time evolution operator for initial value problems are applied in a novel way to the numerical solution of these problems by explicitly factoring the polynomials of the approximation. A remarkable gain over conventional methods in efficiency and accuracy of solution is obtained. 20 refs., 3 figs., 1 tab

  1. A test of the adhesion approximation for gravitational clustering

    Science.gov (United States)

    Melott, Adrian L.; Shandarin, Sergei; Weinberg, David H.

    1993-01-01

    We quantitatively compare a particle implementation of the adhesion approximation to fully non-linear, numerical 'N-body' simulations. Our primary tool, cross-correlation of N-body simulations with the adhesion approximation, indicates good agreement, better than that found by the same test performed with the Zel-dovich approximation (hereafter ZA). However, the cross-correlation is not as good as that of the truncated Zel-dovich approximation (TZA), obtained by applying the Zel'dovich approximation after smoothing the initial density field with a Gaussian filter. We confirm that the adhesion approximation produces an excessively filamentary distribution. Relative to the N-body results, we also find that: (a) the power spectrum obtained from the adhesion approximation is more accurate than that from ZA or TZA, (b) the error in the phase angle of Fourier components is worse than that from TZA, and (c) the mass distribution function is more accurate than that from ZA or TZA. It appears that adhesion performs well statistically, but that TZA is more accurate dynamically, in the sense of moving mass to the right place.

  2. Hydrogen: Beyond the Classic Approximation

    International Nuclear Information System (INIS)

    Scivetti, Ivan

    2003-01-01

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

  3. Simultaneous approximation in scales of Banach spaces

    International Nuclear Information System (INIS)

    Bramble, J.H.; Scott, R.

    1978-01-01

    The problem of verifying optimal approximation simultaneously in different norms in a Banach scale is reduced to verification of optimal approximation in the highest order norm. The basic tool used is the Banach space interpolation method developed by Lions and Peetre. Applications are given to several problems arising in the theory of finite element methods

  4. Tracking black holes in numerical relativity

    International Nuclear Information System (INIS)

    Caveny, Scott A.; Anderson, Matthew; Matzner, Richard A.

    2003-01-01

    This work addresses the problem of generically tracking black hole event horizons in computational simulation of black hole interactions. Solutions of the hyperbolic eikonal equation, solved on a curved spacetime manifold containing black hole sources, are employed in development of a robust tracking method capable of continuously monitoring arbitrary changes of topology in the event horizon as well as arbitrary numbers of gravitational sources. The method makes use of continuous families of level set viscosity solutions of the eikonal equation with identification of the black hole event horizon obtained by the signature feature of discontinuity formation in the eikonal's solution. The method is employed in the analysis of the event horizon for the asymmetric merger in a binary black hole system. In this first such three dimensional analysis, we establish both qualitative and quantitative evidence for our method and its application to the asymmetric problem. We focus attention on (1) the topology of the throat connecting the holes following merger, (2) the time of merger, and (3) continuing to account for the surface of section areas of the black hole sources

  5. On transparent potentials: a Born approximation study

    International Nuclear Information System (INIS)

    Coudray, C.

    1980-01-01

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

  6. Approximate supernova remnant dynamics with cosmic ray production

    Science.gov (United States)

    Voelk, H. J.; Drury, L. O.; Dorfi, E. A.

    1985-01-01

    Supernova explosions are the most violent and energetic events in the galaxy and have long been considered probably sources of Cosmic Rays. Recent shock acceleration models treating the Cosmic Rays (CR's) as test particles nb a prescribed Supernova Remnant (SNR) evolution, indeed indicate an approximate power law momentum distribution f sub source (p) approximation p(-a) for the particles ultimately injected into the Interstellar Medium (ISM). This spectrum extends almost to the momentum p = 1 million GeV/c, where the break in the observed spectrum occurs. The calculated power law index approximately less than 4.2 agrees with that inferred for the galactic CR sources. The absolute CR intensity can however not be well determined in such a test particle approximation.

  7. Approximate supernova remnant dynamics with cosmic ray production

    International Nuclear Information System (INIS)

    Voelk, H.J.; Drury, L.O.; Dorfi, E.A.

    1985-01-01

    Supernova explosions are the most violent and energetic events in the galaxy and have long been considered probable sources of cosmic rays. Recent shock acceleration models treating the cosmic rays (CR's) as test particles nb a prescribed supernova remnant (SNR) evolution, indeed indicate an approximate power law momentum distribution f sub source (p) approximation p(-a) for the particles ultimately injected into the interstellar medium (ISM). This spectrum extends almost to the momentum p = 1 million GeV/c, where the break in the observed spectrum occurs. The calculated power law index approximately less than 4.2 agrees with that inferred for the galactic CR sources. The absolute CR intensity can however not be well determined in such a test particle approximation

  8. Geometric convergence of some two-point Pade approximations

    International Nuclear Information System (INIS)

    Nemeth, G.

    1983-01-01

    The geometric convergences of some two-point Pade approximations are investigated on the real positive axis and on certain infinite sets of the complex plane. Some theorems concerning the geometric convergence of Pade approximations are proved, and bounds on geometric convergence rates are given. The results may be interesting considering the applications both in numerical computations and in approximation theory. As a specific case, the numerical calculations connected with the plasma dispersion function may be performed. (D.Gy.)

  9. Standard filter approximations for low power Continuous Wavelet Transforms.

    Science.gov (United States)

    Casson, Alexander J; Rodriguez-Villegas, Esther

    2010-01-01

    Analogue domain implementations of the Continuous Wavelet Transform (CWT) have proved popular in recent years as they can be implemented at very low power consumption levels. This is essential for use in wearable, long term physiological monitoring systems. Present analogue CWT implementations rely on taking mathematical a approximation of the wanted mother wavelet function to give a filter transfer function that is suitable for circuit implementation. This paper investigates the use of standard filter approximations (Butterworth, Chebyshev, Bessel) as an alternative wavelet approximation technique. This extends the number of approximation techniques available for generating analogue CWT filters. An example ECG analysis shows that signal information can be successfully extracted using these CWT approximations.

  10. Ordering, symbols and finite-dimensional approximations of path integrals

    International Nuclear Information System (INIS)

    Kashiwa, Taro; Sakoda, Seiji; Zenkin, S.V.

    1994-01-01

    We derive general form of finite-dimensional approximations of path integrals for both bosonic and fermionic canonical systems in terms of symbols of operators determined by operator ordering. We argue that for a system with a given quantum Hamiltonian such approximations are independent of the type of symbols up to terms of O(ε), where ε of is infinitesimal time interval determining the accuracy of the approximations. A new class of such approximations is found for both c-number and Grassmannian dynamical variables. The actions determined by the approximations are non-local and have no classical continuum limit except the cases of pq- and qp-ordering. As an explicit example the fermionic oscillator is considered in detail. (author)

  11. Hardness of approximation for strip packing

    DEFF Research Database (Denmark)

    Adamaszek, Anna Maria; Kociumaka, Tomasz; Pilipczuk, Marcin

    2017-01-01

    Strip packing is a classical packing problem, where the goal is to pack a set of rectangular objects into a strip of a given width, while minimizing the total height of the packing. The problem has multiple applications, for example, in scheduling and stock-cutting, and has been studied extensively......)-approximation by two independent research groups [FSTTCS 2016,WALCOM 2017]. This raises a questionwhether strip packing with polynomially bounded input data admits a quasi-polynomial time approximation scheme, as is the case for related twodimensional packing problems like maximum independent set of rectangles or two...

  12. Adaptive control using neural networks and approximate models.

    Science.gov (United States)

    Narendra, K S; Mukhopadhyay, S

    1997-01-01

    The NARMA model is an exact representation of the input-output behavior of finite-dimensional nonlinear discrete-time dynamical systems in a neighborhood of the equilibrium state. However, it is not convenient for purposes of adaptive control using neural networks due to its nonlinear dependence on the control input. Hence, quite often, approximate methods are used for realizing the neural controllers to overcome computational complexity. In this paper, we introduce two classes of models which are approximations to the NARMA model, and which are linear in the control input. The latter fact substantially simplifies both the theoretical analysis as well as the practical implementation of the controller. Extensive simulation studies have shown that the neural controllers designed using the proposed approximate models perform very well, and in many cases even better than an approximate controller designed using the exact NARMA model. In view of their mathematical tractability as well as their success in simulation studies, a case is made in this paper that such approximate input-output models warrant a detailed study in their own right.

  13. Analytical models approximating individual processes: a validation method.

    Science.gov (United States)

    Favier, C; Degallier, N; Menkès, C E

    2010-12-01

    Upscaling population models from fine to coarse resolutions, in space, time and/or level of description, allows the derivation of fast and tractable models based on a thorough knowledge of individual processes. The validity of such approximations is generally tested only on a limited range of parameter sets. A more general validation test, over a range of parameters, is proposed; this would estimate the error induced by the approximation, using the original model's stochastic variability as a reference. This method is illustrated by three examples taken from the field of epidemics transmitted by vectors that bite in a temporally cyclical pattern, that illustrate the use of the method: to estimate if an approximation over- or under-fits the original model; to invalidate an approximation; to rank possible approximations for their qualities. As a result, the application of the validation method to this field emphasizes the need to account for the vectors' biology in epidemic prediction models and to validate these against finer scale models. Copyright © 2010 Elsevier Inc. All rights reserved.

  14. The Hartree-Fock seniority approximation

    International Nuclear Information System (INIS)

    Gomez, J.M.G.; Prieto, C.

    1986-01-01

    A new self-consistent method is used to take into account the mean-field and the pairing correlations in nuclei at the same time. We call it the Hartree-Fock seniority approximation, because the long-range and short-range correlations are treated in the frameworks of Hartree-Fock theory and the seniority scheme. The method is developed in detail for a minimum-seniority variational wave function in the coordinate representation for an effective interaction of the Skyrme type. An advantage of the present approach over the Hartree-Fock-Bogoliubov theory is the exact conservation of angular momentum and particle number. Furthermore, the computational effort required in the Hartree-Fock seniority approximation is similar to that ofthe pure Hartree-Fock picture. Some numerical calculations for Ca isotopes are presented. (orig.)

  15. Quasi-fractional approximation to the Bessel functions

    International Nuclear Information System (INIS)

    Guerrero, P.M.L.

    1989-01-01

    In this paper the authors presents a simple Quasi-Fractional Approximation for Bessel Functions J ν (x), (- 1 ≤ ν < 0.5). This has been obtained by extending a method published which uses simultaneously power series and asymptotic expansions. Both functions, exact and approximated, coincide in at least two digits for positive x, and ν between - 1 and 0,4

  16. Scattering theory and effective medium approximations to heterogeneous materials

    International Nuclear Information System (INIS)

    Gubernatis, J.E.

    1977-01-01

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

  17. Approximate modal analysis using Fourier decomposition

    International Nuclear Information System (INIS)

    Kozar, Ivica; Jericevic, Zeljko; Pecak, Tatjana

    2010-01-01

    The paper presents a novel numerical approach for approximate solution of eigenvalue problem and investigates its suitability for modal analysis of structures with special attention on plate structures. The approach is based on Fourier transformation of the matrix equation into frequency domain and subsequent removal of potentially less significant frequencies. The procedure results in a much reduced problem that is used in eigenvalue calculation. After calculation eigenvectors are expanded and transformed back into time domain. The principles are presented in Jericevic [1]. Fourier transform can be formulated in a way that some parts of the matrix that should not be approximated are not transformed but are fully preserved. In this paper we present formulation that preserves central or edge parts of the matrix and compare it with the formulation that performs transform on the whole matrix. Numerical experiments on transformed structural dynamic matrices describe quality of the approximations obtained in modal analysis of structures. On the basis of the numerical experiments, from the three approaches to matrix reduction one is recommended.

  18. A Gaussian Approximation Potential for Silicon

    Science.gov (United States)

    Bernstein, Noam; Bartók, Albert; Kermode, James; Csányi, Gábor

    We present an interatomic potential for silicon using the Gaussian Approximation Potential (GAP) approach, which uses the Gaussian process regression method to approximate the reference potential energy surface as a sum of atomic energies. Each atomic energy is approximated as a function of the local environment around the atom, which is described with the smooth overlap of atomic environments (SOAP) descriptor. The potential is fit to a database of energies, forces, and stresses calculated using density functional theory (DFT) on a wide range of configurations from zero and finite temperature simulations. These include crystalline phases, liquid, amorphous, and low coordination structures, and diamond-structure point defects, dislocations, surfaces, and cracks. We compare the results of the potential to DFT calculations, as well as to previously published models including Stillinger-Weber, Tersoff, modified embedded atom method (MEAM), and ReaxFF. We show that it is very accurate as compared to the DFT reference results for a wide range of properties, including low energy bulk phases, liquid structure, as well as point, line, and plane defects in the diamond structure.

  19. Development of the relativistic impulse approximation

    International Nuclear Information System (INIS)

    Wallace, S.J.

    1985-01-01

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

  20. Local approximation of a metapopulation's equilibrium.

    Science.gov (United States)

    Barbour, A D; McVinish, R; Pollett, P K

    2018-04-18

    We consider the approximation of the equilibrium of a metapopulation model, in which a finite number of patches are randomly distributed over a bounded subset [Formula: see text] of Euclidean space. The approximation is good when a large number of patches contribute to the colonization pressure on any given unoccupied patch, and when the quality of the patches varies little over the length scale determined by the colonization radius. If this is the case, the equilibrium probability of a patch at z being occupied is shown to be close to [Formula: see text], the equilibrium occupation probability in Levins's model, at any point [Formula: see text] not too close to the boundary, if the local colonization pressure and extinction rates appropriate to z are assumed. The approximation is justified by giving explicit upper and lower bounds for the occupation probabilities, expressed in terms of the model parameters. Since the patches are distributed randomly, the occupation probabilities are also random, and we complement our bounds with explicit bounds on the probability that they are satisfied at all patches simultaneously.

  1. Approximate Bayesian recursive estimation

    Czech Academy of Sciences Publication Activity Database

    Kárný, Miroslav

    2014-01-01

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

  2. Pion-nucleus cross sections approximation

    International Nuclear Information System (INIS)

    Barashenkov, V.S.; Polanski, A.; Sosnin, A.N.

    1990-01-01

    Analytical approximation of pion-nucleus elastic and inelastic interaction cross-section is suggested, with could be applied in the energy range exceeding several dozens of MeV for nuclei heavier than beryllium. 3 refs.; 4 tabs

  3. Semiclassical asymptotic behavior and the rearrangement mechanisms for Coulomb particles

    International Nuclear Information System (INIS)

    Bogdanov, A.V.; Gevorkyan, A.S.; Dubrovskii, G.V.

    1986-01-01

    The semiclassical asymptotic behavior of the eikonal amplitude of the resonance rearrangement in a system of three Coulomb particles is studied. It is shown that the general formula for the amplitude correctly describes two classical mechanisms (pickup and knockout) and one nonclassical mechanism (stripping). The classical mechanisms predominate at high energies, while the stripping mechanism predominates at lower energies. In the region of medium energies the dominant mechanism is the pickup (or Thomas) mechanism, which is realized by nonclassical means. For such transitions the classical cross section diverges, and the amplitude must be computed on a complex trajectory. The physical reasons for introducing the approximate complex trajectories are discussed. The contributions of all the mechanisms to the rearrangement cross section are found in their analytic forms

  4. Pauli blocking and medium effects in nucleon knockout reactions

    International Nuclear Information System (INIS)

    Bertulani, C. A.; De Conti, C.

    2010-01-01

    We study medium modifications of the nucleon-nucleon (NN) cross sections and their influence on the nucleon knockout reactions. Using the eikonal approximation, we compare the results obtained with free NN cross sections with those obtained with a purely geometrical treatment of Pauli blocking and with NN obtained with more elaborated Dirac-Bruecker methods. The medium effects are parametrized in terms of the baryon density. We focus on symmetric nuclear matter, although the geometrical Pauli blocking also allows for the treatment of asymmetric nuclear matter. It is shown that medium effects can change the nucleon knockout cross sections and momentum distributions up to 10% in the energy range E lab =50-300 MeV/nucleon. The effect is more evident in reactions involving halo nuclei.

  5. QCD-motivated Pomeron and diffractive hadronic cross sections at high energies

    International Nuclear Information System (INIS)

    Anisovich, V.V.; Dakhno, L.G.; Nikonov, V.A.

    1996-01-01

    The cross sections for soft diffractive processes in pp (or p-barp) and πp collisions are calculated by using the QCD-motivated Pomeron. Unitarization of the s-channel amplitude is performed in the eikonal approximation. Color screening is taken into account in the quark structure of hadrons. The resulting description of diffractive processes leads to the parameters of the bare Pomeron P that are close to the corresponding parameters of the Lipatov Pomeron. The parameters of the bare Pomeron and three-reggeon block PGG (G is a reggeized gluon) are fixed by fitting data at moderately high energies. Predictions for ultrahigh energies are made. The intercept for the bare Pomeron is obtained. It is consistent with data on deep-inelastic scattering at small x

  6. Production of excitons in grazing collisions of protons with LiF surfaces: An onion model

    Energy Technology Data Exchange (ETDEWEB)

    Miraglia, J. E.; Gravielle, M. S. [Instituto de Astronomia y Fisica del Espacio, Consejo Nacional de Investigaciones Cientificas y Tecnicas and Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Casilla de Correo 67, Sucursal 28, (C1428EGA) Buenos Aires (Argentina)

    2011-12-15

    In this work we evaluate the production of excitons of a lithium fluoride crystal induced by proton impact in the intermediate and high energy regime (from 100 keV to 1 MeV). A simple model is proposed to account for the influence of the Coulomb grid of the target by dressing crystal ions to transform them in what we call onions. The excited states of these onions can be interpreted as excitons. Within this model, total cross section and stopping power are calculated by using the first Born and the continuum distorted-wave (CDW) eikonal initial-state (EIS) approximations. We found that between 7 and 30 excitons per incident proton are produced in grazing collisions with LiF surfaces, becoming a relevant mechanism of inelastic transitions.

  7. Doubly differential cross sections of low-energy electrons emitted in the ionization of molecular hydrogen by bare carbon ions

    International Nuclear Information System (INIS)

    Tribedi, L.C.; Richard, P.; Ling, D.; Wang, Y.D.; Lin, C.D.; Moshammer, R.; Kerby, G.W. III; Gealy, M.W.; Rudd, M.E.

    1996-01-01

    We have measured the double differential cross sections (DDCS) (d 2 σ/d var-epsilon ed Ω e ) of low-energy electron emission in the ionization of H 2 bombarded by bare carbon ions of energy 30 MeV. The energy and angular distributions of the electron DDCS have been obtained for 12 different emission angles and for electron energies varying between 0.1 and 300 eV. We have also deduced the single differential and total ionization cross section from the measured DDCS. The data have been compared with the predictions of first Born approximations and the CDW-EIS (continuum distorted wave endash eikonal initial state) model. The CDW-EIS model provides an excellent agreement with the data. copyright 1996 The American Physical Society

  8. Approximal morphology as predictor of approximal caries in primary molar teeth

    DEFF Research Database (Denmark)

    Cortes, A; Martignon, S; Qvist, V

    2018-01-01

    consent was given, participated. Upper and lower molar teeth of one randomly selected side received a 2-day temporarily separation. Bitewing radiographs and silicone impressions of interproximal area (IPA) were obtained. One-year procedures were repeated in 52 children (84%). The morphology of the distal...... surfaces of the first molar teeth and the mesial surfaces on the second molar teeth (n=208) was scored from the occlusal aspect on images from the baseline resin models resulting in four IPA variants: concave-concave; concave-convex; convex-concave, and convex-convex. Approximal caries on the surface...

  9. Finite Element Approximation of the FENE-P Model

    OpenAIRE

    Barrett , John ,; Boyaval , Sébastien

    2017-01-01

    We extend our analysis on the Oldroyd-B model in Barrett and Boyaval [1] to consider the finite element approximation of the FENE-P system of equations, which models a dilute polymeric fluid, in a bounded domain $D $\\subset$ R d , d = 2 or 3$, subject to no flow boundary conditions. Our schemes are based on approximating the pressure and the symmetric conforma-tion tensor by either (a) piecewise constants or (b) continuous piecewise linears. In case (a) the velocity field is approximated by c...

  10. Nuclear data processing, analysis, transformation and storage with Pade-approximants

    International Nuclear Information System (INIS)

    Badikov, S.A.; Gay, E.V.; Guseynov, M.A.; Rabotnov, N.S.

    1992-01-01

    A method is described to generate rational approximants of high order with applications to neutron data handling. The problems considered are: The approximations of neutron cross-sections in resonance region producing the parameters for Adler-Adler type formulae; calculations of resulting rational approximants' errors given in analytical form allowing to compute the error at any energy point inside the interval of approximation; calculations of the correlation coefficient of error values in two arbitrary points provided that experimental errors are independent and normally distributed; a method of simultaneous generation of a few rational approximants with identical set of poles; functionals other than LSM; two-dimensional approximation. (orig.)

  11. The Mathematical Theory of Multifocal Lenses

    Institute of Scientific and Technical Information of China (English)

    Jacob RUBINSTEIN

    2017-01-01

    This paper presents the fundamental optical concepts of designing multifocal ophthalmic lenses and the mathematical methods associated with them.In particular,it is shown that the design methodology is heavily based on differential geometric ideas such as Willmore surfaces.A key role is played by Hamilton's eikonal functions.It is shown that these functions capture all the information on the local blur and distortion created by the lenses.Along the way,formulas for computing the eikonal functions are derived.Finally,the author lists a few intriguing mathematical problems and novel concepts in optics as future projects.

  12. A new description of high energy antiproton (proton)-proton elastic scattering

    International Nuclear Information System (INIS)

    Barshay, S.; Technion-Israel Inst. of Tech., Haifa. Dept. of Physics); Goldberg, J.

    1987-01-01

    We develop a generalization of the geometric picture for high-energy antiproton (proton)-proton elastic scattering. The eikonal at each impact parameter is considered to have fluctuations about an average value, and is thus characterized by a distribution. A connection to parton branching is made through the specific form of the distribution function for the eikonal. A unified physical theory with significant fluctuations accurately describes the anti p(p)-p data at both √s = 546 GeV and 53 GeV. The fluctuation parameter is remarkably well given by that directly observed in multiparticle production. (orig.)

  13. New description of high energy antiproton (proton)-proton elastic scattering

    Energy Technology Data Exchange (ETDEWEB)

    Barshay, S; Goldberg, J

    1987-10-15

    We develop a generalization of the geometric picture for high-energy antiproton (proton)-proton elastic scattering. The eikonal at each impact parameter is considered to have fluctuations about an average value, and is thus characterized by a distribution. A connection to parton branching is made through the specific form of the distribution function for the eikonal. A unified physical theory with significant fluctuations accurately describes the anti p(p)-p data at both ..sqrt..s = 546 GeV and 53 GeV. The fluctuation parameter is remarkably well given by that directly observed in multiparticle production.

  14. Lattice quantum chromodynamics with approximately chiral fermions

    International Nuclear Information System (INIS)

    Hierl, Dieter

    2008-05-01

    In this work we present Lattice QCD results obtained by approximately chiral fermions. We use the CI fermions in the quenched approximation to investigate the excited baryon spectrum and to search for the Θ + pentaquark on the lattice. Furthermore we developed an algorithm for dynamical simulations using the FP action. Using FP fermions we calculate some LECs of chiral perturbation theory applying the epsilon expansion. (orig.)

  15. Lattice quantum chromodynamics with approximately chiral fermions

    Energy Technology Data Exchange (ETDEWEB)

    Hierl, Dieter

    2008-05-15

    In this work we present Lattice QCD results obtained by approximately chiral fermions. We use the CI fermions in the quenched approximation to investigate the excited baryon spectrum and to search for the {theta}{sup +} pentaquark on the lattice. Furthermore we developed an algorithm for dynamical simulations using the FP action. Using FP fermions we calculate some LECs of chiral perturbation theory applying the epsilon expansion. (orig.)

  16. Rollout sampling approximate policy iteration

    NARCIS (Netherlands)

    Dimitrakakis, C.; Lagoudakis, M.G.

    2008-01-01

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

  17. Using function approximation to determine neural network accuracy

    International Nuclear Information System (INIS)

    Wichman, R.F.; Alexander, J.

    2013-01-01

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

  18. Methods of Approximation Theory in Complex Analysis and Mathematical Physics

    CERN Document Server

    Saff, Edward

    1993-01-01

    The book incorporates research papers and surveys written by participants ofan International Scientific Programme on Approximation Theory jointly supervised by Institute for Constructive Mathematics of University of South Florida at Tampa, USA and the Euler International Mathematical Instituteat St. Petersburg, Russia. The aim of the Programme was to present new developments in Constructive Approximation Theory. The topics of the papers are: asymptotic behaviour of orthogonal polynomials, rational approximation of classical functions, quadrature formulas, theory of n-widths, nonlinear approximation in Hardy algebras,numerical results on best polynomial approximations, wavelet analysis. FROM THE CONTENTS: E.A. Rakhmanov: Strong asymptotics for orthogonal polynomials associated with exponential weights on R.- A.L. Levin, E.B. Saff: Exact Convergence Rates for Best Lp Rational Approximation to the Signum Function and for Optimal Quadrature in Hp.- H. Stahl: Uniform Rational Approximation of x .- M. Rahman, S.K. ...

  19. Beyond the random phase approximation

    DEFF Research Database (Denmark)

    Olsen, Thomas; Thygesen, Kristian S.

    2013-01-01

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

  20. Vacancy-rearrangement theory in the first Magnus approximation

    International Nuclear Information System (INIS)

    Becker, R.L.

    1984-01-01

    In the present paper we employ the first Magnus approximation (M1A), a unitarized Born approximation, in semiclassical collision theory. We have found previously that the M1A gives a substantial improvement over the first Born approximation (B1A) and can give a good approximation to a full coupled channels calculation of the mean L-shell vacancy probability per electron, p/sub L/, when the L-vacancies are accompanied by a K-shell vacancy (p/sub L/ is obtained experimentally from measurements of K/sub α/-satellite intensities). For sufficiently strong projectile-electron interactions (sufficiently large Z/sub p/ or small v) the M1A ceases to reproduce the coupled channels results, but it is accurate over a much wider range of Z/sub p/ and v than the B1A. 27 references

  1. Minimax rational approximation of the Fermi-Dirac distribution

    Science.gov (United States)

    Moussa, Jonathan E.

    2016-10-01

    Accurate rational approximations of the Fermi-Dirac distribution are a useful component in many numerical algorithms for electronic structure calculations. The best known approximations use O(log(βΔ)log(ɛ-1)) poles to achieve an error tolerance ɛ at temperature β-1 over an energy interval Δ. We apply minimax approximation to reduce the number of poles by a factor of four and replace Δ with Δocc, the occupied energy interval. This is particularly beneficial when Δ ≫ Δocc, such as in electronic structure calculations that use a large basis set.

  2. Fast wavelet based sparse approximate inverse preconditioner

    Energy Technology Data Exchange (ETDEWEB)

    Wan, W.L. [Univ. of California, Los Angeles, CA (United States)

    1996-12-31

    Incomplete LU factorization is a robust preconditioner for both general and PDE problems but unfortunately not easy to parallelize. Recent study of Huckle and Grote and Chow and Saad showed that sparse approximate inverse could be a potential alternative while readily parallelizable. However, for special class of matrix A that comes from elliptic PDE problems, their preconditioners are not optimal in the sense that independent of mesh size. A reason may be that no good sparse approximate inverse exists for the dense inverse matrix. Our observation is that for this kind of matrices, its inverse entries typically have piecewise smooth changes. We can take advantage of this fact and use wavelet compression techniques to construct a better sparse approximate inverse preconditioner. We shall show numerically that our approach is effective for this kind of matrices.

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

    International Nuclear Information System (INIS)

    Haftel, M.I.; Zankel, H.

    1981-01-01

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

  4. Framework for sequential approximate optimization

    NARCIS (Netherlands)

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

    2004-01-01

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

  5. Perturbative corrections for approximate inference in gaussian latent variable models

    DEFF Research Database (Denmark)

    Opper, Manfred; Paquet, Ulrich; Winther, Ole

    2013-01-01

    Expectation Propagation (EP) provides a framework for approximate inference. When the model under consideration is over a latent Gaussian field, with the approximation being Gaussian, we show how these approximations can systematically be corrected. A perturbative expansion is made of the exact b...... illustrate on tree-structured Ising model approximations. Furthermore, they provide a polynomial-time assessment of the approximation error. We also provide both theoretical and practical insights on the exactness of the EP solution. © 2013 Manfred Opper, Ulrich Paquet and Ole Winther....

  6. Approximating the physical inner product of loop quantum cosmology

    International Nuclear Information System (INIS)

    Bahr, Benjamin; Thiemann, Thomas

    2007-01-01

    In this paper, we investigate the possibility of approximating the physical inner product of constrained quantum theories. In particular, we calculate the physical inner product of a simple cosmological model in two ways: firstly, we compute it analytically via a trick; secondly, we use the complexifier coherent states to approximate the physical inner product defined by the master constraint of the system. We find that the approximation is able to recover the analytic solution of the problem, which consolidates hopes that coherent states will help to approximate solutions of more complicated theories, like loop quantum gravity

  7. Polynomial approximation of functions in Sobolev spaces

    International Nuclear Information System (INIS)

    Dupont, T.; Scott, R.

    1980-01-01

    Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomical plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces

  8. Nernst effect beyond the relaxation-time approximation

    OpenAIRE

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

    2011-01-01

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

  9. 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...

  10. Approximate spatio-temporal top-k publish/subscribe

    KAUST Repository

    Chen, Lisi

    2018-04-26

    Location-based publish/subscribe plays a significant role in mobile information disseminations. In this light, we propose and study a novel problem of processing location-based top-k subscriptions over spatio-temporal data streams. We define a new type of approximate location-based top-k subscription, Approximate Temporal Spatial-Keyword Top-k (ATSK) Subscription, that continuously feeds users with relevant spatio-temporal messages by considering textual similarity, spatial proximity, and information freshness. Different from existing location-based top-k subscriptions, Approximate Temporal Spatial-Keyword Top-k (ATSK) Subscription can automatically adjust the triggering condition by taking the triggering score of other subscriptions into account. The group filtering efficacy can be substantially improved by sacrificing the publishing result quality with a bounded guarantee. We conduct extensive experiments on two real datasets to demonstrate the performance of the developed solutions.

  11. Approximate spatio-temporal top-k publish/subscribe

    KAUST Repository

    Chen, Lisi; Shang, Shuo

    2018-01-01

    Location-based publish/subscribe plays a significant role in mobile information disseminations. In this light, we propose and study a novel problem of processing location-based top-k subscriptions over spatio-temporal data streams. We define a new type of approximate location-based top-k subscription, Approximate Temporal Spatial-Keyword Top-k (ATSK) Subscription, that continuously feeds users with relevant spatio-temporal messages by considering textual similarity, spatial proximity, and information freshness. Different from existing location-based top-k subscriptions, Approximate Temporal Spatial-Keyword Top-k (ATSK) Subscription can automatically adjust the triggering condition by taking the triggering score of other subscriptions into account. The group filtering efficacy can be substantially improved by sacrificing the publishing result quality with a bounded guarantee. We conduct extensive experiments on two real datasets to demonstrate the performance of the developed solutions.

  12. Resummation of perturbative QCD by pade approximants

    International Nuclear Information System (INIS)

    Gardi, E.

    1997-01-01

    In this lecture I present some of the new developments concerning the use of Pade Approximants (PA's) for resuming perturbative series in QCD. It is shown that PA's tend to reduce the renormalization scale and scheme dependence as compared to truncated series. In particular it is proven that in the limit where the β function is dominated by the 1-loop contribution, there is an exact symmetry that guarantees invariance of diagonal PA's under changing the renormalization scale. In addition it is shown that in the large β 0 approximation diagonal PA's can be interpreted as a systematic method for approximating the flow of momentum in Feynman diagrams. This corresponds to a new multiple scale generalization of the Brodsky-Lepage-Mackenzie (BLM) method to higher orders. I illustrate the method with the Bjorken sum rule and the vacuum polarization function. (author)

  13. The log-linear return approximation, bubbles, and predictability

    DEFF Research Database (Denmark)

    Engsted, Tom; Pedersen, Thomas Quistgaard; Tanggaard, Carsten

    We study in detail the log-linear return approximation introduced by Campbell and Shiller (1988a). First, we derive an upper bound for the mean approximation error, given stationarity of the log dividendprice ratio. Next, we simulate various rational bubbles which have explosive conditional expec...

  14. On root mean square approximation by exponential functions

    OpenAIRE

    Sharipov, Ruslan

    2014-01-01

    The problem of root mean square approximation of a square integrable function by finite linear combinations of exponential functions is considered. It is subdivided into linear and nonlinear parts. The linear approximation problem is solved. Then the nonlinear problem is studied in some particular example.

  15. Approximate estimation of system reliability via fault trees

    International Nuclear Information System (INIS)

    Dutuit, Y.; Rauzy, A.

    2005-01-01

    In this article, we show how fault tree analysis, carried out by means of binary decision diagrams (BDD), is able to approximate reliability of systems made of independent repairable components with a good accuracy and a good efficiency. We consider four algorithms: the Murchland lower bound, the Barlow-Proschan lower bound, the Vesely full approximation and the Vesely asymptotic approximation. For each of these algorithms, we consider an implementation based on the classical minimal cut sets/rare events approach and another one relying on the BDD technology. We present numerical results obtained with both approaches on various examples

  16. Usefulness of bound-state approximations in reaction theory

    International Nuclear Information System (INIS)

    Adhikari, S.K.

    1981-01-01

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

  17. Quenched Approximation to ΔS = 1 K Decay

    International Nuclear Information System (INIS)

    Christ, Norman H.

    2005-01-01

    The importance of explicit quark loops in the amplitudes contributing to ΔS = 1, K meson decays raises potential ambiguities when these amplitudes are evaluated in the quenched approximation. Using the factorization of these amplitudes into short- and long-distance parts provided by the standard low-energy effective weak Hamiltonian, we argue that the quenched approximation can be conventionally justified if it is applied to the long-distance portion of each amplitude. The result is a reasonably well-motivated definition of the quenched approximation that is close to that employed in the RBC and CP-PACS calculations of these quantities

  18. Discovering approximate-associated sequence patterns for protein-DNA interactions

    KAUST Repository

    Chan, Tak Ming

    2010-12-30

    Motivation: The bindings between transcription factors (TFs) and transcription factor binding sites (TFBSs) are fundamental protein-DNA interactions in transcriptional regulation. Extensive efforts have been made to better understand the protein-DNA interactions. Recent mining on exact TF-TFBS-associated sequence patterns (rules) has shown great potentials and achieved very promising results. However, exact rules cannot handle variations in real data, resulting in limited informative rules. In this article, we generalize the exact rules to approximate ones for both TFs and TFBSs, which are essential for biological variations. Results: A progressive approach is proposed to address the approximation to alleviate the computational requirements. Firstly, similar TFBSs are grouped from the available TF-TFBS data (TRANSFAC database). Secondly, approximate and highly conserved binding cores are discovered from TF sequences corresponding to each TFBS group. A customized algorithm is developed for the specific objective. We discover the approximate TF-TFBS rules by associating the grouped TFBS consensuses and TF cores. The rules discovered are evaluated by matching (verifying with) the actual protein-DNA binding pairs from Protein Data Bank (PDB) 3D structures. The approximate results exhibit many more verified rules and up to 300% better verification ratios than the exact ones. The customized algorithm achieves over 73% better verification ratios than traditional methods. Approximate rules (64-79%) are shown statistically significant. Detailed variation analysis and conservation verification on NCBI records demonstrate that the approximate rules reveal both the flexible and specific protein-DNA interactions accurately. The approximate TF-TFBS rules discovered show great generalized capability of exploring more informative binding rules. © The Author 2010. Published by Oxford University Press. All rights reserved.

  19. An approximate analytical approach to resampling averages

    DEFF Research Database (Denmark)

    Malzahn, Dorthe; Opper, M.

    2004-01-01

    Using a novel reformulation, we develop a framework to compute approximate resampling data averages analytically. The method avoids multiple retraining of statistical models on the samples. Our approach uses a combination of the replica "trick" of statistical physics and the TAP approach for appr...... for approximate Bayesian inference. We demonstrate our approach on regression with Gaussian processes. A comparison with averages obtained by Monte-Carlo sampling shows that our method achieves good accuracy....

  20. Approximate convex hull of affine iterated function system attractors

    International Nuclear Information System (INIS)

    Mishkinis, Anton; Gentil, Christian; Lanquetin, Sandrine; Sokolov, Dmitry

    2012-01-01

    Highlights: ► We present an iterative algorithm to approximate affine IFS attractor convex hull. ► Elimination of the interior points significantly reduces the complexity. ► To optimize calculations, we merge the convex hull images at each iteration. ► Approximation by ellipses increases speed of convergence to the exact convex hull. ► We present a method of the output convex hull simplification. - Abstract: In this paper, we present an algorithm to construct an approximate convex hull of the attractors of an affine iterated function system (IFS). We construct a sequence of convex hull approximations for any required precision using the self-similarity property of the attractor in order to optimize calculations. Due to the affine properties of IFS transformations, the number of points considered in the construction is reduced. The time complexity of our algorithm is a linear function of the number of iterations and the number of points in the output approximate convex hull. The number of iterations and the execution time increases logarithmically with increasing accuracy. In addition, we introduce a method to simplify the approximate convex hull without loss of accuracy.

  1. The high intensity approximation applied to multiphoton ionization

    International Nuclear Information System (INIS)

    Brandi, H.S.; Davidovich, L.; Zagury, N.

    1980-08-01

    It is shown that the most commonly used high intensity approximations as applied to ionization by strong electromagnetic fields are related. The applicability of the steepest descent method in these approximations, and the relation between them and first-order perturbation theory, are also discussed. (Author) [pt

  2. The Log-Linear Return Approximation, Bubbles, and Predictability

    DEFF Research Database (Denmark)

    Engsted, Tom; Pedersen, Thomas Quistgaard; Tanggaard, Carsten

    2012-01-01

    We study in detail the log-linear return approximation introduced by Campbell and Shiller (1988a). First, we derive an upper bound for the mean approximation error, given stationarity of the log dividend-price ratio. Next, we simulate various rational bubbles which have explosive conditional expe...

  3. 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...

  4. Ultrafast Approximation for Phylogenetic Bootstrap

    NARCIS (Netherlands)

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

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

  5. An Approximate Method for Solving Optimal Control Problems for Discrete Systems Based on Local Approximation of an Attainability Set

    Directory of Open Access Journals (Sweden)

    V. A. Baturin

    2017-03-01

    Full Text Available An optimal control problem for discrete systems is considered. A method of successive improvements along with its modernization based on the expansion of the main structures of the core algorithm about the parameter is suggested. The idea of the method is based on local approximation of attainability set, which is described by the zeros of the Bellman function in the special problem of optimal control. The essence of the problem is as follows: from the end point of the phase is required to find a path that minimizes functional deviations of the norm from the initial state. If the initial point belongs to the attainability set of the original controlled system, the value of the Bellman function equal to zero, otherwise the value of the Bellman function is greater than zero. For this special task Bellman equation is considered. The support approximation and Bellman equation are selected. The Bellman function is approximated by quadratic terms. Along the allowable trajectory, this approximation gives nothing, because Bellman function and its expansion coefficients are zero. We used a special trick: an additional variable is introduced, which characterizes the degree of deviation of the system from the initial state, thus it is obtained expanded original chain. For the new variable initial nonzero conditions is selected, thus obtained trajectory is lying outside attainability set and relevant Bellman function is greater than zero, which allows it to hold a non-trivial approximation. As a result of these procedures algorithms of successive improvements is designed. Conditions for relaxation algorithms and conditions for the necessary conditions of optimality are also obtained.

  6. Insights inot the atomic many-particle dynamics of scattering processes by ab-initio calculations

    International Nuclear Information System (INIS)

    Zapukhlyak, Myroslav

    2008-01-01

    The present thesis gives a theoretical contribution to the understanding of the many-particle dynamics in inelastic ion-atom collisions. Many-electron dynamics in ion-helium collisions and proton-sodium collisions was theoretically studied. The description is based on the semiclassical approximation with the straight orbit for the projectile motion. The ion-atom collision problem is by this reduced to a time-dependent many-electron problem and in the non-relativistic approximation described by the time-dependent Schroedinger equation. The solution of the many-electron problem pursues in the framework of the time-dependent density functional theory. The time-dependent Schroedinger equation for the interacting many-electron problem is transformed to the system of the time-dependent Kohn-Sham equations and solved by the two-center-basis generator method. The unknown time-dependent exchange-correlation one-particle potential forces different approximation int he time-dependent Kohn-Shan scheme. In this thesis the model of the independent electrons was applied as basis model, in which the electron-electron correlation is consistently neglected in all parts and in all steps. Differential cross sections for different one- and two-electron processes were calculated in the so-called eikonal approximation for the collisional systems p-He, He 2+ -He, and Ar q+ -He (q=15-18) [de

  7. Performance approximation of pick-to-belt orderpicking systems

    NARCIS (Netherlands)

    M.B.M. de Koster (René)

    1994-01-01

    textabstractIn this paper, an approximation method is discussed for the analysis of pick-to-belt orderpicking systems. The aim of the approximation method is to provide an instrument for obtaining rapid insight in the performance of designs of pick-to-belt orderpicking systems. It can be used to

  8. Modified semiclassical approximation for trapped Bose gases

    International Nuclear Information System (INIS)

    Yukalov, V.I.

    2005-01-01

    A generalization of the semiclassical approximation is suggested allowing for an essential extension of its region of applicability. In particular, it becomes possible to describe Bose-Einstein condensation of a trapped gas in low-dimensional traps and in traps of low confining dimensions, for which the standard semiclassical approximation is not applicable. The result of the modified approach is shown to coincide with purely quantum-mechanical calculations for harmonic traps, including the one-dimensional harmonic trap. The advantage of the semiclassical approximation is in its simplicity and generality. Power-law potentials of arbitrary powers are considered. The effective thermodynamic limit is defined for any confining dimension. The behavior of the specific heat, isothermal compressibility, and density fluctuations is analyzed, with an emphasis on low confining dimensions, where the usual semiclassical method fails. The peculiarities of the thermodynamic characteristics in the effective thermodynamic limit are discussed

  9. On Born approximation in black hole scattering

    Science.gov (United States)

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

    2011-12-01

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

  10. Efficient solution of parabolic equations by Krylov approximation methods

    Science.gov (United States)

    Gallopoulos, E.; Saad, Y.

    1990-01-01

    Numerical techniques for solving parabolic equations by the method of lines is addressed. The main motivation for the proposed approach is the possibility of exploiting a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action of the evolution operator on a given state vector by means of a projection process onto a Krylov subspace. Thus, the resulting approximation consists of applying an evolution operator of a very small dimension to a known vector which is, in turn, computed accurately by exploiting well-known rational approximations to the exponential. Because the rational approximation is only applied to a small matrix, the only operations required with the original large matrix are matrix-by-vector multiplications, and as a result the algorithm can easily be parallelized and vectorized. Some relevant approximation and stability issues are discussed. We present some numerical experiments with the method and compare its performance with a few explicit and implicit algorithms.

  11. Diversity comparison of Pareto front approximations in many-objective optimization.

    Science.gov (United States)

    Li, Miqing; Yang, Shengxiang; Liu, Xiaohui

    2014-12-01

    Diversity assessment of Pareto front approximations is an important issue in the stochastic multiobjective optimization community. Most of the diversity indicators in the literature were designed to work for any number of objectives of Pareto front approximations in principle, but in practice many of these indicators are infeasible or not workable when the number of objectives is large. In this paper, we propose a diversity comparison indicator (DCI) to assess the diversity of Pareto front approximations in many-objective optimization. DCI evaluates relative quality of different Pareto front approximations rather than provides an absolute measure of distribution for a single approximation. In DCI, all the concerned approximations are put into a grid environment so that there are some hyperboxes containing one or more solutions. The proposed indicator only considers the contribution of different approximations to nonempty hyperboxes. Therefore, the computational cost does not increase exponentially with the number of objectives. In fact, the implementation of DCI is of quadratic time complexity, which is fully independent of the number of divisions used in grid. Systematic experiments are conducted using three groups of artificial Pareto front approximations and seven groups of real Pareto front approximations with different numbers of objectives to verify the effectiveness of DCI. Moreover, a comparison with two diversity indicators used widely in many-objective optimization is made analytically and empirically. Finally, a parametric investigation reveals interesting insights of the division number in grid and also offers some suggested settings to the users with different preferences.

  12. Approximating Preemptive Stochastic Scheduling

    OpenAIRE

    Megow Nicole; Vredeveld Tjark

    2009-01-01

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

  13. Precise analytic approximations for the Bessel function J1 (x)

    Science.gov (United States)

    Maass, Fernando; Martin, Pablo

    2018-03-01

    Precise and straightforward analytic approximations for the Bessel function J1 (x) have been found. Power series and asymptotic expansions have been used to determine the parameters of the approximation, which is as a bridge between both expansions, and it is a combination of rational and trigonometric functions multiplied with fractional powers of x. Here, several improvements with respect to the so called Multipoint Quasirational Approximation technique have been performed. Two procedures have been used to determine the parameters of the approximations. The maximum absolute errors are in both cases smaller than 0.01. The zeros of the approximation are also very precise with less than 0.04 per cent for the first one. A second approximation has been also determined using two more parameters, and in this way the accuracy has been increased to less than 0.001.

  14. Approximate Likelihood

    CERN Multimedia

    CERN. Geneva

    2015-01-01

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

  15. Some properties of dual and approximate dual of fusion frames

    OpenAIRE

    Arefijamaal, Ali Akbar; Neyshaburi, Fahimeh Arabyani

    2016-01-01

    In this paper we extend the notion of approximate dual to fusion frames and present some approaches to obtain dual and approximate alternate dual fusion frames. Also, we study the stability of dual and approximate alternate dual fusion frames.

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

    Science.gov (United States)

    Xu, Feng; Cai, Xiaoshu; Ren, Kuanfang

    2004-03-20

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

  17. Inertial parameters in the interacting boson fermion approximation

    International Nuclear Information System (INIS)

    Dukelsky, J.; Lima, C.

    1986-06-01

    The Hartree-Bose-Fermi and the adiabatic approximations are used to derive analytic formulas for the moment of inertia and the decoupling parameter of the interacting boson fermion approximation for deformed systems. These formulas are applied to the SU(3) dynamical symmetry, obtaining perfect agreement with the exact results. (Authors) [pt

  18. Approximation of bivariate copulas by patched bivariate Fréchet copulas

    KAUST Repository

    Zheng, Yanting; Yang, Jingping; Huang, Jianhua Z.

    2011-01-01

    Bivariate Fréchet (BF) copulas characterize dependence as a mixture of three simple structures: comonotonicity, independence and countermonotonicity. They are easily interpretable but have limitations when used as approximations to general dependence structures. To improve the approximation property of the BF copulas and keep the advantage of easy interpretation, we develop a new copula approximation scheme by using BF copulas locally and patching the local pieces together. Error bounds and a probabilistic interpretation of this approximation scheme are developed. The new approximation scheme is compared with several existing copula approximations, including shuffle of min, checkmin, checkerboard and Bernstein approximations and exhibits better performance, especially in characterizing the local dependence. The utility of the new approximation scheme in insurance and finance is illustrated in the computation of the rainbow option prices and stop-loss premiums. © 2010 Elsevier B.V.

  19. Approximation of bivariate copulas by patched bivariate Fréchet copulas

    KAUST Repository

    Zheng, Yanting

    2011-03-01

    Bivariate Fréchet (BF) copulas characterize dependence as a mixture of three simple structures: comonotonicity, independence and countermonotonicity. They are easily interpretable but have limitations when used as approximations to general dependence structures. To improve the approximation property of the BF copulas and keep the advantage of easy interpretation, we develop a new copula approximation scheme by using BF copulas locally and patching the local pieces together. Error bounds and a probabilistic interpretation of this approximation scheme are developed. The new approximation scheme is compared with several existing copula approximations, including shuffle of min, checkmin, checkerboard and Bernstein approximations and exhibits better performance, especially in characterizing the local dependence. The utility of the new approximation scheme in insurance and finance is illustrated in the computation of the rainbow option prices and stop-loss premiums. © 2010 Elsevier B.V.

  20. 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...

  1. 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...

  2. Approximating Exponential and Logarithmic Functions Using Polynomial Interpolation

    Science.gov (United States)

    Gordon, Sheldon P.; Yang, Yajun

    2017-01-01

    This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is…

  3. PWL approximation of nonlinear dynamical systems, part I: structural stability

    International Nuclear Information System (INIS)

    Storace, M; De Feo, O

    2005-01-01

    This paper and its companion address the problem of the approximation/identification of nonlinear dynamical systems depending on parameters, with a view to their circuit implementation. The proposed method is based on a piecewise-linear approximation technique. In particular, this paper describes the approximation method and applies it to some particularly significant dynamical systems (topological normal forms). The structural stability of the PWL approximations of such systems is investigated through a bifurcation analysis (via continuation methods)

  4. Dynamic Analyses of Result Quality in Energy-Aware Approximate Programs

    Science.gov (United States)

    RIngenburg, Michael F.

    Energy efficiency is a key concern in the design of modern computer systems. One promising approach to energy-efficient computation, approximate computing, trades off output precision for energy efficiency. However, this tradeoff can have unexpected effects on computation quality. This thesis presents dynamic analysis tools to study, debug, and monitor the quality and energy efficiency of approximate computations. We propose three styles of tools: prototyping tools that allow developers to experiment with approximation in their applications, online tools that instrument code to determine the key sources of error, and online tools that monitor the quality of deployed applications in real time. Our prototyping tool is based on an extension to the functional language OCaml. We add approximation constructs to the language, an approximation simulator to the runtime, and profiling and auto-tuning tools for studying and experimenting with energy-quality tradeoffs. We also present two online debugging tools and three online monitoring tools. The first online tool identifies correlations between output quality and the total number of executions of, and errors in, individual approximate operations. The second tracks the number of approximate operations that flow into a particular value. Our online tools comprise three low-cost approaches to dynamic quality monitoring. They are designed to monitor quality in deployed applications without spending more energy than is saved by approximation. Online monitors can be used to perform real time adjustments to energy usage in order to meet specific quality goals. We present prototype implementations of all of these tools and describe their usage with several applications. Our prototyping, profiling, and autotuning tools allow us to experiment with approximation strategies and identify new strategies, our online tools succeed in providing new insights into the effects of approximation on output quality, and our monitors succeed in

  5. An improved corrective smoothed particle method approximation for second‐order derivatives

    NARCIS (Netherlands)

    Korzilius, S.P.; Schilders, W.H.A.; Anthonissen, M.J.H.

    2013-01-01

    To solve (partial) differential equations it is necessary to have good numerical approximations. In SPH, most approximations suffer from the presence of boundaries. In this work a new approximation for the second-order derivative is derived and numerically compared with two other approximation

  6. Blind sensor calibration using approximate message passing

    International Nuclear Information System (INIS)

    Schülke, Christophe; Caltagirone, Francesco; Zdeborová, Lenka

    2015-01-01

    The ubiquity of approximately sparse data has led a variety of communities to take great interest in compressed sensing algorithms. Although these are very successful and well understood for linear measurements with additive noise, applying them to real data can be problematic if imperfect sensing devices introduce deviations from this ideal signal acquisition process, caused by sensor decalibration or failure. We propose a message passing algorithm called calibration approximate message passing (Cal-AMP) that can treat a variety of such sensor-induced imperfections. In addition to deriving the general form of the algorithm, we numerically investigate two particular settings. In the first, a fraction of the sensors is faulty, giving readings unrelated to the signal. In the second, sensors are decalibrated and each one introduces a different multiplicative gain to the measurements. Cal-AMP shares the scalability of approximate message passing, allowing us to treat large sized instances of these problems, and experimentally exhibits a phase transition between domains of success and failure. (paper)

  7. The binary collision approximation: Background and introduction

    International Nuclear Information System (INIS)

    Robinson, M.T.

    1992-08-01

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

  8. An inductive algorithm for smooth approximation of functions

    International Nuclear Information System (INIS)

    Kupenova, T.N.

    2011-01-01

    An inductive algorithm is presented for smooth approximation of functions, based on the Tikhonov regularization method and applied to a specific kind of the Tikhonov parametric functional. The discrepancy principle is used for estimation of the regularization parameter. The principle of heuristic self-organization is applied for assessment of some parameters of the approximating function

  9. Gauge-invariant intense-field approximations to all orders

    International Nuclear Information System (INIS)

    Faisal, F H M

    2007-01-01

    We present a gauge-invariant formulation of the so-called strong-field KFR approximations in the 'velocity' and 'length' gauges and demonstrate their equivalence in all orders. The theory thus overcomes a longstanding discrepancy between the strong-field velocity and the length-gauge approximations for non-perturbative processes in intense laser fields. (fast track communication)

  10. On the convergence of multigroup discrete-ordinates approximations

    International Nuclear Information System (INIS)

    Victory, H.D. Jr.; Allen, E.J.; Ganguly, K.

    1987-01-01

    Our analysis is divided into two distinct parts which we label for convenience as Part A and Part B. In Part A, we demonstrate that the multigroup discrete-ordinates approximations are well-defined and converge to the exact transport solution in any subcritical setting. For the most part, we focus on transport in two-dimensional Cartesian geometry. A Nystroem technique is used to extend the discrete ordinates multigroup approximates to all values of the angular and energy variables. Such an extension enables us to employ collectively compact operator theory to deduce stability and convergence of the approximates. In Part B, we perform a thorough convergence analysis for the multigroup discrete-ordinates method for an anisotropically-scattering subcritical medium in slab geometry. The diamond-difference and step-characteristic spatial approximation methods are each studied. The multigroup neutron fluxes are shown to converge in a Banach space setting under realistic smoothness conditions on the solution. This is the first thorough convergence analysis for the fully-discretized multigroup neutron transport equations

  11. New analytic unitarization schemes

    International Nuclear Information System (INIS)

    Cudell, J.-R.; Predazzi, E.; Selyugin, O. V.

    2009-01-01

    We consider two well-known classes of unitarization of Born amplitudes of hadron elastic scattering. The standard class, which saturates at the black-disk limit includes the standard eikonal representation, while the other class, which goes beyond the black-disk limit to reach the full unitarity circle, includes the U matrix. It is shown that the basic properties of these schemes are independent of the functional form used for the unitarization, and that U matrix and eikonal schemes can be extended to have similar properties. A common form of unitarization is proposed interpolating between both classes. The correspondence with different nonlinear equations are also briefly examined.

  12. Approximation theorems by Meyer-Koenig and Zeller type operators

    International Nuclear Information System (INIS)

    Ali Ozarslan, M.; Duman, Oktay

    2009-01-01

    This paper is mainly connected with the approximation properties of Meyer-Koenig and Zeller (MKZ) type operators. We first introduce a general sequence of MKZ operators based on q-integers and then obtain a Korovkin-type approximation theorem for these operators. We also compute their rates of convergence by means of modulus of continuity and the elements of Lipschitz class functionals. Furthermore, we give an rth order generalization of our operators in order to get some explicit approximation results.

  13. Space-angle approximations in the variational nodal method

    International Nuclear Information System (INIS)

    Lewis, E. E.; Palmiotti, G.; Taiwo, T.

    1999-01-01

    The variational nodal method is formulated such that the angular and spatial approximations maybe examined separately. Spherical harmonic, simplified spherical harmonic, and discrete ordinate approximations are coupled to the primal hybrid finite element treatment of the spatial variables. Within this framework, two classes of spatial trial functions are presented: (1) orthogonal polynomials for the treatment of homogeneous nodes and (2) bilinear finite subelement trial functions for the treatment of fuel assembly sized nodes in which fuel-pin cell cross sections are represented explicitly. Polynomial and subelement trial functions are applied to benchmark water-reactor problems containing MOX fuel using spherical harmonic and simplified spherical harmonic approximations. The resulting accuracy and computing costs are compared

  14. Subquadratic medial-axis approximation in $\\mathbb{R}^3$

    Directory of Open Access Journals (Sweden)

    Christian Scheffer

    2015-09-01

    Full Text Available We present an algorithm that approximates the medial axis of a smooth manifold in $\\mathbb{R}^3$ which is given by a sufficiently dense point sample. The resulting, non-discrete approximation is shown to converge to the medial axis as the sampling density approaches infinity. While all previous algorithms guaranteeing convergence have a running time quadratic in the size $n$ of the point sample, we achieve a running time of at most $\\mathcal{O}(n\\log^3 n$. While there is no subquadratic upper bound on the output complexity of previous algorithms for non-discrete medial axis approximation, the output of our algorithm is guaranteed to be of linear size.

  15. Merging Belief Propagation and the Mean Field Approximation

    DEFF Research Database (Denmark)

    Riegler, Erwin; Kirkelund, Gunvor Elisabeth; Manchón, Carles Navarro

    2010-01-01

    We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al., which allows to use the same objective function (Kullback-Leibler divergence......) as a starting point. In this method message passing fixed point equations (which correspond to the update rules in a message passing algorithm) are then obtained by imposing different region-based approximations and constraints on the mean field and belief propagation parts of the corresponding factor graph....... Our results can be applied, for example, to algorithms that perform joint channel estimation and decoding in iterative receivers. This is demonstrated in a simple example....

  16. Explicitly solvable complex Chebyshev approximation problems related to sine polynomials

    Science.gov (United States)

    Freund, Roland

    1989-01-01

    Explicitly solvable real Chebyshev approximation problems on the unit interval are typically characterized by simple error curves. A similar principle is presented for complex approximation problems with error curves induced by sine polynomials. As an application, some new explicit formulae for complex best approximations are derived.

  17. APPROXIMATION OF PROBABILITY DISTRIBUTIONS IN QUEUEING MODELS

    Directory of Open Access Journals (Sweden)

    T. I. Aliev

    2013-03-01

    Full Text Available For probability distributions with variation coefficient, not equal to unity, mathematical dependences for approximating distributions on the basis of first two moments are derived by making use of multi exponential distributions. It is proposed to approximate distributions with coefficient of variation less than unity by using hypoexponential distribution, which makes it possible to generate random variables with coefficient of variation, taking any value in a range (0; 1, as opposed to Erlang distribution, having only discrete values of coefficient of variation.

  18. An approximate fractional Gaussian noise model with computational cost

    KAUST Repository

    Sørbye, Sigrunn H.

    2017-09-18

    Fractional Gaussian noise (fGn) is a stationary time series model with long memory properties applied in various fields like econometrics, hydrology and climatology. The computational cost in fitting an fGn model of length $n$ using a likelihood-based approach is ${\\\\mathcal O}(n^{2})$, exploiting the Toeplitz structure of the covariance matrix. In most realistic cases, we do not observe the fGn process directly but only through indirect Gaussian observations, so the Toeplitz structure is easily lost and the computational cost increases to ${\\\\mathcal O}(n^{3})$. This paper presents an approximate fGn model of ${\\\\mathcal O}(n)$ computational cost, both with direct or indirect Gaussian observations, with or without conditioning. This is achieved by approximating fGn with a weighted sum of independent first-order autoregressive processes, fitting the parameters of the approximation to match the autocorrelation function of the fGn model. The resulting approximation is stationary despite being Markov and gives a remarkably accurate fit using only four components. The performance of the approximate fGn model is demonstrated in simulations and two real data examples.

  19. Sharp Bounds for Symmetric and Asymmetric Diophantine Approximation

    Institute of Scientific and Technical Information of China (English)

    Cornelis KRAAIKAMP; Ionica SMEETS

    2011-01-01

    In 2004,Tong found bounds for the approximation quality of a regular continued fraction convergent to a rational number,expressed in bounds for both the previous and next approximation.The authors sharpen his results with a geometric method and give both sharp upper and lower bounds.The asymptotic frequencies that these bounds occur are also calculated.

  20. evaluation of approximate design procedures for biaxially loaded

    African Journals Online (AJOL)

    The approximation according to the ACI is based on the work by Parme [9] who chose to approximate a as a logarithmic function 9f a parameter /3 representing an actual point on· the non-dimensional load contour, where the two moment components, . related to the respective uniaxial capacities are equal,. i.e. f3=;: my lmuy ...