Mcaninch, G. L.; Myers, M. K.
1980-01-01
The parabolic approximation for the acoustic equations of motion is applied to the study of the sound field generated by a plane wave at or near grazing incidence to a finite impedance boundary. It is shown how this approximation accounts for effects neglected in the usual plane wave reflection analysis which, at grazing incidence, erroneously predicts complete cancellation of the incident field by the reflected field. Examples are presented which illustrate that the solution obtained by the parabolic approximation contains several of the physical phenomena known to occur in wave propagation near an absorbing boundary.
Probing phase of a scattering amplitude beyond the plane-wave approximation
Karlovets, Dmitry V
2016-01-01
Within a plane-wave approach, a number of scattering events in a generic collision process is insensitive to an overall complex phase of a transition amplitude, although this phase is extremely important for a number of problems, especially in hadronic physics at the LHC energies. In reality, however, the particles are better described as localized wave packets with the mean momenta $p$, their uncertainties $\\sigma$, and here we show that the observables grow dependent upon this phase if one lays aside the simplified plane-wave model. A relative contribution of the phase to the cross section is generally attenuated by a small factor $\\sigma^2/p^2 \\ll 1$, making its experimental measurement a rather challenging task. We discuss two methods for probing how this phase changes with the transferred momentum $t$, either by colliding two beams at a non-zero impact-parameter (say, $pp \\rightarrow X$) or by employing the states with the non-trivial wave functions, for instance, vortex particles carrying orbital angula...
Energy Technology Data Exchange (ETDEWEB)
Caballero, J.A. [Univ. de Sevilla (Spain). Dept. de Fisica Atomica, Molecular y Nucl.]|[Instituto de Estructura de la Materia, Consejo Superior de Investigaciones Cientificas, Serrano 123, Madrid 28006 (Spain); Donnelly, T.W. [Centre for Theoretical Physics, Laboratory for Nuclear Science and Dept. of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139-4307 (United States); Moya de Guerra, E. [Instituto de Estructura de la Materia, Consejo Superior de Investigaciones Cientificas, Serrano 123, Madrid 28006 (Spain); Udias, J.M. [Departamento de Fisica Atomica, Molecular y Nuclear, Universidad Complutense de Madrid, Avda. Complutense s/n, Madrid 28040 (Spain)
1998-03-23
The issue of factorization within the context of coincidence quasi-elastic electron scattering is revisited. Using a relativistic formalism for the entire reaction mechanism and restricting ourselves to the case of plane waves for the outgoing proton, we discuss the role of the negative-energy components of the bound nucleon wave function. (orig.). 30 refs.
Resonant-state expansion Born Approximation
Doost, M B
2015-01-01
The Born Approximation is a fundamental formula in Physics, it allows the calculation of weak scattering via the Fourier transform of the scattering potential. I extend the Born Approximation by including in the formula the Fourier transform of a truncated basis of the infinite number of appropriately normalised resonant states. This extension of the Born Approximation is named the Resonant-State Expansion Born Approximation or RSE Born Approximation. The resonant-states of the system can be calculated using the recently discovered RSE perturbation theory for electrodynamics and normalised correctly to appear in spectral Green's functions via the flux volume normalisation.
On Born approximation in black hole scattering
Energy Technology Data Exchange (ETDEWEB)
Batic, D. [University of West Indies, Department of Mathematics, Kingston (Jamaica); Kelkar, N.G.; Nowakowski, M. [Universidad de los Andes, Departamento de Fisica, Bogota (Colombia)
2011-12-15
A massless field propagating on spherically symmetric black hole metrics such as the Schwarzschild, Reissner-Nordstroem and Reissner-Nordstroem-de Sitter backgrounds is considered. In particular, explicit formulae in terms of transcendental functions for the scattering of massless scalar particles off black holes are derived within a Born approximation. It is shown that the conditions on the existence of the Born integral forbid a straightforward extraction of the quasi normal modes using the Born approximation for the scattering amplitude. Such a method has been used in literature. We suggest a novel, well defined method, to extract the large imaginary part of quasinormal modes via the Coulomb-like phase shift. Furthermore, we compare the numerically evaluated exact scattering amplitude with the Born one to find that the approximation is not very useful for the scattering of massless scalar, electromagnetic as well as gravitational waves from black holes. (orig.)
Approximated solutions to Born-Infeld dynamics
Energy Technology Data Exchange (ETDEWEB)
Ferraro, Rafael [Instituto de Astronomía y Física del Espacio (IAFE, CONICET-UBA),Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires (Argentina); Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires,Ciudad Universitaria, Pabellón I, 1428 Buenos Aires (Argentina); Nigro, Mauro [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires,Ciudad Universitaria, Pabellón I, 1428 Buenos Aires (Argentina)
2016-02-01
The Born-Infeld equation in the plane is usefully captured in complex language. The general exact solution can be written as a combination of holomorphic and anti-holomorphic functions. However, this solution only expresses the potential in an implicit way. We rework the formulation to obtain the complex potential in an explicit way, by means of a perturbative procedure. We take care of the secular behavior common to this kind of approach, by resorting to a symmetry the equation has at the considered order of approximation. We apply the method to build approximated solutions to Born-Infeld electrodynamics. We solve for BI electromagnetic waves traveling in opposite directions. We study the propagation at interfaces, with the aim of searching for effects susceptible to experimental detection. In particular, we show that a reflected wave is produced when a wave is incident on a semi-space containing a magnetostatic field.
Entanglement in the Born-Oppenheimer Approximation
Izmaylov, Artur F
2016-01-01
The role of electron-nuclear entanglement on the validity of the Born-Oppenheimer (BO) approximation is investigated. While nonadiabatic couplings generally lead to entanglement and to a failure of the BO approximation, surprisingly the degree of electron-nuclear entanglement is found to be uncorrelated with the degree of validity of the BO approximation. This is because while the degree of entanglement of BO states is determined by their deviation from the corresponding states in the crude BO approximation, the accuracy of the BO approximation is dictated, instead, by the deviation of the BO states from the exact electron-nuclear states. In fact, in the context of a minimal avoided crossing model, extreme cases are identified where an adequate BO state is seen to be maximally entangled, and where the BO approximation fails but the associated BO state remains approximately unentangled. Further, the BO states are found to not preserve the entanglement properties of the exact electron-nuclear eigenstates, and t...
CMB-lensing beyond the Born approximation
Marozzi, Giovanni; Fanizza, Giuseppe; Di Dio, Enea; Durrer, Ruth
2016-09-01
We investigate the weak lensing corrections to the cosmic microwave background temperature anisotropies considering effects beyond the Born approximation. To this aim, we use the small deflection angle approximation, to connect the lensed and unlensed power spectra, via expressions for the deflection angles up to third order in the gravitational potential. While the small deflection angle approximation has the drawback to be reliable only for multipoles l lesssim 2500, it allows us to consistently take into account the non-Gaussian nature of cosmological perturbation theory beyond the linear level. The contribution to the lensed temperature power spectrum coming from the non-Gaussian nature of the deflection angle at higher order is a new effect which has not been taken into account in the literature so far. It turns out to be the leading contribution among the post-Born lensing corrections. On the other hand, the effect is smaller than corrections coming from non-linearities in the matter power spectrum, and its imprint on CMB lensing is too small to be seen in present experiments.
CMB-lensing beyond the Born approximation
Marozzi, Giovanni; Di Dio, Enea; Durrer, Ruth
2016-01-01
We investigate the weak lensing corrections to the cosmic microwave background temperature anisotropies considering effects beyond the Born approximation. To this aim, we use the small deflection angle approximation, to connect the lensed and unlensed power spectra, via expressions for the deflection angles up to third order in the gravitational potential. While the small deflection angle approximation has the drawback to be reliable only for multipoles $\\ell\\lesssim 2500$, it allows us to consistently take into account the non-Gaussian nature of cosmological perturbation theory beyond the linear level. The contribution to the lensed temperature power spectrum coming from the non-Gaussian nature of the deflection angle at higher order is a new effect which has not been taken into account in the literature so far. It turns out to be the leading contribution among the post-Born lensing corrections. On the other hand, the effect is smaller than corrections coming from non-linearities in the matter power spectrum...
Nanostructures: Scattering beyond the Born approximation
Grigoriev, S. V.; Syromyatnikov, A. V.; Chumakov, A. P.; Grigoryeva, N. A.; Napolskii, K. S.; Roslyakov, I. V.; Eliseev, A. A.; Petukhov, A. V.; Eckerlebe, H.
2010-03-01
The neutron scattering on a two-dimensional ordered nanostructure with the third nonperiodic dimension can go beyond the Born approximation. In our model supported by the exact theoretical solution a well-correlated hexagonal porous structure of anodic aluminum oxide films acts as a peculiar two-dimensional grating for the coherent neutron wave. The thickness of the film L (length of pores) plays important role in the transition from the weak to the strong scattering regimes. It is shown that the coherency of the standard small-angle neutron scattering setups suits to the geometry of the studied objects and often affects the intensity of scattering. The proposed theoretical solution can be applied in the small-angle neutron diffraction experiments with flux lines in superconductors, periodic arrays of magnetic or superconducting nanowires, as well as in small-angle diffraction experiments on synchrotron radiation.
Lin, Chih-Ming; Angot, Ludovic
2008-06-15
The first Born approximation is applied to calculate the angular selectivity for different positions on the reconstructed image as a function of the object beam's optical axis angle theta(ob) and reference beam angle theta(rw) for a holographic data storage system that records the Fourier transform holograms in a medium with an infinite plane-wave reference beam. Results are compared with those calculated by the coupled-wave theory.
Forgács, Péter; Romańczukiewicz, Tomasz
2013-01-01
It is shown that in a large class of systems plane waves can act as tractor beams: i.e., an incident plane wave can exert a pulling force on the scatterer. The underlying physical mechanism for the pulling force is due to the sufficiently strong scattering of the incoming wave into another mode having a larger wave number, in which case excess momentum is created behind the scatterer. Such a tractor beam or negative radiation pressure effect arises naturally in systems where the coupling between the scattering channels is due to Aharonov-Bohm (AB) gauge potentials. It is demonstrated that this effect is also present if the AB potential is an induced, ("artificial") gauge potential such as the one found in J. March-Russell, J. Preskill, F. Wilczek, Phys. Rev. Lett. 58 2567 (1992).
Homogeneity and plane-wave limits
Figueroa-O'Farrill, J M; Philip, S; Farrill, Jos\\'e Figueroa-O'; Meessen, Patrick; Philip, Simon
2005-01-01
We explore the plane-wave limit of homogeneous spacetimes. For plane-wave limits along homogeneous geodesics the limit is known to be homogeneous and we exhibit the limiting metric in terms of Lie algebraic data. This simplifies many calculations and we illustrate this with several examples. We also investigate the behaviour of (reductive) homogeneous structures under the plane-wave limit.
Resonant-state expansion Born Approximation applied to Schrodinger's Equation
Doost, M B
2015-01-01
The RSE Born Approximation is a new scattering formula in Physics, it allows the calculation of strong scattering via the Fourier transform of the scattering potential and Resonant-states. In this paper I apply the RSE Born Approximation to Schr\\"odinger's Equation. The resonant-states of the system can be calculated using the recently discovered RSE perturbation theory and normalised correctly to appear in spectral Green's functions via the flux volume normalisation.
Born approximation in linear-time invariant system
Gumjudpai, Burin
2015-01-01
Linear-time invariant (LTI) oscillation systems such as forced mechanical vibration, series RLC and parallel RLC circuits can be solved by using simplest initial conditions or employing of Green's function of which knowledge of initial condition of the force term is needed. Here we show a mathematical connection of the LTI system and the Helmholtz equation form of the time-independent Schr\\"{o}dinger equation in quantum mechanical scattering problem. We apply Born approximation in quantum mechanics to obtain LTI general solution in form of infinite Born series which can be expressed as a series of one-dimensional Feynman graphs. Conditions corresponding to the approximation are given for the case of harmonic driving force. The Born series of the harmonic forced oscillation case are derived by directly applying the approximation to the LTI system or by transforming the LTI system to Helmholtz equation prior to doing the approximation.
Complex method for approximated solutions to Born-Infeld equation
Ferraro, Rafael
2015-01-01
We display the method to solve the Born-Infeld equation in the complex plane. As the exact solution is obtained in an implicit form, we turn it into an explicit form by means of a perturbative procedure which takes care of secular behaviors common to this kind of approximations. We apply the method to build solutions to Born-Infeld electrodynamics. In particular, we study BI electromagnetic waves at interfaces, with the aim of searching for effects susceptible of experimental detection.
Causal inheritence in plane wave quotients
Energy Technology Data Exchange (ETDEWEB)
Hubeny, Veronika E.; Rangamani, Mukund; Ross, Simon F.
2003-11-24
We investigate the appearance of closed timelike curves in quotients of plane waves along spacelike isometries. First we formulate a necessary and sufficient condition for a quotient of a general spacetime to preserve stable causality. We explicitly show that the plane waves are stably causal; in passing, we observe that some pp-waves are not even distinguishing. We then consider the classification of all quotients of the maximally supersymmetric ten-dimensional plane wave under a spacelike isometry, and show that the quotient will lead to closed timelike curves iff the isometry involves a translation along the u direction. The appearance of these closed timelike curves is thus connected to the special properties of the light cones in plane wave spacetimes. We show that all other quotients preserve stable causality.
Energy Technology Data Exchange (ETDEWEB)
Jin, Jinshuang, E-mail: jsjin@hznu.edu.cn [Department of Physics, Hangzhou Normal University, Hangzhou 310036 (China); Li, Jun [Department of Physics, Hangzhou Normal University, Hangzhou 310036 (China); College of Physics and Electronic Engineering, Dezhou University, Dezhou 253023 (China); Liu, Yu [State Key Laboratory for Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083 (China); Li, Xin-Qi, E-mail: lixinqi@bnu.edu.cn [State Key Laboratory for Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083 (China); Department of Physics, Beijing Normal University, Beijing 100875 (China); Department of Chemistry, Hong Kong University of Science and Technology, Kowloon (Hong Kong); Yan, YiJing, E-mail: yyan@ust.hk [Department of Chemistry, Hong Kong University of Science and Technology, Kowloon (Hong Kong); Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026 (China)
2014-06-28
Beyond the second-order Born approximation, we propose an improved master equation approach to quantum transport under self-consistent Born approximation. The basic idea is to replace the free Green's function in the tunneling self-energy diagram by an effective reduced propagator under the Born approximation. This simple modification has remarkable consequences. It not only recovers the exact results for quantum transport through noninteracting systems under arbitrary voltages, but also predicts the challenging nonequilibrium Kondo effect. Compared to the nonequilibrium Green's function technique that formulates the calculation of specific correlation functions, the master equation approach contains richer dynamical information to allow more efficient studies for such as the shot noise and full counting statistics.
Jin, Jinshuang; Li, Jun; Liu, Yu; Li, Xin-Qi; Yan, YiJing
2014-06-28
Beyond the second-order Born approximation, we propose an improved master equation approach to quantum transport under self-consistent Born approximation. The basic idea is to replace the free Green's function in the tunneling self-energy diagram by an effective reduced propagator under the Born approximation. This simple modification has remarkable consequences. It not only recovers the exact results for quantum transport through noninteracting systems under arbitrary voltages, but also predicts the challenging nonequilibrium Kondo effect. Compared to the nonequilibrium Green's function technique that formulates the calculation of specific correlation functions, the master equation approach contains richer dynamical information to allow more efficient studies for such as the shot noise and full counting statistics.
Electronic Flux Density beyond the Born-Oppenheimer Approximation.
Schild, Axel; Agostini, Federica; Gross, E K U
2016-05-19
In the Born-Oppenheimer approximation, the electronic wave function is typically real-valued and hence the electronic flux density (current density) seems to vanish. This is unfortunate for chemistry, because it precludes the possibility to monitor the electronic motion associated with the nuclear motion during chemical rearrangements from a Born-Oppenheimer simulation of the process. We study an electronic flux density obtained from a correction to the electronic wave function. This correction is derived via nuclear velocity perturbation theory applied in the framework of the exact factorization of electrons and nuclei. To compute the correction, only the ground state potential energy surface and the electronic wave function are needed. For a model system, we demonstrate that this electronic flux density approximates the true one very well, for coherent tunneling dynamics as well as for over-the-barrier scattering, and already for mass ratios between electrons and nuclei that are much larger than the true mass ratios.
Coulomb-Born-Oppenheimer approximation in Ps-H scattering
Indian Academy of Sciences (India)
Hasi Ray
2006-02-01
To improve the Coulomb-Born approximation (CBA) theory of ionization in positronium (Ps) and atom scattering, the effect of exchange is introduced. The nine-dimensional exchange amplitude for ionization of Ps in Ps-H scattering is reduced to a two-dimensional integral using the present Coulomb-Born-Oppenheimer approximation (CBOA). The methodology is extremely useful to evaluate ionization parameters for different target systems and for different types of ionization processes. It is then applied to evaluate the Ps-ionization cross-section and to estimate the effect of exchange on Ps-ionization in Ps-H system. We establish the importance of exchange at lower energy region.
Properties of strongly dipolar Bose gases beyond the Born approximation
Ołdziejewski, Rafał
2016-01-01
Strongly dipolar Bose gases can form liquid droplets stabilized by quantum fluctuations. In theoretical description of this phenomenon, low energy scattering amplitude is utilized as an effective potential. We show that for magnetic atoms corrections with respect to Born approximation arise, and derive modified pseudopotential using realistic interaction model. We discuss the resulting changes in collective mode frequencies and droplet stability diagram. Our results are relevant for recent experiments with erbium and dysprosium atoms.
On Corrections to the Born-Oppenheimer Approximation
Kerley, Gerald I
2013-01-01
This report presents a new approach for treating the coupling of electrons and nuclei in quantum mechanical calculations for molecules and condensed matter. It includes the standard "Born-Oppenheimer approximation" as a special case but treats both adiabatic and non-adiabatic corrections using perturbation theory. The adiabatic corrections include all terms that do not explicitly involve the nuclear wavefunctions, so that the nuclei move on a single electronic potential surface. The non-adiabatic corrections, which allow the nuclei to move on more than one potential surface, include coupling between the electronic and nuclear wavefunctions. The method is related to an approach first proposed by Born and Huang, but it differs in the methodology and in the definition of the electronic wavefunctions and potential surfaces. A simple example is worked out to illustrate the mechanics of the technique. The report also includes a review of previous work.
Horizons and plane waves: A review
Hubeny, V E; Hubeny, Veronika E.; Rangamani, Mukund
2003-01-01
We review the attempts to construct black hole/string solutions in asymptotically plane wave spacetimes. First, we demonstrate that geometries admitting a covariantly constant null Killing vector cannot admit event horizons, which implies that pp-waves can't describe black holes. However, relaxing the symmetry requirements allows us to generate solutions which do possess regular event horizons while retaining the requisite asymptotic properties. In particular, we present two solution generating techniques and use them to construct asymptotically plane wave black string/brane geometries.
Free string evolution across plane wave singularities
Craps, Ben; Evnin, Oleg
2009-01-01
In these proceedings, we summarize our studies of free string propagation in (near-)singular scale-invariant plane wave geometries. We analyze the singular limit of the evolution for the center-of-mass motion and all excited string modes. The requirement that the entire excitation energy of the string should be finite excludes consistent propagation across the singularity, in case no dimensionful scales are introduced at the singular locus (in an otherwise scale-invariant space-time).
Breakdown of the adiabatic Born-Oppenheimer approximation in graphene
Pisana, Simone; Lazzeri, Michele; Casiraghi, Cinzia; Novoselov, Kostya S.; Geim, A. K.; Ferrari, Andrea C.; Mauri, Francesco
2007-03-01
The adiabatic Born-Oppenheimer approximation (ABO) has been the standard ansatz to describe the interaction between electrons and nuclei since the early days of quantum mechanics. ABO assumes that the lighter electrons adjust adiabatically to the motion of the heavier nuclei, remaining at any time in their instantaneous ground state. ABO is well justified when the energy gap between ground and excited electronic states is larger than the energy scale of the nuclear motion. In metals, the gap is zero and phenomena beyond ABO (such as phonon-mediated superconductivity or phonon-induced renormalization of the electronic properties) occur. The use of ABO to describe lattice motion in metals is, therefore, questionable. In spite of this, ABO has proved effective for the accurate determination of chemical reactions, molecular dynamics and phonon frequencies in a wide range of metallic systems. Here, we show that ABO fails in graphene. Graphene, recently discovered in the free state, is a zero-bandgap semiconductor that becomes a metal if the Fermi energy is tuned applying a gate voltage, Vg. This induces a stiffening of the Raman G peak that cannot be described within ABO.
Colliding Plane Waves in String Theory
Chen, B; Furuta, K; Lin, F L; Chen, Bin; Chu, Chong-Sun; Furuta, Ko; Lin, Feng-Li
2004-01-01
We construct colliding plane wave solutions in higher dimensional gravity theory with dilaton and higher form flux, which appears naturally in the low energy theory of string theory. Especially, the role of the junction condition in constructing the solutions is emphasized. Our results not only include the previously known CPW solutions, but also provide a wide class of new solutions that is not known in the literature before. We find that late time curvature singularity is always developed for the solutions we obtained in this paper. This supports the generalized version of Tipler's theorem in higher dimensional supergravity.
Blackfolds, plane waves and minimal surfaces
Armas, Jay; Blau, Matthias
2015-01-01
Minimal surfaces in Euclidean space provide examples of possible non-compact horizon geometries and topologies in asymptotically flat space-time. On the other hand, the existence of limiting surfaces in the space-time provides a simple mechanism for making these configurations compact. Limiting surfaces appear naturally in a given space-time by making minimal surfaces rotate but they are also inherent to plane wave or de Sitter space-times in which case minimal surfaces can be static and comp...
Blackfolds, Plane Waves and Minimal Surfaces
Armas, Jay
2015-01-01
Minimal surfaces in Euclidean space provide examples of possible non-compact horizon geometries and topologies in asymptotically flat space-time. On the other hand, the existence of limiting surfaces in the space-time provides a simple mechanism for making these configurations compact. Limiting surfaces appear naturally in a given space-time by making minimal surfaces rotate but they are also inherent to plane wave or de Sitter space-times in which case minimal surfaces can be static and compact. We use the blackfold approach in order to scan for possible black hole horizon geometries and topologies in asymptotically flat, plane wave and de Sitter space-times. In the process we uncover several new configurations, such as black helicoids and catenoids, some of which have an asymptotically flat counterpart. In particular, we find that the ultraspinning regime of singly-spinning Myers-Perry black holes, described in terms of the simplest minimal surface (the plane), can be obtained as a limit of a black helicoid...
Blackfolds, plane waves and minimal surfaces
Armas, Jay; Blau, Matthias
2015-07-01
Minimal surfaces in Euclidean space provide examples of possible non-compact horizon geometries and topologies in asymptotically flat space-time. On the other hand, the existence of limiting surfaces in the space-time provides a simple mechanism for making these configurations compact. Limiting surfaces appear naturally in a given space-time by making minimal surfaces rotate but they are also inherent to plane wave or de Sitter space-times in which case minimal surfaces can be static and compact. We use the blackfold approach in order to scan for possible black hole horizon geometries and topologies in asymptotically flat, plane wave and de Sitter space-times. In the process we uncover several new configurations, such as black helicoids and catenoids, some of which have an asymptotically flat counterpart. In particular, we find that the ultraspinning regime of singly-spinning Myers-Perry black holes, described in terms of the simplest minimal surface (the plane), can be obtained as a limit of a black helicoid, suggesting that these two families of black holes are connected. We also show that minimal surfaces embedded in spheres rather than Euclidean space can be used to construct static compact horizons in asymptotically de Sitter space-times.
Improved beamforming performance using pulsed plane wave decomposition
DEFF Research Database (Denmark)
Munk, Peter; Jensen, Jørgen Arendt
2000-01-01
A tool for calculating the beamformer setup associated with a specified pulsed acoustic field is presented. The method is named Pulsed Plane Wave Decomposition (PPWD) and is based on the decomposition of a pulsed acoustic field into a set of PPWs at a given depth. Each PPW can be propagated...... to the location of the elements of an array transducer by a time delay. The contribution of each propagated PPW is summed to form one time function for each array element (the BMF matrix). This approach gives the beamformer setup needed to obtain a close approximation to the desired bounded pulsed acoustic field...... without involving any optimization scheme. The approximation arises due to the limited size of the acoustic aperture and the spatial sampling property of the array transducer. Thus, the acoustical field can be designed according to the imaging needs. The method is demonstrated by examples in the 2D space...
On the plane-wave cubic vertex
Lucietti, J; Sinha, A K; Lucietti, James; Schäfer-Nameki, Sakura; Sinha, Aninda
2004-01-01
The exact bosonic Neumann matrices of the cubic vertex in plane-wave light-cone string field theory are derived using the contour integration techniques developed in our earlier paper. This simplifies the original derivation of the vertex. In particular, the Neumann matrices are written in terms of \\mu-deformed Gamma-functions, thus casting them into a form that elegantly generalizes the well-known flat-space solution. The asymptotics of the \\mu-deformed Gamma-functions allow one to determine the large-\\mu behaviour of the Neumann matrices including exponential corrections. We provide an explicit expression for the first exponential correction and make a conjecture for the subsequent exponential correction terms.
The plane wave spectrum representation of electromagnetic fields
Clemmow, P C
1966-01-01
The Plane Wave Spectrum Representation of Electromagnetic Fields presents the theory of the electromagnetic field with emphasis to the plane wave. This book explains how fundamental electromagnetic fields can be represented by the superstition of plane waves traveling in different directions. Organized into two parts encompassing eight chapters, this book starts with an overview of the methods whereby plane wave spectrum representation can be used in attacking different characteristic problems belonging to the theories of radiation, diffraction, and propagation. This book then discusses the co
Efficient computation of GW energy level corrections for molecules described in a plane wave basis
Rousseau, Bruno; Laflamme Janssen, Jonathan; Côté, Michel
2013-03-01
An efficient computational approach is presented to compute the ionisation energy and quasiparticle band gap at the level of the GW approximation when the Hilbert space is described in terms of plane waves. The method relies on ab initio calculations as a starting point. Then, the use of the Sternheimer equation eliminates slowly convergent sums on conduction states. Further, the Lanczos method is used to efficiently extract the most important eigenstates of the dielectric operator. This approach avoids the explicit computation of matrix elements of the dielectric operator in the plane wave basis, a crippling bottleneck of the brute force approach. The method is initially applied to organic molecules of current interest in the field of organic photovoltaics. Given the completeness of the plane wave basis, systematic convergence studies can be conducted. Furthermore, the method can readily be extended to describe polymers, which are also of interest for photovoltaic applications, but remain a significant computational challenge for methods based on localized basis sets.
Nuclear Rotations and the Born-Oppenheimer Approximation
Zettili, Nouredine
2011-10-01
We deal here with the application of the Nuclear Born Oppenheimer (NBO) method to the description of nuclear rotations. As an edifying illustration, we apply the NBO formalism to study the rotational motion of nuclei which are axially-symmetric and even, but whose shells are not closed. We focus, in particular, on the derivation of expressions for the rotational energy and for the moment of inertia. Additionally, we examine the connection between the NBO method and the self-consistent cranking (SCC) model. Finally, we compare the moment of inertia generated by the NBO method with the Thouless-Valantin formula and hence establish a connection between the NBO method and the large body of experimental data.
Electron-Helium Scattering in a Bichromatic Laser Field in the Second-Order Born Approximation
Institute of Scientific and Technical Information of China (English)
ZHOU Bin; LI Shu-Min
2009-01-01
@@ The elastic scattering of electrons in atomic helium assisted by a bichromatic laser field is investigated in the second order Born approximation. The target atom is approximated by a simple screening potential. The dependence of the differential cross section on the relative phase between the two laser components is calculated, and compared with the recent results of first order Born approximation [Sun J F, Liang M C and Zhu Z L 2007Chin. Phys. Lett. 24 2572].
Energy Technology Data Exchange (ETDEWEB)
W. Xu; B. Anderson; L. Auberbach; T. Averett; W. Bertozzi; T. Black; J. Calarco; L. Cardman; G.D. Cates; Z.W. Chai; J.P. Chen; S. Choi; E. Chudakov; S. Churchwell; G.S. Corrado; C. Crawford; D. Dale; A. Deur; P. Djawotho; T.W. Donnelly; D. Dutta; J.M. Finn; H. Gao; R. Gilman; A.V. Glamazdin; C. Glashausser; Walter Gloeckle; J. Golak; J. Gomez; V.G. Gorbenko; J.O. Hansen; F.W. Hersman; D.W. Higinbotham; R. Holmes; C.R. Howell; E. Hughes; B. Humensky; S. Incerti; C.W. de Jager; J.S. Jensen; X. Jiang; C.E. Jones; M. Jones; R. Kahl; H. Kamada; A. Kievsky; I. Kominis; W. Korsch; K. Kramer; G. Kumbartzki; M. Kuss; E. Lakuriqi; M. Liang; N. Liyanage; J. LeRose; S. Malov; D.J. Margaziotis; J.W. Martin; K. McCormick; R. D. McKeown; K. McIlhany; Z.E. Meziani; R. Michaels; G.W. Miller; J. Mitchell; S. Nanda; E. Pace; T. Pavlin; G.G. Petratos; R.I. Pomatsalyuk; D. Pripstein; D. Prout; R.D. Ransome; Y. Roblin; M. Rvachev; A. Saha; G. Salme; M. Schnee; T. Shin; K. Slifer; P.A. Souder; S. Strauch; R. Suleiman; M. Sutter; B. Tipton; L. Todor; M. Viviani; B. Vlahovic; J. Watson; C.F. Williamson; H. Witala; B. Wojtsekhowski; F. Xiong; J. Yeh; P. Zolnierczuk
2003-02-01
A high precision measurement of the transverse spin-dependent asymmetry A{sub T} in {sup 3}{rvec H}e({rvec e},e{prime}) quasielastic scattering was performed in Hall A at Jefferson Lab at values of the squared four-momentum transfer, Q{sup 2}, between 0.1 and 0.6 (GeV/c){sup 2}. A{sub T} is sensitive to the neutron magnetic form factor, G{sub M}{sup n}. Values of G{sub M}{sup n} at Q{sup 2} = 0.1 and 0.2 (GeV/c){sup 2}, extracted using Faddeev calculations, were reported previously. Here, we report the extraction of G{sub M}{sup n} for the remaining Q{sup 2}-values in the range from 0.3 to 0.6 (GeV/c){sup 2} using a Plane-Wave Impulse Approximation calculation. The results are in good agreement with recent precision data from experiments using a deuterium target.
Plane-wave least-squares reverse-time migration
Dai, Wei
2013-06-03
A plane-wave least-squares reverse-time migration (LSRTM) is formulated with a new parameterization, where the migration image of each shot gather is updated separately and an ensemble of prestack images is produced along with common image gathers. The merits of plane-wave prestack LSRTM are the following: (1) plane-wave prestack LSRTM can sometimes offer stable convergence even when the migration velocity has bulk errors of up to 5%; (2) to significantly reduce computation cost, linear phase-shift encoding is applied to hundreds of shot gathers to produce dozens of plane waves. Unlike phase-shift encoding with random time shifts applied to each shot gather, plane-wave encoding can be effectively applied to data with a marine streamer geometry. (3) Plane-wave prestack LSRTM can provide higher-quality images than standard reverse-time migration. Numerical tests on the Marmousi2 model and a marine field data set are performed to illustrate the benefits of plane-wave LSRTM. Empirical results show that LSRTM in the plane-wave domain, compared to standard reversetime migration, produces images efficiently with fewer artifacts and better spatial resolution. Moreover, the prestack image ensemble accommodates more unknowns to makes it more robust than conventional least-squares migration in the presence of migration velocity errors. © 2013 Society of Exploration Geophysicists.
On the validity of the Born approximation for weak cosmic flexions
Schaefer, Bjoern Malte; Kalovidouris, Angelos Fotios; Bacon, David J
2011-01-01
Weak lensing calculations are often made under the assumption of the Born approximation, where the ray path is approximated as a straight radial line. In addition, lens-lens couplings where there are several deflections along the light ray are often neglected. We examine the effect of dropping the Born approximation and taking lens-lens couplings into account, for weak lensing effects up to second order (cosmic flexion), by making a perturbative expansion in the light path. We present a diagrammatic representation of the resulting corrections to the lensing effects. The flexion signal, which measures the derivative of the density field, acquires correction terms proportional to the squared gravitational shear; we also find that by dropping the Born approximation, two further degrees of freedom of the lensing distortion can be excited (the twist components), in addition to the four standard flexion components. We derive angular power spectra of the flexion and twist, with and without the Born-approximation and...
The second Born approximation in electron-atom collisions in the presence of a laser field
Energy Technology Data Exchange (ETDEWEB)
Makhoute, A. [UFR de Physique Atomique, Moleculaire et Optique Appliquee, Faculte des Sciences, Universite Moulay Ismail, Meknes (Morocco)]. E-mail: makhoute@fsmek.ac.ma; Khalil, D.; Zitane, M.; Bouzidi, M. [UFR de Physique Atomique, Moleculaire et Optique Appliquee, Faculte des Sciences, Universite Moulay Ismail, Meknes (Morocco)
2002-02-28
The second-order Born approximation (SBA) has been used to calculate the differential cross section for electron-hydrogen collisions in the presence of a linearly polarized laser field. We present a more precise treatment of the small-energy region of an incident electron by improving the calculation of the second Born term in this energy region. Detailed calculations of the scattering amplitudes are performed by using the Sturmian basis expansion. Our SBA results agree very well with those obtained in the first-order Born approximation at larger incident electron energies. (author)
On the validity of the Born approximation for weak cosmic flexions
Schäfer, Björn Malte; Heisenberg, Lavinia; Kalovidouris, Angelos F.; Bacon, David J.
2012-02-01
Weak lensing calculations are often made under the assumption of the Born approximation, where the ray path is approximated as a straight radial line. In addition, lens-lens couplings where there are several deflections along the light ray are often neglected. We examine the effect of dropping the Born approximation and taking lens-lens couplings into account, for weak lensing effects up to second order (cosmic flexion), by making a perturbative expansion in the light path. We present a diagrammatic representation of the resulting corrections to the lensing effects. The flexion signal, which measures the derivative of the density field, acquires correction terms proportional to the squared gravitational shear; we also find that by dropping the Born approximation, two further degrees of freedom of the lensing distortion can be excited (the twist components), in addition to the four standard flexion components. We derive angular power spectra of the flexion and twist, with and without the Born approximation and lens-lens couplings and confirm that the Born approximation is an excellent approximation for weak cosmic flexions, but may fail in the strong lensing regime.
Regularized plane-wave least-squares Kirchhoff migration
Wang, Xin
2013-09-22
A Kirchhoff least-squares migration (LSM) is developed in the prestack plane-wave domain to increase the quality of migration images. A regularization term is included that accounts for mispositioning of reflectors due to errors in the velocity model. Both synthetic and field results show that: 1) LSM with a reflectivity model common for all the plane-wave gathers provides the best image when the migration velocity model is accurate, but it is more sensitive to the velocity errors, 2) the regularized plane-wave LSM is more robust in the presence of velocity errors, and 3) LSM achieves both computational and IO saving by plane-wave encoding compared to shot-domain LSM for the models tested.
The second Born approximation of electron-argon elastic scattering in a Bichromatic laser field
Zhou, Bin; Wen, Da-Yong
2013-01-01
We study the elastic scattering of atomic argon by electron in the presence of a bichromatic laser field in the second Born approximation. The target atom is approximated by a simple screening potential and the continuum states of the impinging and emitting electrons are described as Volkov states. We evaluate the S-matrix elements numerically. The dependence of differential cross section on the relative phase between the two laser components is presented. The results obtained in the first and second Born approximation are compared and analysed.
Plane-wave scattering from half-wave dipole arrays
DEFF Research Database (Denmark)
Jensen, Niels E.
1970-01-01
A matrix equation for determination of plane-wave scattering from arrays of thin short-circuited dipoles of lengths about half a wavelength is derived. Numerical and experimental results are presented for linear, circular, and concentric circular arrays.......A matrix equation for determination of plane-wave scattering from arrays of thin short-circuited dipoles of lengths about half a wavelength is derived. Numerical and experimental results are presented for linear, circular, and concentric circular arrays....
3D plane-wave least-squares Kirchhoff migration
Wang, Xin
2014-08-05
A three dimensional least-squares Kirchhoff migration (LSM) is developed in the prestack plane-wave domain to increase the quality of migration images and the computational efficiency. Due to the limitation of current 3D marine acquisition geometries, a cylindrical-wave encoding is adopted for the narrow azimuth streamer data. To account for the mispositioning of reflectors due to errors in the velocity model, a regularized LSM is devised so that each plane-wave or cylindrical-wave gather gives rise to an individual migration image, and a regularization term is included to encourage the similarities between the migration images of similar encoding schemes. Both synthetic and field results show that: 1) plane-wave or cylindrical-wave encoding LSM can achieve both computational and IO saving, compared to shot-domain LSM, however, plane-wave LSM is still about 5 times more expensive than plane-wave migration; 2) the regularized LSM is more robust compared to LSM with one reflectivity model common for all the plane-wave or cylindrical-wave gathers.
Resonant-state-expansion Born approximation with a correct eigen-mode normalisation
Doost, M. B.
2016-08-01
The Born approximation (Born 1926 Z. Phys. 38 802) is a fundamental result in physics, it allows the calculation of weak scattering via the Fourier transform of the scattering potential. As was done by previous authors (Ge et al 2014 New J. Phys. 16 113048) the Born approximation is extended by including in the formula the resonant-states (RSs) of the scatterer. However in this study unlike previous studies the included eigen-modes are correctly normalised with dramatic positive consequences for the accuracy of the method. The normalisation of RSs used in the previous RS expansion Born approximation or resonant-state expansion (RSE) Born approximation made in Ge et al (2014 New J. Phys. 16 113048) has been shown to be numerically unstable in Muljarov et al (2014 arXiv:1409.6877) and by analytics here. The RSs of the system can be calculated using my recently discovered RSE perturbation theory for dispersive electrodynamic scatterers (Muljarov et al 2010 Europhys. Lett. 92 50010; Doost et al 2012 Phys. Rev. A 85 023835; Doost et al 2013 Phys. Rev. A 87 043827; Armitage et al 2014 Phys. Rev. A 89; Doost et al 2014 Phys. Rev. A 90 013834) and normalised correctly to appear in spectral Green's functions and hence the RSE Born approximation via the flux-volume normalisation which I recently rigorously derived in Armitage et al (2014 Phys. Rev. A 89), Doost et al (2014 Phys. Rev. A 90 013834), Doost (2016 Phys. Rev. A 93 023835). In the case of effectively one-dimensional systems I find a RSE Born approximation alternative to the scattering matrix method.
Energy Technology Data Exchange (ETDEWEB)
Dal Cappello, C [Laboratoire de Physique Moleculaire et des Collisions, ICPMB (FR 2843), Institut de Physique, Universite Paul Verlaine-Metz, 1 rue Arago, 57078 Metz Cedex 3 (France); Haddadou, A; Menas, F [Laboratoire de Physique et Chimie, Universite Mouloud MAMMERI Tizi-Ouzou, Quantique, BP 17, 15000 Tizi-Ouzou (Algeria); Roy, A C, E-mail: cappello@univ-metz.fr [School of Mathematical Sciences, Ramakrishna Mission Vivekananda University, Belur Math 711202, West Bengal (India)
2011-01-14
Recently, Lahmam-Bennani et al (2010 J. Phys. B: At. Mol. Opt. Phys. 43 105201) have shown that the second Born approximation is necessary to describe the experimental results of the double ionization of atoms and molecules. The second Born approximation needs a difficult triple numerical integration and often many authors find some controversial results. We now investigate, in greater detail, the application of the second Born approximation for the easier case: the ionization of atomic hydrogen by electrons. The ionization of atomic hydrogen allows us to check accurately this approximation because the wavefunctions describing the target are known exactly. Moreover, sophisticated models such as convergent close coupling (CCC) and the continuum distorted wave eikonal initial state (CDW-EIS) exist and give closer results leading to easier comparisons. We report accurate second Born results for differential cross sections for the ionization of atomic hydrogen using a basis including 100 discrete states, and another basis including 32 discrete states and pseudo-states. The results of the present method are compared with other calculations and experiment. The single ionization of helium is also investigated in order to answer an old controversy between two different theoretical results. Finally, an application of the second Born approximation to the double ionization of helium has been performed.
Scattering of electromagnetic plane waves by a buried vertical dike
Directory of Open Access Journals (Sweden)
Batista Lurimar S.
2003-01-01
Full Text Available The complete and exact solution of the scattering of a TE mode frequency domain electromagnetic plane wave by a vertical dike under a conductive overburden has been established. An integral representation composed of one-sided Fourier transforms describes the scattered electric field components in each one of the five media: air, overburden, dike, and the country rocks on both sides of the dike. The determination of the terms of the series that represents the spectral components of the Fourier integrals requires the numerical inversion of a sparse matrix, and the method of successive approaches. The zero-order term of the series representation for the spectral components of the overburden, for given values of the electrical and geometrical parameters of the model, has been computed. This result allowed to determine an approximate value of the variation of the electric field on the top of the overburden in the direction perpendicular to the strike of the dike. The results demonstrate the efficiency of this forward electromagnetic modeling, and are fundamental for the interpretation of VLF and Magnetotelluric data.
Exact exchange plane-wave-pseudopotential calculations for slabs.
Engel, Eberhard
2014-05-14
The exact exchange of density functional theory is applied to both free-standing graphene and a Si(111) slab, using the plane-wave pseudopotential (PWPP) approach and a periodic repetition of the supercell containing the slab. It is shown that (i) PWPP calculations with exact exchange for slabs in supercell geometry are basically feasible, (ii) the width of the vacuum required for a decoupling of the slabs is only moderately larger than in the case of the local-density approximation, and (iii) the resulting exchange potential vx shows an extended region, both far outside the surface of the slab and far from the middle of the vacuum region between the slabs, in which vx behaves as -e(2)/z, provided the width of the vacuum is chosen sufficiently large. This last result is corroborated by an analytical analysis of periodically repeated jellium slabs. The intermediate -e(2)/z behavior of vx can be used for an absolute normalization of vx and the total Kohn-Sham potential, which, in turn, allows the determination of the work function.
Karlovets, D V; Serbo, V G
2015-01-01
Laser photons carrying non-zero orbital angular momentum are known and exploited during the last twenty years. Recently it has been demonstrated experimentally that such (twisted) electrons can be produced and even focused to a subnanometer scale. Thus, twisted electrons emerge as a new tool in atomic physics. The state of a twisted electron can be considered as a specific wave packet of plane waves. In the present paper-I we consider elastic scattering of the wave packets of fast non-relativistic particles on a potential field. We obtain simple and convenient formulae for a number of events in such a scattering. The equations derived represent, in fact, generalization of the well-known Born approximation for the case when finite sizes and inhomogeneity of the initial packet should be taken into account. To illustrate the obtained results, we consider two simple models corresponding to scattering of a Gaussian wave packet on the Gaussian potential and on the hydrogen atom. The scattering of twisted electrons ...
Aperture domain model image reconstruction (ADMIRE) with plane wave synthesis
Dei, Kazuyuki; Tierney, Jaime; Byram, Brett
2017-03-01
In our previous studies, we demonstrated that our aperture domain model-based clutter suppression algorithm improved image quality of in vivo B-mode data obtained from focused transmit beam sequences. Our approach suppresses off-axis clutter and reverberation and tackles limitations of related algorithms because it preserves RF channel signals and speckle statistics. We call the algorithm aperture domain model image reconstruction (ADMIRE). We previously focused on reverberation suppression, but ADMIRE is also effective at suppressing off-axis clutter. We are interested in how ADMIRE performs on plane wave sequences and the impact of AD- MIRE applied before and after synthetic beamforming of steered plane wave sequences. We employed simulated phantoms using Field II and tissue-mimicking phantoms to evaluate ADMIRE applied to plane wave sequencing. We generated images acquired from plane waves with and without synthetic aperture synthesis and measured contrast and contrast-to-noise ratio (CNR). For simulated cyst images formed from single plane waves, the contrast for delay-and-sum (DAS) and ADMIRE are 15.64 dB and 28.34 dB, respectively, while the CNR are 1.76 dB and 3.90 dB, respectively. Based on these findings, ADMIRE improves plane wave image quality. We also applied ADMIRE to resolution phantoms having a point target at 3 cm depth on-axis, simulating the point spread functions from data obtained from 1 and 75 steered plane waves, along with linear scan at focus of 3 and 4 cm depth. We then examined the outcome of applying ADMIRE before and after synthetic aperture processing. Finally, we applied this to an in vivo carotid artery.
Multiple-scattering corrections in diluted magnetic semiconductors: A plane-wave expansion
Scalbert, D.; Ghazali, A.; Benoit à la Guillaume, C.
1993-12-01
Energy levels of band edges in diluted magnetic semiconductors are calculated in the effective-mass approximation, retaining off-diagonal terms in the exchange interaction and using a plane-wave expansion. This model accounts qualitatively for the observed asymmetry in the splitting of the A exciton in a magnetic field in Cd1-xMnxS for which multiple-scattering corrections are expected to be important.
On the mass of atoms in molecules: Beyond the Born-Oppenheimer approximation
Scherrer, Arne; Sebastiani, Daniel; Gross, E K U; Vuilleumier, Rodolphe
2016-01-01
Describing the dynamics of nuclei in molecules requires a potential energy surface, which is traditionally provided by the Born-Oppenheimer or adiabatic approximation. However, we also need to assign masses to the nuclei. There, the Born-Oppenheimer picture does not account for the inertia of the electrons and only bare nuclear masses are considered. Nowadays, experimental accuracy challenges the theoretical predictions of rotational and vibrational spectra and requires to include the participation of electrons in the internal motion of the molecule. More than 80 years after the original work of Born and Oppenheimer, this issue still is not solved in general. Here, we present a theoretical and numerical framework to address this problem in a general and rigorous way. Starting from the exact factorization of the electron-nuclear wave function, we include electronic effects beyond the Born-Oppenheimer regime in a perturbative way via position-dependent corrections to the bare nuclear masses. This maintains an a...
Object-dependent cloaking in the first-order Born approximation
Setälä, Tero; Hakkarainen, Timo; Friberg, Ari T.; Hoenders, Bernhard J.; Setälä, Tero
2010-01-01
We consider the cloaking of a slab object in scalar wave theory within the first-order Born approximation. We show that in the forward direction cloaking is achieved for any transversally invariant, positively refracting, and absorbing object by using a lossy, negative-index metamaterial cloak. Cloa
AdS plane waves, entanglement and mutual information
Mukherjee, Debangshu
2014-01-01
$AdS$ plane wave backgrounds are dual to CFT excited states with energy momentum density $T_{++}=Q$. Building on previous work on entanglement entropy in these and nonconformal brane plane wave backgrounds, we first describe a phenomenological scaling picture for entanglement in terms of "entangling partons". We then study aspects of holographic mutual information in these backgrounds for two strip shaped subsystems, aligned parallel or orthogonal to the flux. We focus on the wide ($Ql^d\\gg 1$) and narrow ($Ql^d\\ll 1$) strip regimes. In the wide strip regime, mutual information exhibits growth with the individual strip sizes and a disentangling transition as the separation between the strips increases, whose behaviour is distinct from the ground and thermal states. In the narrow strip case, our calculations have parallels with "entanglement thermodynamics" for these $AdS$ plane wave deformations. We also discuss some numerical analysis.
Plane-Wave Imaging Challenge in Medical Ultrasound
DEFF Research Database (Denmark)
Liebgott, Herve; Molares, Alfonso Rodriguez; Cervenansky, F.
2016-01-01
for this effect, but comparing the different methods is difficult due to the lack of appropriate tools. PICMUS, the Plane-Wave Imaging Challenge in Medical Ultrasound aims to provide these tools. This paper describes the PICMUS challenge, its motivation, implementation, and metrics.......Plane-Wave imaging enables very high frame rates, up to several thousand frames per second. Unfortunately the lack of transmit focusing leads to reduced image quality, both in terms of resolution and contrast. Recently, numerous beamforming techniques have been proposed to compensate...
Plane waves in a thermally conducting viscous liquid
Indian Academy of Sciences (India)
Baljeet Singh
2004-02-01
The aim of this paper is to investigate plane waves in a thermally conducting viscous liquid half-space with thermal relaxation times. There exist three basic waves, namely; thermal wave, longitudinal wave and transverse wave in a thermally conducting viscous liquid half-space. Reﬂection of plane waves from the free surface of a thermally conducting viscous liquid half-space is studied. The results are obtained in terms of amplitude ratios and are compared with those without viscosity and thermal disturbances.
Thermally-induced vacuum instability in a single plane wave
King, B; Di Piazza, A
2012-01-01
Ever since Schwinger published his influential paper [J. Schwinger, Phys. Rev. \\textbf{82}, 664 (1951)], it has been unanimously accepted that the vacuum is stable in the presence of an electromagnetic plane wave. However, we advance an analysis that indicates this statement is not rigorously valid in a real situation, where thermal effects are present. We show that the thermal vacuum, in the presence of a single plane-wave field, even in the limit of zero frequency (a constant crossed field), decays into electron-positron pairs. Interestingly, the pair-production rate is found to depend nonperturbatively on both the amplitude of the constant crossed field and on the temperature.
Polarization operator for plane-wave background fields
Meuren, S; Di Piazza, A
2013-01-01
We derive an alternative representation of the leading-order contribution to the polarization operator in strong-field QED with a plane-wave electromagnetic background field, which is manifestly symmetric with respect to the external photon momenta. Our derivation is based on a direct evaluation of the corresponding Feynman diagram, using the Volkov-representation of the dressed fermion propagator. Furthermore, the validity of the Ward-Takahashi identity is shown for general loop diagrams in an external plane-wave background field.
An Apparatus for Constructing an Electromagnetic Plane Wave Model
Kneubil, Fabiana Botelho; Loures, Marcus Vinicius Russo; Amado, William
2015-01-01
In this paper we report on an activity aimed at building an electromagnetic wave. This was part of a class on the concept of mass offered to a group of 20 pre-service Brazilian physics teachers. The activity consisted of building a plane wave using an apparatus in which it is possible to fit some rods representing electric and magnetic fields into…
An Apparatus for Constructing an Electromagnetic Plane Wave Model
Kneubil, Fabiana Botelho; Loures, Marcus Vinicius Russo; Amado, William
2015-01-01
In this paper we report on an activity aimed at building an electromagnetic wave. This was part of a class on the concept of mass offered to a group of 20 pre-service Brazilian physics teachers. The activity consisted of building a plane wave using an apparatus in which it is possible to fit some rods representing electric and magnetic fields into…
Metaphysics of colliding self-gravitating plane waves
Energy Technology Data Exchange (ETDEWEB)
Matzner, R.A.; Tipler, F.J.
1984-04-15
We discuss certain global features of colliding plane-wave solutions to Einstein's equations. In particular, we show that the apparently local curvature singularities both in the Khan-Penrose solution and in the Bell-Szekeres solution are actually global. These global singularities are associated with the breakdown of nondegenerate planar symmetry in the characteristic initial data sets.
Metaphysics of colliding self-gravitating plane waves
Matzner, Richard A.; Tipler, Frank J.
1984-04-01
We discuss certain global features of colliding plane-wave solutions to Einstein's equations. In particular, we show that the apparently local curvature singularities both in the Khan-Penrose solution and in the Bell-Szekeres solution are actually global. These global singularities are associated with the breakdown of nondegenerate planar symmetry in the characteristic initial data sets.
Strings On Plane-waves And Spin Chains On Orbifolds
Sadri, D
2005-01-01
This thesis covers a number of topics in string theory focusing on various aspects of the AdS/CFT duality in various guises and regimes. In the first chapter we present a self-contained review of the Plane- wave/super-Yang-Mills duality. This duality is a specification of the usual AdS/CFT correspondence in the “Penrose limit”. In chapter two we study the most general parallelizable pp-wave backgrounds which are non-dilatonic solutions in the NS-NS sector of type IIA and IIB string theories. We demonstrate that parallelizable pp-wave backgrounds are necessarily homogeneous plane-waves, and that a large class of homogeneous plane-waves are parallelizable, stating the necessary conditions. Quantization of string modes, their compactification and behaviour under T- duality are also studied, as are BPS Dp- branes on such backgrounds. In chapter three we consider giant gravitons on the maximally supersymmetric plane-wave background. We deduce the low energy effective light-cone Hamiltonian of ...
Supersymmetry and Branes in M-theory Plane-waves
Kim, N; Kim, Nakwoo; Yee, Jung-Tay
2003-01-01
We study brane embeddings in M-theory plane-waves and their supersymmetry. The relation with branes in AdS backgrounds via the Penrose limit is also explored. Longitudinal planar branes are originated from AdS branes while giant gravitons of AdS spaces become spherical branes which are realized as fuzzy spheres in the massive matrix theory.
Solitary plane waves in an isotropic hexagonal lattice
DEFF Research Database (Denmark)
Zolotaryuk, Yaroslav; Savin, A.V.; Christiansen, Peter Leth
1998-01-01
Solitary plane-wave solutions in a two-dimensional hexagonal lattice which can propagate in different directions on the plane are found by using the pseudospectral method. The main point of our studies is that the lattice model is isotropic and we show that the sound velocity is the same for diff...
Plane-Wave Propagation in Extreme Magnetoelectric (EME) Media
Lindell, I V; Favaro, A
2016-01-01
The extreme magnetoelectric medium (EME medium) is defined in terms of two medium dyadics, $\\alpha$, producing electric polarization by the magnetic field and $\\beta$, producing magnetic polarization by the electric field. Plane-wave propagation of time-harmonic fields of fixed finite frequency in the EME medium is studied. It is shown that (if $\\omega\
Iles-Smith, Jake; Lambert, Neill; Nazir, Ahsan
2015-01-01
We explore excitonic energy transfer dynamics in a molecular dimer system coupled to both structured and unstructured oscillator environments. By extending the reaction coordinate master equation technique developed in [J. Iles-Smith, N. Lambert, and A. Nazir, Phys. Rev. A 90, 032114 (2014)], we go beyond the commonly used Born-Markov approximations to incorporate system-environment correlations and the resultant non-Markovian dynamical effects. We obtain energy transfer dynamics for both underdamped and overdamped oscillator environments that are in perfect agreement with the numerical hierarchical equations of motion over a wide range of parameters. Furthermore, we show that the Zusman equations, which may be obtained in a semiclassical limit of the reaction coordinate model, are often incapable of describing the correct dynamical behaviour. This demonstrates the necessity of properly accounting for quantum correlations generated between the system and its environment when the Born-Markov approximations no ...
Second-order Born approximation for the ionization of molecules by electron and positron impact
Energy Technology Data Exchange (ETDEWEB)
Dal Cappello, C. [Universite Paul Verlaine-Metz, Laboratoire de Physique Moleculaire et des Collisions, Institut Jean Barriol (FR2843), 1 Boulevard Arago, F-57078 Metz Cedex 3 (France); Rezkallah, Z.; Houamer, S. [Laboratoire de Physique Quantique et Systemes Dynamiques, Departement de Physique, Faculte des Sciences Universite Ferhat Abbas, Setif 19000 (Algeria); Charpentier, I. [Universite Paul Verlaine-Metz, Laboratoire de Physique et Mecanique des Materiaux UMR 7554, Ile du Saulcy, F-57045 Metz Cedex 1 (France); Hervieux, P. A. [Institut de Physique et Chimie des Materiaux de Strasbourg, 23 Rue du Loess, BP 43, F-67034 Strasbourg Cedex 2 (France); Ruiz-Lopez, M. F. [Nancy-University, Equipe de Chimie et Biochimie Theoriques, UMR CNRS-UHP 7565, BP 239, F-54506 Vandoeuvre-les-Nancy (France); Dey, R. [Max-Planck Institut fuer Plasmaphysik, Boltzmannstr. 2, D-85748 Garching (Germany); Roy, A. C. [School of Mathematical Sciences, Ramakrishna Mission Vivekananda University, Belur Math 711202, West Bengal (India)
2011-09-15
Second-order Born approximation is applied to study the ionization of molecules. The initial and final states are described by single-center wave functions. For the initial state a Gaussian wave function is used while for the ejected electron it is a distorted wave. Results of the present model are compared with recent (e,2e) experiments on the water molecule. Preliminary results are also presented for the ionization of the thymine molecule by electrons and positrons.
Institute of Scientific and Technical Information of China (English)
孙昌璞
1995-01-01
The generalized Born-Oppenheimer approximation theory is applied to the localization control of state tunneling of a two-level atom in a cavity field with single mode. The nonadiabatic effect of tunneling of atomic chiral states in coherent cavity field is analyzed quantitatively and the condition for realizing localization is given strictly. Besides, the influence of variation in temperature on tunneling of atomic state is discussed.
DEFF Research Database (Denmark)
Tolstikhin, Oleg I.; Madsen, Lars Bojer
2013-01-01
We show that retardation in adjusting an electronic state to an instantaneous internuclear configuration caused by the finiteness of the electron’s velocity breaks the validity of the Born-Oppenheimer (BO) approximation at large electron-nuclei distances. This applies even to the ground state....... As a result, the BO approximation in the theory of tunneling ionization of molecules breaks down at sufficiently weak fields. We also show that to account for nuclear motion the weak-field asymptotic expansion for the tunneling ionization rate must be restructured. The predictions for the rate using the BO...
Zhang, Hou-Dao; Yan, YiJing
2015-12-07
The issue of efficient hierarchy truncation is related to many approximate theories. In this paper, we revisit this issue from both the numerical efficiency and quantum mechanics prescription invariance aspects. The latter requires that the truncation approximation made in Schrödinger picture, such as the quantum master equations and their self-consistent-Born-approximation improvements, should be transferable to their Heisenberg-picture correspondences, without further approximations. We address this issue with the dissipaton equation of motion (DEOM), which is a unique theory for the dynamics of not only reduced systems but also hybrid bath environments. We also highlight the DEOM theory is not only about how its dynamical variables evolve in time, but also the underlying dissipaton algebra. We demonstrate this unique feature of DEOM with model systems and report some intriguing nonlinear Fano interferences characteristics that are experimentally measurable.
The second Born approximation for the double ionization of N2 by electron impact
Lamy, P.; Dal Cappello, C.; Charpentier, I.; Ruiz-Lopez, M. F.; Hervieux, P. A.
2016-07-01
In their (e,3e) and (e,3-1e) experiments of the double ionization (DI) of the outermost orbital of N2, Li et al (2012 J. Phys. B: At. Mol. Opt. Phys. 45 135201) recently showed that the process is largely dominated by a two-step-2 mechanism, which is a double interaction of the incident electron with the target. From a theoretical point of view, this should entail the use of the second Born approximation. In the past, very few theoretical calculations had been carried out this way because it requires a difficult numerical triple integration. We propose here to take into account the second Born approximation for the DI of N2 by using the closure approximation. The initial state is described by a single-center wave function derived from the usual multi-center wave function obtained in the self-consistent-field Hartree-Fock method using the linear combination of atomic orbitals-molecular orbital (LCAO-MO) approximation. The final state describes the interaction between each of the ejected electrons and the target by a Coulomb wave and the interaction between the two ejected electrons with the use of the Gamow factor. We calculate differential cross sections using the same kinematic conditions as Li et al (intermediate incident energy about 600 eV) for (e,3e) and (e,3-1e) DI of N2. The results show that the model does not allow a shift of the variation of the four-fold differential cross section near the momentum transfer to be obtained nor its opposite when we include the contribution given by the second Born approximation, as in (e,3-1e) experiments.
Plane Waves in a Transparent Isotropic Chiral Medium
Fisanov, V. V.
2015-04-01
A homogeneous isotropic transparent chiral medium supports two normal plane waves with left and right circular polarization and differently valued positive wave numbers. The presence or absence of forward and backward Beltrami waves and their helicity are regulated by the signs of the permittivity and permeability and the strength of the chirality. The ray refractive index is a universal parameter whose sign differentiates the forward and backward waves.
Scattering of a CW plane wave by a pulse
Trivett, D. H.; Rogers, P. H.
1982-05-01
A procedure similar to the CW crossed-beam calculation of Ingard and Pridmore-Brown (1956) is used to calculate the far field scattered sound pressure of a pulse interacting with a plane wave. The scattered sound is found to be at neither the sum nor the difference frequency. It is suggested that this type of interaction is ideal for investigating the scattering of sound by sound, and a numerical solution is used to discuss the general features of the nearfield waveform.
Two-Flux Colliding Plane Waves in String Theory
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
We construct the two-flux colliding plane wave solutions in higher-dimensional gravity theory with dilaton,and two complementary fluxes. Two kinds of solutions have been obtained: Bell-Szekeres (BS) type and homogeneous type. After imposing the junction condition, we find that only the BS type solution is physically well-defined. Furthermore, we show that the future curvature singularity is always developed for our solutions.
The worldline approach to helicity flip in plane waves
Ilderton, Anton
2016-01-01
We apply worldline methods to the study of vacuum polarisation effects in plane wave backgrounds, in both scalar and spinor QED. We calculate helicity-flip probabilities to one loop order and treated exactly in the background field, and provide a toolkit of methods for use in investigations of higher-order processes. We also discuss the connections between the worldline, S-matrix, and lightfront approaches to vacuum polarisation effects.
DEFF Research Database (Denmark)
Tolstikhin, Oleg I.; Madsen, Lars Bojer
2013-01-01
We show that retardation in adjusting an electronic state to an instantaneous internuclear configuration caused by the finiteness of the electron’s velocity breaks the validity of the Born-Oppenheimer (BO) approximation at large electron-nuclei distances. This applies even to the ground state....... As a result, the BO approximation in the theory of tunneling ionization of molecules breaks down at sufficiently weak fields. We also show that to account for nuclear motion the weak-field asymptotic expansion for the tunneling ionization rate must be restructured. The predictions for the rate using the BO...... approximation and the asymptotic expansion are compared with numerical results for a one-dimensional three-body system modeling a diatomic molecule, with both electronic and nuclear motions treated exactly....
Plane-wave Least-squares Reverse Time Migration
Dai, Wei
2012-11-04
Least-squares reverse time migration is formulated with a new parameterization, where the migration image of each shot is updated separately and a prestack image is produced with common image gathers. The advantage is that it can offer stable convergence for least-squares migration even when the migration velocity is not completely accurate. To significantly reduce computation cost, linear phase shift encoding is applied to hundreds of shot gathers to produce dozens of planes waves. A regularization term which penalizes the image difference between nearby angles are used to keep the prestack image consistent through all the angles. Numerical tests on a marine dataset is performed to illustrate the advantages of least-squares reverse time migration in the plane-wave domain. Through iterations of least-squares migration, the migration artifacts are reduced and the image resolution is improved. Empirical results suggest that the LSRTM in plane wave domain is an efficient method to improve the image quality and produce common image gathers.
Plane wave method for elastic wave scattering by a heterogeneous fracture
Energy Technology Data Exchange (ETDEWEB)
Nakagawa, Seiji; Nihei, Kurt T.; Myer, Larry R.
2003-02-21
A plane-wave method for computing the three-dimensional scattering of propagating elastic waves by a planar fracture with heterogeneous fracture compliance distribution is presented. This method is based upon the spatial Fourier transform of the seismic displacement-discontinuity (SDD) boundary conditions (also called linear slip interface conditions), and therefore, called the wave-number-domain SDD method (wd-SDD method). The resulting boundary conditions explicitly show the coupling between plane waves with an incident wave number component (specular component) and scattered waves which do not follow Snell's law (nonspecular components) if the fracture is viewed as a planar boundary. For a spatially periodic fracture compliance distribution, these boundary conditions can be cast into a linear system of equations that can be solved for the amplitudes of individual wave modes and wave numbers. We demonstrate the developed technique for a simulated fracture with a stochastic (correlated) surface compliance distribution. Low- and high-frequency solutions of the method are also compared to the predictions by low-order Born series in the weak and strong scattering limit.
On the local plane wave methods for in situ measurement of acoustic absorption
Wijnant, Y.H.
2015-01-01
In this paper we address a series of so-called local plane wave methods (LPW) to measure acoustic absorption. As opposed to other methods, these methods do not rely on assumptions of the global sound field, like e.g. a plane wave or diffuse field, but are based on a local plane wave assumption. Ther
On the Mass of Atoms in Molecules: Beyond the Born-Oppenheimer Approximation
Scherrer, Arne; Agostini, Federica; Sebastiani, Daniel; Gross, E. K. U.; Vuilleumier, Rodolphe
2017-07-01
Describing the dynamics of nuclei in molecules requires a potential energy surface, which is traditionally provided by the Born-Oppenheimer or adiabatic approximation. However, we also need to assign masses to the nuclei. There, the Born-Oppenheimer picture does not account for the inertia of the electrons, and only bare nuclear masses are considered. Nowadays, experimental accuracy challenges the theoretical predictions of rotational and vibrational spectra and requires the participation of electrons in the internal motion of the molecule. More than 80 years after the original work of Born and Oppenheimer, this issue has still not been solved, in general. Here, we present a theoretical and numerical framework to address this problem in a general and rigorous way. Starting from the exact factorization of the electron-nuclear wave function, we include electronic effects beyond the Born-Oppenheimer regime in a perturbative way via position-dependent corrections to the bare nuclear masses. This maintains an adiabaticlike point of view: The nuclear degrees of freedom feel the presence of the electrons via a single potential energy surface, whereas the inertia of electrons is accounted for and the total mass of the system is recovered. This constitutes a general framework for describing the mass acquired by slow degrees of freedom due to the inertia of light, bounded particles; thus, it is applicable not only in electron-nuclear systems but in light-heavy nuclei or ions as well. We illustrate this idea with a model of proton transfer, where the light particle is the proton and the heavy particles are the oxygen atoms to which the proton is bounded. Inclusion of the light-particle inertia allows us to gain orders of magnitude in accuracy. The electron-nuclear perspective is adopted, instead, to calculate position-dependent mass corrections using density functional theory for a few polyatomic molecules at their equilibrium geometry. These data can serve as input for the
Energy Technology Data Exchange (ETDEWEB)
Iles-Smith, Jake, E-mail: Jakeilessmith@gmail.com [Controlled Quantum Dynamics Theory, Imperial College London, London SW7 2PG (United Kingdom); Photon Science Institute and School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester M13 9PL (United Kingdom); Department of Photonics Engineering, DTU Fotonik, Ørsteds Plads, 2800 Kongens Lyngby (Denmark); Dijkstra, Arend G. [Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg (Germany); Lambert, Neill [CEMS, RIKEN, Saitama 351-0198 (Japan); Nazir, Ahsan, E-mail: ahsan.nazir@manchester.ac.uk [Photon Science Institute and School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester M13 9PL (United Kingdom)
2016-01-28
We explore excitonic energy transfer dynamics in a molecular dimer system coupled to both structured and unstructured oscillator environments. By extending the reaction coordinate master equation technique developed by Iles-Smith et al. [Phys. Rev. A 90, 032114 (2014)], we go beyond the commonly used Born-Markov approximations to incorporate system-environment correlations and the resultant non-Markovian dynamical effects. We obtain energy transfer dynamics for both underdamped and overdamped oscillator environments that are in perfect agreement with the numerical hierarchical equations of motion over a wide range of parameters. Furthermore, we show that the Zusman equations, which may be obtained in a semiclassical limit of the reaction coordinate model, are often incapable of describing the correct dynamical behaviour. This demonstrates the necessity of properly accounting for quantum correlations generated between the system and its environment when the Born-Markov approximations no longer hold. Finally, we apply the reaction coordinate formalism to the case of a structured environment comprising of both underdamped (i.e., sharply peaked) and overdamped (broad) components simultaneously. We find that though an enhancement of the dimer energy transfer rate can be obtained when compared to an unstructured environment, its magnitude is rather sensitive to both the dimer-peak resonance conditions and the relative strengths of the underdamped and overdamped contributions.
Stolt's f-k migration for plane wave ultrasound imaging.
Garcia, Damien; Le Tarnec, Louis; Muth, Stéphan; Montagnon, Emmanuel; Porée, Jonathan; Cloutier, Guy
2013-09-01
Ultrafast ultrasound is an emerging modality that offers new perspectives and opportunities in medical imaging. Plane wave imaging (PWI) allows one to attain very high frame rates by transmission of planar ultrasound wave-fronts. As a plane wave reaches a given scatterer, the latter becomes a secondary source emitting upward spherical waves and creating a diffraction hyperbola in the received RF signals. To produce an image of the scatterers, all the hyperbolas must be migrated back to their apexes. To perform beamforming of plane wave echo RFs and return high-quality images at high frame rates, we propose a new migration method carried out in the frequency-wavenumber (f-k) domain. The f-k migration for PWI has been adapted from the Stolt migration for seismic imaging. This migration technique is based on the exploding reflector model (ERM), which consists in assuming that all the scatterers explode in concert and become acoustic sources. The classical ERM model, however, is not appropriate for PWI. We showed that the ERM can be made suitable for PWI by a spatial transformation of the hyperbolic traces present in the RF data. In vitro experiments were performed to outline the advantages of PWI with Stolt's f-k migration over the conventional delay-and-sum (DAS) approach. The Stolt's f-k migration was also compared with the Fourier-based method developed by J.-Y. Lu. Our findings show that multi-angle compounded f-k migrated images are of quality similar to those obtained with a stateof- the-art dynamic focusing mode. This remained true even with a very small number of steering angles, thus ensuring a highly competitive frame rate. In addition, the new FFT-based f-k migration provides comparable or better contrast-to-noise ratio and lateral resolution than the Lu's and DAS migration schemes. Matlab codes for the Stolt's f-k migration for PWI are provided.
Plane Wave Medical Ultrasound Imaging Using Adaptive Beamforming
DEFF Research Database (Denmark)
Holfort, Iben Kraglund; Gran, Fredrik; Jensen, Jørgen Arendt
2008-01-01
In this paper, the adaptive, minimum variance (MV) beamformer is applied to medical ultrasound imaging. The Significant resolution and contrast gain provided by the adaptive, minimum variance (MV) beamformer, introduces the possibility of plane wave (PW) ultrasound imaging. Data is obtained using...... Field H and a 7 MHz, 128-elements, linear array transducer with lambda/2-spacing. MV is compared to the conventional delay-and-sum (DS) beamformer with Boxcar and Hanning weights. Furthermore, the PW images are compared to the a conventional ultrasound image, obtained from a linear scan sequence...
Plane waves and spherical means applied to partial differential equations
John, Fritz
2004-01-01
Elementary and self-contained, this heterogeneous collection of results on partial differential equations employs certain elementary identities for plane and spherical integrals of an arbitrary function, showing how a variety of results on fairly general differential equations follow from those identities. The first chapter deals with the decomposition of arbitrary functions into functions of the type of plane waves. Succeeding chapters introduce the first application of the Radon transformation and examine the solution of the initial value problem for homogeneous hyperbolic equations with con
Plane-Wave Propagation in Electromagnetic PQ Medium
Lindell, Ismo V
2015-01-01
Two basic classes of electromagnetic media, recently defined and labeled as those of P media and Q media, are generalized to define the class of PQ media. Plane wave propagation in the general PQ medium is studied and the quartic dispersion equation is derived in analytic form applying four-dimensional dyadic formalism. The result is verified by considering various special cases of PQ media for which the dispersion equation is known to decompose to two quadratic equations or be identically satisfied (media with no dispersion equation). As a numerical example, the dispersion surface of a PQ medium with non-decomposable dispersion equation is considered.
Energy Relations for Plane Waves Reflected from Moving Media
DEFF Research Database (Denmark)
Daly, P.; Gruenberg, Harry
1967-01-01
When a plane wave is obliquely incident from vacuum on a semi-infinite moving medium, the energy flow carried by the incident wave, is in general, not carried away by the reflected and transmitted waves. This is only the case when the medium velocity is parallel to its vacuum interface. Otherwise...... there is a net inflow or outflow of electromagnetic energy, which can be accounted for by the change of stored energy in the system, and the work done by the mechanical forces acting on the medium. A detailed energy balance is drawn up for two different media moving normal to their vacuum interfaces: (a...
Chen, Jianhan
2010-09-14
The generalized Born (GB) theory is a prime choice for implicit treatment of solvent that provides a favorable balance between efficiency and accuracy for reliable simulation of protein conformational equilibria. In GB, the dielectric boundary is a key physical property that needs to be properly described. While it is widely accepted that the molecular surface (MS) should provide the most physical description, most existing GB models are based on van der Waals (vdW)-like surfaces for computational simplicity and efficiency. A simple and effective approximation to molecular volume is explored here using atom-centered dielectric functions within the context of a generalized Born model with simple switching (GBSW). The new model, termed GBSW/MS2, is as efficient as the original vdW-like-surface-based GBSW model, but is able to reproduce the Born radii calculated from the "exact" Poisson-Boltzmann theory with a correlation of 0.95. More importantly, examination of the potentials of mean force of hydrogen-bonding and charge-charge interactions demonstrates that GBSW/MS2 correctly captures the first desolvation peaks, a key signature of true MS. Physical parameters including atomic input radii and peptide backbone torsion were subsequently optimized on the basis of solvation free energies of model compounds, potentials of mean force of their interactions, and conformational equilibria of a set of helical and β-hairpin model peptides. The resulting GBSW/MS2 protein force field reasonably recapitulates the structures and stabilities of these model peptides. Several remaining limitations and possible future developments are also discussed.
Parkhill, John A; Markovich, Thomas; Tempel, David G; Aspuru-Guzik, Alan
2012-12-14
In this work, we develop an approach to treat correlated many-electron dynamics, dressed by the presence of a finite-temperature harmonic bath. Our theory combines a small polaron transformation with the second-order time-convolutionless master equation and includes both electronic and system-bath correlations on equal footing. Our theory is based on the ab initio Hamiltonian, and is thus well-defined apart from any phenomenological choice of basis states or electronic system-bath coupling model. The equation-of-motion for the density matrix we derive includes non-markovian and non-perturbative bath effects and can be used to simulate environmentally broadened electronic spectra and dissipative dynamics, which are subjects of recent interest. The theory also goes beyond the adiabatic Born-Oppenheimer approximation, but with computational cost scaling such as the Born-Oppenheimer approach. Example propagations with a developmental code are performed, demonstrating the treatment of electron-correlation in absorption spectra, vibronic structure, and decay in an open system. An untransformed version of the theory is also presented to treat more general baths and larger systems.
Parkhill, John A; Tempel, David G; Aspuru-Guzik, Alan
2012-01-01
In this work we develop a theory of correlated many-electron dynamics dressed by the presence of a finite-temperature harmonic bath. The theory is based on the ab-initio Hamiltonian, and thus well-defined apart from any phenomenological choice of collective basis states or electronic coupling model. The equation-of-motion includes some bath effects non-perturbatively, and can be used to simulate line- shapes beyond the Markovian approximation and open electronic dynamics which are subjects of renewed recent interest. Energy conversion and transport depend critically on the ratio of electron-electron coupling to bath-electron coupling, which is a fitted parameter if a phenomenological basis of many-electron states is used to develop an electronic equation of motion. Since the present work doesn't appeal to any such basis, it avoids this ambiguity. The new theory produces a level of detail beyond the adiabatic Born-Oppenheimer states, but with cost scaling like the Born-Oppenheimer approach. While developing th...
Waveguide characteristics of coupled in-plane waves.
Pan, Jie; Lu, Jing; Qiu, Xiaojun
2012-06-01
In-plane waves in a waveguide made from a thin plate are described by a superposition of a set of orthogonal functions that satisfy the edge conditions of the waveguide. Due to the Poisson and shear effects, the displacement components of the in-plane waves along the two in-plane orthogonal coordinates are coupled and this coupling affects the propagation and spatial properties of the waveguide modes. The orthogonal functions and their associated wavenumbers represent the characteristics of the uncoupled modes of the waveguide where the above mentioned couplings are ignored. This study demonstrates that the characteristics of the waveguide modes are determined by the couplings of the uncoupled mode pairs, which become significant when the pairs satisfy the conditions of spatial coincidence. At some frequencies, certain waveguide modes can be determined by a single pair of uncoupled modes. For this case, the analytical solution for the waveguide modes exists and provides both a qualitative and quantitative interpretation of the characteristics of the waveguide mode.
The second Born approximation in electron-helium scattering in a Nd-YAG laser field
Energy Technology Data Exchange (ETDEWEB)
Khalil, D.; Makhoute, A.; Rahali, G.; Zitane, M. [Universite Moulay Ismail, UFR de Physique Atomique, Moleculaire et Optique Appliquee, Faculte des Sciences (Morocco); Rahali, G.; Makhoute, A. [The Abdus Salam International Centre for Theoretical Physics, Trieste (Italy); Maquet, A. [Universite Pierre et Marie Curie, Lab. de Chimie Physique, Matiere et Rayonnement, 75 - Paris (France)
2007-02-15
The dynamics of laser-assisted elastic collisions in helium is studied using the second-order Born approximation. Detailed calculations of the scattering amplitudes are performed by using the Sturmian basis expansion. Differential cross sections for elastic scattering with the net absorption/emission of up to two photons are calculated for collision energies of 5 eV, 10 eV, and 20 eV. We discuss the influence of the low-energy electrons on the differential cross section (DCS) as a function of the scattering angle for selected choices of the laser frequency and the number of photons exchanged between the external field and electron-helium system. (authors)
Large-scale parameter extraction in electrocardiology models through Born approximation
He, Yuan; Keyes, David E.
2013-01-01
One of the main objectives in electrocardiology is to extract physical properties of cardiac tissues from measured information on electrical activity of the heart. Mathematically, this is an inverse problem for reconstructing coefficients in electrocardiology models from partial knowledge of the solutions of the models. In this work, we consider such parameter extraction problems for two well-studied electrocardiology models: the bidomain model and the FitzHugh-Nagumo model. We propose a systematic reconstruction method based on the Born approximation of the original nonlinear inverse problem. We describe a two-step procedure that allows us to reconstruct not only perturbations of the unknowns, but also the backgrounds around which the linearization is performed. We show some numerical simulations under various conditions to demonstrate the performance of our method. We also introduce a parameterization strategy using eigenfunctions of the Laplacian operator to reduce the number of unknowns in the parameter extraction problem.
Large-scale parameter extraction in electrocardiology models through Born approximation
He, Yuan
2012-12-04
One of the main objectives in electrocardiology is to extract physical properties of cardiac tissues from measured information on electrical activity of the heart. Mathematically, this is an inverse problem for reconstructing coefficients in electrocardiology models from partial knowledge of the solutions of the models. In this work, we consider such parameter extraction problems for two well-studied electrocardiology models: the bidomain model and the FitzHugh-Nagumo model. We propose a systematic reconstruction method based on the Born approximation of the original nonlinear inverse problem. We describe a two-step procedure that allows us to reconstruct not only perturbations of the unknowns, but also the backgrounds around which the linearization is performed. We show some numerical simulations under various conditions to demonstrate the performance of our method. We also introduce a parameterization strategy using eigenfunctions of the Laplacian operator to reduce the number of unknowns in the parameter extraction problem. © 2013 IOP Publishing Ltd.
Ahmadi, H; Maghari, A
2016-01-01
The underlying physics behind the molecular harmonic emission in relatively long sin$^2$-like laser pulses is investigated. We numerically solved the full-dimensional electronic time-dependent Schr\\"{o}dinger equation beyond the Born-Oppenheimer approximation for simple molecular ion H$_2^+$. The occurrence and the effect of electron localization, non-adiabatic redshift and spatially asymmetric emission are evaluated to understand better complex patterns appearing in the high-order harmonic generation (HHG) spectrum. Results show that the complex patterns in the HHG spectrum originate mainly from a non-adiabatic response of the molecule to the rapidly changing laser field and also from a spatially asymmetric emission along the polarization direction. The effect of electron localization on the HHG spectrum was not observed as opposed to what is reported in the literature.
Borzdov
2000-04-01
Vector plane-wave superpositions defined by a given set of orthonormal scalar functions on a two- or three-dimensional manifold-beam manifold-are treated. We present a technique for composing orthonormal beams and some other specific types of fields such as three-dimensional standing waves, moving and evolving whirls. It can be used for any linear fields, in particular, electromagnetic fields in complex media and elastic fields in crystals. For electromagnetic waves in an isotropic medium or free space, unique families of exact solutions of Maxwell's equations are obtained. The solutions are illustrated by calculating fields, energy densities, and energy fluxes of beams defined by the spherical harmonics. It is shown that the obtained results can be used for a transition from the plane-wave approximation to more accurate models of real incident beams in free-space techniques for characterizing complex media. A mathematical formalism convenient for the treatment of various beams defined by the spherical harmonics is presented.
Yong, Peng; Huang, Jianping; Li, Zhenchun; Liao, Wenyuan; Qu, Luping; Li, Qingyang; Liu, Peijun
2017-02-01
In finite-difference (FD) method, numerical dispersion is the dominant factor influencing the accuracy of seismic modelling. Various optimized FD schemes for scalar wave modelling have been proposed to reduce grid dispersion, while the optimized time-space domain FD schemes for elastic wave modelling have not been fully investigated yet. In this paper, an optimized FD scheme with Equivalent Staggered Grid (ESG) for elastic modelling has been developed. We start from the constant P- and S-wave speed elastic wave equations and then deduce analytical plane wave solutions in the wavenumber domain with eigenvalue decomposition method. Based on the elastic plane wave solutions, three new time-space domain dispersion relations of ESG elastic modelling are obtained, which are represented by three equations corresponding to P-, S- and converted-wave terms in the elastic equations, respectively. By using these new relations, we can study the dispersion errors of different spatial FD terms independently. The dispersion analysis showed that different spatial FD terms have different errors. It is therefore suggested that different FD coefficients to be used to approximate the three spatial derivative terms. In addition, the relative dispersion error in L2-norm is minimized through optimizing FD coefficients using Newton's method. Synthetic examples have demonstrated that this new optimal FD schemes have superior accuracy for elastic wave modelling compared to Taylor-series expansion and optimized space domain FD schemes.
2, Pulse-mode expansions and refractive indices in plane-wave propagation
Energy Technology Data Exchange (ETDEWEB)
Shore, B.W.; Sacks, R.; Karr, T.; Morris, J.; Paisner, J.A.
1987-06-20
This memo presents basic background theory for treating simultaneous propagation of electromagnetic pulses of various colors, directed along a common ray, through a molecular vapor. The memo discusses some techniques for expanding the positive frequency part of the transverse electric field into pulse modes, characterized by carrier frequencies within a modulated envelope. We discuss, in the approximation of plane waves with slowly varying envelopes, a set of uncoupled envelope equations in which a polarization mode-envelope acts as a source for an electric-field envelope. These equations, when taken with a prescription for the polarization field, are the basic equations of plane-wave pulse propagation through a molecular medium. We discuss two ways of treating dispersive media, one based upon expansions in the frequency domain and the other based in the time domain. In both cases we find envelope equations that involve group velocities. This memo represents a portion of a more extensive treatment of propagation to be presented separately. Many of the equations presented here have been described in various books and articles. They are collected and described here as a summary and review of contemporary theory.
The second Born approximation of electron–argon elastic scattering in a bichromatic laser ﬁeld
Indian Academy of Sciences (India)
Bin Zhou; Ming-Yang Zheng; Da-Yong Wen
2012-03-01
We study the elastic scattering of atomic argon by electron in the presence of a bichromatic laser ﬁeld in the second Born approximation. The target atom is approximated by a simple screening potential and the continuum states of the impinging and emitting electrons are described as Volkov states. We evaluate the S-matrix elements numerically. The dependence of differential cross-section on the relative phase between the two laser components is presented. The results obtained in the ﬁrst and second Born approximations are compared and analysed.
Gravitational scattering of zero-rest-mass plane waves
De Logi, W. K.; Kovacs, S. J., Jr.
1977-01-01
The Feyman-diagram technique is used to calculate the differential cross sections for the scattering of zero-rest-mass plane waves of spin 0, 1, and 2 by linearized Schwarzschild and Kerr geometries in the long-wavelength weak-field limit. It is found that the polarization of right (or left) circularly polarized electromagnetic waves is unaffected by the scattering process (i.e., helicity is conserved) and that the two helicity (polarization) states of the photon are scattered differently by the Kerr geometry. This coupling between the photon helicity and the angular momentum of the scatterer also leads to a partial polarization of unpolarized incident light. For gravitational waves, on the other hand, there is neither helicity conservation nor helicity-dependent scattering; the angular momentum of the scatterer has no polarizing effect on incident unpolarized gravitational waves.
Hu, Min; Wang, Hailong; Gong, Qian; Wang, Shumin
2017-04-01
A comparison is made between the plane wave basis and variational method. Within the framework of effective-mass approximation theory, the variational and plane wave basis method are used to calculate ground state energy and ground state binding energy in low-dimensional nano-structures under the external electric field. Comparing calculation results, the donor binding energies of ground state display the consistent trend, both of them are strongly dependent on the quantum size, impurity position and external electric field. However, the impurity ground state energy calculated using variational method may be larger than the real value and it results in the smaller binding energy for variational method. In addition, the binding energy is more sensitive to the external electric field for the variational method, which can be seen more clearly from Stark shift.
Fully converged plane-wave-based self-consistent G W calculations of periodic solids
Cao, Huawei; Yu, Zhongyuan; Lu, Pengfei; Wang, Lin-Wang
2017-01-01
The G W approximation is a well-known method to obtain the quasiparticle and spectral properties of systems ranging from molecules to solids. In practice, G W calculations are often employed with many different approximations and truncations. In this work, we describe the implementation of a fully self-consistent G W approach based on the solution of the Dyson equation using a plane wave basis set. Algorithmic, numerical, and technical details of the self-consistent G W approach are presented. The fully self-consistent G W calculations are performed for GaAs, ZnO, and CdS including semicores in the pseudopotentials. No further approximations and truncations apart from the truncation on the plane wave basis set are made in our implementation of the G W calculation. After adopting a special potential technique, a ˜100 Ry energy cutoff can be used without the loss of accuracy. We found that the self-consistent G W (sc-G W ) significantly overestimates the bulk band gaps, and this overestimation is likely due to the underestimation of the macroscopic dielectric constants. On the other hand, the sc-G W accurately predicts the d -state positions, most likely because the d -state screening does not sensitively depend on the macroscopic dielectric constant. Our work indicates the need to include the high-order vertex term in order for the many-body perturbation theory to accurately predict the semiconductor band gaps. It also sheds some light on why, in some cases, the G0W0 bulk calculation is more accurate than the fully self-consistent G W calculation, because the initial density-functional theory has a better dielectric constant compared to experiments.
On the types and number of plane waves in hypoelastic materials
Rushchitsky, J. J.
2005-11-01
General principles are formulated for modeling the elastic deformation of materials and analyzing plane waves in nonlinearly elastic materials such as hyperelastic, hypoelastic, and those governed by the general law of elasticity. The results of studying the propagation of plane waves in hypoelastic materials are further outlined. The influence of initial stresses and initial velocities on the types and number of plane waves is studied. Wave effects characteristic of hypoelastic materials are predicted theoretically. One of such effects is blocking of certain types of plane waves by initial stresses
Four-body corrected first Born approximation for single charge exchange at high impact energies
Mančev, Ivan
1995-06-01
Single electron capture is investigated by means of the four-body boundary corrected first Born approximation (CB1-4B). The "post" form of the transition amplitude for a general heteronuclear case (Zp; e1) + (ZT; e2) → (Zp; e1, e2) + ZT is derived in the form of readily obtainable two-dimensional real integrals. We investigate the sensitivity of the total cross sections to the choice of ground state wave function for helium-like atoms. Also, the influence of non-captured electron on the final results is studied. As an illustration, the CB1-4B method is used to compute the total cross sections for reactions: H(1s) + H(1s) → H-(1s2) + H+, He+(1s) + H(1s) → He(1s2) + H+ and He+(1s) + He+(1s) → He(1s2) + α. The theoretical cross sections are found to be in good agreement with the available experimental data.
Cavity Born-Oppenheimer Approximation for Correlated Electron-Nuclear-Photon Systems
Flick, Johannes; Ruggenthaler, Michael; Rubio, Angel
2016-01-01
In this work, we illustrate the recently introduced concept of the cavity Born-Oppenheimer approximation for correlated electron-nuclear-photon problems in detail. We demonstrate how an expansion in terms of conditional electronic and photon-nuclear wave functions accurately describes eigenstates of strongly correlated light-matter systems. For a GaAs quantum ring model in resonance with a photon mode we highlight how the ground-state electronic potential-energy surface changes the usual harmonic potential of the free photon mode to a dressed mode with a double-well structure. This change is accompanied by a splitting of the electronic ground-state density. For a model where the photon mode is in resonance with a vibrational transition, we observe in the excited-state electronic potential-energy surface a splitting from a single minimum to a double minimum. Furthermore, for a time-dependent setup, we show how the dynamics in correlated light-matter systems can be understood in terms of population transfer bet...
Nonlinear dynamics and band transport in a superlattice driven by a plane wave
Apostolakis, A.; Awodele, M. K.; Alekseev, K. N.; Kusmartsev, F. V.; Balanov, A. G.
2017-06-01
A quantum particle transport induced in a spatially periodic potential by a propagating plane wave has a number of important implications in a range of topical physical systems. Examples include acoustically driven semiconductor superlattices and cold atoms in an optical crystal. Here we apply a kinetic description of the directed transport in a superlattice beyond standard linear approximation, and utilize exact path-integral solutions of the semiclassical transport equation. We show that the particle drift and average velocities have nonmonotonic dependence on the wave amplitude with several prominent extrema. Such nontrivial kinetic behavior is related to global bifurcations developing with an increase of the wave amplitude. They cause dramatic transformations of the system phase space and lead to changes of the transport regime. We describe different types of phase trajectories contributing to the directed transport and analyze their spectral content.
PARTICLE DISPLACEMENTS ON THE WALL OF A BOREHOLE FROM INCIDENT PLANE WAVES.
Lee, M.W.
1987-01-01
Particle displacements from incident plane waves at the wall of a fluid-filled borehole are formulated by applying the seismic reciprocity theorem to far-field displacement fields. Such displacement fields are due to point forces acting on a fluid-filled borehole under the assumption of long wavelengths. The displacement fields are analyzed to examine the effect of the borehole on seismic wave propagation, particularly for vertical seismic profiling (VSP) measurements. When the shortest wavelength of interest is approximately 25 times longer than the borehole's diameter, the scattered displacements are proportional to the first power of incident frequency and borehole diameter. When the shortest wavelength of interest is about 40 times longer than the borehole's diameter, borehole effects on VSP measurements using a wall-locking geophone are negligible.
Implementation of LDA+DMFT with the pseudo-potential-plane-wave method
Institute of Scientific and Technical Information of China (English)
Zhao Jian-Zhou; Zhuang Jia-Ning; Deng Xiao-Yu; Bi Yan; Cai Ling-Cang; Fang Zhong; Dai Xi
2012-01-01
We propose an efficient implementation of combining dynamical mean field theory(DMFT)with electronic structural calculation based on the local density approximation(LDA).The pseudo-potential-plane-wave method is used in the LDA part,which enables it to be applied to large systems.The full loop self consistency of the charge density has been reached in our implementation,which allows us to compute the total energy related properties.The procedure of LDA+DMFT is introduced in detail with a complete flow chart.We have also applied our code to study the electronic structure of several typical strong correlated materials,including cerium,americium and NiO.Our results fit quite well with both the experimental data and previous studies.
A comparison of exact TM plane wave diffraction by coated wedges and impedance wedges
DEFF Research Database (Denmark)
Andersen, Lars S.; Breinbjerg, Olav; Moore, John T.
1996-01-01
without interference from direct fields or reflected fields. Results have been obtained in the case of illumination by a transverse magnetic (TM) uniform plane wave. The analysis of the coated wedge is based on an integral equation formulation combined with a hybrid technique, while the analysis......The purpose of this work is to numerically investigate the accuracy of the standard impedance boundary condition (SIBC) approximation for edge diffraction. To this end, we compare the scattering by coated wedges and SIBC wedges for which the diffracted field from a single edge can be observed...... of the SIBC wedge is based on Maliuzhinets' solution. Comparisons have been carried out for a series of configurations including lossy coatings as well as lossless coatings permitting unattenuated propagation of surface waves. The results show that the presence of an edge in a coated structure does...
The plain truth about forming a plane wave of neutrons
Energy Technology Data Exchange (ETDEWEB)
Wagh, Apoorva G., E-mail: nintsspd@barc.gov.i [Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai 400 085 (India); Abbas, Sohrab [Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai 400 085 (India); Treimer, Wolfgang [Helmholtz Zentrum Berlin, Glienicker Str. 100, D-14109 Berlin (Germany)
2011-04-01
We have attained the first sub-arcsecond collimation of a monochromatic neutron beam by diffracting neutrons from a Bragg prism, viz. a single crystal prism operating in the vicinity of Bragg incidence. Analytical as well numerical computations based on the dynamical diffraction theory, led to the optimised collimator configuration of a silicon {l_brace}1 1 1{r_brace} Bragg prism for 5.26 A neutrons. We fabricated a Bragg prism to these specifications, tested and operated it at the double diffractometer setup in Helmholtz Zentrum Berlin to produce a 0.58 arcsec wide monochromatic neutron beam. With a similarly optimised Bragg prism analyser of opposite asymmetry, we recorded a 0.62 arcsec wide virgin rocking curve for this ultra-parallel beam. With this nearly plane-wave neutron beam, we have recorded the first ever USANS spectrum in Q{approx}10{sup -6} A{sup -1} range with a hydroxyapatite casein protein sample and demonstrated the instrument capability to characterise agglomerates up to 150 {mu}m in size. The super-collimated monochromatic beam has also enabled us to record the first neutron diffraction pattern from a macroscopic grating of 200 {mu}m period. The transverse coherence length of 175 {mu}m (FWHM) of the ultra-parallel beam derived from the analysis of this pattern, is the greatest achieved to date for A wavelength neutrons.
The Lukash Plane-Wave Attractor and Relative Energy
Korunur, M; Salti, M; Aydogdu, Oktay; Korunur, Murat; Salti, Mustafa
2006-01-01
We study energy distribution in the context of teleparallel theory of gravity, due to matter and fields including gravitation, of the universe based on the plane-wave Bianchi VII$_{\\delta}$ spacetimes described by the Lukash metric. In order to make this calculation we consider the teleparallel gravity analogs of the energy-momentum formulations of Einstein, Bergmann-Thomson and Landau-Lifshitz. We find that Einstein and Bergmann-Thomson prescriptions agree with each other and give the same results for the energy distribution in a given spacetime, but the Landau-Lifshitz complex does not. Energy density turns out to be non-vanishing in all of these prescriptions. It is interesting to mention that the results can be reduced to the already available results for the Milne universe when we write $\\omega=1$ and $\\Xi^2=1$ in the metric of the Lukash spacetime, and for this special case, we get the same relation among the energy-momentum formulations of Einstein, Bergmann-Thomson and Landau-Lifshitz as obtained for ...
Dispersive photonic crystals from the plane wave method
Energy Technology Data Exchange (ETDEWEB)
Guevara-Cabrera, E.; Palomino-Ovando, M.A. [Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Apdo. Post. 165, Puebla, Pue. 72000, México (Mexico); Flores-Desirena, B., E-mail: bflores@fcfm.buap.mx [Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Apdo. Post. 165, Puebla, Pue. 72000, México (Mexico); Gaspar-Armenta, J.A. [Departamento de Investigación en Física de la Universidad de Sonora Apdo, Post 5-088, Hermosillo Sonora 83190, México (Mexico)
2016-03-01
Nowadays photonic crystals are widely used in many different applications. One of the most used methods to compute their band structure is the plane wave method (PWM). However, it can only be applied directly to non-dispersive media and be extended to systems with a few model dielectric functions. We explore an extension of the PWM to photonic crystals containing dispersive materials, that solves an eigenvalue equation for the Bloch wave vectors. First we compare our calculation with analytical results for one dimensional photonic crystals containing Si using experimental values of its optical parameters, and obtainig very well agreement, even for the spectrum region with strong absorption. Then, using the same method, we computed the band structure for a two dimensional photonic crystal without absorption, formed by an square array of MgO cylinders in air. The optical parameters for MgO were modeled with the Lorentz dielectric function. Finally, we studied an array of MgO cylinders in a metal, using Drude model without absorption, for the metal dielectric function. For this last case, we study the gap–midgap ratio as a function of the filling fraction for both the square and triangular lattice. The gap–midgap ratio is larger for the triangular lattice, with a maximum value of 10% for a filling fraction of 0.6. Our results show that the method can be applied to dispersive materials, and then to a wide range of applications where photonic crystals can be used.
Ground penetrating radar antenna measurements based on plane-wave expansions
DEFF Research Database (Denmark)
Lenler-Eriksen, Hans-Rudolph; Meincke, Peter
2005-01-01
The plane-wave transmitting spectrum of the system consisting of the ground penetrating radar (GPR) antenna and the air-soil interface is measured using a loop buried in the soil. The plane-wave spectrum is used to determine various parameters characterizing the radiation of the GPR antenna...
Wave-equation Migration Velocity Analysis Using Plane-wave Common Image Gathers
Guo, Bowen
2017-06-01
Wave-equation migration velocity analysis (WEMVA) based on subsurface-offset, angle domain or time-lag common image gathers (CIGs) requires significant computational and memory resources because it computes higher dimensional migration images in the extended image domain. To mitigate this problem, a WEMVA method using plane-wave CIGs is presented. Plane-wave CIGs reduce the computational cost and memory storage because they are directly calculated from prestack plane-wave migration, and the number of plane waves is often much smaller than the number of shots. In the case of an inaccurate migration velocity, the moveout of plane-wave CIGs is automatically picked by a semblance analysis method, which is then linked to the migration velocity update by a connective function. Numerical tests on two synthetic datasets and a field dataset validate the efficiency and effectiveness of this method.
Energy Technology Data Exchange (ETDEWEB)
Meziane, M; Brash, E J; Jones, M K; Luo, W; Pentchev, L; Perdrisat, C F; Puckett, A J.R.; Punjabi, V; Wesselmann, F R; Ahmidouch, A; Albayrak, I; Aniol, K A; Arrington, J; Asaturyan, A; Ates, O; Baghdasaryan, H; Benmokhtar, F; Bertozzi, W; Bimbot, L; Bosted, P; Boeglin, W; Butuceanu, C; Carter, P; Chernenko, S; Christy, E; Commisso, M; Cornejo, J C; Covrig, S; Danagoulian, S; Daniel, A; Davidenko, A; Day, D; Dhamija, S; Dutta, D; Ent, R; Frullani, S; Fenker, H; Frlez, E; Garibaldi, F; Gaskell, D; Gilad, S; Goncharenko, Y; Hafidi, K; Hamilton, D; Higinbothan, D W; Hinton, W; Horn, T; Hu, B; Huang, J; Huber, G M; Jensen, E; Kang, H; Keppel, C; Khandaker, M; King, P; Kirillov, D; Kohl, M; Kravtsov, V; Kumbartzki, G; Li, Y; Mamyan, V; Margaziotis, D J; Markowitz, P; Marsh, A; Matulenko, Y; Maxwell, J; Mbianda, G; Meekins, D; Melnick, Y; Miller, J; Mkrtchyan, A; Mkrtchyan, H; Moffit, B; Moreno, O; Mulholland, J; Narayan, A; Nuruzzaman,; Nedev, S; Piasetzky, E; Pierce, W; Piskunov, N M; Prok, Y; Ransome, R D; Razin, D S; Reimer, P E; Reinhold, J; Rondon, O; Shabestari, M; Shahinyan, A; Shestermanov, K; Sirca, S; Sitnik, I; Smykov, L; Smith, G; Solovyev, L; Solvignon, P; Subedi, R; Suleiman, R; Tomasi-Gustafsson, E; Vasiliev, A; Vanderhaeghen, M; Veilleux, M; Wojtsekhowski, B B; Wood, S; Ye, Z; Zanevsky, Y; Zhang, X; Zhang, Y; Zheng, X; Zhu, L
2011-04-01
Intensive theoretical and experimental efforts over the past decade have aimed at explaining the discrepancy between data for the proton electric to magnetic form factor ratio, $G_{E}/G_{M}$, obtained separately from cross section and polarization transfer measurements. One possible explanation for this difference is a two-photon-exchange (TPEX) contribution. In an effort to search for effects beyond the one-photon-exchange or Born approximation, we report measurements of polarization transfer observables in the elastic $H(\\vec{e},e'\\vec{p})$ reaction for three different beam energies at a fixed squared momentum transfer $Q^2 = 2.5$ GeV$^2$, spanning a wide range of the virtual photon polarization parameter, $\\epsilon$. From these measured polarization observables, we have obtained separately the ratio $R$, which equals $\\mu_p G_{E}/G_{M}$ in the Born approximation, and the longitudinal polarization transfer component $P_\\ell$, with statistical and systematic uncertainties of $\\Delta R \\approx \\pm 0.01 \\mbox{(stat)} \\pm 0.013 \\mbox{(syst)}$ and $\\Delta P_\\ell/P^{Born}_{\\ell} \\approx \\pm 0.006 \\mbox{(stat)}\\pm 0.01 \\mbox{(syst)}$. The ratio $R$ is found to be independent of $\\epsilon$ at the 1.5% level, while the $\\epsilon$ dependence of $P_\\ell$ shows an enhancement of $(2.3 \\pm 0.6) %$ relative to the Born approximation at large $\\epsilon$.
A new GTD slope diffraction coefficient for plane wave illumination of a wedge
DEFF Research Database (Denmark)
Lumholt, Michael; Breinbjerg, Olav
1997-01-01
Two wedge problems including slope diffraction are solved: one in which the incident field is a non-uniform plane wave, and one in which it is an inhomogeneous plane wave. The two solutions lead to the same GTD slope diffraction coefficient. This coefficient reveals the existence of a coupling...... effect between a transverse magnetic (or transverse electric) incident plane wave and the transverse electric (or transverse magnetic) slope-diffracted field. The coupling effect is not described by the existing GTD slope diffraction coefficient...
No pair production of open strings in a plane-wave background
Sakaguchi, Makoto; Yoshida, Kentaroh
2014-01-01
We consider whether an external electric field may cause the pair production of open strings in a type IIA plane-wave background. The boundary states of D-branes with condensates are constructed in the Green-Schwarz formulation of superstring with the light-cone gauge. The cylinder diagrams are computed with massive theta functions. Although the value of the electric field is bounded by the upper value as usual, there is no pole in the amplitudes and it indicates that no pair production occurs in the plane-wave background. This result would be universal for a class of plane-wave backgrounds.
Parallel 3-dim fast Fourier transforms with load balancing of the plane waves
Gao, Xingyu; Fang, Jun; Wang, Han
2016-01-01
The plane wave method is most widely used for solving the Kohn-Sham equations in first-principles materials science computations. In this procedure, the three-dimensional (3-dim) trial wave functions' fast Fourier transform (FFT) is a regular operation and one of the most demanding algorithms in terms of the scalability on a parallel machine. We propose a new partitioning algorithm for the 3-dim FFT grid to accomplish the trade-off between the communication overhead and load balancing of the plane waves. It is shown by qualitative analysis and numerical results that our approach could scale the plane wave first-principles calculations up to more nodes.
On the Hagedorn Behaviour of Singular Scale-Invariant Plane Waves
Blau, Matthias; O'Loughlin, M; Blau, Matthias; Borunda, Monica; Loughlin, Martin O'
2005-01-01
As a step towards understanding the properties of string theory in time-dependent and singular spacetimes, we study the divergence of density operators for string ensembles in singular scale-invariant plane waves, i.e. those plane waves that arise as the Penrose limits of generic spacetime singularities. We show that the scale invariance implies that the Hagedorn behaviour of bosonic and supersymmetric strings in these backgrounds, even with the inclusion of RR or NS fields, is the same as that of strings in flat space. This is in marked contrast to the behaviour of strings in the BFHP plane wave which exhibit quantitatively and qualitatively different thermodynamic properties.
Mustroph, Heinz
2016-09-05
The concept of a potential-energy surface (PES) is central to our understanding of spectroscopy, photochemistry, and chemical kinetics. However, the terminology used in connection with the basic approximations is variously, and somewhat confusingly, represented with such phrases as "adiabatic", "Born-Oppenheimer", or "Born-Oppenheimer adiabatic" approximation. Concerning the closely relevant and important Franck-Condon principle (FCP), the IUPAC definition differentiates between a classical and quantum mechanical formulation. Consequently, in many publications we find terms such as "Franck-Condon (excited) state", or a vertical transition to the "Franck-Condon point" with the "Franck-Condon geometry" that relaxes to the excited-state equilibrium geometry. The Born-Oppenheimer approximation and the "classical" model of the Franck-Condon principle are typical examples of misused terms and lax interpretations of the original theories. In this essay, we revisit the original publications of pioneers of the PES concept and the FCP to help stimulate a lively discussion and clearer thinking around these important concepts.
Meziane, M; Brash, E J; Gilman, R; Jones, M K; Luo, W; Pentchev, L; Perdrisat, C F; Puckett, A J R; Punjabi, V; Wesselmann, F R; Ahmidouch, A; Albayrak, I; Aniol, K A; Arrington, J; Asaturyan, A; Ates, O; Baghdasaryan, H; Benmokhtar, F; Bertozzi, W; Bimbot, L; Bosted, P; Boeglin, W; Butuceanu, C; Carter, P; Chernenko, S; Christy, E; Commisso, M; Cornejo, J C; Covrig, S; Danagoulian, S; Daniel, A; Davidenko, A; Day, D; Dhamija, S; Dutta, D; Ent, R; Frullani, S; Fenker, H; Frlez, E; Garibaldi, F; Gaskell, D; Gilad, S; Goncharenko, Y; Hafidi, K; Hamilton, D; Higinbotham, D W; Hinton, W; Horn, T; Hu, B; Huang, J; Huber, G M; Jensen, E; Kang, H; Keppel, C; Khandaker, M; King, P; Kirillov, D; Kohl, M; Kravtsov, V; Kumbartzki, G; Li, Y; Mamyan, V; Margaziotis, D J; Markowitz, P; Marsh, A; Matulenko, Y; Maxwell, J; Mbianda, G; Meekins, D; Melnik, Y; Miller, J; Mkrtchyan, A; Mkrtchyan, H; Moffit, B; Moreno, O; Mulholland, J; Narayan, A; Nuruzzaman; Nedev, S; Piasetzky, E; Pierce, W; Piskunov, N M; Prok, Y; Ransome, R D; Razin, D S; Reimer, P E; Reinhold, J; Rondon, O; Shabestari, M; Shahinyan, A; Shestermanov, K; Širca, S; Sitnik, I; Smykov, L; Smith, G; Solovyev, L; Solvignon, P; Subedi, R; Suleiman, R; Tomasi-Gustafsson, E; Vasiliev, A; Vanderhaeghen, M; Veilleux, M; Wojtsekhowski, B B; Wood, S; Ye, Z; Zanevsky, Y; Zhang, X; Zhang, Y; Zheng, X; Zhu, L
2011-04-01
Intensive theoretical and experimental efforts over the past decade have aimed at explaining the discrepancy between data for the proton electric to magnetic form factor ratio, G(E)/G(M), obtained separately from cross section and polarization transfer measurements. One possible explanation for this difference is a two-photon-exchange contribution. In an effort to search for effects beyond the one-photon-exchange or Born approximation, we report measurements of polarization transfer observables in the elastic H(e[over →],e(')p[over →]) reaction for three different beam energies at a Q(2)=2.5 GeV(2), spanning a wide range of the kinematic parameter ε. The ratio R, which equals μ(p)G(E)/G(M) in the Born approximation, is found to be independent of ε at the 1.5% level. The ε dependence of the longitudinal polarization transfer component P(ℓ) shows an enhancement of (2.3±0.6)% relative to the Born approximation at large ε.
Institute of Scientific and Technical Information of China (English)
ZHOU Bin; LI Shu-Min
2010-01-01
@@ We study the elastic scattering of atomic argon by an electron in the presence of a bichromatic laser field in the second Born approximation.The target atom is approximated by a simple screening potential.We explore the dependences of the differential cross sections on the relative phase (φ) between the two components of the radiation field and discuss the influence of the number of photons exchanged on the phase-dependence effect.Moreover,for different scattering angles and incident electron energies,the differential cross sections are notably different.
Ab initio Sternheimer-GW method for quasiparticle calculations using plane waves
Lambert, Henry; Giustino, Feliciano
2013-08-01
We report on the extension and implementation of the Sternheimer-GW method introduced by Giustino [Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.81.115105 81, 115105 (2010)] to the case of first-principles pseudopotential calculations based on a plane-waves basis. The Sternheimer-GW method consists of calculating the GW self-energy operator without resorting to the standard expansion over unoccupied Kohn-Sham electronic states. The Green's function is calculated by solving linear systems for frequencies along the real axis. The screened Coulomb interaction is calculated for frequencies along the imaginary axis by using the Sternheimer equation. Analytic continuation to the real axis is performed using Padé approximants. The generalized plasmon-pole approximation is avoided by performing explicit calculations at multiple frequencies using Frommer's multishift solver. We demonstrate our methodology by reporting tests on common insulators and semiconductors, including Si, diamond, LiCl, and SiC. Our calculated quasiparticle energies are in agreement with the results of fully converged calculations based on the sum-over-states approach. As the Sternheimer-GW method yields the complete self-energy Σ(r,r',ω) and not only its expectation values on Kohn-Sham states, this work opens the way to nonperturbative GW calculations and to direct calculations of spectral functions for angle-resolved photoemission spectroscopy. As an example of the capabilities of the method we calculate the G0W0 spectral functions of silicon and diamond.
Plane wave holonomies in quantum gravity. II. A sine wave solution
Neville, Donald E.
2015-08-01
This paper constructs an approximate sinusoidal wave packet solution to the equations of canonical gravity. The theory uses holonomy-flux variables with support on a lattice (LHF =lattice-holonomy flux ). There is an SU(2) holonomy on each edge of the LHF simplex, and the goal is to study the behavior of these holonomies under the influence of a passing gravitational wave. The equations are solved in a small sine approximation: holonomies are expanded in powers of sines and terms beyond sin2 are dropped; also, fields vary slowly from vertex to vertex. The wave is unidirectional and linearly polarized. The Hilbert space is spanned by a set of coherent states tailored to the symmetry of the plane wave case. Fixing the spatial diffeomorphisms is equivalent to fixing the spatial interval between vertices of the loop quantum gravity lattice. This spacing can be chosen such that the eigenvalues of the triad operators are large, as required in the small sine limit, even though the holonomies are not large. Appendices compute the energy of the wave, estimate the lifetime of the coherent state packet, discuss circular polarization and coarse-graining, and determine the behavior of the spinors used in the U(N) SHO realization of LQG.
On plane-wave relativistic electrodynamics in plasmas and in vacuum
Fiore, Gaetano
2016-01-01
We revisit the exact microscopic equations (in differential, and equivalent integral form) ruling a relativistic cold plasma after the plane-wave Ansatz, without customary approximations. We show that in the Eulerian description the motion of a very diluted plasma initially at rest and excited by an arbitrary transverse plane electromagnetic travelling-wave has a very simple and explicit dependence on the transverse electromagnetic potential; for a non-zero density plasma the above motion is a good approximation of the real one as long as the back-reaction of the charges on the electromagnetic field can be neglected, i.e. for a time lapse decreasing with the plasma density, and can be used as initial step in an iterative resolution scheme. As one of many possible applications, we use these results to describe how the ponderomotive force of a very intense and short plane laser pulse hitting normally the surface of a plasma boosts the surface electrons into the ion background. Because of this penetration the el...
An Analytical Method of Auxiliary Sources Solution for Plane Wave Scattering by Impedance Cylinders
DEFF Research Database (Denmark)
Larsen, Niels Vesterdal; Breinbjerg, Olav
2004-01-01
Analytical Method of Auxiliary Sources solutions for plane wave scattering by circular impedance cylinders are derived by transformation of the exact eigenfunction series solutions employing the Hankel function wave transformation. The analytical Method of Auxiliary Sources solution thus obtained...
Diffraction of an inhomogeneous plane wave by an impedance wedge in a lossy medium
CSIR Research Space (South Africa)
Manara, G
1998-11-01
Full Text Available The diffraction of an inhomogeneous plane wave by an impedance wedge embedded in a lossy medium is analyzed. The rigorous integral representation for the field is asymptotically evaluated in the context of the uniform geometrical theory...
Directory of Open Access Journals (Sweden)
Melissa E. Libertus
2017-07-01
Full Text Available Preterm children are at increased risk for poor academic achievement, especially in math. In the present study, we examined whether preterm children differ from term-born children in their intuitive sense of number that relies on an unlearned, approximate number system (ANS and whether there is a link between preterm children’s ANS acuity and their math abilities. To this end, 6.5-year-old extremely preterm (i.e., <27 weeks gestation, n = 82 and term-born children (n = 89 completed a non-symbolic number comparison (ANS acuity task and a standardized math test. We found that extremely preterm children had significantly lower ANS acuity than term-born children and that these differences could not be fully explained by differences in verbal IQ, perceptual reasoning skills, working memory, or attention. Differences in ANS acuity persisted even when demands on visuo-spatial skills and attention were reduced in the ANS task. Finally, we found that ANS acuity and math ability are linked in extremely preterm children, similar to previous results from term-born children. These results suggest that deficits in the ANS may be at least partly responsible for the deficits in math abilities often observed in extremely preterm children.
Application of Plane Wave Method to the Calculation of Electronic States of Nano-Structures
Institute of Scientific and Technical Information of China (English)
LI Shu-Shen; XIA Jian-Bai
2006-01-01
@@ The electronic states of nano-structures are studied in the framework of effective-mass envelope-function theory using the plane wave basis. The barrier width and the number of plane waves are proposed to be 2.5 times the effective Bohr radius and 15n, respectively, for n-dimensional nano-structures (n = 1, 2, 3). Our proposals can be widely applied in the design of various nano-structure devices.
Energy Technology Data Exchange (ETDEWEB)
Zhang, Hou-Dao [Department of Chemistry, Hong Kong University of Science and Technology, Hong Kong (China); Yan, YiJing, E-mail: yyan@ust.hk [Department of Chemistry, Hong Kong University of Science and Technology, Hong Kong (China); iChEM and Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026 (China)
2015-12-07
The issue of efficient hierarchy truncation is related to many approximate theories. In this paper, we revisit this issue from both the numerical efficiency and quantum mechanics prescription invariance aspects. The latter requires that the truncation approximation made in Schrödinger picture, such as the quantum master equations and their self–consistent–Born–approximation improvements, should be transferable to their Heisenberg–picture correspondences, without further approximations. We address this issue with the dissipaton equation of motion (DEOM), which is a unique theory for the dynamics of not only reduced systems but also hybrid bath environments. We also highlight the DEOM theory is not only about how its dynamical variables evolve in time, but also the underlying dissipaton algebra. We demonstrate this unique feature of DEOM with model systems and report some intriguing nonlinear Fano interferences characteristics that are experimentally measurable.
Electron-positron pair production in ion collisions at low velocity beyond Born approximation
Lee, R N
2016-01-01
We derive the spectrum and the total cross section of electromagnetic $e^{+}e^{-}$ pair production in the collisions of two nuclei at low relative velocity $\\beta$. Both free-free and bound-free $e^{+}e^{-}$ pair production is considered. The parameters $\\eta_{A,B}=Z_{A,B}\\alpha$ are assumed to be small compared to unity but arbitrary compared to $\\beta$ ($Z_{A,B}$ are the charge numbers of the nuclei and $\\alpha$ is the fine structure constant). Due to a suppression of the Born term by high power of $\\beta$, the first Coulomb correction to the amplitude appears to be important at $\\eta_{A,B}\\gtrsim \\beta$. The effect of a finite nuclear mass is discussed. In contrast to the result obtained in the infinite nuclear mass limit, the terms $\\propto M^{-2}$ are not suppressed by the high power of $\\beta$ and may easily dominate at sufficiently small velocities.
Hospital-Bravo, Raúl; Sarrate, Josep; Díez, Pedro
2016-05-01
A new 2D numerical model to predict the underwater acoustic propagation is obtained by exploring the potential of the Partition of Unity Method (PUM) enriched with plane waves. The aim of the work is to obtain sound pressure level distributions when multiple operational noise sources are present, in order to assess the acoustic impact over the marine fauna. The model takes advantage of the suitability of the PUM for solving the Helmholtz equation, especially for the practical case of large domains and medium frequencies. The seawater acoustic absorption and the acoustic reflectance of the sea surface and sea bottom are explicitly considered, and perfectly matched layers (PML) are placed at the lateral artificial boundaries to avoid spurious reflexions. The model includes semi-analytical integration rules which are adapted to highly oscillatory integrands with the aim of reducing the computational cost of the integration step. In addition, we develop a novel strategy to mitigate the ill-conditioning of the elemental and global system matrices. Specifically, we compute a low-rank approximation of the local space of solutions, which in turn reduces the number of degrees of freedom, the CPU time and the memory footprint. Numerical examples are presented to illustrate the capabilities of the model and to assess its accuracy.
Quartic scaling MP2 for solids: A highly parallelized algorithm in the plane-wave basis
Schäfer, Tobias; Kresse, Georg
2016-01-01
We present a low-complexity algorithm to calculate the correlation energy of periodic systems in second-order M{\\o}ller-Plesset perturbation theory (MP2). In contrast to previous approximation-free MP2 codes, our implementation possesses a quartic scaling, $\\mathcal O(N^4$), with respect to the system size $N$ and offers an almost ideal parallelization efficiency. The general issue that the correlation energy converges slowly with the number of basis functions is solved by an internal basis set extrapolation. The key concept to reduce the scaling of the algorithm is to eliminate all summations over virtual bands which can be elegantly achieved in the Laplace transformed MP2 (LTMP2) formulation using plane-wave basis sets. Analogously, this approach could allow to calculate second order screened exchange (SOSEX) as well as particle-hole ladder diagrams with a similar low complexity. Hence, the presented method can be considered as a step towards systematically improved correlation energies.
Towards a generalized iso-density continuum model for molecular solvents in plane-wave DFT
Gunceler, Deniz; Arias, T. A.
2017-01-01
Implicit electron-density solvation models offer a computationally efficient solution to the problem of calculating thermodynamic quantities of solvated systems from first-principles quantum mechanics. However, despite much recent interest in such models, to date the applicability of such models in the plane-wave context to non-aqueous solvents has been limited because the determination of the model parameters requires fitting to a large database of experimental solvation energies for each new solvent considered. This work presents a simple approach to quickly find approximations to the non-electrostatic contributions to the solvation energy, allowing for development of new iso-density models for a large class of protic and aprotic solvents from only simple, single-molecule ab initio calculations and readily available bulk thermodynamic data. Finally, to illustrate the capabilities of the resulting theory, we also calculate the surface solvation energies of crystalline LiF in various different non-aqueous solvents, and discuss the observed trends and their relevance to lithium battery technology.
Proton-impact excitation of helium to the n = 2 sublevels in the distorted-wave Born approximation
Khurana, I.; Srivastava, R.; Tripathi, A. N.
1986-05-01
Differential and total cross sections for proton-impact excitation of helium to the n = 2 sublevels are calculated in the distorted-wave Born approximation. Many-parameter correlated wave functions are used to describe the helium atom. A comparison with recent theories and experimental measurements is made. The present calculations for differential cross sections for the n = 2 substates yield good agreement with the measured values of Park et al. (1978) and Kvale et al. (1985) and the multistate eikonal calculations of Flannery and McCann (1974).
Energy Technology Data Exchange (ETDEWEB)
Hamman, E.; Zorgati, R.
1995-12-31
Eddy current non-destructive testing is used by EDF to detect flaws affecting conductive objects such as steam generator tubes. With a view to obtaining ever more accurate information on equipment integrity, thereby facilitating diagnosis, studies aimed at using measurements to reconstruct an image of the flaw have been proceeding now for about ten years. In this context, our approach to eddy current imaging is based on inverse problem formalism. The direct problem, involving a mathematical model linking measurements provided by a probe with variables characterizing the defect, is dealt with elsewhere. Using the model results, we study the possibility of inverting it, i.e. of reconstructing an image of the flaw from the measurements. We first give an overview of the different inversion techniques, representative of the state of the art and all based on linearization of the inverse problem by means of the Born approximation. The model error resulting from an excessive Born approximation nevertheless severely limits the quantity of the images which can be obtained. In order to counteract this often critical error and extend the eddy current imaging application field, we have to del with the non-linear inverse problem. A method derived from recent research is proposed and implemented to ensure consistency with the exact model. Based on an `optimization` type approach and provided with a convergence theorem, the method is highly efficient. (authors). 17 refs., 7 figs., 1 append.
THE USE OF PLANE WAVES TO APPROXIMATE WAVE PROPAGATION IN ANISOTROPIC MEDIA
Institute of Scientific and Technical Information of China (English)
Tomi Huttunen; Peter Monk
2007-01-01
In this paper we extend the standard Ultra Weak Variational Formulation (UWVF) of Maxwell's equations in an isotropic medium to the case of an anisotropic medium. We verify that the underlying theoretical framework carries over to anisotropic media (however error estimates are not yet available) and completely describe the new scheme. We then consider TM mode scattering, show how this results in a Helmholtz equation in two dimensions with an anisotropic coefficient and demonstrate how to formulate the UWVF for it. In one special case, convergence can be proved. We then show some numerical results that suggest that the UWVF can successfully simulate wave propagation in anisotropic media.
Libertus, Melissa E; Forsman, Lea; Adén, Ulrika; Hellgren, Kerstin
2017-01-01
Preterm children are at increased risk for poor academic achievement, especially in math. In the present study, we examined whether preterm children differ from term-born children in their intuitive sense of number that relies on an unlearned, approximate number system (ANS) and whether there is a link between preterm children's ANS acuity and their math abilities. To this end, 6.5-year-old extremely preterm (i.e., preterm children had significantly lower ANS acuity than term-born children and that these differences could not be fully explained by differences in verbal IQ, perceptual reasoning skills, working memory, or attention. Differences in ANS acuity persisted even when demands on visuo-spatial skills and attention were reduced in the ANS task. Finally, we found that ANS acuity and math ability are linked in extremely preterm children, similar to previous results from term-born children. These results suggest that deficits in the ANS may be at least partly responsible for the deficits in math abilities often observed in extremely preterm children.
Coherent states, quantum gravity, and the Born- Oppenheimer approximation. II. Compact Lie groups
Stottmeister, Alexander; Thiemann, Thomas
2016-07-01
In this article, the second of three, we discuss and develop the basis of a Weyl quantisation for compact Lie groups aiming at loop quantum gravity-type models. This Weyl quantisation may serve as the main mathematical tool to implement the program of space adiabatic perturbation theory in such models. As we already argued in our first article, space adiabatic perturbation theory offers an ideal framework to overcome the obstacles that hinder the direct implementation of the conventional Born-Oppenheimer approach in the canonical formulation of loop quantum gravity. Additionally, we conjecture the existence of a new form of the Segal-Bargmann-Hall "coherent state" transform for compact Lie groups G, which we prove for G = U(1)n and support by numerical evidence for G = SU(2). The reason for conjoining this conjecture with the main topic of this article originates in the observation that the coherent state transform can be used as a basic building block of a coherent state quantisation (Berezin quantisation) for compact Lie groups G. But, as Weyl and Berezin quantisation for ℝ2d are intimately related by heat kernel evolution, it is natural to ask whether a similar connection exists for compact Lie groups as well. Moreover, since the formulation of space adiabatic perturbation theory requires a (deformation) quantisation as minimal input, we analyse the question to what extent the coherent state quantisation, defined by the Segal-Bargmann-Hall transform, can serve as basis of the former.
Mass distribution of fission fragments within the Born-Oppenheimer approximation
Energy Technology Data Exchange (ETDEWEB)
Pomorski, K.; Nerlo-Pomorska, B. [M.C.S. University, Department of Theoretical Physics, Lublin (Poland); Ivanyuk, F.A. [Institute for Nuclear Research, Kiev (Ukraine)
2017-03-15
The fission fragments mass-yield of {sup 236} U is obtained by an approximate solution of the eigenvalue problem of the collective Hamiltonian that describes the dynamics of the fission process whose degrees of freedom are: the fission (elongation), the neck and mass-asymmetry modes. The macroscopic-microscopic method is used to evaluate the potential energy surface. The macroscopic energy part is calculated using the liquid drop model and the microscopic corrections are obtained using a Woods-Saxon single-particle levels. The four-dimensional modified Cassini ovals shape parametrization is used to describe the shape of the fissioning nucleus. The mass tensor is taken within a cranking-type approximation. The final fragment mass distribution is obtained by weighting the adiabatic density distribution in the collective space with the neck-dependent fission probability. The neck degree of freedom is found to play a significant role in determining the final fragment mass distribution. (orig.)
Gao, Jing Kun; Qin, Yu Liang; Deng, Bin; Wang, Hong Qiang; Li, Jin; Li, Xiang
2016-04-01
This paper presents two parts of work around terahertz imaging applications. The first part aims at solving the problems occurred with the increasing of the rotation angle. To compensate for the nonlinearity of terahertz radar systems, a calibration signal acquired from a bright target is always used. Generally, this compensation inserts an extra linear phase term in the intermediate frequency (IF) echo signal which is not expected in large-rotation angle imaging applications. We carried out a detailed theoretical analysis on this problem, and a minimum entropy criterion was employed to estimate and compensate for the linear-phase errors. In the second part, the effects of spherical wave on terahertz inverse synthetic aperture imaging are analyzed. Analytic criteria of plane-wave approximation were derived in the cases of different rotation angles. Experimental results of corner reflectors and an aircraft model based on a 330-GHz linear frequency-modulated continuous wave (LFMCW) radar system validated the necessity and effectiveness of the proposed compensation. By comparing the experimental images obtained under plane-wave assumption and spherical-wave correction, it also showed to be highly consistent with the analytic criteria we derived.
Three-dimensional, prestack, plane wave migration of teleseismic P-to-S converted phases: 1. Theory
Poppeliers, Christian; Pavlis, Gary L.
2003-02-01
We present the theoretical foundations for a prestack migration technique to image teleseismic P-to-S converted phases. The method builds on teleseismic P wave deconvolution, pseudostation stacking [, 1999] and on the idea of using a plane wave decomposition for imaging as introduced by [1982]. Deconvolution operators are constructed by pseudostation stacking of the array aligned to the incident P wave arrival times to produce a space-variable deconvolution operator. The resulting data are then muted to remove the deconvolved direct P wave pulse and pseudostation stacked over a grid of feasible slowness vectors. The pseudostation stack interpolates the wave field onto a regular grid along Earth's surface producing a series (one per slowness vector) of uniformly sampled three-dimensional data cubes (two space variables and time). The plane wave components can be propagated downward using a form of approximate ray tracing with a three-dimensional Earth model. This yields a series of distorted cubes topologically equivalent to the original uniformly sampled data cubes. These data volumes are summed as a weighted stack with the weights derived from an integration formula for inverse scattering based on the generalized Radon transform. This allows an image of the subsurface to be constructed on an event by event basis beneath the array. We apply this technique to data from the Lodore array that was deployed in northwestern Colorado. The results suggest the presence of a major lithospheric-scale discontinuity defined by a south dipping boundary.
The Born Approximation and Eikonal Approximation of the Quantum Scattering%量子散射的玻恩近似和程函近似
Institute of Scientific and Technical Information of China (English)
徐中辉; 周祥; 廖昱博
2011-01-01
The theory of scattering is a very important part of the quantum mechanics.The Born approximation and Eikonal approximation of the Scattering cross-section are calculated with the Gauss potential and Lenzjensen potential under a particular incident energy.The results show that the bigger the Electronic energy is,the smaller the total scattering crossection is and the weaker the electron scattering of potential field is.There is little influence of potential to the energetic particle about the Lenz-jensen potential.And the majority of scattered particles are concentrated on a narrow range.%散射理论是量子力学的一项重要内容.在规定的入射能量下,分别给定Gauss位势和Lenz-jensen位势,计算了散射总截面的玻恩近似和程函近似.结果表明对于Gauss位势,电子能量越大,总散射截面越小,势场对电子的散射越弱.对于Lenz-jensen位势,势对高能粒子的影响比较小,大部分散射的粒子集中在小角度范围内.
A numerical method for determining the radial wave motion correction in plane wave couplers
DEFF Research Database (Denmark)
Cutanda Henriquez, Vicente; Barrera Figueroa, Salvador; Torras Rosell, Antoni
2016-01-01
solution is an analytical expression that estimates the difference between the ideal plane wave sound field and a more complex lossless sound field created by a non-planar movement of the microphone’s membranes. Alternatively, a correction may be calculated numerically by introducing a full model......Microphones are used for realising the unit of sound pressure level, the pascal (Pa). Electro-acoustic reciprocity is the preferred method for the absolute determination of the sensitivity. This method can be applied in different sound fields: uniform pressure, free field or diffuse field. Pressure...... calibration, carried out in plane wave couplers, is the most extended. Here plane wave propagation is assumed. While this assumption is valid at low and mid frequencies, it fails at higher frequencies because the membrane of the microphones is not moving uniformly, and there are viscous losses. An existing...
Computation of the electronic flux density in the Born-Oppenheimer approximation.
Diestler, D J; Kenfack, A; Manz, J; Paulus, B; Pérez-Torres, J F; Pohl, V
2013-09-12
A molecule in the electronic ground state described in the Born–Oppenheimer approximation (BOA) by the wave function ΨBO = Φ0χ0 (where Φ0 is the time-independent electronic energy eigenfunction and χ0 is a time-dependent nuclear wave packet) exhibits a nonzero nuclear flux density, whereas it always displays zero electronic flux density (EFD), because the electrons are in a stationary state. A hierarchical approach to the computation of the EFD within the context of the BOA, which utilizes only standard techniques of quantum chemistry (to obtain Φ0) and quantum dynamics (to describe the evolution of χ0 on the ground-state potential energy surface), provides a resolution of this puzzling, nonintuitive result. The procedure is applied to H2(+) oriented parallel with the z-axis and vibrating in the ground state (2)Σg(+). First, Φ0 and χ0 are combined by the coupled-channels technique to give the normally dominant z-component of the EFD. Imposition of the constraints of electronic continuity, cylindrical symmetry of Φ0 and two boundary conditions on the EFD through a scaling procedure yields an improved z-component, which is then used to compute the complementary orthogonal ρ-component. The resulting EFD agrees with its highly accurate counterpart furnished by a non-BOA treatment of the system.
Yum, H N; Jang, Y J; Liu, X; Shahriar, M S
2012-08-13
In a white light cavity (WLC), the group velocity is superluminal over a finite bandwidth. For a WLC-based data buffering system we recently proposed, it is important to visualize the behavior of pulses inside such a cavity. The conventional plane wave transfer functions, valid only over space that is translationally invariant, cannot be used for the space inside WLC or any cavity, which is translationally variant. Here, we develop the plane wave spatio temporal transfer function (PWSTTF) method to solve this problem, and produce visual representations of a Gaussian input pulse incident on a WLC, for all times and positions.
In-Vivo Synthetic Aperture and Plane Wave High Frame Rate Cardiac Imaging
DEFF Research Database (Denmark)
Stuart, Matthias Bo; Jensen, Jonas; Brandt, Andreas Hjelm;
2014-01-01
A comparison of synthetic aperture imaging using spherical and plane waves with low number of emission events is presented. For both wave types, a 90 degree sector is insonified using 15 emission events giving a frame rate of 200 frames per second. Field II simulations of point targets show simil.......43 for spherical and 0.70 for plane waves. All measures are well within FDA limits for cardiac imaging. In-vivo images of the heart of a healthy 28-year old volunteer are shown....
Diestler, D J
2013-06-01
Intuition suggests that a molecular system in the electronic ground state Φ0 should exhibit an electronic flux density (EFD) in response to the motion of its nuclei. If that state is described by the Born-Oppenheimer approximation (BOA), however, a straightforward calculation of the EFD yields zero, since the electrons are in a stationary state, regardless of the state of the nuclear motion. Here an alternative pathway to a nonzero EFD from a knowledge of only the BOA ground-state wave function is proposed. Via perturbation theory a complete set of approximate vibronic eigenfunctions of the whole Hamiltonian is generated. If the complete non-BOA wave function is expressed in the basis of these vibronic eigenfunctions, the ground-state contribution to the EFD is found to involve a summation over excited states. Evaluation of this sum through the so-called "average excitation energy approximation" produces a nonzero EFD. An explicit formula for the EFD for the prototypical system, namely, oriented H2+ vibrating in the electronic ground state, is derived.
Meziane, M; Jones, M K; Luo, W; Pentchev, L; Perdrisat, C F; Puckett, A J R; Punjabi, V; Wesselmann, F R; Ahmidouch, A; Albayrak, I; Aniol, K A; Arrington, J; Asaturyan, A; Ates, O; Baghdasaryan, H; Benmokhtar, F; Bertozzi, W; Bimbot, L; Bosted, P; Boeglin, W; Butuceanu, C; Carter, P; Chernenko, S; Christy, E; Commisso, M; Cornejo, J C; Covrig, S; Danagoulian, S; Daniel, A; Davidenko, A; Day, D; Dhamija, S; Dutta, D; Ent, R; Frullani, S; Fenker, H; Frlez, E; Garibaldi, F; Gaskell, D; Gilad, S; Gilman, R; Goncharenko, Y; Hafidi, K; Hamilton, D; Higinbotham, D W; Hinton, W; Horn, T; Hu, B; Huang, J; Huber, G M; Jensen, E; Kang, H; Keppel, C; Khandaker, M; King, P; Kirillov, D; Kohl, M; Kravtsov, V; Kumbartzki, G; Li, Y; Mamyan, V; Margaziotis, D J; Markowitz, P; Marsh, A; Matulenko, Y; Maxwell, J; Mbianda, G; Meekins, D; Melnik, Y; Miller, J; Mkrtchyan, A; Mkrtchyan, H; Moffit, B; Moreno, O; Mulholland, J; Narayan, A; Nuruzzaman,; Nedev, S; Piasetzky, E; Pierce, W; Piskunov, N M; Prok, Y; Ransome, R D; Razin, D S; Reimer, P E; Reinhold, J; Rondon, O; Shabestari, M; Shahinyan, A; Shestermanov, K; Sirca, S; Sitnik, I; Smykov, L; Smith, G; Solovyev, L; Solvignon, P; Subedi, R; Suleiman, R; Tomasi-Gustafsson, E; Vasiliev, A; Vanderhaeghen, M; Veilleux, M; Wojtsekhowski, B B; Wood, S; Ye, Z; Zanevsky, Y; Zhang, X; Zhang, Y; Zheng, X; Zhu, L
2010-01-01
Intensive theoretical and experimental efforts over the past decade have aimed at explaining the discrepancy between data for the proton form factor ratio $G_{Ep}/G_{Mp}$ obtained from cross section and polarization measurements. One possible explanation for this difference is a two-photon-exchange contribution. We report the results of the JLab Hall C $GEp2\\gamma$ experiment, which measured the kinematical dependence of polarization transfer observables in elastic electron-proton scattering at $Q^2=2.5$ GeV$^2$, in search of effects beyond the Born approximation. For a wide range of values of the kinematic factor $\\epsilon$ ($\\epsilon=$0.15, 0.63, and 0.77), the proton polarization component ratio and the longitudinal polarization transfer component were measured with statistical uncertainties of $\\pm$0.01 and $\\pm$0.006 and systematic uncertainties of 0.013 and 0.01, respectively.
Band structure of thin films by the linear augmented-plane-wave method
DEFF Research Database (Denmark)
Jepsen, O.; Madsen, J.; Andersen, Ole Krogh
1978-01-01
We present a linear augmented-plane-wave method for solving the band-structure problem in thin crystalline films. The potential is separated into a muffin-tin potential inside the film, a potential depending exclusively on the normal coordinate outside the film, and corrections in both regions...
The Relativistic Transformation for an Electromagnetic Plane Wave with General Time Dependence
Smith, Glenn S.
2012-01-01
In special relativity, the transformation between inertial frames for an electromagnetic plane wave is usually derived for the time-harmonic case (the field is a sinusoid of infinite duration), even though all practical waves are of finite duration and may not even contain a dominant sinusoid. This paper presents an alternative derivation in which…
Linear GPR Imaging Based on Electromagnetic Plane-Wave Spectra and Diffraction Tomography
DEFF Research Database (Denmark)
Meincke, Peter
2004-01-01
in the forward model. The two inversion schemes include an accurate electromagnetic description of the GPR antennas through their plane-wave transmitting and receiving spectra. The performance of the FTM is investigated through a numerical example involving a 2.5-dimensional configuration in which the GPR...
Optimized Plane Wave Imaging for Fast and High-Quality Ultrasound Imaging
DEFF Research Database (Denmark)
Jensen, Jonas; Stuart, Matthias Bo; Jensen, Jørgen Arendt
2016-01-01
This paper presents a method for optimizing parameters affecting the image quality in plane wave imaging. More specifically, the number of emissions and steering angles is optimized to attain the best images with the highest frame rate possible. The method is applied to a specific problem, where ...
Simplified description of out-of-plane waves in thin annular elastic plates
DEFF Research Database (Denmark)
Zadeh, Maziyar Nesari; Sorokin, Sergey
2013-01-01
Dispersion relations are derived for the out-of-plane wave propagation in planar elastic plates with constant curvature using the classical Kirchhoff thin plate theory. The dispersion diagrams and the mode shapes are compared with their counterparts for a straight plate strip and the role of curv...
DEFF Research Database (Denmark)
Hansen, Hendrik H.G.; Stuart, Matthias Bo; Villagómez Hoyos, Carlos Armando
2014-01-01
using linear array ultrasound data of a pulsating concentric homogeneous artery simulated using Field II . The transducer ( f c = 9 MHz, pitch = 197.9 μ m, 192 elements, f s = 180 MHz) transmitted plane waves at 3 sequentially alternating angles (0°, + θ , - θ ) at a PRF of 2 kHz. Simulations were...
Measurement of Plane-Wave Spectra of Ground Penetrating Radar Antennas
DEFF Research Database (Denmark)
Lenler-Eriksen, Hans-Rudolph; Meincke, Peter
2005-01-01
The plane-wave transmitting spectrum of a ground penetrating radar (GPR) loop antenna close to the air-soil interface is measured by means of a probe buried in soil. Probe correction is implemented based upon knowledge about the complex permittivity of the soil and the current distribution...
A numerical method for determining the radial wave motion correction in plane wave couplers
DEFF Research Database (Denmark)
Cutanda Henriquez, Vicente; Barrera Figueroa, Salvador; Torras Rosell, Antoni
2016-01-01
solution is an analytical expression that estimates the difference between the ideal plane wave sound field and a more complex lossless sound field created by a non-planar movement of the microphone’s membranes. Alternatively, a correction may be calculated numerically by introducing a full model...
Z sup 0 -boson contribution in anomalous electron momenta in plane-wave electromagnetic field
Klimenko, E Y
2002-01-01
The Z sup 0 -boson contribution to the mass of electron moving in plane-wave field is considered. The dependence of the Z sup 0 -boson contribution to electron anomalous magnetic momentum and anomalous electric momentum on the external field parameters is studied within the frames of the Weinberg-Salam-Glashow standard model
Measurement of Plane-Wave Spectra of Ground Penetrating Radar Antennas
DEFF Research Database (Denmark)
Lenler-Eriksen, Hans-Rudolph; Meincke, Peter
2005-01-01
The plane-wave transmitting spectrum of a ground penetrating radar (GPR) loop antenna close to the air-soil interface is measured by means of a probe buried in soil. Probe correction is implemented based upon knowledge about the complex permittivity of the soil and the current distribution...
Fast color flow mode imaging using plane wave excitation and temporal encoding
DEFF Research Database (Denmark)
Udesen, Jesper; Gran, Fredrik; Jensen, Jørgen Arendt
2005-01-01
velocity image is presented. The method is based on using a plane wave excitation with temporal encoding to compensate for the decreased SNR, resulting from the lack of focusing. The temporal encoding is done with a linear frequency modulated signal. To decrease lateral sidelobes, a Tukey window is used...
LDA+DMFT implemented with the pseudopotential plane-wave approach
Energy Technology Data Exchange (ETDEWEB)
Trimarchi, G; Leonov, I; Binggeli, N [Abdus Salam International Centre for Theoretical Physics, Trieste 34014 (Italy); Korotin, Dm; Anisimov, V I [Institute of Metal Physics, Russian Academy of Sciences, Ural Division, 620219 Yekaterinburg GSP-170 (Russian Federation)], E-mail: binggeli@ictp.it
2008-04-02
We present a joint implementation of dynamical-mean-field theory (DMFT) with the pseudopotential plane-wave approach, via Wannier functions, for the determination of the electronic properties of strongly correlated materials. The scheme uses, as input for the DMFT calculations, a tight-binding Hamiltonian obtained from the plane-wave calculations by projection onto atomic-centered symmetry-constrained Wannier functions for the correlated orbitals. We apply this scheme to two prototype systems: a paramagnetic correlated metal, SrVO{sub 3}, and a paramagnetic correlated system, V{sub 2}O{sub 3}, which exhibits a metal-insulator transition. Comparisons with available linear-muffin-tin-orbital (LMTO) plus DMFT calculations demonstrate the suitability of the joint DMFT pseudopotential plane-wave approach to describe the electronic properties of strongly correlated materials. This opens the way to future developments using the pseudopotential plane-wave DMFT approach to address total-energy properties, such as structural properties.
Shepherd, James J.; Grüneis, Andreas; Booth, George H.; Kresse, Georg; Alavi, Ali
2012-07-01
Using the finite simulation-cell homogeneous electron gas (HEG) as a model, we investigate the convergence of the correlation energy to the complete-basis-set (CBS) limit in methods utilizing plane-wave wave-function expansions. Simple analytic and numerical results from second-order Møller-Plesset theory (MP2) suggest a 1/M decay of the basis-set incompleteness error where M is the number of plane waves used in the calculation, allowing for straightforward extrapolation to the CBS limit. As we shall show, the choice of basis-set truncation when constructing many-electron wave functions is far from obvious, and here we propose several alternatives based on the momentum transfer vector, which greatly improve the rate of convergence. This is demonstrated for a variety of wave-function methods, from MP2 to coupled-cluster doubles theory and the random-phase approximation plus second-order screened exchange. Finite basis-set energies are presented for these methods and compared with exact benchmarks. A transformation can map the orbitals of a general solid state system onto the HEG plane-wave basis and thereby allow application of these methods to more realistic physical problems. We demonstrate this explicitly for solid and molecular lithium hydride.
Ye, Qian; Jiang, Yikun; Lin, Haoze
2017-03-01
In most textbooks, after discussing the partial transmission and reflection of a plane wave at a planar interface, the power (energy) reflection and transmission coefficients are introduced by calculating the normal-to-interface components of the Poynting vectors for the incident, reflected and transmitted waves, separately. Ambiguity arises among students since, for the Poynting vector to be interpreted as the energy flux density, on the incident (reflected) side, the electric and magnetic fields involved must be the total fields, namely, the sum of incident and reflected fields, instead of the partial fields which are just the incident (reflected) fields. The interpretation of the cross product of partial fields as energy flux has not been obviously justified in most textbooks. Besides, the plane wave is actually an idealisation that is only ever found in textbooks, then what do the reflection and transmission coefficients evaluated for a plane wave really mean for a real beam of limited extent? To provide a clearer physical picture, we exemplify a light beam of finite transverse extent by a fundamental Gaussian beam and simulate its reflection and transmission at a planar interface. Due to its finite transverse extent, we can then insert the incident fields or reflected fields as total fields into the expression of the Poynting vector to evaluate the energy flux and then power reflection and transmission coefficients. We demonstrate that the power reflection and transmission coefficients of a beam of finite extent turn out to be the weighted sum of the corresponding coefficients for all constituent plane wave components that form the beam. The power reflection and transmission coefficients of a single plane wave serve, in turn, as the asymptotes for the corresponding coefficients of a light beam as its width expands infinitely.
From plane waves to local Gaussians for the simulation of correlated periodic systems
Booth, George H.; Tsatsoulis, Theodoros; Chan, Garnet Kin-Lic; Grüneis, Andreas
2016-08-01
We present a simple, robust, and black-box approach to the implementation and use of local, periodic, atom-centered Gaussian basis functions within a plane wave code, in a computationally efficient manner. The procedure outlined is based on the representation of the Gaussians within a finite bandwidth by their underlying plane wave coefficients. The core region is handled within the projected augment wave framework, by pseudizing the Gaussian functions within a cutoff radius around each nucleus, smoothing the functions so that they are faithfully represented by a plane wave basis with only moderate kinetic energy cutoff. To mitigate the effects of the basis set superposition error and incompleteness at the mean-field level introduced by the Gaussian basis, we also propose a hybrid approach, whereby the complete occupied space is first converged within a large plane wave basis, and the Gaussian basis used to construct a complementary virtual space for the application of correlated methods. We demonstrate that these pseudized Gaussians yield compact and systematically improvable spaces with an accuracy comparable to their non-pseudized Gaussian counterparts. A key advantage of the described method is its ability to efficiently capture and describe electronic correlation effects of weakly bound and low-dimensional systems, where plane waves are not sufficiently compact or able to be truncated without unphysical artifacts. We investigate the accuracy of the pseudized Gaussians for the water dimer interaction, neon solid, and water adsorption on a LiH surface, at the level of second-order Møller-Plesset perturbation theory.
On the exact open-closed vertex in plane-wave light-cone string field theory
Lucietti, J; Sinha, A K; Lucietti, James; Schafer-Nameki, Sakura; Sinha, Aninda
2003-01-01
The open-closed vertex in the maximally supersymmetric type IIB plane-wave light-cone string field theory is considered and an explicit solution for the bosonic part of the vertex is derived, valid for all values of the mass parameter, \\mu. This vertex is of relevance to IIB plane-wave orientifolds, as well as IIB plane-wave strings in the presence of D-branes, and their gauge theory duals. Methods of complex analysis are used to develop a systematic procedure for obtaining the solution. This procedure is first applied to the vertex in flat space, and then extended to the plane-wave case. The plane-wave solution for the vertex requires introducing certain ``\\mu-deformed Gamma functions'', which are generalizations of the ordinary Gamma function. The behaviour of the Neumann matrices is graphically illustrated and their large-\\mu asymptotics are analysed.
Métris, Aline; George, Susie M; Ropers, Delphine
2017-01-02
Addition of salt to food is one of the most ancient and most common methods of food preservation. However, little is known of how bacterial cells adapt to such conditions. We propose to use piecewise linear approximations to model the regulatory adaptation of Escherichiacoli to osmotic stress. We apply the method to eight selected genes representing the functions known to be at play during osmotic adaptation. The network is centred on the general stress response factor, sigma S, and also includes a module representing the catabolic repressor CRP-cAMP. Glutamate, potassium and supercoiling are combined to represent the intracellular regulatory signal during osmotic stress induced by salt. The output is a module where growth is represented by the concentration of stable RNAs and the transcription of the osmotic gene osmY. The time course of gene expression of transport of osmoprotectant represented by the symporter proP and of the osmY is successfully reproduced by the network. The behaviour of the rpoS mutant predicted by the model is in agreement with experimental data. We discuss the application of the model to food-borne pathogens such as Salmonella; although the genes considered have orthologs, it seems that supercoiling is not regulated in the same way. The model is limited to a few selected genes, but the regulatory interactions are numerous and span different time scales. In addition, they seem to be condition specific: the links that are important during the transition from exponential to stationary phase are not all needed during osmotic stress. This model is one of the first steps towards modelling adaptation to stress in food safety and has scope to be extended to other genes and pathways, other stresses relevant to the food industry, and food-borne pathogens. The method offers a good compromise between systems of ordinary differential equations, which would be unmanageable because of the size of the system and for which insufficient data are available
Flach, S
1995-01-01
We study tangent bifurcation of band edge plane waves in nonlinear Hamiltonian lattices. The lattice is translationally invariant. We argue for the breaking of permutational symmetry by the new bifurcated periodic orbits. The case of two coupled oscillators is considered as an example for the perturbation analysis, where the symmetry breaking can be traced using Poincare maps. Next we consider a lattice and derive the dependence of the bifurcation energy on the parameters of the Hamiltonian function in the limit of large system sizes. A necessary condition for the occurence of the bifurcation is the repelling of the band edge plane wave's frequency from the linear spectrum with increasing energy. We conclude that the bifurcated orbits will consequently exponentially localize in the configurational space.
Radiation of de-excited electrons at large times in a strong electromagnetic plane wave
Kazinski, P O
2013-01-01
The late time asymptotics of the physical solutions to the Lorentz-Dirac equation in the electromagnetic external fields of simple configurations -- the constant homogeneous field, the linearly polarized plane wave (in particular, the constant uniform crossed field), and the circularly polarized plane wave -- are found. The solutions to the Landau-Lifshitz equation for the external electromagnetic fields admitting a two-parametric symmetry group, which include as a particular case the above mentioned field configurations, are obtained. General properties of the total radiation power of a charged particle are established. In particular, for a circularly polarized wave and constant uniform crossed fields, the total radiation power in the asymptotic regime is independent of the charge and the external field strength, when expressed in terms of the proper-time, and equals a half of the rest energy of a charged particle divided by its proper-time. The spectral densities of the radiation power formed on the late ti...
Dynamics of a spiral pair source and its interaction with plane waves.
Rabinovitch, A; Biton, Y; Gutman, M; Aviram, I
2009-05-01
Spiral pair creation and dynamics is a widely occurring phenomenon in nature. It can appear in the heart tissue, causing severe arrhythmia, known as a figure-eight reentry. We consider the appearance of a spiral pair source, its minimal strength for survival, and the possible results of its interaction with a plane wave. In particular, its ability to outlast such an encounter is of interest. We also consider the question of exposing the source to a train of pulses, in terms of the frequency and angle of encounter. Results show different regimes of behavior, e.g. source annihilation, motion of the source away from, or towards the origin of the plane waves, its breaking and multiplication. Relevance of these results to heart arrhythmia and their possible cancellation by external pacing are briefly discussed.
Well-posedness and generalized plane waves simulations of a 2D mode conversion model
Imbert-Gérard, Lise-Marie
2015-01-01
Certain types of electro-magnetic waves propagating in a plasma can undergo a mode conversion process. In magnetic confinement fusion, this phenomenon is very useful to heat the plasma, since it permits to transfer the heat at or near the plasma center. This work focuses on a mathematical model of wave propagation around the mode conversion region, from both theoretical and numerical points of view. It aims at developing, for a well-posed equation, specific basis functions to study a wave mode conversion process. These basis functions, called generalized plane waves, are intrinsically based on variable coefficients. As such, they are particularly adapted to the mode conversion problem. The design of generalized plane waves for the proposed model is described in detail. Their implementation within a discontinuous Galerkin method then provides numerical simulations of the process. These first 2D simulations for this model agree with qualitative aspects studied in previous works.
Tiny graviton matrix theory: DLCQ of IIB plane-wave string theory, a conjecture
Energy Technology Data Exchange (ETDEWEB)
Sheikh-Jabbari, Mohammad M. [Department of Physics, Stanford University, 382 via Pueblo Mall, Stanford CA 94305-4060 (United States)]. E-mail: jabbari@itp.stanford.edu
2004-09-01
We conjecture that the discrete light-cone quantization (DLCQ) of strings on the maximally supersymmetric type IIB plane-wave background in the sector with J units of light-cone momentum is a supersymmetric 0+1 dimensional U(J) gauge theory (quantum mechanics) with PSU(2|2) x PSU(2|2) x U(1) superalgebra. The conjectured hamiltonian for the plane-wave matrix (string) theory, the tiny graviton matrix theory, is the quantized (regularized) three brane action on the same background. We present some pieces of evidence for this conjecture through analysis of the hamiltonian , its vacua, spectrum and coupling constant. Moreover, we discuss an extension of our conjecture to the DLCQ of type IIB strings on AdS{sub 5} x S{sup 5} geometry. (author)
Simulations and cold-test results of a prototype plane wave transformer linac structure
Directory of Open Access Journals (Sweden)
Arvind Kumar
2002-03-01
Full Text Available We have built a 4-cell prototype plane wave transformer (PWT linac structure. We discuss here details of the design and fabrication of the PWT linac structure. We present results from superfish and gdfidl simulations as well as cold tests, which are in good agreement with each other. We also present detailed tolerance maps for the PWT structure. We discuss beam dynamics simulation studies performed using parmela.
Institute of Scientific and Technical Information of China (English)
宋海斌; 马在田; 张关泉
1996-01-01
A layer-stripping method is presented for simultaneous inversion of compressional velocity and shear velocity in layered medium from single precritical-incident-angle data of P-P and P-SV plane wave seismogram. A finite bandwidth algorithm is provided and results obviously better than previous research work are obtained by the numerical experiments for band-limited seismogram and synthetic data including noise.
Contributions in anomalous fermion momenta of neutral vector boson in plane-wave field
Klimenko, E Y
2002-01-01
The contributions of the neutral vector boson to the anomalous magnetic and electric momenta of the polarized fermion moving in the plane-wave electromagnetic field are considered in this paper. The contributions are divided by the fermion spin polarization states, which makes it possible to investigate the important problem on the contributions to the fermion anomalous momenta, coming from the the fermion transition to the intermediate state spin-nonflip or spin flip of fermion
CMS-Wave Model: Part 5. Full-plane Wave Transformation and Grid Nesting
2012-04-01
are available in previous reports and CHETNs (Lin et al. 2006; Demirbilek et al. 2007). CMS -Wave is part of the Coastal Modeling System ( CMS ...the U.S. Army Corps of Engineers’ (USACE) Surface-water Modeling System (SMS). The CMS -Wave FP option is available in SMS Version 11.1 and higher...ERDC/CHL CHETN-IV-81 April 2012 Approved for public release; distribution is unlimited. CMS -Wave Model: Part 5. Full-plane Wave Transformation
Li, Chuang; Huang, Jian-Ping; Li, Zhen-Chun; Wang, Rong-Rong
2017-03-01
Least squares migration can eliminate the artifacts introduced by the direct imaging of irregular seismic data but is computationally costly and of slow convergence. In order to suppress the migration noise, we propose the preconditioned prestack plane-wave least squares reverse time migration (PLSRTM) method with singular spectrum constraint. Singular spectrum analysis (SSA) is used in the preconditioning of the take-offangle-domain common-image gathers (TADCIGs). In addition, we adopt randomized singular value decomposition (RSVD) to calculate the singular values. RSVD reduces the computational cost of SSA by replacing the singular value decomposition (SVD) of one large matrix with the SVD of two small matrices. We incorporate a regularization term into the preconditioned PLSRTM method that penalizes misfits between the migration images from the plane waves with adjacent angles to reduce the migration noise because the stacking of the migration results cannot effectively suppress the migration noise when the migration velocity contains errors. The regularization imposes smoothness constraints on the TADCIGs that favor differential semblance optimization constraints. Numerical analysis of synthetic data using the Marmousi model suggests that the proposed method can efficiently suppress the artifacts introduced by plane-wave gathers or irregular seismic data and improve the imaging quality of PLSRTM. Furthermore, it produces better images with less noise and more continuous structures even for inaccurate migration velocities.
Study of simple plane wave generator with an air-metal barrier
Directory of Open Access Journals (Sweden)
Wei Xiong
2014-06-01
Full Text Available Plane wave generators (PWGs are used to accelerate flyer plates to high velocities with their generated plane waves, which are widely used in the test of dynamic properties of materials. The traditional PWG is composed of two explosives with different detonation velocities. It is difficult to implement the related fabrication processes and control the generated waves due to its complicated structures. A simple plane wave generator is presented in this paper, which is composed of two identical cylindrical high explosive (HE charges and an air-metal barrier. A theoretical model was established based on two different paths of the propagation of detonation waves, based on which the size of air-metal barrier was calculated for a given charge. The corresponding numerical simulations were also carried out by AUTODYN-2D® based on the calculated results, which were used to compare with the theoretical calculations. A detonation wave with a flatness of 0.039 μs within the range of 70-percent diameter of the main charge was obtained through the simulations.
Study of simple plane wave generator with an air-metal barrier
Institute of Scientific and Technical Information of China (English)
Wei XIONG; Xian-feng ZHANG; Zhong-wei GUAN; Yong HE; Liang QIAO; Li-li GUO
2014-01-01
Plane wave generators (PWGs) are used to accelerate flyer plates to high velocities with their generated plane waves, which are widely used in the test of dynamic properties of materials. The traditional PWG is composed of two explosives with different detonation velocities. It is difficult to implement the related fabrication processes and control the generated waves due to its complicated structures. A simple plane wave generator is presented in this paper, which is composed of two identical cylindrical high explosive (HE) charges and an air-metal barrier. A theoretical model was established based on two different paths of the propagation of detonation waves, based on which the size of air-metal barrier was calculated for a given charge. The corresponding numerical simulations were also carried out by AUTODYN-2D® based on the calculated results, which were used to compare with the theoretical calculations. A detonation wave with a flatness of 0.039 ms within the range of 70-percent diameter of the main charge was obtained through the simulations.
On the integrability of large N plane-wave matrix theory
Energy Technology Data Exchange (ETDEWEB)
Klose, Thomas E-mail: thklose@aei.mpg.de; Plefka, Jan E-mail: plefka@aei.mpg.de
2004-02-16
We show the three-loop integrability of large N plane-wave matrix theory in a subsector of states comprised of two complex light scalar fields. This is done by diagonalizing the theory's Hamiltonian in perturbation theory and taking the large N limit. At one-loop level the result is known to be equal to the Heisenberg spin-1/2 chain, which is a well-known integrable system. Here, integrability implies the existence of hidden conserved charges and results in a degeneracy of parity pairs in the spectrum. In order to confirm integrability at higher loops, we show that this degeneracy is not lifted and that (corrected) conserved charges exist. Plane-wave matrix theory is intricately connected to N=4 super-Yang-Mills, as it arises as a consistent reduction of the gauge theory on a three-sphere. We find that after appropriately renormalizing the mass parameter of the plane-wave matrix theory the effective Hamiltonian is identical to the dilatation operator of N=4 super-Yang-Mills theory in the considered subsector. Our results therefore represent a strong support for the conjectured three-loop integrability of planar N=4 SYM and are in disagreement with a recent dual string theory finding. Finally, we study the stability of the large N integrability against nonsupersymmetric deformations of the model.
Energy Technology Data Exchange (ETDEWEB)
Khenata, R.; Baltache, H.; Sahnoun, M.; Driz, M.; Rerat, M.; Abbar, B
2003-08-01
A theoretical study of structural and electronic properties of GeC, SnC and GeSn is presented using the full potential linearized augmented plane wave method. In this approach, the generalized gradient approximation was used for the exchange-correlation potential. Results are given for lattice constant, bulk modulus and its pressure derivative in both zinc-blende and rocksalt structures. Band structure, density of states and band gap pressure coefficients in zinc-blende structure are also given. The results are compared with previous calculations and with experimental measurements.
Superresolution Imaging Using Resonant Multiples and Plane-wave Migration Velocity Analysis
Guo, Bowen
2017-08-28
Seismic imaging is a technique that uses seismic echoes to map and detect underground geological structures. The conventional seismic image has the resolution limit of λ/2, where λ is the wavelength associated with the seismic waves propagating in the subsurface. To exceed this resolution limit, this thesis develops a new imaging method using resonant multiples, which produces superresolution images with twice or even more the spatial resolution compared to the conventional primary reflection image. A resonant multiple is defined as a seismic reflection that revisits the same subsurface location along coincident reflection raypath. This reverberated raypath is the reason for superresolution imaging because it increases the differences in reflection times associated with subtle changes in the spatial location of the reflector. For the practical implementation of superresolution imaging, I develop a post-stack migration technique that first enhances the signal-to-noise ratios (SNRs) of resonant multiples by a moveout-correction stacking method, and then migrates the post-stacked resonant multiples with the associated Kirchhoff or wave-equation migration formula. I show with synthetic and field data examples that the first-order resonant multiple image has about twice the spatial resolution compared to the primary reflection image. Besides resolution, the correct estimate of the subsurface velocity is crucial for determining the correct depth of reflectors. Towards this goal, wave-equation migration velocity analysis (WEMVA) is an image-domain method which inverts for the velocity model that maximizes the similarity of common image gathers (CIGs). Conventional WEMVA based on subsurface-offset, angle domain or time-lag CIGs requires significant computational and memory resources because it computes higher dimensional migration images in the extended image domain. To mitigate this problem, I present a new WEMVA method using plane-wave CIGs. Plane-wave CIGs reduce the
On AdS/CFT correspondence beyond SUGRA: plane waves, free CFTs and double-trace deformations
Energy Technology Data Exchange (ETDEWEB)
Diaz Vazquez, D.E.
2007-09-13
This thesis deals with three corners of the AdS/CFT Correspondence that lie one step beyond the classical supergravity (SUGRA) approximation. We first explore the BMN limit of the duality and study, in particular, the behavior of field theoretic propagators in the corresponding Penrose limit. We unravel the semiclassical (WKB-) exactness of the propagators in the resulting plane wave background metric. Then, we address the limit of vanishing coupling of the conformal field theory (CFT) at large N. In the simplified scenario of Higher Spin/O(N) Vector Model duality, the conformal partial wave (CPW) expansion of scalar four-point functions are reorganized to make them suggestive of a bulk interpretation in term of a consistent truncated massless higher spin theory and their corresponding exchange Witten graphs. We also explore the connection to the interacting O(N) Vector Model at its infra-red fixed point, at leading large N. Finally, coming back to the gauge theory, we study the effect of a relevant double-trace deformations of the boundary CFT on the partition function and its dual bulk interpretation. We show how the one-loop computation in the Anti-de Sitter (AdS) space correctly reproduces the partition function and conformal anomaly of the boundary theory. In all, we get a clean test of the duality beyond the classical SUGRA approximation in the AdS bulk and at the corresponding next-to-leading 1/N order of the CFT at the conformal boundary. (orig.)
N=4 Supersymmetric Yang-Mills on S^3 in Plane Wave Matrix Model at Finite Temperature
Kitazawa, Yoshihisa
2008-01-01
We investigate the large N reduced model of gauge theory on a curved spacetime through the plane wave matrix model. We formally derive the action of the N=4 supersymmetric Yang-Mills theory on R \\times S^3 from the plane wave matrix model in the large N limit. Furthermore, we evaluate the effective action of the plane wave matrix model up to the two-loop level at finite temperature. We find that the effective action is consistent with the free energy of the N=4 supersymmetric Yang-Mills theory on S^3 at high temperature limit where the planar contributions dominate. We conclude that the plane wave matrix model can be used as a large N reduced model to investigate nonperturbative aspects of the N=4 supersymmetric Yang-Mills theory on R \\times S^3.
Institute of Scientific and Technical Information of China (English)
Wang Yang; Zhou Ya-Jun; Jiao Li-Guang
2012-01-01
The standard distorted wave Born approximation (DWBA) method has been extended to second-order Born amplitude in order to describe the multiple interactions between the projectile and the atomic target.Second-order DWBA calculations have been preformed to investigate the triple differential cross sections (TDCS) of coplanar doubly symmetric (e,2e) collisions for the alkali target potassium at excess energies of 6 eV-60 eV.Compared with the previous first-order DWBA calculations,the present theoretical model improves the degree of agreement with experiments,especially for the backward scattering angle region of TDCS.This indicates that the present second-order Born term is capable of giving a reasonable correction to the DWBA model in studying coplanar symmetric (e,2e) problems in low and intermediate energy ranges.
Sum, K S; Pan, J
2007-07-01
Distributions of sound pressure and intensity on the surface of a flat impedance strip flush-mounted on a rigid baffle are studied for a grazing incident plane wave. The distributions are obtained by superimposing the unperturbed wave (the specularly reflected wave as if the strip is rigid plus the incident wave) with the radiated wave from the surface vibration of the strip excited by the unperturbed pressure. The radiated pressure interferes with the unperturbed pressure and distorts the propagating plane wave. When the plane wave propagates in the baffle-strip-baffle direction, it encounters discontinuities in acoustical impedance at the baffle-strip and strip-baffle interfaces. The radiated pressure is highest around the baffle-strip interface, but decreases toward the strip-baffle interface where the plane wave distortion reduces accordingly. As the unperturbed and radiated waves have different magnitudes and superimpose out of phase, the surface pressure and intensity increase across the strip in the plane wave propagation direction. Therefore, the surface absorption of the strip is nonzero and nonuniform. This paper provides an understanding of the surface pressure and intensity behaviors of a finite impedance strip for a grazing incident plane wave, and of how the distributed intensity determines the sound absorption coefficient of the strip.
Propagation of plane waves in thermoelastic cubic crystal material with two relaxation times
Institute of Scientific and Technical Information of China (English)
Rajneesh Kumar; Manjeet Singh
2007-01-01
A problem concerned with the reflection and refraction of thermoelastic plane waves an imperfect interface between two generalized thermally conducting cutimes has been investigated.The generalized thermoelastic theory with two relaxation of retiected and refracted waves to the amplitude of incident waves are obtained for an imperfect boundary and deduced for normal stiffness,transverse stiffness,themlal contact conductance,slip and welded boundaries. Amplitude ratios of different reflected and graphically for different incident waves.It is observed that the amplitude ratios of reflected and refracted waves are affected by the stiffness and thermal properties of the media.
Reflection of plane waves from free surface of a microstretch elastic solid
Indian Academy of Sciences (India)
Baljeet Singh
2002-03-01
In the present investigation, it is shown that there exists five basic waves in a microstretch elastic solid half-space. The problem of reflection of plane waves from free surface of a microstretch elastic solid half-space is studied. The energy ratios for various reflected waves are obtained for aluminium- epoxy composite as a microstretch elastic solid half-space. The variations of the energy ratios with the angle of incidence are shown graphically. The microstretch effect is shown on various reflected waves.
Fisanov, V. V.
2017-09-01
Analytical expressions for complex values of the wave number, refractive index, and the characteristic wave impedance of homogeneous electromagnetic plane waves propagating in a linear, homogeneous, isotropic medium with losses and gain are derived. Formulas for determining the type of normal wave as a function of the values of the real and imaginary parts of the permittivity and permeability are obtained, and conditions for the appearance of positive and negative refraction at the interface of two isotropic media are indicated. In the approach applied here, the concept of a negative refractive index is not used.
Directory of Open Access Journals (Sweden)
Zhang Rong
2013-01-01
Full Text Available This paper analyzes the reflection and refraction of plane wave incidences at the interface between magnetoelectroelastic (MEE and liquid media. The MEE medium is assumed to be transversely isotropic and the liquid medium to be nonviscous. Three cases, i.e., the coupled quasipressure wave incidence from the MEE medium, the coupled quasi-shear vertical wave incidence from the MEE medium, and the pressure wave incidence from the liquid medium, are discussed. The expressions of reflection and transmission coefficients varying with the incident angle are obtained. This investigation would be useful to the MEE acoustic device field.
Relativistic two-boson system in presence of electromagnetic plane waves
Droz-Vincent, Philippe
2015-01-01
The relativistic two-body problem is considered for spinless particles subject to an external macroscopic electromagnetic field. When this field is made of the monochromatic superposition of two conter-propagating plane waves (and provided the mutual interaction between particles is known), it is possible to write down explicitly a pair of coupled wave equations (corresponding to a pair of mass-shell constraints) which takes into account also the field contribution. These equations are manifestly covariant; constants of the motion are exhibited, so one ends up with a reduced problem concerning five degrees of freedom.
Nonlocal Effects on D-branes in Plane-Wave Backgrounds
Ganor, O J; Ganor, Ori J.; Varadarajan, Uday
2002-01-01
We argue that the effective field theory on D3-branes in a plane-wave background with 3-form flux is a nonlocal deformation of Yang-Mills theory. In the case of NSNS flux, it is a dipole field theory with lightlike dipole vectors. For an RR 3-form flux the dipole theory is strongly coupled. We propose a weakly coupled S-dual description for it. The S-dual description is local at any finite order in string perturbation theory but becomes nonlocal when all perturbation theory orders are summed together.
Abramov, Arnold; Kostikov, Alexander
2017-03-01
We report the effect of scattering of electromagnetic plane waves by two cylinders on whispering gallery mode (WGM) formation in a cylinder. WGM can occur because of the presence of additional cylinder scatterers at specific location, while WGMs can only form in a single cylinder for specific cylinder radius and/or wavelength values, the matching accuracy required would be much greater than that required in our model for the additional cylinders locations. Analysis of the general solution to the problem showed that the effect can be explained by the interference of waves scattered by additional cylinders and incident on the main cylinder.
DEFF Research Database (Denmark)
Cappellin, Cecilia; Breinbjerg, Olav; Frandsen, Aksel
2008-01-01
An effective technique for extracting the singularity of plane wave spectra in the computation of antenna aperture fields is proposed. The singular spectrum is first factorized into a product of a finite function and a singular function. The finite function is inverse Fourier transformed...... numerically using the Inverse Fast Fourier Transform, while the singular function is inverse Fourier transformed analytically, using the Weyl-identity, and the two resulting spatial functions are then convolved to produce the antenna aperture field. This article formulates the theory of the singularity...
NC plane waves, Casimir effect and flux tube potential with L\\"uscher terms
Kováčik, Samuel
2016-01-01
We analyze plane waves in a model of quantum mechanics in a three dimensional noncommutative (NC) space $R^3_{\\lambda}$. Signature features of NC models are impossibility of probing distances smaller than a certain length scale {\\lambda} and a presence of natural energetic cut-off at energy scale of order $1/{\\lambda}^2$ (in convenient units). We analyze consequences of such restrictions on a 1 dimensional Casimir effect. The result shows resemblance to flux tube potential for quark-antiquark pairs and to effective bosonic string theories with L\\"uscher terms. Such behavior might effect the radius of possible compact (fuzzy) dimensions.
Plane wave matrix theory vs. N=4 D=4 super Yang-Mills
Energy Technology Data Exchange (ETDEWEB)
Kim, N. [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Am Muehlenberg 1, 14476 Golm (Germany)
2004-06-01
A mass deformed, supersymmetric, Yang-Mills quantum mechanics has been introduced recently as the matrix model of M-theory on plane-wave backgrounds. Here we point out that the massive matrix model can be obtained as a dimensional reduction of N=4, D=4 Super Yang-Mills theory on S{sup 3}. The hamiltonian of the matrix model can be matched with the dilatation operator of the conformal field theory, and we discuss how they behave in the perturbative computations. (Abstract Copyright [2004], Wiley Periodicals, Inc.)
Electromagnetic plane-wave pulse transmission into a Lorentz half-space.
Cartwright, Natalie A
2011-12-01
The propagation of an electromagnetic plane-wave signal obliquely incident upon a Lorentz half-space is studied analytically. Time-domain asymptotic expressions that increase in accuracy with propagation distance are derived by application of uniform saddle point methods on the Fourier-Laplace integral representation of the transmitted field. The results are shown to be continuous in time and comparable with numerical calculations of the field. Arrival times and angles of refraction are given for prominent transient pulse features and the steady-state signal.
Indian Academy of Sciences (India)
Baljeet Singh; Anand Kumar Yadav
2013-08-01
Reflection of plane waves is studied at a free surface of a perfectly conducting transversely isotropic elastic solid half-space with initial stress. The governing equations are solved to obtain the velocity equation which indicates the existence of two quasi planar waves in the medium. Reflection coefficients and energy ratios for reflected qP and qSV waves are derived and computed numerically for a particular material. Effects of the initial stress and magnetic field are shown graphically on these reflection coefficients and energy ratios.
Yaakob, M. K.; Taib, M. F. M.; Lu, L.; Hassan, O. H.; Yahya, M. Z. A.
2015-11-01
The structural, electronic, elastic, and optical properties of BiFeO3 were investigated using the first-principles calculation based on the local density approximation plus U (LDA + U) method in the frame of plane-wave pseudopotential density functional theory. The application of self-interaction corrected LDA + U method improved the accuracy of the calculated properties. Results of structural, electronic, elastic, and optical properties of BiFeO3, calculated using the LDA + U method were in good agreement with other calculation and experimental data; the optimized choice of on-site Coulomb repulsion U was 3 eV for the treatment of strong electronic localized Fe 3d electrons. Based on the calculated band structure and density of states, the on-site Coulomb repulsion U had a significant effect on the hybridized O 2p and Fe 3d states at the valence and the conduction band. Moreover, the elastic stiffness tensor, the longitudinal and shear wave velocities, bulk modulus, Poisson’s ratio, and the Debye temperature were calculated for U = 0, 3, and 6 eV. The elastic stiffness tensor, bulk modulus, sound velocities, and Debye temperature of BiFeO3 consistently decreased with the increase of the U value.
Tremblay-Darveau, Charles; Williams, Ross; Milot, Laurent; Bruce, Matthew; Burns, Peter N
2014-12-01
Plane-wave imaging offers image acquisition rates at the pulse repetition frequency, effectively increasing the imaging frame rates by up to two orders of magnitude over conventional line-by-line imaging. This form of acquisition can be used to achieve very long ensemble lengths in nonlinear modes such as pulse inversion Doppler, which enables new imaging trade-offs that were previously unattainable. We first demonstrate in this paper that the coherence of microbubble signals under repeated exposure to acoustic pulses of low mechanical index can be as high as 204 ± 5 pulses, which is long enough to allow an accurate power Doppler measurement. We then show that external factors, such as tissue acceleration, restrict the detection of perfusion at the capillary level with linear Doppler, even if long Doppler ensembles are considered. Hence, perfusion at the capillary level can only be detected with ultrasound through combined microbubbles and Doppler imaging. Finally, plane-wave contrast-enhanced power and color Doppler are performed on a rabbit kidney in vivo as a proof of principle. We establish that long pulse-inversion Doppler sequences and conventional wall-filters can create an image that simultaneously resolves both the vascular morphology of veins and arteries, and perfusion at the capillary level with frame rates above 100 Hz.
Plane-Wave Least-Squares Reverse Time Migration for Rugged Topography
Institute of Scientific and Technical Information of China (English)
Jianping Huang; Chuang Li; Rongrong Wang; Qingyang Li
2015-01-01
We present a method based on least-squares reverse time migration with plane-wave encod-ing (P-LSRTM) for rugged topography. Instead of modifying the wave field before migration, we modify the plane-wave encoding function and fill constant velocity to the area above rugged topography in the model so that P-LSRTM can be directly performed from rugged surface in the way same to shot domain reverse time migration. In order to improve efficiency and reduce I/O (input/output) cost, the dynamic en-coding strategy and hybrid encoding strategy are implemented. Numerical test on SEG rugged topography model show that P-LSRTM can suppress migration artifacts in the migration image, and compensate am-plitude in the middle-deep part efficiently. Without data correction, P-LSRTM can produce a satisfying image of near-surface if we could get an accurate near-surface velocity model. Moreover, the pre-stack P-LSRTM is more robust than conventional RTM in the presence of migration velocity errors.
Energy Technology Data Exchange (ETDEWEB)
Abramov, Arnold, E-mail: qulaser@gmail.com [Kuang-Chi Institute of Advanced Technology, Shenzhen, 518057 (China); Kostikov, Alexander [Donbass State Engineering Academy, 84303, Kramatorsk, Donetsk (Ukraine)
2017-03-26
We report the effect of scattering of electromagnetic plane waves by two cylinders on whispering gallery mode (WGM) formation in a cylinder. WGM can occur because of the presence of additional cylinder scatterers at specific location, while WGMs can only form in a single cylinder for specific cylinder radius and/or wavelength values, the matching accuracy required would be much greater than that required in our model for the additional cylinders locations. Analysis of the general solution to the problem showed that the effect can be explained by the interference of waves scattered by additional cylinders and incident on the main cylinder. - Highlights: • We consider scattering of electromagnetic plane waves by two cylinders. • WGMs occur because of the presence of additional cylinder at specific location. • The accuracy for the locations is much less than required for specific values of single cylinder. • The interference of waves scattered by additional cylinders and incident on the main is responsible for the effect.
Concepts and Tradeoffs in Velocity Estimation With Plane-Wave Contrast-Enhanced Doppler.
Tremblay-Darveau, Charles; Williams, Ross; Sheeran, Paul S; Milot, Laurent; Bruce, Matthew; Burns, Peter N
2016-11-01
While long Doppler ensembles are, in principle, beneficial for velocity estimates, short acoustic pulses must be used in microbubble contrast-enhanced (CE) Doppler to mitigate microbubble destruction. This introduces inherent tradeoffs in velocity estimates with autocorrelators, which are studied here. A model of the autocorrelation function adapted to the microbubble Doppler signal accounting for transit time, the echo frequency uncertainty, and contrast-agent destruction is derived and validated in vitro. It is further demonstrated that a local measurement of the center frequency of the microbubble echo is essential in order to avoid significant bias in velocity estimates arising from the linear and nonlinear frequency-dependent scattering of microbubbles and compensate for the inherent speckle nature of the received echo frequency. For these reasons, broadband Doppler estimators (2-D autocorrelator and Radon projection) are better suited than simpler narrow-band estimators (1-D autocorrelator and 1-D Fourier transform) for CE flow assessment. A case study of perfusion in a VX-2 carcinoma using CE plane-wave Doppler is also shown. We demonstrate that even when considering all uncertainties associated with microbubble-related decorrelation (destruction, pulse bandwidth, transit time, and flow gradient) and the need for real-time imaging, a coefficient of variation of 4% on the axial velocity is achievable with plane-wave imaging.
Lectures on the Plane-Wave String/Gauge Theory Duality
Plefka, J
2004-01-01
These lectures give an introduction to the novel duality relating type IIB string theory in a maximally supersymmetric plane-wave background to N=4, d=4, U(N) Super Yang-Mills theory in a particular large N and large R-charge limit due to Berenstein, Maldacena and Nastase. In the first part of these lectures the duality is derived from the AdS/CFT correspondence by taking a Penrose limit of the AdS_5 x S^5 geometry and studying the corresponding double-scaling limit on the gauge theory side. The resulting free plane-wave superstring is then quantized in light-cone gauge. On the gauge theory side of the correspondence the composite Super Yang-Mills operators dual to string excitations are identified, and it is shown how the string spectrum can be mapped to the planar scaling dimensions of these operators. In the second part of these lectures we study the correspondence at the interacting respectively non-planar level. On the gauge theory side it is demonstrated that the large N large R-charge limit in question...
Radiation of de-excited electrons at large times in a strong electromagnetic plane wave
Kazinski, P. O.
2013-12-01
The late time asymptotics of the physical solutions to the Lorentz-Dirac equation in the electromagnetic external fields of simple configurations-the constant homogeneous field, the linearly polarized plane wave (in particular, the constant uniform crossed field), and the circularly polarized plane wave-are found. The solutions to the Landau-Lifshitz equation for the external electromagnetic fields admitting a two-parametric symmetry group, which include as a particular case the above mentioned field configurations, are obtained. Some general properties of the total radiation power of a charged particle are established. In particular, for a circularly polarized wave and constant uniform crossed fields, the total radiation power in the asymptotic regime is independent of the charge and the external field strength, when expressed in terms of the proper-time, and equals a half the rest energy of a charged particle divided by its proper-time. The spectral densities of the radiation power formed on the late time asymptotics are derived for a charged particle moving in the external electromagnetic fields of the simple configurations pointed above. This provides a simple method to verify experimentally that the charged particle has reached the asymptotic regime.
Fast solution of elliptic partial differential equations using linear combinations of plane waves
Pérez-Jordá, José M.
2016-02-01
Given an arbitrary elliptic partial differential equation (PDE), a procedure for obtaining its solution is proposed based on the method of Ritz: the solution is written as a linear combination of plane waves and the coefficients are obtained by variational minimization. The PDE to be solved is cast as a system of linear equations A x =b , where the matrix A is not sparse, which prevents the straightforward application of standard iterative methods in order to solve it. This sparseness problem can be circumvented by means of a recursive bisection approach based on the fast Fourier transform, which makes it possible to implement fast versions of some stationary iterative methods (such as Gauss-Seidel) consuming O (N logN ) memory and executing an iteration in O (N log2N ) time, N being the number of plane waves used. In a similar way, fast versions of Krylov subspace methods and multigrid methods can also be implemented. These procedures are tested on Poisson's equation expressed in adaptive coordinates. It is found that the best results are obtained with the GMRES method using a multigrid preconditioner with Gauss-Seidel relaxation steps.
Plane Wave Imaging for ultrasonic non-destructive testing: Generalization to multimodal imaging.
Le Jeune, Léonard; Robert, Sébastien; Lopez Villaverde, Eduardo; Prada, Claire
2016-01-01
This paper describes a new ultrasonic array imaging method for Non-Destructive Testing (NDT) which is derived from the medical Plane Wave Imaging (PWI) technique. The objective is to perform fast ultrasound imaging with high image quality. The approach is to transmit plane waves at several angles and to record the back-scattered signals with all the array elements. Focusing in receive is then achieved by coherent summations of the signals in every point of a region of interest. The medical PWI is generalized to immersion setups where water acts as a coupling medium and to multimodal (direct, half-skip modes) imaging in order to detect different types of defects (inclusions, porosities, cracks). This method is compared to the Total Focusing Method (TFM) which is the reference imaging technique in NDT. First, the two post-processing algorithms are described. Then experimental results with the array probe either in contact or in immersion are presented. A good agreement between the TFM and the PWI is observed, with three to ten times less transmissions required for the PWI.
Planar plane-wave matrix theory at the four loop order: integrability without BMN scaling
Energy Technology Data Exchange (ETDEWEB)
Fischbacher, Thomas [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Am Muehlenberg 1, D-14476 Potsdam (Germany); Physique Theorique et Mathematique and International Solvay Institutes, Universite Libre de Bruxelles, Campus Plaine C.P. 231, B-1050 Brussels (Belgium); Klose, Thomas; Plefka, Jan [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Am Muehlenberg 1, D-14476 Potsdam (Germany)]. E-mail: jan.plefka@aei.mpg.de
2005-02-01
We study SU(N) plane-wave matrix theory up to fourth perturbative order in its large N planar limit. The effective hamiltonian in the closed su(2) subsector of the model is explicitly computed through a specially tailored computer program to perform large scale distributed symbolic algebra and generation of planar graphs. The number of graphs here was in the deep billions. The outcome of our computation establishes the four-loop integrability of the planar plane-wave matrix model. To elucidate the integrable structure we apply the recent technology of the perturbative asymptotic Bethe ansatz to our model. The resulting S-matrix turns out to be structurally similar but nevertheless distinct to the so far considered long-range spin-chain S-matrices of Inozemtsev, Beisert-Dippel-Staudacher and Arutyunov-Frolov-Staudacher in the AdS/CFT context. In particular our result displays a breakdown of BMN scaling at the four-loop order. That is, while there exists an appropriate identification of the matrix theory mass parameter with the coupling constant of the N=4 superconformal Yang-Mills theory which yields an eighth order lattice derivative for well separated impurities (naively implying BMN scaling) the detailed impurity contact interactions ruin this scaling property at the four-loop order. Moreover we study the issue of 'wrapping' interactions, which show up for the first time at this loop-order through a Konishi descendant length four operator. (author)
Trail-Needs pseudopotentials in quantum Monte Carlo calculations with plane-wave/blip basis sets
Drummond, N. D.; Trail, J. R.; Needs, R. J.
2016-10-01
We report a systematic analysis of the performance of a widely used set of Dirac-Fock pseudopotentials for quantum Monte Carlo (QMC) calculations. We study each atom in the periodic table from hydrogen (Z =1 ) to mercury (Z =80 ), with the exception of the 4 f elements (57 ≤Z ≤70 ). We demonstrate that ghost states are a potentially serious problem when plane-wave basis sets are used in density functional theory (DFT) orbital-generation calculations, but that this problem can be almost entirely eliminated by choosing the s channel to be local in the DFT calculation; the d channel can then be chosen to be local in subsequent QMC calculations, which generally leads to more accurate results. We investigate the achievable energy variance per electron with different levels of trial wave function and we determine appropriate plane-wave cutoff energies for DFT calculations for each pseudopotential. We demonstrate that the so-called "T-move" scheme in diffusion Monte Carlo is essential for many elements. We investigate the optimal choice of spherical integration rule for pseudopotential projectors in QMC calculations. The information reported here will prove crucial in the planning and execution of QMC projects involving beyond-first-row elements.
Institute of Scientific and Technical Information of China (English)
章韦芳; 贾昌春; 肖全志; 陈姣姣
2011-01-01
在玻恩近似理论中分别采用扭曲波、平面波、库仑波,计算在250、150、54.4 eV三种入射能下氢原子(e,2e)反应的三重微分截面(TDCS),并与实验数据进行对比.发现在这些入射能下,采用扭曲波和平面波描述入射电子所得的TDCS相差不大;但当考虑散射电子与核的库仑相互作用时,其计算结果比扭曲波描述的更符合实验数据.%In the(e,2e)reaction of hydrogen,distorted wave,plane wave and Coulomb wave in the Born approximation theory were to calculate the triple differential cross sections(TDCS)at incident energies of 250,150 and 54.4 eV respectively,and the theoretical results were compared with experiments.The authors found that there was little difference between the results from the two models,one using the description of plane wave and the other of distorted wave.However,if the interaction between the scattered electron and the nucleus was considered,the result of the calculation coincided with the result of the experiments was better-than the calculation resulted from the description of distorted wave.
Shepherd, James J; Booth, George H; Kresse, Georg; Alavi, Ali
2012-01-01
Using the finite simulation-cell homogeneous electron gas (HEG) as a model, we investigate the convergence of the correlation energy to the complete basis set (CBS) limit in methods utilising plane-wave wavefunction expansions. Simple analytic and numerical results from second-order M{\\o}ller-Plesset theory (MP2) suggest a 1/M decay of the basis-set incompleteness error where M is the number of plane waves used in the calculation, allowing for straightforward extrapolation to the CBS limit. As we shall show, the choice of basis set truncation when constructing many-electron wavefunctions is far from obvious, and here we propose several alternatives based on the momentum transfer vector, which greatly improve the rate of convergence. This is demonstrated for a variety of wavefunction methods, from MP2 to coupled-cluster doubles theory (CCD) and the random-phase approximation plus second-order screened exchange (RPA+SOSEX). Finite basis-set energies are presented for these methods and compared with exact benchm...
Kuznetsov, G. N.; Lebedev, O. V.
2012-09-01
The possibility of approximating the sound field in the region of interference maxima using the equivalent plane wave model with the actual amplitude and the average "effective" phase velocity calculated or measured by the phase gradient at the array aperture is discussed. The method is substantiated by studying the mode, interference, and phase structures of the low-frequency sound field along with the spatial responses of an extended linear array. For bottom-moored or towed geophysical arrays whose sizes are large compared to the wavelength, both the necessity and the possibility of reducing the error in taking the bearing of a sound source in a waveguide are justified. The use of the proposed model is recommended for approximate matching of the array to the transfer function of the waveguide to reduce the bearing error.
Oberhofer, Harald; Blumberger, Jochen
2010-12-01
We present a plane wave basis set implementation for the calculation of electronic coupling matrix elements of electron transfer reactions within the framework of constrained density functional theory (CDFT). Following the work of Wu and Van Voorhis [J. Chem. Phys. 125, 164105 (2006)], the diabatic wavefunctions are approximated by the Kohn-Sham determinants obtained from CDFT calculations, and the coupling matrix element calculated by an efficient integration scheme. Our results for intermolecular electron transfer in small systems agree very well with high-level ab initio calculations based on generalized Mulliken-Hush theory, and with previous local basis set CDFT calculations. The effect of thermal fluctuations on the coupling matrix element is demonstrated for intramolecular electron transfer in the tetrathiafulvalene-diquinone (Q-TTF-Q-) anion. Sampling the electronic coupling along density functional based molecular dynamics trajectories, we find that thermal fluctuations, in particular the slow bending motion of the molecule, can lead to changes in the instantaneous electron transfer rate by more than an order of magnitude. The thermal average, ( { } )^{1/2} = 6.7 {mH}, is significantly higher than the value obtained for the minimum energy structure, | {H_ab } | = 3.8 {mH}. While CDFT in combination with generalized gradient approximation (GGA) functionals describes the intermolecular electron transfer in the studied systems well, exact exchange is required for Q-TTF-Q- in order to obtain coupling matrix elements in agreement with experiment (3.9 mH). The implementation presented opens up the possibility to compute electronic coupling matrix elements for extended systems where donor, acceptor, and the environment are treated at the quantum mechanical (QM) level.
Cheng, Qiang; Cui, Tie Jun
2006-12-01
We have investigated the reflection and refraction properties of plane waves incident from free space into a uniaxially anisotropic chiral medium, where the chirality appears only in one direction and the host medium can be either an isotropic dielectric or an anisotropic electric plasma. We show that the reflection and refraction properties are closely related to the dispersion relation of the chiral medium and that negative phase refractions and/or negative group refractions may occur. We further demonstrate that the two eigenwaves within the uniaxially anisotropic chiral medium behave differently with respect to the incident angle, and in some cases only one of them can be supported and transmitted. We have studied the critical angle and Brewster's angle with some special properties. We have also discussed the potential application of the uniaxially anisotropic chiral medium for the polarization beam splitter. Numerical results are given to validate our analysis.
LOBSTER: A tool to extract chemical bonding from plane-wave based DFT.
Maintz, Stefan; Deringer, Volker L; Tchougréeff, Andrei L; Dronskowski, Richard
2016-04-30
The computer program LOBSTER (Local Orbital Basis Suite Towards Electronic-Structure Reconstruction) enables chemical-bonding analysis based on periodic plane-wave (PAW) density-functional theory (DFT) output and is applicable to a wide range of first-principles simulations in solid-state and materials chemistry. LOBSTER incorporates analytic projection routines described previously in this very journal [J. Comput. Chem. 2013, 34, 2557] and offers improved functionality. It calculates, among others, atom-projected densities of states (pDOS), projected crystal orbital Hamilton population (pCOHP) curves, and the recently introduced bond-weighted distribution function (BWDF). The software is offered free-of-charge for non-commercial research. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.
Resonant plane waves in metamaterials with dipoles and quadrupoles coupled with quantum system
Chipouline, A; Pertsch, T
2013-01-01
Here the multipole approach [13], in combination with the density matrix formalism is used for establishing of the model for MMs with gain. This approach allows us to investigate analytically or semi-analytically the interplay between gain and magnetic properties of the MMs, the influence of internally unstable operation mode for spasers (MAs coupled with emitters, which the MMs consist of) on the propagation characteristics, and finally to optimize MM design. Moreover, the presented model is in line with the previously presented approach [16] (actually is its natural extension on the problem of plane wave propagation) and from the other side pretty clear and observable. The results presented in this paper resolve the discussion excited by [12] followed by [35-38].
Schwab, Hans-Martin; Beckmann, Martin F; Schmitz, Georg
2016-04-01
Photoacoustic imaging aims to visualize light absorption properties of biological tissue by receiving a sound wave that is generated inside the observed object as a result of the photoacoustic effect. In clinical applications, the strong light absorption in human skin is a major problem. When high amplitude photoacoustic waves that originate from skin absorption propagate into the tissue, they are reflected back by acoustical scatterers and the reflections contribute to the received signal. The artifacts associated with these reflected waves are referred to as clutter or skin echo and limit the applicability of photoacoustic imaging for medical applications severely. This study seeks to exploit the acoustic tissue information gained by plane wave ultrasound measurements with a linear array in order to correct for reflections in the photoacoustic image. By deriving a theory for clutter waves in k-space and a matching inversion approach, photoacoustic measurements compensated for clutter are shown to be recovered.
Institute of Scientific and Technical Information of China (English)
Lu Ke-Qing; Zhao Wei; Yang Yan-Long; Zhu Xiang-Ping; Li Jin-Ping; Zhang Yan-Peng
2004-01-01
We investigate the modulation instability of quasi-plane-wave optical beams in biased photorefractive-photovoltaic crystals by globally treating the space-charge field. The modulation instability growth rate is obtained, which depends on the external bias field, on the bulk photovoltaic effect, and on the ratio of the optical beam's intensity to that of the dark irradiance. Our analysis indicates that this modulation instability growth rate is identical to the modulation instability growth rate studied previously in biased photorefractive-nonphotovoltaic crystals when the bulk photovoltaic effect is negligible for shorted circuits, and predicts the modulation instability growth rate in open- and closed-circuit photorefractive-photovoltaic crystals when the external bias field is absent.
DFT LCAO and plane wave calculations of SrZrO{sub 3}
Energy Technology Data Exchange (ETDEWEB)
Evarestov, R.A.; Bandura, A.V.; Alexandrov, V.E. [Department of Quantum Chemistry, St. Petersburg State University, 26 Universitetskiy Prospekt, Stary Peterhof 198504 (Russian Federation); Kotomin, E.A. [Max-Planck-Institut fuer Festkoerperforschung, Heisenbergstr. 1, 70569, Stuttgart (Germany)
2005-02-01
The results of the density functional (DFT) LCAO and plane wave (PW) calculations of the electronic and structural properties of four known SrZrO{sub 3} phases (Pm3m, I4/mcm, Cmcm and Pbnm) are presented and discussed. The calculated unit cell energies and relative stability of these phases agree well with the experimental sequence of SrZrO{sub 3} phases as the temperature increases. The lattice structure parameters optimized in the PW calculations for all four phases are in good agreement with the experimental neutron diffraction data. The LCAO and PW results for the electronic structure, density of states and chemical bonding in the cubic phase (Pm3m) are discussed in detail and compared with the results of previous PW calculations. (copyright 2005 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Cavity-based linear polarizer immune to the polarization direction of an incident plane wave.
Wang, Jiang; Shen, Zhongxiang; Gao, Xiang; Wu, Wen
2016-01-15
We herein report a linear polarizer based on a 2D array of substrate integrated waveguide cavities, which can convert an arbitrary linearly polarized (LP) incident wave into an outgoing LP wave in a specified polarization direction with constant transmittance. Two orthogonal slots etched on the front surface of the cavity are utilized to couple a wave of arbitrary polarization into the cavity, while another slot on the back side helps to couple the field out along a desired polarization direction. Microwave experiments are performed as a proof of concept. The proposed polarizer exhibits very good performance with stable transmittance as 50% and a polarization extinction ratio over 45 dB. The new polarizer is potentially useful in novel polarization-selective devices that are immune to the polarization direction of an incident plane wave.
An efficient algorithm for time propagation as applied to linearized augmented plane wave method
Dewhurst, J. K.; Krieger, K.; Sharma, S.; Gross, E. K. U.
2016-12-01
An algorithm for time propagation of the time-dependent Kohn-Sham equations is presented. The algorithm is based on dividing the Hamiltonian into small time steps and assuming that it is constant over these steps. This allows for the time-propagating Kohn-Sham wave function to be expanded in the instantaneous eigenstates of the Hamiltonian. The method is particularly efficient for basis sets which allow for a full diagonalization of the Hamiltonian matrix. One such basis is the linearized augmented plane waves. In this case we find it is sufficient to perform the evolution as a second-variational step alone, so long as sufficient number of first variational states are used. The algorithm is tested not just for non-magnetic but also for fully non-collinear magnetic systems. We show that even for delicate properties, like the magnetization density, fairly large time-step sizes can be used demonstrating the stability and efficiency of the algorithm.
Diffraction of a Shear Plane Wave in Elastic Medium with Piecewise Homogeneous Infinite Inclusion
Directory of Open Access Journals (Sweden)
Voskanyan A. R.
2007-06-01
Full Text Available Diffraction of shear plane wave incident from infinity at arbitrary angle on infinite inclusion is considered. The infinite inclusion consists of two semi-infinite parts made of different materials. The problem’s solution is presented in the form of sum of its even and odd problems. The case of long waves is considered and these problems (the even and odd ones are modelled in a corresponding way after which each of them is reduced to the solution of Wiener-Hopf functional equation. Asymptotic formulas are obtained for displacement’s amplitude and contacts stresses in the far field. The behaviors of contact stresses in the neighborhood of the bonding line of the semi-infinite parts of the inclusion are also obtained.
Integrable Open Spin Chain in Super Yang-Mills and the Plane-wave/SYM duality
Chen, B; Wu, Y S; Chen, Bin; Wang, Xiao-Jun; Wu, Yong-Shi
2004-01-01
We investigate the integrable structures in an N=2 superconfomal Sp(N) Yang-Mills theory with matter, which is dual to an open+closed string system. We restrict ourselves to the BMN operators that correspond to free string states. In the closed string sector, an integrable structure is inherited from its parent theory, N=4 SYM. For the open string sector, the planar one-loop mixing matrix for gauge invariant holomorphic operators is identified with the Hamiltonian of an integrable SU(3) open spin chain. Using the K-matrix formalism we identify the integrable open-chain boundary conditions that correspond to string boundary conditions. The solutions to the algebraic Bethe ansatz equations (ABAE) with a few impurities are shown to recover the anomalous dimensions that exactly match the spectrum of free open string in the plane-wave background. We also discuss the properties of the solutions of ABAE beyond the BMN regime.
Reflection for three-dimensional plane waves in triclinic crystalline medium
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The propagation of three-dimensional plane waves at a traction free boundary of a half-space composed of triclinic crystalline material is discussed. A method has been developed to find the analytical expressions of all the three phase velocities of quasi-P (qP), quasi-SV (qSV) and quasi-SH (qSH) in three dimensions. Closed form expressions in three dimensions for the amplitude ratios of reflection coefficients of qP, qSV and qSH waves in a triclinic medium are obtained. These expressions are used for numerically studying the variation of the reflection coefficients with the angle of incidence. The graphs are drawn for different polar angle and azimuth. Numerical results presented indicate that the anisotropy affect the reflection coefficients significantly in the three dimensional case compared to the two-dimensional case.
Progress in parallel implementation of the multilevel plane wave time domain algorithm
Liu, Yang
2013-07-01
The computational complexity and memory requirements of classical schemes for evaluating transient electromagnetic fields produced by Ns dipoles active for Nt time steps scale as O(NtN s 2) and O(Ns 2), respectively. The multilevel plane wave time domain (PWTD) algorithm [A.A. Ergin et al., Antennas and Propagation Magazine, IEEE, vol. 41, pp. 39-52, 1999], viz. the extension of the frequency domain fast multipole method (FMM) to the time domain, reduces the above costs to O(NtNslog2Ns) and O(Ns α) with α = 1.5 for surface current distributions and α = 4/3 for volumetric ones. Its favorable computational and memory costs notwithstanding, serial implementations of the PWTD scheme unfortunately remain somewhat limited in scope and ill-suited to tackle complex real-world scattering problems, and parallel implementations are called for. © 2013 IEEE.
Integrable open spin chain in super Yang-Mills and the plane-wave/SYM duality
Chen, Bin; Wang, Xiao-Jun; Wu, Yong-Shi
2004-02-01
We investigate the integrable structures in an Script N = 2 superconformal Sp(N) Yang-Mills theory with matter, which is dual to an open+closed string system. We restrict ourselves to the BMN operators that correspond to free string states. In the closed string sector, an integrable structure is inherited from its parent theory, Script N = 4 SYM. For the open string sector, the planar one-loop mixing matrix for gauge invariant holomorphic scalar operators is identified with the hamiltonian of an integrable SU(3) open spin chain. Using the K-matrix formalism we identify the integrable open-chain boundary conditions that correspond to string boundary conditions. The solutions to the algebraic Bethe ansatz equations (ABAE) with a few impurities are shown to recover the anomalous dimensions that exactly match the spectrum of free open string in the plane-wave background. We also discuss the properties of the solutions of ABAE beyond the BMN regime.
Sánchez, N G
2003-01-01
Key issues of classical and quantum strings in gravitational plane waves, shock waves and spacetime singularities are synthetically understood. This includes the string mass and mode number excitations, energy-momentum tensor, scattering amplitudes, vacuum polarization and wave-string polarization effect. The role of the real pole singularities characteristic of the tree level string spectrum (real mass resonances) and that of spacetime singularities is clearly exhibited. This throws light on the issue of singularities in string theory which can be thus classified and fully physically characterized in two different sets: strong singularities (poles of order equal or larger than 2, and black holes), where the string motion is collective and non oscillating in time, outgoing and scattering states do not appear, the string does not cross the singularities, and weak singularities (poles of order smaller than 2, Dirac delta, and conic/orbifold singularities) where the whole string motion is oscillatory in time, ou...
Ding, Chaoliang; Cai, Yangjian; Zhang, Yongtao; Pan, Liuzhan
2012-06-01
The scattering of a stochastic electromagnetic plane-wave pulse on a deterministic spherical medium is investigated. An analytical formula for the degree of polarization (DOP) of the scattered field in the far zone is derived. Letting pulse duration T(0) → ∞, our formula can be applied to study the scattering of a stationary stochastic electromagnetic light wave. Numerical results show that the DOP of the far zone field is closely determined by the size of the spherical medium when the incident field is a stochastic electromagnetic plane-wave pulse. This is much different from the case when the incident field is a stationary stochastic electromagnetic light wave, where the DOP of the far zone field is independent of the size of the medium. One may obtain the information of the spherical medium by measuring the scattering-induced changes in the DOP of a stochastic electromagnetic plane-wave pulse.
Directory of Open Access Journals (Sweden)
Maity N.
2017-06-01
Full Text Available The article is concernedwith the possibility of plane wave propagation in a rotating elastic medium under the action of magnetic and thermal fields. The material is assumed to be fibre-reinforced with increased stiffness, strength and load bearing capacity. Green and Nagdhi’s concepts of generalized thermoelastic models II and III have been followed in the governing equations expressed in tensor notation. The effects of various parameters of the applied fields on the plane wave velocity have been shown graphically.
Evarestov, Robert A.; Blokhin, Evgeny; Gryaznov, Denis; Kotomin, Eugene A.; Maier, Joachim
2011-04-01
The atomic, electronic structure and phonon frequencies have been calculated in cubic and low-temperature tetragonal SrTiO3 phases at the ab initio level. We demonstrate that the use of the hybrid exchange-correlation PBE0 functional gives the best agreement with experimental data. The results for the standard generalized gradient approximation (PBE) and hybrid PBE0 functionals are compared for the two types of approaches: a linear combination of atomic orbitals (CRYSTAL09 computer code) and plane waves (VASP5.2 code). The relation between cubic and tetragonal phases and the relevant antiferrodistortive phase transition is discussed in terms of group theory and is illustrated with analysis of calculated soft-mode frequencies at the Γ and R points in the Brillouin zone. Based on phonon calculations, the temperature dependence of the heat capacity is in good agreement with experiment.
Energy Technology Data Exchange (ETDEWEB)
Petzold, Vivien; Rosner, Helge [Max-Planck-Institut fuer Chemische Physik fester Stoffe, Dresden (Germany)
2011-07-01
Electronic band structure calculations are routinely applied to many problems in chemistry and physics. The methods rely on a number of approximations, where the treatment of exchange and correlation is a very prominent issue, probably the most prominent in the development of new density functionals in the framework of density functional theory (DFT). The present work highlights effects that arise from the more fundamental Born-Oppenheimer approximation. Based on this approximation, the original problem - the quantum-mechanical description of matter consisting of nuclei and electrons - is decomposed into a nuclear and an electronic problem, the latter of which is treated by electronic band structure methods. Utilizing the most common density functionals, the local density approximation (LDA) and the generalized gradient approximation (GGA), we observe deviations between experimental and theoretical de Haas van Alphen (dHvA) frequencies for MgB{sub 2} and ZrB{sub 2} that can be consistently understood by electron-phonon coupling effects, which the theory is lacking. The explanation is based on a highly accurate computation of dHvA frequencies indicating an electron-phonon coupling-induced shift of the electronic bands.
Terada, Takahide; Yamanaka, Kazuhiro; Suzuki, Atsuro; Tsubota, Yushi; Wu, Wenjing; Kawabata, Ken-ichi
2017-07-01
Ultrasound computed tomography (USCT) is promising for a non-invasive, painless, operator-independent and quantitative system for breast-cancer screening. Assembly error, production tolerance, and aging-degradation variations of the hardwire components, particularly of plane-wave-based USCT systems, may hamper cost effectiveness, precise imaging, and robust operation. The plane wave is transmitted from a ring-shaped transducer array for receiving the signal at a high signal-to-noise-ratio and fast aperture synthesis. There are four signal-delay components: response delays in the transmitters and receivers and propagation delays depending on the positions of the transducer elements and their directivity. We developed a highly precise calibration method for calibrating these delay components and evaluated it with our prototype plane-wave-based USCT system. Our calibration method was found to be effective in reducing delay errors. Gaps and curves were eliminated from the plane wave, and echo images of wires were sharpened in the entire imaging area.
Plane-wave matrix theory from N=4 super-Yang-Mills on RxS{sup 3}
Energy Technology Data Exchange (ETDEWEB)
Kim, Nakwoo E-mail: kim@aei.mpg.de; Klose, Thomas E-mail: thklose@aei.mpg.de; Plefka, Jan E-mail: plefka@aei.mpg.de
2003-11-03
Recently a mass deformation of the maximally supersymmetric Yang-Mills quantum mechanics has been constructed from the supermembrane action in eleven-dimensional plane-wave backgrounds. However, the origin of this plane-wave matrix theory in terms of a compactification of a higher-dimensional super-Yang-Mills model has remained obscure. In this paper we study the Kaluza-Klein reduction of D=4, N=4 super-Yang-Mills theory on a round three-sphere, and demonstrate that the plane-wave matrix theory arises through a consistent truncation to the lowest lying modes. We further explore the relation between the dilatation operator of the conformal field theory and the Hamiltonian of the quantum mechanics through perturbative calculations up to two-loop order. In particular, we find that the one-loop anomalous dimensions of pure scalar operators are completely captured by the plane-wave matrix theory. At two-loop level this property ceases to exist.
Ould-Lahoucine, H. K.; Chetouani, L.
2012-07-01
Exact Green function for a Dirac particle subject to a couple of orthogonal plane wave fields is obtained throughout a path integral approach. In addition, a suitable representation of the Dirac matrices is deduced so that the initial problem becomes the one of a free particle.
The strain in the array is mainly in the plane (waves below ~1 Hz)
Gomberg, J.; Pavlis, G.; Bodin, P.
1999-01-01
We compare geodetic and single-station methods of measuring dynamic deformations and characterize their causes in the frequency bands 0.5-1.0 Hz and 4.0-8.0 Hz. The geodetic approach utilizes data from small-aperture seismic arrays, applying techniques from geodesy. It requires relatively few assumptions and a priori information. The single-station method uses ground velocities recorded at isolated or single stations and assumes all the deformation is due to plane-wave propagation. It also requires knowledge of the azimuth and horizontal velocity of waves arriving at the recording station. Data employed come from a small-aperture, dense seismic array deployed in Geyokcha, Turkmenistan, and include seismograms recorded by broadband STS2 and short-period L28 sensors. Poor agreement between geodetic and single-station estimates in the 4.0-8.0 Hz passband indicates that the displacement field may vary nonlinearly with distance over distances of ~50 m. STS2 geodetic estimates provide a robust standard in the 0.5-1.0 Hz passband because they appear to be computationally stable and require fewer assumptions than single-station estimates. The agreement between STS2 geodetic estimates and single-station L28 estimates is surprisingly good for the S-wave and early surface waves, suggesting that the single-station analysis should be useful with commonly available data. These results indicate that, in the 0.5 to 1.0 Hz passband, the primary source of dynamic deformation is plane-wave propagation along great-circle source-receiver paths. For later arriving energy, the effects of scattering become important. The local structure beneath the array exerts a strong control on the geometry of the dynamic deformation, implying that it may be difficult to infer source characteristics of modern or paleoearthquakes from indicators of dynamic deformations. However, strong site control also suggests that the dynamic deformations may be predictable, which would be useful for engineering
Kawashima, Yukio; Hirao, Kimihiko
2017-02-24
We introduced two methods to correct the singularity in the calculation of long-range Hartree-Fock (HF) exchange for long-range-corrected density functional theory (LC-DFT) calculations in plane-wave basis sets. The first method introduces an auxiliary function to cancel out the singularity. The second method introduces a truncated long-range Coulomb potential, which has no singularity. We assessed the introduced methods using the LC-BLYP functional by applying it to isolated systems of naphthalene and pyridine. We first compared the total energies and the HOMO energies of the singularity-corrected and uncorrected calculations and confirmed that singularity correction is essential for LC-DFT calculations using plane-wave basis sets. The LC-DFT calculation results converged rapidly with respect to the cell size as the other functionals, and their results were in good agreement with the calculated results obtained using Gaussian basis sets. LC-DFT succeeded in obtaining accurate orbital energies and excitation energies. We next applied LC-DFT with singularity correction methods to the electronic structure calculations of the extended systems, Si and SiC. We confirmed that singularity correction is important for calculations of extended systems as well. The calculation results of the valence and conduction bands by LC-BLYP showed good convergence with respect to the number of k points sampled. The introduced methods succeeded in overcoming the singularity problem in HF exchange calculation. We investigated the effect of the singularity correction on the excitation state calculation and found that careful treatment of the singularities is required compared to ground-state calculations. We finally examined the excitonic effect on the band gap of the extended systems. We calculated the excitation energies to the first excited state of the extended systems using a supercell model at the Γ point and found that the excitonic binding energy, supposed to be small for
Plane-wave transverse oscillation for high-frame-rate 2-D vector flow imaging.
Lenge, Matteo; Ramalli, Alessandro; Tortoli, Piero; Cachard, Christian; Liebgott, Hervé
2015-12-01
Transverse oscillation (TO) methods introduce oscillations in the pulse-echo field (PEF) along the direction transverse to the ultrasound propagation direction. This may be exploited to extend flow investigations toward multidimensional estimates. In this paper, the TOs are coupled with the transmission of plane waves (PWs) to reconstruct high-framerate RF images with bidirectional oscillations in the pulse-echo field. Such RF images are then processed by a 2-D phase-based displacement estimator to produce 2-D vector flow maps at thousands of frames per second. First, the capability of generating TOs after PW transmissions was thoroughly investigated by varying the lateral wavelength, the burst length, and the transmission frequency. Over the entire region of interest, the generated lateral wavelengths, compared with the designed ones, presented bias and standard deviation of -3.3 ± 5.7% and 10.6 ± 7.4% in simulations and experiments, respectively. The performance of the ultrafast vector flow mapping method was also assessed by evaluating the differences between the estimated velocities and the expected ones. Both simulations and experiments show overall biases lower than 20% when varying the beam-to-flow angle, the peak velocity, and the depth of interest. In vivo applications of the method on the common carotid and the brachial arteries are also presented.
Quantum Larmor radiation from a moving charge in an electromagnetic plane wave background
Nakamura, Gen; 10.1142/S0217751X12501424
2012-01-01
We extend our previous work [Phys. Rev. D83 045030 (2011)], which investigated the first-order quantum effect in the Larmor radiation from a moving charge in a spatially homogeneous time-dependent electric field. Specifically, we investigate the quantum Larmor radiation from a moving charge in a monochromatic electromagnetic plane wave background based on the scalar quantum electrodynamics at the lowest order of the perturbation theory. Using the in-in formalism, we derive the theoretical formula of the total radiation energy from a charged particle in the initial states being at rest and being in a relativistic motion. Expanding the theoretical formula in terms of the Planck constant \\hbar, we obtain the first-order quantum effect on the Larmor radiation. The quantum effect generally suppresses the total radiation energy compared with the prediction of the classical Larmor formula, which is a contrast to the previous work. The reason is explained by the fact that the radiation from a moving charge in a monoc...
Scaling of plane-wave functions in statistically optimized near-field acoustic holography.
Hald, Jørgen
2014-11-01
Statistically Optimized Near-field Acoustic Holography (SONAH) is a Patch Holography method, meaning that it can be applied in cases where the measurement area covers only part of the source surface. The method performs projections directly in the spatial domain, avoiding the use of spatial discrete Fourier transforms and the associated errors. First, an inverse problem is solved using regularization. For each calculation point a multiplication must then be performed with two transfer vectors--one to get the sound pressure and the other to get the particle velocity. Considering SONAH based on sound pressure measurements, existing derivations consider only pressure reconstruction when setting up the inverse problem, so the evanescent wave amplification associated with the calculation of particle velocity is not taken into account in the regularized solution of the inverse problem. The present paper introduces a scaling of the applied plane wave functions that takes the amplification into account, and it is shown that the previously published virtual source-plane retraction has almost the same effect. The effectiveness of the different solutions is verified through a set of simulated measurements.
Zhang, Xiao-Zheng; Thomas, Jean-Hugh; Bi, Chuan-Xing; Pascal, Jean-Claude
2012-10-01
A time-domain plane wave superposition method is proposed to reconstruct nonstationary sound fields. In this method, the sound field is expressed as a superposition of time convolutions between the estimated time-wavenumber spectrum of the sound pressure on a virtual source plane and the time-domain propagation kernel at each wavenumber. By discretizing the time convolutions directly, the reconstruction can be carried out iteratively in the time domain, thus providing the advantage of continuously reconstructing time-dependent pressure signals. In the reconstruction process, the Tikhonov regularization is introduced at each time step to obtain a relevant estimate of the time-wavenumber spectrum on the virtual source plane. Because the double infinite integral of the two-dimensional spatial Fourier transform is discretized directly in the wavenumber domain in the proposed method, it does not need to perform the two-dimensional spatial fast Fourier transform that is generally used in time domain holography and real-time near-field acoustic holography, and therefore it avoids some errors associated with the two-dimensional spatial fast Fourier transform in theory and makes possible to use an irregular microphone array. The feasibility of the proposed method is demonstrated by numerical simulations and an experiment with two speakers.
On the formation of shocks of electromagnetic plane waves in non-linear crystals
Christodoulou, Demetrios
2015-01-01
An influential result of F. John states that no genuinely non-linear strictly hyperbolic quasi-linear first order system of partial differential equations in two variables has a global $C^2$-solution for small enough initial data. Inspired by recent work of D. Christodoulou, we revisit John's original proof and extract a more precise description of the behaviour of solutions at the time of shock. We show that John's singular first order quantity, when expressed in characteristic coordinates, remains bounded until the final time, which is then characterised by an inverse density of characteristics tending to zero in one point. Moreover, we study the derivatives of second order, showing again their boundedness when expressed in appropriate coordinates. We also recover John's upper bound for the time of shock formation and complement it with a lower bound. Finally, we apply these results to electromagnetic plane waves in a crystal with no magnetic properties and cubic electric non-linearity in the energy density...
On the formation of shocks of electromagnetic plane waves in non-linear crystals
Christodoulou, Demetrios; Perez, Daniel Raoul
2016-08-01
An influential result of F. John states that no genuinely non-linear strictly hyperbolic quasi-linear first order system of partial differential equations in two variables has a global C2-solution for small enough initial data. Inspired by recent work of D. Christodoulou, we revisit John's original proof and extract a more precise description of the behaviour of solutions at the time of shock. We show that John's singular first order quantity, when expressed in characteristic coordinates, remains bounded until the final time, which is then characterised by an inverse density of characteristics tending to zero in one point. Moreover, we study the derivatives of second order, showing again their boundedness when expressed in appropriate coordinates. We also recover John's upper bound for the time of shock formation and complement it with a lower bound. Finally, we apply these results to electromagnetic plane waves in a crystal with no magnetic properties and cubic electric non-linearity in the energy density, assuming no dispersion.
Effects of Non-Elevation-Focalized Linear Array Transducer on Ultrasound Plane-Wave Imaging
Directory of Open Access Journals (Sweden)
Congzhi Wang
2016-11-01
Full Text Available Plane-wave ultrasound imaging (PWUS has become an important method of ultrasound imaging in recent years as its frame rate has exceeded 10,000 frames per second, allowing ultrasound to be used for two-dimensional shear wave detection and functional brain imaging. However, compared to the traditional focusing and scanning method, PWUS images always suffer from a degradation of lateral resolution and contrast. To improve the image quality of PWUS, many different beamforming algorithms have been proposed and verified. Yet the influence of transducer structure is rarely studied. For this paper, the influence of using an acoustic lens for PWUS was evaluated. Two linear array transducers were fabricated. One was not self-focalized in the elevation direction (non-elevation-focalized transducer, NEFT; the other one was a traditional elevation-focalized transducer (EFT. An initial simulation was conducted to show the influence of elevation focusing. Then the images obtained with NEFT on a standard ultrasound imaging phantom were compared with those obtained with EFT. It was demonstrated that, in a relatively deep region, the contrast of an NEFT image is better than that of an EFT image. These results indicate that a more sophisticated design of ultrasound transducer would further improve the image quality of PWUS.
Fast color flow mode imaging using plane wave excitation and temporal encoding
Udesen, Jesper; Gran, Fredrik; Jensen, Jorgen A.
2005-04-01
In conventional ultrasound color flow mode imaging, a large number (~500) of pulses have to be emitted in order to form a complete velocity map. This lowers the frame-rate and temporal resolution. A method for color flow imaging in which a few (~10) pulses have to be emitted to form a complete velocity image is presented. The method is based on using a plane wave excitation with temporal encoding to compensate for the decreased SNR, resulting from the lack of focusing. The temporal encoding is done with a linear frequency modulated signal. To decrease lateral sidelobes, a Tukey window is used as apodization on the transmitting aperture. The data are beamformed along the direction of the flow, and the velocity is found by 1-D cross correlation of these data. First the method is evaluated in simulations using the Field II program. Secondly, the method is evaluated using the experimental scanner RASMUS and a 7 MHz linear array transducer, which scans a circulating flowrig. The velocity of the blood mimicking fluid in the flowrig is constant and parabolic, and the center of the scanned area is situated at a depth of 40 mm. A CFM image of the blood flow in the flowrig is estimated from two pulse emissions. At the axial center line of the CFM image, the velocity is estimated over the vessel with a mean relative standard deviation of 2.64% and a mean relative bias of 6.91%. At an axial line 5 mm to the right of the center of the CFM image, the velocity is estimated over the vessel with a relative standard deviation of 0.84% and a relative bias of 5.74%. Finally the method is tested on the common carotid artery of a healthy 33-year-old male.
Radiation of de-excited electrons at large times in a strong electromagnetic plane wave
Energy Technology Data Exchange (ETDEWEB)
Kazinski, P.O., E-mail: kpo@phys.tsu.ru
2013-12-15
The late time asymptotics of the physical solutions to the Lorentz–Dirac equation in the electromagnetic external fields of simple configurations–the constant homogeneous field, the linearly polarized plane wave (in particular, the constant uniform crossed field), and the circularly polarized plane wave–are found. The solutions to the Landau–Lifshitz equation for the external electromagnetic fields admitting a two-parametric symmetry group, which include as a particular case the above mentioned field configurations, are obtained. Some general properties of the total radiation power of a charged particle are established. In particular, for a circularly polarized wave and constant uniform crossed fields, the total radiation power in the asymptotic regime is independent of the charge and the external field strength, when expressed in terms of the proper-time, and equals a half the rest energy of a charged particle divided by its proper-time. The spectral densities of the radiation power formed on the late time asymptotics are derived for a charged particle moving in the external electromagnetic fields of the simple configurations pointed above. This provides a simple method to verify experimentally that the charged particle has reached the asymptotic regime. -- Highlights: •Late time asymptotics of the solutions to the Lorentz–Dirac equation are studied. •General properties of the total radiation power of electrons are established. •The total radiation power equals a half the rest energy divided by the proper-time. •Spectral densities of radiation formed on the late time asymptotics are derived. •Possible experimental verification of the results is proposed.
Maity, Narottam; Barik, S. P.; Chaudhuri, P. K.
2016-09-01
In this paper, plane wave propagation in a rotating anisotropic material of general nature under the action of a magnetic field of constant magnitude has been investigated. The material is supposed to be porous in nature and contains voids. Following the concept of [Cowin S. C. and Nunziato, J. W. [1983] “Linear elastic materials with voids,” J. Elasticity 13, 125-147.] the governing equations of motion have been written in tensor notation taking account of rotation, magnetic field effect and presence of voids in the medium and the possibility of plane wave propagation has been examined. A number of particular cases have been derived from our general results to match with previously obtained results in this area. Effects of various parameters on the velocity of wave propagation have been presented graphically.
Li, Xiang-Guo; Zhang, X -G; Cheng, Hai-Ping
2015-01-01
Electron transport in graphene is along the sheet but junction devices are often made by stacking different sheets together in a "side-contact" geometry which causes the current to flow perpendicular to the sheets within the device. Such geometry presents a challenge to first-principles transport methods. We solve this problem by implementing a plane-wave based multiple scattering theory for electron transport. This implementation improves the computational efficiency over the existing plane-wave transport code, scales better for parallelization over large number of nodes, and does not require the current direction to be along a lattice axis. As a first application, we calculate the tunneling current through a side-contact graphene junction formed by two separate graphene sheets with the edges overlapping each other. We find that transport properties of this junction depend strongly on the AA or AB stacking within the overlapping region as well as the vacuum gap between two graphene sheets. Such transport beh...
Liquid Water through Density-Functional Molecular Dynamics: Plane-Wave vs Atomic-Orbital Basis Sets
Miceli, Giacomo; Pasquarello, Alfredo
2016-01-01
We determine and compare structural, dynamical, and electronic properties of liquid water at near ambient conditions through density-functional molecular dynamics simulations, when using either plane-wave or atomic-orbital basis sets. In both frameworks, the electronic structure and the atomic forces are self-consistently determined within the same theoretical scheme based on a nonlocal density functional accounting for van der Waals interactions. The overall properties of liquid water achieved within the two frameworks are in excellent agreement with each other. Thus, our study supports that implementations with plane-wave or atomic-orbital basis sets yield equivalent results and can be used indiscriminately in study of liquid water or aqueous solutions.
Vadali, Ramkumar V; Shi, Yan; Kumar, Sameer; Kale, Laxmikant V; Tuckerman, Mark E; Martyna, Glenn J
2004-12-01
Many systems of great importance in material science, chemistry, solid-state physics, and biophysics require forces generated from an electronic structure calculation, as opposed to an empirically derived force law to describe their properties adequately. The use of such forces as input to Newton's equations of motion forms the basis of the ab initio molecular dynamics method, which is able to treat the dynamics of chemical bond-breaking and -forming events. However, a very large number of electronic structure calculations must be performed to compute an ab initio molecular dynamics trajectory, making the efficiency as well as the accuracy of the electronic structure representation critical issues. One efficient and accurate electronic structure method is the generalized gradient approximation to the Kohn-Sham density functional theory implemented using a plane-wave basis set and atomic pseudopotentials. The marriage of the gradient-corrected density functional approach with molecular dynamics, as pioneered by Car and Parrinello (R. Car and M. Parrinello, Phys Rev Lett 1985, 55, 2471), has been demonstrated to be capable of elucidating the atomic scale structure and dynamics underlying many complex systems at finite temperature. However, despite the relative efficiency of this approach, it has not been possible to obtain parallel scaling of the technique beyond several hundred processors on moderately sized systems using standard approaches. Consequently, the time scales that can be accessed and the degree of phase space sampling are severely limited. To take advantage of next generation computer platforms with thousands of processors such as IBM's BlueGene, a novel scalable parallelization strategy for Car-Parrinello molecular dynamics is developed using the concept of processor virtualization as embodied by the Charm++ parallel programming system. Charm++ allows the diverse elements of a Car-Parrinello molecular dynamics calculation to be interleaved with low
Sato, Haruo; Emoto, Kentaro
2017-10-01
In high-frequency seismograms of small earthquakes, we clearly see the excitation of long lasting coda waves and the envelope broadening of an S-wavelet with travel distance increasing. We can interpret those phenomena resulting from scattering by random inhomogeneities distributed in the earth medium. Those phenomena have been theoretically studied by stochastic methods, which deal with velocity inhomogeneities as random media. As a simple mathematical model, we study the propagation of a scalar wavelet for the spherical radiation from a point source in 3-D von Kármán-type random media, of which the power spectral density function (PSDF) decreases according to a power-law higher than the corner wavenumber. Our objective is to propose a method to synthesize the wavelet intensity time trace, the mean square amplitude trace, at a given travel distance by using statistical parameters characterizing the PSDF and the centre wavenumber of the wavelet. When the phase shift is small, we can use the Born approximation to calculate the non-isotropic scattering coefficient representing the scattering power per unit volume. Using the scattering coefficient in the radiative transfer equation (RTE), we are able to synthesize the wavelet intensity time trace. When the centre wavenumber increases in the power-law spectral range, however, we often face the situation of a large phase shift, where the Born approximation is inapplicable, but we are able to use the Markov approximation based on the parabolic approximation. It well explains the intensity time traces showing envelope broadening with peak delay due to multiple scattering around the forward direction and the wandering effect caused by travel time fluctuations; however, it fails to explain rich coda waves composed of scattered waves in wide angles. In such a case, here, we newly propose the spectrum division method as follows: at first, taking the centre wavenumber with a tuning parameter as a reference, we divide the
Dreissigacker, Ingo; Lein, Manfred
2014-05-01
Motivated by recent experiments on circular dichroism in the photoelectron momentum distributions from strong-field ionization of chiral molecules [C. Lux et al., Angew. Chem. Int. Ed. 51, 5001 (2012), 10.1002/anie.201109035; C. S. Lehmann et al., J. Chem. Phys. 139, 234307 (2013), 10.1063/1.4844295], we investigate the origin of this effect theoretically. We show that it is not possible to describe photoelectron circular dichroism with the commonly used strong-field approximation due to its plane-wave nature. We therefore apply the Born approximation to the scattering state and use this as a continuum-state correction in the strong-field approximation. We obtain electron distributions for the molecules camphor and fenchone. In order to gain physical insight into the process, we study the contributions of individual molecular orientations.
Self-consistent theory for a plane wave in a moving medium and light-momentum criterion
Wang, Changbiao
2014-01-01
A self-consistent theory is developed based on the principle of relativity for a plane wave in a moving non-dispersive, lossless, non-conducting, isotropic uniform medium. Light-momentum criterion is set up for the first time, which states that the momentum of light in a medium is parallel to the wave vector in all inertial frames of reference. By rigorous analysis, novel basic properties of the plane wave are exposed: (1) Poynting vector does not necessarily represent the electromagnetic (EM) power flow when a medium moves, (2) Minkowski light momentum and energy constitute a Lorentz four-vector in a form of single EM-field cell or single photon, and Planck constant is a Lorentz invariant, (3) there is no momentum transfer taking place between the plane wave and the uniform medium, and the EM momentum conservation equation cannot be uniquely determined without resort to the principle of relativity, and (4) the moving medium behaves as a so-called "negative index medium" when it moves opposite to the wave vec...
Ovsiyuk, E M; Red'kov, V M
2010-01-01
The aim of the article to clarify the status of Shapiro plane wave solutions of the Schr\\"odinger's equation in the frames of the well-known general method of separation of variables. To solve this task, we use the well-known cylindrical coordinates in Riemann and Lobachevsky spaces, naturally related with Euler angle-parameters. Conclusion may be drawn: the general method of separation of variables embraces the all plane wave solutions; the plane waves in Lobachevsky and Riemann space consist of a small part of the whole set of basis wave functions of Schr\\"odinger equation. In space of constant positive curvature $S_{3}$, a complex analog of horospherical coordinates of Lobachevsky space $H_{3}$ is introduced. To parameterize real space $S_{3}$, two complex coordinates $(r,z)$ must obey additional restriction in the form of the equation $r^{2} = e^{z-z^{*}} - e^{2z} $. The metrical tensor of space $S_{3}$ is expressed in terms of $(r,z)$ with additional constraint, or through pairs of conjugate variables $(...
Born approximation, scattering, and algorithm
Martinez, Alex; Hu, Mengqi; Gu, Haicheng; Qiao, Zhijun
2015-05-01
In the past few decades, there were many imaging algorithms designed in the case of the absence of multiple scattering. Recently, we discussed an algorithm for removing high order scattering components from collected data. This paper is a continuation of our previous work. First, we investigate the current state of multiple scattering in SAR. Then, we revise our method and test it. Given an estimate of our target reflectivity, we compute the multi scattering effects in the target region for various frequencies. Furthermore, we propagate this energy through free space towards our antenna, and remove it from the collected data.
Magnetoelastic plane waves in rotating media in thermoelasticity of type II (G-N model
Directory of Open Access Journals (Sweden)
S. K. Roychoudhuri
2004-01-01
Full Text Available A study is made of the propagation of time-harmonic plane waves in an infinite, conducting, thermoelastic solid permeated by a uniform primary external magnetic field when the entire medium is rotating with a uniform angular velocity. The thermoelasticity theory of type II (G-N model (1993 is used to study the propagation of waves. A more general dispersion equation is derived to determine the effects of rotation, thermal parameters, characteristic of the medium, and the external magnetic field. If the primary magnetic field has a transverse component, it is observed that the longitudinal and transverse motions are linked together. For low frequency (χ≪1, χ being the ratio of the wave frequency to some standard frequency ω∗, the rotation and the thermal field have no effect on the phase velocity to the first order of χ and then this corresponds to only one slow wave influenced by the electromagnetic field only. But to the second order of χ, the phase velocity, attenuation coefficient, and the specific energy loss are affected by rotation and depend on the thermal parameters cT, cT being the nondimensional thermal wave speed of G-N theory, and the thermoelastic coupling εT, the electromagnetic parameters εH, and the transverse magnetic field RH. Also for large frequency, rotation and thermal field have no effect on the phase velocity, which is independent of primary magnetic field to the first order of (1/χ (χ≫1, and the specific energy loss is a constant, independent of any field parameter. However, to the second order of (1/χ, rotation does exert influence on both the phase velocity and the attenuation factor, and the specific energy loss is affected by rotation and depends on the thermal parameters cT and εT, electromagnetic parameter εH, and the transverse magnetic field RH, whereas the specific energy loss is independent of any field parameters to the first order of (1/χ.
Zhang, Baile; Wu, Bae-Ian; Chen, Hongsheng; Kong, Jin Au
2008-08-08
We demonstrate some interesting phenomena associated with a nonmonochromatic plane wave passing through a spherical invisibility cloak whose radial permittivity and permeability are of Drude and Lorentz types. We observe that the frequency center of a quasimonochromatic incident wave will suffer a blueshift in the forward scattering direction. Different frequency components have different depths of penetration, causing a rainbowlike effect within the cloak. The concept of group velocity at the inner boundary of the cloak needs to be revisited. Extremely low scattering can still be achieved within a narrow band.
Evarestov, Robert A.; Blokhin, Evgeny; Gryaznov, Denis; Kotomin, Eugene A.; Maier, Joachim
2010-01-01
The atomic, electronic structure and phonon frequencies have been calculated in a cubic and low-temperature tetragonal SrTiO3 phases at the ab initio level. We demonstrate that the use of hybrid exchange-correlation PBE0 functional gives the best agreement with experimental data. The results for the standard PBE and hybrid PBE0 are compared for the two types of basis sets: a linear combination of atomic orbitals (LCAO, CRYSTAL09 computer code) and plane waves (PW, VASP 5.2 code). Relation bet...
Wilson, Chick C.; Morrison, Carole A.
2002-08-01
Low temperature neutron diffraction and high level computational methods have been applied to investigate the short hydrogen bond in urea-phosphoric acid. It is found that isolated molecule calculations predict a `normal' O-H⋯O hydrogen bond, in strong disagreement with the very short, 3 c-4 e hydrogen bond found from the neutron diffraction. Extending these calculations into a periodic environment using plane-wave DFT methods give much improved agreement with experiment, with a much shorter, stronger hydrogen bond, and significant elongation of the O-H `covalent' bond.
Institute of Scientific and Technical Information of China (English)
FengYangde; WangYuesheng; ZhangZimao; CuiJunzhi
2003-01-01
A 2D time domain boundary element method (BEM) is developed to solve the transient scattering of plane waves by a unilaterally frictionally constrained inclusion. Coulomb friction is assumed along the contact interface. The incident wave is assumed strong enough so that localized slip and separation take place along the interface. The present problem is in effect a nonlinear boundary value problem since the mixed boundary conditions involve unknown intervals (slip, separation and stick regions). In order to determine the unknown intervals, an iterative technique is developed. As an example, we consider the scattering of a circular cylinder embeddedin an infinite solid.
Al-Saidi, W A; Krakauer, Henry; Zhang, Shiwei
2007-05-21
The authors present phaseless auxiliary-field (AF) quantum Monte Carlo (QMC) calculations of the ground states of some hydrogen-bonded systems. These systems were selected to test and benchmark different aspects of the new phaseless AF QMC method. They include the transition state of H+H(2) near the equilibrium geometry and in the van der Walls limit, as well as the H(2)O, OH, and H(2)O(2) molecules. Most of these systems present significant challenges for traditional independent-particle electronic structure approaches, and many also have exact results available. The phaseless AF QMC method is used either with a plane wave basis with pseudopotentials or with all-electron Gaussian basis sets. For some systems, calculations are done with both to compare and characterize the performance of AF QMC under different basis sets and different Hubbard-Stratonovich decompositions. Excellent results are obtained using as input single Slater determinant wave functions taken from independent-particle calculations. Comparisons of the Gaussian based AF QMC results with exact full configuration interaction show that the errors from controlling the phase problem with the phaseless approximation are small. At the large basis-size limit, the AF QMC results using both types of basis sets are in good agreement with each other and with experimental values.
Nikolaev, A. V.; Lamoen, D.; Partoens, B.
2016-07-01
In order to increase the accuracy of the linearized augmented plane wave (LAPW) method, we present a new approach where the plane wave basis function is augmented by two different atomic radial components constructed at two different linearization energies corresponding to two different electron bands (or energy windows). We demonstrate that this case can be reduced to the standard treatment within the LAPW paradigm where the usual basis set is enriched by the basis functions of the tight binding type, which go to zero with zero derivative at the sphere boundary. We show that the task is closely related with the problem of extended core states which is currently solved by applying the LAPW method with local orbitals (LAPW+LO). In comparison with LAPW+LO, the number of supplemented basis functions in our approach is doubled, which opens up a new channel for the extension of the LAPW and LAPW+LO basis sets. The appearance of new supplemented basis functions absent in the LAPW+LO treatment is closely related with the existence of the u ˙ l -component in the canonical LAPW method. We discuss properties of additional tight binding basis functions and apply the extended basis set for computation of electron energy bands of lanthanum (face and body centered structures) and hexagonal close packed lattice of cadmium. We demonstrate that the new treatment gives lower total energies in comparison with both canonical LAPW and LAPW+LO, with the energy difference more pronounced for intermediate and poor LAPW basis sets.
Directory of Open Access Journals (Sweden)
Marta Cavagnaro
2013-01-01
Full Text Available The safety aspects of the exposure of people to uniform plane waves in the frequency range from 900 MHz to 5 GHz are analyzed. Starting from a human body model available in the literature, representing a man in resting state, two new anatomical models are considered, representing different phases of the respiratory activity: tidal breath and deep breath. These models have been used to evaluate the whole body Specific Absorption Rate (SAR and the 10-g averaged and 1-g averaged SAR. The analysis is performed using a parallel implementation of the finite difference time domain method. A uniform plane wave, with vertical polarization, is used as an incident field since this is the canonical exposure situation used in safety guidelines. Results show that if the incident electromagnetic field is compliant with the reference levels promulgated by the International Commission on Non-Ionizing Radiation Protection and by IEEE, the computed SAR values are lower than the corresponding basic restrictions, as expected. On the other side, when the Federal Communications Commission reference levels are considered, 1-g SAR values exceeding the basic restrictions for exposure at 4 GHz and above are obtained. Furthermore, results show that the whole body SAR values increase passing from the resting state model to the deep breath model, for all the considered frequencies.
Torres, Ana M; Lopez, Jose J; Pueo, Basilio; Cobos, Maximo
2013-04-01
Plane-wave decomposition (PWD) methods using microphone arrays have been shown to be a very useful tool within the applied acoustics community for their multiple applications in room acoustics analysis and synthesis. While many theoretical aspects of PWD have been previously addressed in the literature, the practical advantages of the PWD method to assess the acoustic behavior of real rooms have been barely explored so far. In this paper, the PWD method is employed to analyze the sound field inside a selected set of real rooms having a well-defined purpose. To this end, a circular microphone array is used to capture and process a number of impulse responses at different spatial positions, providing angle-dependent data for both direct and reflected wavefronts. The detection of reflected plane waves is performed by means of image processing techniques applied over the raw array response data and over the PWD data, showing the usefulness of image-processing-based methods for room acoustics analysis.
Reﬂection of plane waves at the free surface of a ﬁbre-reinforced elastic half-space
Indian Academy of Sciences (India)
Baljeet Singh; Sarva Jit Singh
2004-06-01
The propagation of plane waves in ﬁbre-reinforced, anisotropic, elastic media is discussed. The expressions for the phase velocity of quasi-$P(qP)$ and quasi-$SV(qSV)$ waves propagating in a plane containing the reinforcement direction are obtained as functions of the angle between the propagation and reinforcement directions. Closed form expressions for the amplitude ratios for qP and qSV waves reﬂected at the free surface of a ﬁbre-reinforced, anisotropic, homogeneous, elastic half-space are obtained. These expressions are used to study the variation of amplitude ratios with angle of incidence. It is found that reinforcement has a signiﬁcant effect on the amplitude ratios and critical angle.
Kim, V T; Pivovarov, G B; Vary, J P; Kim, Victor T.; Matveev, Victor A.; Pivovarov, Grigorii B.; Vary, James P.
2001-01-01
Without a gauge fixing, canonical variables for the light-front SU(2) gluodynamics are determined. The Gauss law is written in terms of the canonical variables. The system is qualified as a generalized dynamical system with first class constraints. Abeliazation is a specific feature of the formulation (most of the canonical variables transform nontrivially only under the action of an Abelian subgroup of the gauge transformations). At finite volume, a discrete spectrum of the light-front Hamiltonian $P_+$ is obtained in the sector of vanishing $P_-$. We obtain, therefore, a quantized form of the classical solutions previously known as non-Abelian plane waves. Then, considering the infinite volume limit, we find that the presence of the mass gap depends on the way the infinite volume limit is taken, which may suggest the presence of different ``phases'' of the infinite volume theory.
Energy Technology Data Exchange (ETDEWEB)
D`yachkov, P.N. [Kurnakov Institute of General and Inorganic Chemistry, Moscow (Russian Federation); Nikolaev, A.V. [Institute of Physcial Chemistry, Moscow (Russian Federation)
1995-10-01
The advent of carbon nanotubes, which are graphite layers convoluted in cylinders several nanometers in diameter and several micrometers in length, as well as the experiments on implanting metal atoms in such tubes open the way to producing nanoconductors and other materials with unique properties. For theorists, the basic challenge is interpreting and predicting the structure and properties of these systems. The linearized augmented-plane-wave method (LAPW) is one of the most accurate methods in the theory of the electronic structure of solids. A generalization of this method for quasi-two-dimensional systems, surface electronic states, and layered crystals is known. The LAPW theory for quasi-unidimensional systems, which exhibit translational symmetry in one direction, has been absent thus far. In this paper, the authors suggest a version of such a theory and use this method to calculate the electronic structure of carbyne (a linear chain of carbon atoms) and carbon nanotube with implanted Sc atoms.
Directory of Open Access Journals (Sweden)
C. H. Schmidt
2009-05-01
Full Text Available The radiation of large antennas and those operating at low frequencies can be determined efficiently by near-field measurement techniques and a subsequent near-field far-field transformation. Various approaches and algorithms have been researched but for electrically large antennas and irregular measurement contours advanced algorithms with low computation complexity are required. In this paper an algorithm employing plane waves as equivalent sources and utilising efficient diagonal translation operators is presented. The efficiency is further enhanced using simple far-field translations in combination with the expensive near-field translations. In this way a low complexity near-field transformation is achieved, which works for arbitrary sample point distributions and incorporates a full probe correction without increasing the complexity.
Mobile Ultrasound Plane Wave Beamforming on iPhone or iPad using Metal- based GPU Processing
Hewener, Holger J.; Tretbar, Steffen H.
Mobile and cost effective ultrasound devices are being used in point of care scenarios or the drama room. To reduce the costs of such devices we already presented the possibilities of consumer devices like the Apple iPad for full signal processing of raw data for ultrasound image generation. Using technologies like plane wave imaging to generate a full image with only one excitation/reception event the acquisition times and power consumption of ultrasound imaging can be reduced for low power mobile devices based on consumer electronics realizing the transition from FPGA or ASIC based beamforming into more flexible software beamforming. The massive parallel beamforming processing can be done with the Apple framework "Metal" for advanced graphics and general purpose GPU processing for the iOS platform. We were able to integrate the beamforming reconstruction into our mobile ultrasound processing application with imaging rates up to 70 Hz on iPad Air 2 hardware.
Dorn, H
2003-01-01
Projecting on a suitable subset of coordinates, a picture is constructed in which the conformal boundary of AdS sub 5 xS sup 5 and that of the plane wave resulting in the Penrose limit are located at the same line. In a second line of arguments all AdS sub 5 xS sup 5 and plane wave geodesics are constructed in their integrated form. Performing the Penrose limit, the approach of null geodesics reaching the conformal boundary of AdS sub 5 xS sup 5 to that of the plane wave is studied in detail. At each point these null geodesics of AdS sub 5 xS sup 5 form a cone which degenerates in the limit. (author)
Maintz, Stefan; Deringer, Volker L; Tchougréeff, Andrei L; Dronskowski, Richard
2013-11-05
Quantum-chemical computations of solids benefit enormously from numerically efficient plane-wave (PW) basis sets, and together with the projector augmented-wave (PAW) method, the latter have risen to one of the predominant standards in computational solid-state sciences. Despite their advantages, plane waves lack local information, which makes the interpretation of local densities-of-states (DOS) difficult and precludes the direct use of atom-resolved chemical bonding indicators such as the crystal orbital overlap population (COOP) and the crystal orbital Hamilton population (COHP) techniques. Recently, a number of methods have been proposed to overcome this fundamental issue, built around the concept of basis-set projection onto a local auxiliary basis. In this work, we propose a novel computational technique toward this goal by transferring the PW/PAW wavefunctions to a properly chosen local basis using analytically derived expressions. In particular, we describe a general approach to project both PW and PAW eigenstates onto given custom orbitals, which we then exemplify at the hand of contracted multiple-ζ Slater-type orbitals. The validity of the method presented here is illustrated by applications to chemical textbook examples-diamond, gallium arsenide, the transition-metal titanium-as well as nanoscale allotropes of carbon: a nanotube and the C60 fullerene. Remarkably, the analytical approach not only recovers the total and projected electronic DOS with a high degree of confidence, but it also yields a realistic chemical-bonding picture in the framework of the projected COHP method.
DEFF Research Database (Denmark)
Udesen, J.; Gran, F.; Hansen, K.L.
2008-01-01
Conventional ultrasound methods for acquiring color images of blood velocity are limited by a relatively low frame-rate and are restricted to give velocity estimates along the ultrasound beam direction only. To circumvent these limitations, the method presented in this paper uses 3 techniques: 1...... carotid artery of a healthy male was scanned with a scan sequence that satisfies the limits set by the Food and Drug Administration. Vector velocity images were obtained with a frame-rate of 100 Hz where 40 speckle images are used for each vector velocity image. It was found that the blood flow...... approximately followed the vessel wall, and that maximum velocity was approximately 1 m/s, which is a normal value for a healthy person. To further evaluate the method, the test person was scanned with magnetic resonance (MR) angiography. The volume flow derived from the MR scanning was compared with that from...
Takahashi, Yukio; Nishino, Yoshinori; Tsutsumi, Ryosuke; Kubo, Hideto; Furukawa, Hayato; Mimura, Hidekazu; MATSUYAMA, Satoshi; Zettsu, Nobuyuki; Matsubara, Eiichiro; Ishikawa, Tetsuya; Yamauchi, Kazuto
2009-01-01
X-ray waves in the center of the beam waist of nearly diffraction limited focused x-ray beams can be considered to have amplitude and phase that are both almost uniform, i.e., they are x-ray plane waves. Here we report the results of an experimental demonstration of high-resolution diffraction microscopy using the x-ray plane wave of the synchrotron x-ray beam focused using Kirkpatrik-Baez mirrors. A silver nanocube with an edge length of ∼100 nm is illuminated with the x-ray beam focused to ...
The motion of charged particles in strong plane waves including radiation reaction
Leinemann, R.; Herold, H.; Ruder, H.; Kegel, W. H.
The Lorentz-Dirac equation in the Landau approximation is used to study the motion of charged particles in strong plane vacuum waves. It is shown that integration for circularly polarized waves can be used to determine analytically the curves of the particle trajectories. The solution is used to investigate the particle trajectories and energy evolution for various strong waves. The initial conditions for the motion are chosen so that the particles start from a radiation-free path and the growing effect of the radiation reaction on the particle trajectory is highlighted.
Scattering and Absorption of Gravitational Plane Waves by Rotating Black Holes
Dolan, Sam R
2008-01-01
In this study, we investigate scattering and absorption of planar gravitational waves by a Kerr black hole in vacuum. We compute cross sections for radiation incident along the rotation axis, and consider both co- and counter-rotating circular polarizations. We show that, if a novel series reduction method is employed, the partial wave approach developed by Matzner and coworkers yields accurate results. Phase shifts are computed via a Sasaki-Nakamura transformation, and spheroidal harmonics via a spectral decomposition method. A catalogue of cross sections is presented for a range of parameters ($M\\omega \\le 4$ and $a \\le 0.99M$). In the long- and short-wavelength regimes we find good agreement with perturbative and semi-classical approximations. We confirm that helicity is not conserved: flux scattered in the backward direction has the opposite polarization to the incident radiation. At low frequencies, fast-rotating holes generate superradiance in the $l = 2$, $m = 2$ mode which enhances the back-scattered ...
Energy Technology Data Exchange (ETDEWEB)
Boudjedaa, T. [Ecole Normale Superieure, Jijel (Algeria). Dept. de Physique; Chetouani, L. [Dept. de Physique Theorique, Inst. de Physique, Univ. de Constantine (Algeria); Guechi, L. [Dept. de Physique Theorique, Inst. de Physique, Univ. de Constantine (Algeria); Hammann, T.F. [Lab. de Mathematiques et Physique Mathematique, Faculte des Sciences et Techniques, 68 Mulhouse (France)
1995-07-01
The Green`s functions for charged particles of spin zero and 1/2, subjected to the action of a Redmond field which is the combination of an electromagnetic plane wave plus a parallel constant magnetic field, are calculated via the Schwinger action principle. The Heisenberg equations are then exactly solved. The spectrum and the waves are deduced in both cases. (orig.).
DEFF Research Database (Denmark)
Alvarez, Yuri; Cappellin, Cecilia; Las-Heras, Fernando
2008-01-01
A comparison between two recently developed methods for antenna diagnostics is presented. On one hand, the Spherical Wave Expansion-to-Plane Wave Expansion (SWE-PWE), based on the relationship between spherical and planar wave modes. On the other hand, the Sources Reconstruction Method (SRM), based...
Voss, D. E.; Koslover, R. A.; Cremer, C. D.; Silvestro, J.; Miner, L. M.
1990-05-01
The High Power Microwaves (HPM) susceptibility testing often requires irradiating test objects at the highest fluences possible. For aperture antennas, the highest fluences are generally found in the radiating near field region. For valid effects testing, the energy coupled to the object interior must accurately replicate that which would occur in a true weapon environment (plane wave illumination). Some believe that valid testing requires object placement at distances from the aperture exceeding 2 D squared/lambda (D=antenna effective diameter). Many also believe testing at farther away than 2 D squared/lambda guarantees plane wave-like coupling conditions. Neither view is correct. Testing in the reactive field region (less than lambda from the aperture) is generally invalid due to dominance of reactive coupling. For testing in the radiating near field, determination of validity is less trivial. An investigation was performed quantifying deviations from plane wave coupling. The measurements, using an instrumented Maverick missile in an anechoic chamber, and supported by theory, indicate conditions for which testing the Maverick missile accurately simulates plane wave coupling.
Anisotropic effects of background fields on Born-Infeld electromagnetic waves
Aiello, Matias; Bengochea, Gabriel; Ferraro, Rafael
2006-01-01
We show exact solutions of Born-Infeld theory for electromagnetic plane waves propagating in the presence of static background fields. The non-linear character of Born-Infeld equations generates an interaction between background and wave that changes the speed of propagation and adds a longitudinal component to the wave. As a consequence, in a magnetic background the ray direction differs from the propagation direction --a behavior resembling the one of a wave in an anisotropic medium--. This...
Do, V. Nam; Le, H. Anh; Vu, V. Thieu
2017-04-01
We propose a computational approach to combining the plane-wave method and the real-space treatment to describe the periodic variation in the material plane and the decay of wave functions from the material surfaces. The proposed approach is natural for two-dimensional material systems and thus may circumvent some intrinsic limitations involving the artificial replication of material layers in traditional supercell methods. In particular, we show that the proposed method is easy to implement and, especially, computationally effective since low-cost computational algorithms, such as iterative and recursive techniques, can be used to treat matrices with block tridiagonal structure. Using this approach we show first-principles features that supplement the current knowledge of some fundamental issues in bilayer graphene systems, including the coupling between the two graphene layers, the preservation of the σ band of monolayer graphene in the electronic structure of the bilayer system, and the differences in low-energy band structure between the AA- and AB-stacked configurations.
Institute of Scientific and Technical Information of China (English)
Ni Zhen; Feng-Lian Li; Yue-Sheng Wang; Chuan-Zeng Zhang
2012-01-01
In this paper,a method based on the Dirichletto-Neumann map is developed for bandgap calculation of mixed in-plane waves propagating in 2D phononic crystals with square and triangular lattices.The method expresses the scattered fields in a unit cell as the cylindrical wave expansions and imposes the Bloch condition on the boundary of the unit cell.The Dirichlet-to-Neumann (DtN) map is applied to obtain a linear eigenvalue equation,from which the Bloch wave vectors along the irreducible Brillouin zone are calculated for a given frequency.Compared with other methods,the present method is memory-saving and time-saving.It can yield accurate results with fast convergence for various material combinations including those with large acoustic mismatch without extra computational cost.The method is also efficient for mixed fluid-solid systems because it considers the different wave modes in the fluid and solid as well as the proper fluid-solid interface condition.
Akhlagh Moayed, Alireza; Dang, Shannon; Ramahi, Omar M.; Bizheva, Kostadinka K.
2009-02-01
The early stages of ocular diseases such as Diabetic Retinopathy are manifested by morphological changes in retinal tissue occurring on cellular level. Therefore, a number of ophthalmic diseases can be diagnosed at an early stage by detecting spatial and temporal variations in the scattering profile of retinal tissue. It was recently demonstrated that, OCT can be used to probe the functional response of retinal photoreceptors to external light stimulation [1]-[3]. fUHROCT measures localized differential changes in the retina reflectivity over time resulting from external light stimulation of the retina. Currently the origins of the observed reflectivity changes are not well understood. However, due to the complex nature of retinal physiology using purely experimental approaches in this case is problematic. For example fUHROCT is sensitive to small changes in the refractive index of biological tissue which as demonstrated previously, can result from a number of processes such as membrane hyperpolarization, osmotic swelling, metabolic changes, etc. In this paper, we present a computational model of interaction between photoreceptor cells and optical plane wave based on the Finite Integration Technique (FIT).
Bakker, J F; Paulides, M M; Christ, A; Kuster, N; van Rhoon, G C
2010-06-07
To avoid potentially adverse health effects of electromagnetic fields (EMF), the International Commission on Non-Ionizing Radiation Protection (ICNIRP) has defined EMF reference levels from the basic restrictions on the induced whole-body-averaged specific absorption rate (SAR(wb)) and the peak 10 g spatial-averaged SAR (SAR(10g)). The objective of this study is to assess if the SAR in children remains below the basic restrictions upon exposure at the reference levels. Finite difference time domain (FDTD) modeling was used to calculate the SAR in six children and two adults when exposed to all 12 orthogonal plane wave configurations. A sensitivity study showed an expanded uncertainty of 53% (SAR(wb)) and 58% (SAR(10g)) due to variations in simulation settings and tissue properties. In this study, we found that the basic restriction on the SAR(wb) is occasionally exceeded for children, up to a maximum of 45% in small children. The maximum SAR(10g) values, usually found at body protrusions, remain under the limit for all scenarios studied. Our results are in good agreement with the literature, suggesting that the recommended ICNIRP reference levels may need fine tuning.
Bakker, J. F.; Paulides, M. M.; Christ, A.; Kuster, N.; van Rhoon, G. C.
2010-06-01
To avoid potentially adverse health effects of electromagnetic fields (EMF), the International Commission on Non-Ionizing Radiation Protection (ICNIRP) has defined EMF reference levels from the basic restrictions on the induced whole-body-averaged specific absorption rate (SARwb) and the peak 10 g spatial-averaged SAR (SAR10g). The objective of this study is to assess if the SAR in children remains below the basic restrictions upon exposure at the reference levels. Finite difference time domain (FDTD) modeling was used to calculate the SAR in six children and two adults when exposed to all 12 orthogonal plane wave configurations. A sensitivity study showed an expanded uncertainty of 53% (SARwb) and 58% (SAR10g) due to variations in simulation settings and tissue properties. In this study, we found that the basic restriction on the SARwb is occasionally exceeded for children, up to a maximum of 45% in small children. The maximum SAR10g values, usually found at body protrusions, remain under the limit for all scenarios studied. Our results are in good agreement with the literature, suggesting that the recommended ICNIRP reference levels may need fine tuning.
Bahar, Ezekiel
2010-09-01
The common definition of the Brewster angles for dielectric and magnetic achiral materials are the angles at which the vertically and horizontally polarized reflection coefficients vanish. We examine broader definitions of the Brewster conditions for waves that are incident on a free-space-chiral interface. Besides the common definition, the Brewster angles have been defined as the angles at which the polarizations of the reflected waves are independent of the polarizations of the incident waves. We consider total transmission of incident plane waves that satisfy the Brewster conditions at a free-space-chiral medium planar interface. In this case we determine the polarization of the incident wave for which the reflected vertically and horizontally polarized waves vanish simultaneously. Thus with this definition of the Brewster conditions the polarization of the reflected wave is undefined. The conditions for the excitation of surface waves are considered. The characteristic polarizations that are the same for the reflected and incident waves are also examined subject to the Brewster conditions. Potential applications of this analysis are to experimentally determine the chiral or geotropic measure of the medium and to identify and characterize biological and chemical materials through their optical activity in real time. Several independent measurements can be taken with the same polarimetric instrument to avoid false identifications. Since measurements can be conducted in the reflection mode they can be nonintrusive.
A 1D time-domain method for in-plane wave motions in a layered half-space
Institute of Scientific and Technical Information of China (English)
Jingbo Liu; Yan Wang
2007-01-01
A 1D finite element method in time domain is developed in this paper and applied to calculate in-plane wave motions of free field exited by SV or P wave oblique incidence in an elastic layered half-space. First, the layered half-space is discretized on the basis of the propagation cha-racteristic of elastic wave according to the Snell law. Then, the finite element method with lumped mass and the cen-tral difference method are incorporated to establish 2D wave motion equations, which can be transformed into 1D equa-tions by discretization principle and explicit finite element method. By solving the 1D equations, the displacements of nodes in any vertical line can be obtained, and the wave motions in layered half-space are finally determined based on the characteristic of traveling wave. Both the theoretical ana-lysis and the numerical results demonstrate that the proposed method has high accuracy and good stability.
Plane Wave-Perturbative Method for Evaluating the Effective Speed of Sound in 1D Phononic Crystals
Directory of Open Access Journals (Sweden)
J. Flores Méndez
2016-01-01
Full Text Available A method for calculating the effective sound velocities for a 1D phononic crystal is presented; it is valid when the lattice constant is much smaller than the acoustic wave length; therefore, the periodic medium could be regarded as a homogeneous one. The method is based on the expansion of the displacements field into plane waves, satisfying the Bloch theorem. The expansion allows us to obtain a wave equation for the amplitude of the macroscopic displacements field. From the form of this equation we identify the effective parameters, namely, the effective sound velocities for the transverse and longitudinal macroscopic displacements in the homogenized 1D phononic crystal. As a result, the explicit expressions for the effective sound velocities in terms of the parameters of isotropic inclusions in the unit cell are obtained: mass density and elastic moduli. These expressions are used for studying the dependence of the effective, transverse and longitudinal, sound velocities for a binary 1D phononic crystal upon the inclusion filling fraction. A particular case is presented for 1D phononic crystals composed of W-Al and Polyethylene-Si, extending for a case solid-fluid.
Papadakis, Panagiotis I; Piperakis, George S; Kalogerakis, Michael A
2015-02-01
This work studies the reflection coefficient of a plane wave incident on a seafloor consisting of two layers (sediment and substrate), whose interface is linear but not parallel to the water-sediment interface. This is an extension of the well-established and studied reflection coefficient concept for seafloors with parallel layers. Moreover this study introduces the concept of the Coherent Reflection Coefficient (CRC) that extends the usual Rayleigh reflection coefficient definition not only at the water-sediment interface but inside the water column as well. The mathematical formulation of the CRC is derived and its numerical implementation is explained. Based on this implementation a numerical code is developed and incorporated-among other codes-in a user-friendly graphics toolbox that was built to facilitate CRC calculations. Numerical examples for realistic seafloors are presented and the derived results are compared to similar ones for parallel layers, indicating that even for small inclination angles the reflection coefficient difference between parallel and slanted interface layers is substantial, hence cannot be ignored. An imminent application of the extended seafloor model and the CRC introduced in this work is the enhancement of geophysics inversion schemes for the estimation of the seafloor parameters.
Institute of Scientific and Technical Information of China (English)
何兵红; 吴国忱
2015-01-01
常规τ值法假设应力松弛时间与应变延迟时间近似相等，造成了常 Q 模型拟合精度低。本文利用精确的广义流变体模型 Q 值计算公式，研究改进的τ值法求解常 Q 模型参数。根据地震波散射理论，推导了基于广义流变体模型的黏滞性介质一阶波恩近似方程，结合位移-速度关系得到了含卷积完全匹配层边界条件的黏滞性介质应力-速度方程的一阶波恩近似表达式。通过数值实验验证并对比了黏滞性介质中全波波动方程、一阶波恩近似方程以及单程波波动方程的波场特征，讨论了基于流变体模型的黏滞性介质一阶波恩近似方程对速度扰动和 Q 扰动的适应性，以及对旅行时和振幅精度的影响。%The conventionalτmethod assumes that the stress relaxation time is approximately equal to the strain delay time,leading to the constant Q model with low precision.In this study,an improvedτmethod is proposed by an accu-rate equation of Q value based on generalized rheological body so as to solve the parameters of constant Q model.According to the seismic wave scattering theo-ry,the first-order Born approximation equation in viscoacoustic media is derived based on generalized rheological body and then the first-order Born approxima-tion of stress-velocity equation is obtained for the viscoacoustic media with con-volutional perfect matched layer (CPML ) boundary.The wave fields and records are compared through numerical simulation by full wave equation,first-order Born approximation equation and one-way wave equation.And it is also discussed that the precision of travel time and amplitude of the seismic wave obtained by the viscoacoustic first-order Born approximation equation with velocity perturbation and Q perturbation.
Filippov, A. I.; Akhmetova, O. V.; Koval‧skii, A. A.
2016-11-01
The filtration-wave process in the central layer of a three-layer anisotropic medium is described as an equivalent plane wave with a modified asymptotic method accurate in the mean. The initial problem is parametrized and broken down into simpler problems for the coefficients of expansion in an asymptotic parameter. The zero expansion coefficient describes the sought plane wave, whereas the first coefficient ensures refinement of the wave-front geometry. The exact solution of the parametrized problem is obtained on the basis of the Fourier sine transformation. The correctness of the developed method is confirmed by comparing the obtained asymptotic solutions and the coefficients of Maclaurin-series expansion of the exact solution of the parametrized problem in a formal parameter.
Staszewska, G.
1981-06-01
A new approach to the solution of coupled equations involved in electron-ion and electron-atom scattering problems is proposed. This method is a combination of iteration and variation procedures. The main advantage of this method is that exchange terms can be calculated in a direct and straightforward manner. The method is based on the Lippmann-Schwinger equation and does not require trial functions satisfying appropriate boundary conditions. Using the Volterra formulation one can find the solution on an interval determined by the range of the exchange potential and the long-range potential terms can be taken into account by a projection procedure giving the asymptotic value of the reactance matrix. The method is tested on the case of electron-hydrogen atom scattering in the 1s-2s and 1s-2s-2p approximation. We have adapted the method proposed originally by Rayski to obtain solutions of coupled equations involved in electron-ion and electron-atom scattering. As mentioned in section 1 the construction of the method secures an automatic fulfilment of the boundary conditions. It allows an easy calculation of the exchange potential as well as an estimation of the introduced approximation. It gives also a possibility of detecting any spurious convergence. Moreover, it is important that this formalism can be applied in the case of normalized as well as unnormalized initial integral equations. This fact is of special importance in the case of long-range interactions. When the method is used for unnormalized (Volterra) equations it allows application of a very convenient projection procedure for treating the long-range terms in the direct potential. Electron-hydrogen atom collisions are investigated as a numerical illustration of the method. In the 1s-2s approximation the normalized equations were solved, while in the 1s-2s-2p approximation the solution was obtained with the help of Volterra equations and the long-range terms of the direct potential were taken into account
Singh, Mithun Kuniyil Ajith; Jaeger, Michael; Frenz, Martin; Steenbergen, Wiendelt
2017-01-01
Reflection artifacts caused by acoustic inhomogeneities constitute a major problem in epi-mode biomedical photoacoustic imaging. Photoacoustic transients from the skin and superficial optical absorbers traverse into the tissue and reflect off echogenic structures to generate reflection artifacts. These artifacts cause difficulties in the interpretation of images and reduce contrast and imaging depth. We recently developed a method called PAFUSion (photoacoustic-guided focused ultrasound) to circumvent the problem of reflection artifacts in photoacoustic imaging. We already demonstrated that the photoacoustic signals can be backpropagated using synthetic aperture pulse-echo data for identifying and reducing reflection artifacts in vivo. In this work, we propose an alternative variant of PAFUSion in which synthetic backpropagation of photoacoustic signals is based on multi-angled plane-wave ultrasound measurements. We implemented plane-wave and synthetic aperture PAFUSion in a handheld ultrasound/photoacoustic imaging system and demonstrate reduction of reflection artifacts in phantoms and in vivo measurements on a human finger using both approaches. Our results suggest that, while both approaches are equivalent in terms of artifact reduction efficiency, plane-wave PAFUSion requires less pulse echo acquisitions when the skin absorption is the main cause of reflection artifacts. PMID:28736669
Directory of Open Access Journals (Sweden)
O. W. Roberts
2014-08-01
Full Text Available Recent observations of astrophysical magnetic fields have shown the presence of fluctuations being wave-like (propagating in the plasma frame and those described as being structure-like (advected by the plasma bulk velocity. Typically with single spacecraft missions it is impossible to differentiate between these two fluctuations, due to the inherent spatio-temporal ambiguity associated with a single point measurement. However missions such as Cluster which contain multiple spacecraft have allowed temporal and spatial changes to be resolved, with techniques such as the k-filtering technique. While this technique does not assume Taylor's hypothesis as is necessary with single spacecraft missions, it does require weak stationarity of the time series, and that the fluctuations can be described by a superposition of plane waves with random phase. In this paper we test whether the method can cope with a synthetic signal which is composed of a combination of non-random phase coherent structures with a mean radius d and a mean separation λ, as well as plane waves with random phase.
Directory of Open Access Journals (Sweden)
O. W. Roberts
2014-12-01
Full Text Available Recent observations of astrophysical magnetic fields have shown the presence of fluctuations being wave-like (propagating in the plasma frame and those described as being structure-like (advected by the plasma bulk velocity. Typically with single-spacecraft missions it is impossible to differentiate between these two fluctuations, due to the inherent spatio-temporal ambiguity associated with a single point measurement. However missions such as Cluster which contain multiple spacecraft have allowed for temporal and spatial changes to be resolved, using techniques such as k filtering. While this technique does not assume Taylor's hypothesis it requires both weak stationarity of the time series and that the fluctuations can be described by a superposition of plane waves with random phases. In this paper we test whether the method can cope with a synthetic signal which is composed of a combination of non-random-phase coherent structures with a mean radius d and a mean separation λ, as well as plane waves with random phase.
Energy Technology Data Exchange (ETDEWEB)
Hou Zhilin [Laboratoire de Physique des Milieux Ionises et Applications (LPMIA), Nancy University, CNRS Boulevard des Aiguillettes, BP 239 F-54506, Vandoeuvre-les-Nancy (France)], E-mail: zhilin.hou@lpmi.uhp-nancy.fr; Assouar, Badreddine M. [Laboratoire de Physique des Milieux Ionises et Applications (LPMIA), Nancy University, CNRS Boulevard des Aiguillettes, BP 239 F-54506, Vandoeuvre-les-Nancy (France)
2008-03-17
We show that the conversional three-dimensional plane wave expansion method can be revised to investigate the lamb wave propagation in the plate with two-dimensional phononic crystal layer coated on uniform substrate. We find that an imaginary three-dimensional periodic system can be constructed by stacking the studied plates and vacuum layers alternately, and then the Fourier series expansion can be performed. The difference between our imaginary periodic system and the true three-dimensional one is that, in our system, the Bloch feature of the wave along the thickness direction is broken. Three different systems are investigated by the proposed method as examples. The principle and reliability of the method are also discussed.
Preston, Thomas C; Reid, Jonathan P
2015-06-01
The angular scattering of light from a homogeneous spherical particle in a zeroth-order Bessel beam is calculated using a generalized Lorenz-Mie theory. We investigate the dependence of the angular scattering on the semi-apex angle of the Bessel beam and discuss the major features of the resulting scattering plots. We also compare Bessel beam scattering to plane wave scattering and provide criterion for when the difference between the two cases can be considered negligible. Finally, we discuss a method for characterizing spherical particles using angular light scattering. This work is useful to researchers who are interested in characterizing particles trapped in optical beams using angular dependent light scattering measurements.
Unz, H.; Roskam, J.
1979-01-01
The theory of acoustic plane wave normally incident on a clamped panel in a rectangular duct is developed. The coupling theory between the elastic vibrations of the panel (plate) and the acoustic wave propagation in infinite space and in the rectangular duct is considered. The partial differential equation which governs the vibration of the panel (plate) is modified by adding to its stiffness (spring) forces and damping forces, and the fundamental resonance frequency and the attenuation factor are discussed. The noise reduction expression based on the theory is found to agree well with the corresponding experimental data of a sample aluminum panel in the mass controlled region, the damping controlled region, and the stiffness controlled region. All the frequency positions of the upward and downward resonance spikes in the sample experimental data are identified theoretically as resulting from four cross interacting major resonance phenomena: the cavity resonance, the acoustic resonance, the plate resonance, and the wooden back panel resonance.
Lester, H. C.; Posey, J. W.
1976-01-01
A discrete frequency study is made of the influence of source characteristics on the optimal properties of acoustically lined uniform and two section ducts. Two simplified sources, a plane wave and a monopole, are considered in some detail and over a greater frequency range than has been previously studied. Source and termination impedance effects are given limited examination. An example of a turbomachinery source and three associated source variants is also presented. Optimal liner designs based on modal theory approach the Cremer criterion at low frequencies and the geometric acoustics limit at high frequencies. Over an intermediate frequency range, optimal two section liners produced higher transmission losses than did the uniform configurations. Source distribution effects were found to have a significant effect on optimal liner design, but source and termination impedance effects appear to be relatively unimportant.
DEFF Research Database (Denmark)
Larsen, Niels Vesterdal; Breinbjerg, Olav
2004-01-01
To facilitate the validation of the numerical Method of Auxiliary Sources an analytical Method of Auxiliary Sources solution is derived in this paper. The Analytical solution is valid for transverse magnetic, and electric, plane wave scattering by circular impedance Cylinders, and it is derived...... by transformation of the exact eigenfunction series solution. The transformation employs the Hankel function wave transformation to express the eigenfunction series of higher-order Hankel functions, with their singularities at the coordinate system origin as a superposition of zero-order Hankel functions...... with their singularities at different positions away from the origin. The transformation necessitates a truncation of the wave transformation but the inaccuracy introduced hereby is shown to be negligible. The analytical Method of Auxiliary Sources solution is employed as a reference to investigate the accuracy...
Energy Technology Data Exchange (ETDEWEB)
Alshits, V.I.; Darinskii, A.N. [Russian Academy of Sciences, Moscow (Russian Federation); Radovich, A. [Kielce Technological Univ., Kielce (Poland)
1995-05-01
The specific features of acoustic wave reflection are analyzed at the interface between two hexagonal crystals with a sliding contact between them. Attention is focused on the angles of incidence corresponding to excitation of the leaky wave. The conditions supporting the existence of leaky waves are found. The expressions illustrating the behavior of plane wave transformation coefficients for reflection, refraction, and excitation of interfacial oscillations are found in analytic form. In addition, the features of nonmirror reflection are studied for a slightly diverging acoustic beam having initially a rectangular profile. The study deals with the case when the tangential projection of the {open_quotes}mean{close_quotes} wavevector for the beam is close to or coincides with the real part of the wavevector of the leaky wave. 9 refs., 10 figs.
Accurate and efficient computation of nonlocal potentials based on Gaussian-sum approximation
Exl, Lukas; Mauser, Norbert J.; Yong ZHANG
2015-01-01
We introduce an accurate and efficient method for a class of nonlocal potential evaluations with free boundary condition, including the 3D/2D Coulomb, 2D Poisson and 3D dipolar potentials. Our method is based on a Gaussian-sum approximation of the singular convolution kernel and Taylor expansion of the density. Starting from the convolution formulation, for smooth and fast decaying densities, we make a full use of the Fourier pseudospectral (plane wave) approximation of the density and a sepa...
Yao, Yi; Kanai, Yosuke
2017-06-01
We present the implementation and performance of the strongly constrained and appropriately normed, SCAN, meta-GGA exchange-correlation (XC) approximation in the planewave-pseudopotential (PW-PP) formalism using the Troullier-Martins pseudopotential scheme. We studied its performance by applying the PW-PP implementation to several practical applications of interest in condensed matter sciences: (a) crystalline silicon and germanium, (b) martensitic phase transition energetics of phosphorene, and (c) a single water molecule physisorption on a graphene sheet. Given the much-improved accuracy over the GGA functionals and its relatively low computational cost compared to hybrid XC functionals, the SCAN functional is highly promising for various practical applications of density functional theory calculations for condensed matter systems. At same time, the SCAN meta-GGA functional appears to require more careful attention to numerical details. The meta-GGA functional shows more significant dependence on the fast Fourier transform grid, which is used for evaluating the XC potential in real space in the PW-PP formalism, than other more conventional GGA functionals do. Additionally, using pseudopotentials that are generated at a different/lower level of XC approximation could introduce noticeable errors in calculating some properties such as phase transition energetics.
Generating exact solutions to Einstein's equation using linearized approximations
Harte, Abraham I.; Vines, Justin
2016-10-01
We show that certain solutions to the linearized Einstein equation can—by the application of a particular type of linearized gauge transformation—be straightforwardly transformed into solutions of the exact Einstein equation. In cases with nontrivial matter content, the exact stress-energy tensor of the transformed metric has the same eigenvalues and eigenvectors as the linearized stress-energy tensor of the initial approximation. When our gauge exists, the tensorial structure of transformed metric perturbations identically eliminates all nonlinearities in Einstein's equation. As examples, we derive the exact Kerr and gravitational plane wave metrics from standard harmonic-gauge approximations.
Generating exact solutions to Einstein's equation using linearized approximations
Harte, Abraham I
2016-01-01
We show that certain solutions to the linearized Einstein equation can---by the application of a particular type of linearized gauge transformation---be straightforwardly transformed into solutions of the exact Einstein equation. In cases with nontrivial matter content, the exact stress-energy tensor of the transformed metric has the same eigenvalues and eigenvectors as the linearized stress-energy tensor of the initial approximation. When our gauge exists, the tensorial structure of transformed metric perturbations identically eliminates all nonlinearities in Einstein's equation. As examples, we derive the exact Kerr and gravitational plane wave metrics from standard harmonic-gauge approximations.
Energy Technology Data Exchange (ETDEWEB)
Bednarski, M; Pszczola, J; Bodnar, W [Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, A Mickiewicza Avenue 30, 30-059 Krakow (Poland); Stoch, P; Zachariasz, P; Suwalski, J, E-mail: pszczola@agh.edu.pl [Institute of Atomic Energy, 05-400 Swierk-Otwock (Poland)
2011-05-01
{sup 57}Fe Moessbauer effect spectra were collected at 4.2 K for the Ho(Fe{sub 1-x}Co{sub x}){sub 2} C15 Laves phases. The hyperfine interaction parameters, i.e. isomer shift, the magnetic hyperfine field and the quadrupole interaction parameter, were determined for the individual Fe/Co nearest neighbourhoods of iron atoms and also as average values for the sample as bulk. As a result of Fe/Co substitution, Slater-Pauling-type dependences for magnetic hyperfine fields corresponding to both the local area and the sample as bulk were observed, and a linear correlation between the local magnetic hyperfine field and the average magnetic hyperfine field was observed. Magnetic moments of atoms were obtained from band structure calculations using the full-potential linearized augmented plane wave method. The magnetic hyperfine field obtained from the experiment correlates linearly (but separately for weak and strong ferromagnetic areas) with the magnetic moment calculated per transition metal atom.
Kattawar, G. W.
1980-01-01
The multipole expansion obtained by Morita et al. (1968) of the Gaussian laser beam used to levitate an aerosol particle in order that its complete phase matrix may be measured is compared with that of Tsai and Pogorzelski (1975) in order to demonstrate the effect of the incorrect expansion used by Morita. Errors incurred by the use of an equation in which one side satisfies the scalar wave equation while the other side does not and can be reduced to a plane wave amplitude are calculated as functions of the inverse of the wave number times the beam waist, the wave number times the radial spherical coordinate and the angular spherical coordinate. Errors on the order of a few percent, considered undetectable are obtained in the squared-field amplitudes due to the expansion, however, they are found to become significant (several tens of percent) when the angle is zero. It is concluded that the expansion of Morita should only be used in the regions where the spherical angle is less than 0.01 and its product with the wave number and the radial spherical coordinate is less than unity.
Wagner, L. S.; Forsyth, D. W.; Fouch, M. J.; James, D. E.
2009-12-01
The High Lava Plains (HLP) of eastern Oregon represent an unusual track of bimodal volcanism extending from the southeastern-most corner of the state to its current position beneath the Newberry Volcano on the eastern margin of the Cascades. The silicic volcanism is time progressive along this track, beginning some 15 Ma near the Owyhee plateau and then trending to the north east. The timing and location of the start of the HLP coincides with that of the initial volcanism associated with the Yellowstone/Snake River Plain track (YSRP). While the YSRP has often been interpreted as the classic intra-continental hot spot track, the HLP, which trends almost normal to absolute plate motion, is harder to explain. This study uses the 100+ stations associated with the HLP seismic deployment together with another ~100 Earthscope Transportable Array stations (TA) to perform a high resolution inversion for Rayleigh wave phase velocities using the 2-plane-wave methodology of Forsyth and Li (2004). Because of the comparatively small grid spacing of this study, we are able to discern much finer scale structures than studies looking at the entire western U.S. with only TA stations. Preliminary results indicate very low velocities across the study area, especially at upper mantle depths. Especially low velocities are seen beneath the Owyhee plateau and along both the HLP and YSRP tracks. Final details about the exact geometries of these features will help constrain possible scenarios for the formation of the HLP volcanic sequence.
Fang, Changming; Li, Wun-Fan; Koster, Rik S; Klimeš, Jiří; van Blaaderen, Alfons; van Huis, Marijn A
2015-01-07
Knowledge about the intrinsic electronic properties of water is imperative for understanding the behaviour of aqueous solutions that are used throughout biology, chemistry, physics, and industry. The calculation of the electronic band gap of liquids is challenging, because the most accurate ab initio approaches can be applied only to small numbers of atoms, while large numbers of atoms are required for having configurations that are representative of a liquid. Here we show that a high-accuracy value for the electronic band gap of water can be obtained by combining beyond-DFT methods and statistical time-averaging. Liquid water is simulated at 300 K using a plane-wave density functional theory molecular dynamics (PW-DFT-MD) simulation and a van der Waals density functional (optB88-vdW). After applying a self-consistent GW correction the band gap of liquid water at 300 K is calculated as 7.3 eV, in good agreement with recent experimental observations in the literature (6.9 eV). For simulations of phase transformations and chemical reactions in water or aqueous solutions whereby an accurate description of the electronic structure is required, we suggest to use these advanced GW corrections in combination with the statistical analysis of quantum mechanical MD simulations.
Hsu, Jin-Chen; Wu, Tsung-Tsong
2008-02-01
Based on Mindlin's piezoelectric plate theory and the plane wave expansion method, a formulation is proposed to study the frequency band gaps and dispersion relations of the lower-order Lamb waves in two-dimensional piezoelectric phononic plates. The method is applied to analyze the phononic plates composed of solid-solid and airsolid constituents with square and triangular lattices, respectively. Factors that influence the opening and width of the complete Lamb wave gaps are identified and discussed. For solid/solid phononic plates, it is suggested that the filling material be chosen with larger mass density, proper stiffness, and weak anisotropic factor embedded in a soft matrix in order to obtain wider complete band gaps of the lower-order Lamb waves. By comparing to the calculated results without considering the piezoelectricity, the influences of piezoelectric effect on Lamb waves are analyzed as well. On the other hand, for air/solid phononic plates, a background material itself with proper anisotropy and a high filling fraction of air may favor the opening of the complete Lamb wave gaps.
Bandura, A V; Sofo, J O; Kubicki, J D
2006-04-27
Plane-wave density functional theory (DFT-PW) calculations were performed on bulk SnO2 (cassiterite) and the (100), (110), (001), and (101) surfaces with and without H2O present. A classical interatomic force field has been developed to describe bulk SnO2 and SnO2-H2O surface interactions. Periodic density functional theory calculations using the program VASP (Kresse et al., 1996) and molecular cluster calculations using Gaussian 03 (Frisch et al., 2003) were used to derive the parametrization of the force field. The program GULP (Gale, 1997) was used to optimize parameters to reproduce experimental and ab initio results. The experimental crystal structure and elastic constants of SnO2 are reproduced reasonably well with the force field. Furthermore, surface atom relaxations and structures of adsorbed H2O molecules agree well between the ab initio and force field predictions. H2O addition above that required to form a monolayer results in consistent structures between the DFT-PW and classical force field results as well.
Zhang, Tian; Chen, Lin; Wang, Bing; Li, Xun
2015-06-01
We investigate optical field enhancement for a wide mid-infrared range, originating from the excitation of graphene plasmons, by introducing a graded dielectric grating of varying period underneath a graphene monolayer. Excitation of the plasmonic mode can be achieved by illuminating a normal-incidence plane wave on the gratings due to guided-mode resonance. The gratings of varying period enable the excitation of the plasmonic mode with a very high field enhancement factor (to the order of magnitude of 1000) within a wide spectral band, which leads to the frequency-dependent spatially separated localization of the infrared spectrum modes. We also demonstrate that the excitation position of the plasmonic mode can be freely tuned by varying the thickness of the interlayer as well as the chemical potential of the graphene monolayer. This structure enables the design of two-dimensional plasmonic photonic circuits and metamaterials targeted towards numerous potential applications including optoelectronic detectors, light-harvest devices, on-chip optical interconnects, biosensors, and light-matter interactions.
Directory of Open Access Journals (Sweden)
Larry W. Burggraf
2013-07-01
Full Text Available To find low energy SinCn structures out of hundreds to thousands of isomers we have developed a general method to search for stable isomeric structures that combines Stochastic Potential Surface Search and Pseudopotential Plane-Wave Density Functional Theory Car-Parinello Molecular Dynamics simulated annealing (PSPW-CPMD-SA. We enhanced the Sunders stochastic search method to generate random cluster structures used as seed structures for PSPW-CPMD-SA simulations. This method ensures that each SA simulation samples a different potential surface region to find the regional minimum structure. By iterations of this automated, parallel process on a high performance computer we located hundreds to more than a thousand stable isomers for each SinCn cluster. Among these, five to 10 of the lowest energy isomers were further optimized using B3LYP/cc-pVTZ method. We applied this method to SinCn (n = 4–12 clusters and found the lowest energy structures, most not previously reported. By analyzing the bonding patterns of low energy structures of each SinCn cluster, we observed that carbon segregations tend to form condensed conjugated rings while Si connects to unsaturated bonds at the periphery of the carbon segregation as single atoms or clusters when n is small and when n is large a silicon network spans over the carbon segregation region.
Liu, Y. H.; Ma, Y. M.; He, Z.; Cui, T.; Liu, B. B.; Zou, G. T.
2007-10-01
We present a detailed investigation of CaCl2 under high pressure in CaCl2 (Pnnm,Z = 2) and α-PbO2 (Pbcn, Z = 4) phases, respectively. Theoretical calculations are performed by using the ab initio pseudopotential plane-wave method based on the density functional method. We estimate the transition pressure between the two phases by the crossing point of their enthalpies, which are equivalent to the Gibbs free energy at zero temperature, after optimizing the structures under high pressure. Our results show that the transition happens at about 2.9 GPa, which is in agreement with the experimental data. We calculate the structural parameters, charge transfers, bond structures, density of states and optical properties. The calculated results show that there are no charge transfers in CaCl2 structure under high pressure. It is found that the transitions from the Cl 3p to Ca 4s and Cl 3s to Ca 3p orbitals contribute mainly to the dielectric function. The optical properties of CaCl2 (Pnnm, Z = 2) do not vary much under pressure. However, some of the dispersion curves of optical constants in the α-PbO2 (Pbcn, Z = 4) phase are changed significantly under pressure.
Energy Technology Data Exchange (ETDEWEB)
Liu, Y H; Ma, Y M; He, Z; Cui, T; Liu, B B; Zou, G T [National Lab of Superhard Materials, Jilin University, Changchun 130012 (China)
2007-10-24
We present a detailed investigation of CaCl{sub 2} under high pressure in CaCl{sub 2} (Pnnm,Z = 2) and {alpha}-PbO{sub 2} (Pbcn, Z = 4) phases, respectively. Theoretical calculations are performed by using the ab initio pseudopotential plane-wave method based on the density functional method. We estimate the transition pressure between the two phases by the crossing point of their enthalpies, which are equivalent to the Gibbs free energy at zero temperature, after optimizing the structures under high pressure. Our results show that the transition happens at about 2.9 GPa, which is in agreement with the experimental data. We calculate the structural parameters, charge transfers, bond structures, density of states and optical properties. The calculated results show that there are no charge transfers in CaCl{sub 2} structure under high pressure. It is found that the transitions from the Cl 3p to Ca 4s and Cl 3s to Ca 3p orbitals contribute mainly to the dielectric function. The optical properties of CaCl{sub 2} (Pnnm, Z = 2) do not vary much under pressure. However, some of the dispersion curves of optical constants in the {alpha}-PbO{sub 2} (Pbcn, Z = 4) phase are changed significantly under pressure.
Rivero, Pablo; Loschen, Christoph; Moreira, Ibério De P R; Illas, Francesc
2009-11-15
This work explores the performance of periodic plane wave density functional theory calculations with an on-site Coulomb correction to the standard LDA and GGA exchange-correlation potential--commonly used to describe strongly correlated solids--in describing the magnetic coupling constant of a series of molecular compounds representative of dinuclear Cu complexes and of organic diradicals. The resulting LDA+U or GGA+U formalisms, lead to results comparable to experiment and to those obtained by means of standard hybrid functionals provided that the value of the U parameter is adequately chosen. Hence, these methods offer an alternative efficient computational scheme to correct LDA and GGA approaches to adequately describe the electronic structure and magnetic coupling in large molecular magnetic systems, although at the expenses of introducing an empirical (U) parameter. For all investigated copper dinuclear systems, the LDA+U and GGA+U approaches lead to an improvement in the description of magnetic properties over the original LDA and GGA schemes with an accuracy similar to that arising from the hybrid B3LYP functional, by increasing the on-site Coulomb repulsion with a moderate U value. Nevertheless, the introduction of an arbitrary U value in the 0-10 eV range most often provides the correct ground-state spin distribution and the correct sign of the magnetic coupling constant.
Simsic, P. L.
1974-01-01
Excitation of neutral atoms by inelastic scattering of incident electrons in gaseous nebulae were investigated using Slater Wave functions to describe the initial and final states of the atom. Total cross sections using the Born Approximation are calculated for: Li(2s yields 2p), Na(3s yields 4p), k(4s yields 4p). The intensity of emitted radiation from gaseous nebulae is also calculated, and Maxwell distribution is employed to average the kinetic energy of electrons.
Del Ben, Mauro; Hutter, Jürg; VandeVondele, Joost
2015-09-01
The forces acting on the atoms as well as the stress tensor are crucial ingredients for calculating the structural and dynamical properties of systems in the condensed phase. Here, these derivatives of the total energy are evaluated for the second-order Møller-Plesset perturbation energy (MP2) in the framework of the resolution of identity Gaussian and plane waves method, in a way that is fully consistent with how the total energy is computed. This consistency is non-trivial, given the different ways employed to compute Coulomb, exchange, and canonical four center integrals, and allows, for example, for energy conserving dynamics in various ensembles. Based on this formalism, a massively parallel algorithm has been developed for finite and extended system. The designed parallel algorithm displays, with respect to the system size, cubic, quartic, and quintic requirements, respectively, for the memory, communication, and computation. All these requirements are reduced with an increasing number of processes, and the measured performance shows excellent parallel scalability and efficiency up to thousands of nodes. Additionally, the computationally more demanding quintic scaling steps can be accelerated by employing graphics processing units (GPU's) showing, for large systems, a gain of almost a factor two compared to the standard central processing unit-only case. In this way, the evaluation of the derivatives of the RI-MP2 energy can be performed within a few minutes for systems containing hundreds of atoms and thousands of basis functions. With good time to solution, the implementation thus opens the possibility to perform molecular dynamics (MD) simulations in various ensembles (microcanonical ensemble and isobaric-isothermal ensemble) at the MP2 level of theory. Geometry optimization, full cell relaxation, and energy conserving MD simulations have been performed for a variety of molecular crystals including NH3, CO2, formic acid, and benzene.
Energy Technology Data Exchange (ETDEWEB)
Del Ben, Mauro, E-mail: mauro.delben@chem.uzh.ch; Hutter, Jürg, E-mail: hutter@chem.uzh.ch [Department of Chemistry, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich (Switzerland); VandeVondele, Joost, E-mail: Joost.VandeVondele@mat.ethz.ch [Department of Materials, ETH Zürich, Wolfgang-Pauli-Strasse 27, CH-8093 Zürich (Switzerland)
2015-09-14
The forces acting on the atoms as well as the stress tensor are crucial ingredients for calculating the structural and dynamical properties of systems in the condensed phase. Here, these derivatives of the total energy are evaluated for the second-order Møller-Plesset perturbation energy (MP2) in the framework of the resolution of identity Gaussian and plane waves method, in a way that is fully consistent with how the total energy is computed. This consistency is non-trivial, given the different ways employed to compute Coulomb, exchange, and canonical four center integrals, and allows, for example, for energy conserving dynamics in various ensembles. Based on this formalism, a massively parallel algorithm has been developed for finite and extended system. The designed parallel algorithm displays, with respect to the system size, cubic, quartic, and quintic requirements, respectively, for the memory, communication, and computation. All these requirements are reduced with an increasing number of processes, and the measured performance shows excellent parallel scalability and efficiency up to thousands of nodes. Additionally, the computationally more demanding quintic scaling steps can be accelerated by employing graphics processing units (GPU’s) showing, for large systems, a gain of almost a factor two compared to the standard central processing unit-only case. In this way, the evaluation of the derivatives of the RI-MP2 energy can be performed within a few minutes for systems containing hundreds of atoms and thousands of basis functions. With good time to solution, the implementation thus opens the possibility to perform molecular dynamics (MD) simulations in various ensembles (microcanonical ensemble and isobaric-isothermal ensemble) at the MP2 level of theory. Geometry optimization, full cell relaxation, and energy conserving MD simulations have been performed for a variety of molecular crystals including NH{sub 3}, CO{sub 2}, formic acid, and benzene.
Electromagnetic Characteristics of Microstrip Circuits Under Plane Wave Illumination%平面波照射下微带电路的电磁特性
Institute of Scientific and Technical Information of China (English)
李守荣; 李莹; 孙震; 王帆
2013-01-01
基于十字结微带结构的等效电路,建立了平面波照射下不连续微带电路的电磁敏感性模型.利用场耦合理论计算入射平面波在微带电路终端产生的等效源表达式,并分别对十字结微带结构和单级放大器等电路的电磁敏感性模型进行计算和仿真验证.结果显示,仿真结果与测量结果具有很好的一致性,且仿真时间短,有助于设计者更加快速准确地预测电磁干扰对不连续微带电路的影响.%Based on the equivalent circuit of the microstrip cross bend, the electromagnetic sensitivity model of discontinuous microstrip circuits with the presence of a uniform plane incident wave is estab-lished,.First,the analytical expressions are modeled as equivalent voltage and current sources for discussing the global effect of the incident plane wave on the associated interconnects. Then,these field-induced equiv alent source expressions are incorporated into ADS circuit solver,and a fast model is established for analy zing the output responses of microstrip circuits,such as the cross bend and the single-stage amplifier. The corresponding simulated results from the proposed model are also validated by comparing the results from the measurements. With the merit of short simulation time, the proposed approach would be an efficient method to solve the electromagnetic susceptibility problems associated with the discontinuous microstrip circuits.
Del Ben, Mauro; Hutter, Jürg; VandeVondele, Joost
2015-09-14
The forces acting on the atoms as well as the stress tensor are crucial ingredients for calculating the structural and dynamical properties of systems in the condensed phase. Here, these derivatives of the total energy are evaluated for the second-order Møller-Plesset perturbation energy (MP2) in the framework of the resolution of identity Gaussian and plane waves method, in a way that is fully consistent with how the total energy is computed. This consistency is non-trivial, given the different ways employed to compute Coulomb, exchange, and canonical four center integrals, and allows, for example, for energy conserving dynamics in various ensembles. Based on this formalism, a massively parallel algorithm has been developed for finite and extended system. The designed parallel algorithm displays, with respect to the system size, cubic, quartic, and quintic requirements, respectively, for the memory, communication, and computation. All these requirements are reduced with an increasing number of processes, and the measured performance shows excellent parallel scalability and efficiency up to thousands of nodes. Additionally, the computationally more demanding quintic scaling steps can be accelerated by employing graphics processing units (GPU's) showing, for large systems, a gain of almost a factor two compared to the standard central processing unit-only case. In this way, the evaluation of the derivatives of the RI-MP2 energy can be performed within a few minutes for systems containing hundreds of atoms and thousands of basis functions. With good time to solution, the implementation thus opens the possibility to perform molecular dynamics (MD) simulations in various ensembles (microcanonical ensemble and isobaric-isothermal ensemble) at the MP2 level of theory. Geometry optimization, full cell relaxation, and energy conserving MD simulations have been performed for a variety of molecular crystals including NH3, CO2, formic acid, and benzene.
Amplitude-preserving plane-wave prestack time migration for AVO analysis%用于AVO分析的振幅保真平面波叠前时间偏移
Institute of Scientific and Technical Information of China (English)
王棣; 程玖兵; 郑晓东; 王华忠; 马在田
2008-01-01
To support amplitude variation with offset (AVO) analysis in complex structure areas, we introduce an amplitude-preserving plane-wave prestack time migration approach based on the double-square-root wave equation in media with little lateral velocity variation.In its implementation, a data mapping algorithm is used to obtain offset-plane-wave data sets from the common-midpoint gathers followed by a non-recursive phase-shift solution with amplitude correction to generate common-image gathers in offset-ray-parameter domain and a structural image. Theoretical model tests and a real data example show that our prestack time migration approach is helpful for AVO analysis in complex geological environments.
基于低相干光平面波照明的数字全息显微测量%Digital holographic microscopy illuminated by low-coherent plane waves
Institute of Scientific and Technical Information of China (English)
卢文龙; 游雾; 刘晓军
2012-01-01
提出将基于低相干光平面波照明的离轴数字全息显微方法应用于微纳表面测量,结合角谱算法,可在更近的距离以高分辨率重建由平面波记录的数字全息图.在发光二极管平面波照明全息实验中,通过单幅离轴全息图对标准刻线板进行了强度像和相位像的重建.在重建过程中,未发生频谱重叠的现象.对其三维表面形貌的评定结果显示重建的横向参数值与纵向参数值均与标准值具有很好的一致性.%Off-axis digital holographic microscopy in mirco-nano surface measurement was proposed, which was based on the illumination of low coherent plane wave. Compared with sphere-wave inter- ferometry illuminated by lasers, low-coherent plane-wave interferometry could effectively avoid the influence of freckles and multiple-reflections. Combined with angular spectrum algorithm, digital holo- grams illuminated by plane wave could be reconstructed with smaller distances and higher resolutions. In the experiment illuminated by LED（light emitting diode）rs plane wave, the intensity-contrast and phase contrast images of a standard grating plate were reconstructed by a single off-axis hologram. Overlaps did not appear in the frequency spectrum during the reconstructed process. The evaluation of the three dimensional surface topography reveals that the reconstructed axial and lateral parameters are both in good accordance with their standard values.
Heats of Segregation of BCC Binaries from ab Initio and Quantum Approximate Calculations
Good, Brian S.
2004-01-01
We compare dilute-limit heats of segregation for selected BCC transition metal binaries computed using ab initio and quantum approximate energy methods. Ab initio calculations are carried out using the CASTEP plane-wave pseudopotential computer code, while quantum approximate results are computed using the Bozzolo-Ferrante-Smith (BFS) method with the most recent LMTO-based parameters. Quantum approximate segregation energies are computed with and without atomistic relaxation, while the ab initio calculations are performed without relaxation. Results are discussed within the context of a segregation model driven by strain and bond-breaking effects. We compare our results with full-potential quantum calculations and with available experimental results.
Approximate Representations and Approximate Homomorphisms
Moore, Cristopher
2010-01-01
Approximate algebraic structures play a defining role in arithmetic combinatorics and have found remarkable applications to basic questions in number theory and pseudorandomness. Here we study approximate representations of finite groups: functions f:G -> U_d such that Pr[f(xy) = f(x) f(y)] is large, or more generally Exp_{x,y} ||f(xy) - f(x)f(y)||^2$ is small, where x and y are uniformly random elements of the group G and U_d denotes the unitary group of degree d. We bound these quantities in terms of the ratio d / d_min where d_min is the dimension of the smallest nontrivial representation of G. As an application, we bound the extent to which a function f : G -> H can be an approximate homomorphism where H is another finite group. We show that if H's representations are significantly smaller than G's, no such f can be much more homomorphic than a random function. We interpret these results as showing that if G is quasirandom, that is, if d_min is large, then G cannot be embedded in a small number of dimensi...
CERN. Geneva
2015-01-01
Most physics results at the LHC end in a likelihood ratio test. This includes discovery and exclusion for searches as well as mass, cross-section, and coupling measurements. The use of Machine Learning (multivariate) algorithms in HEP is mainly restricted to searches, which can be reduced to classification between two fixed distributions: signal vs. background. I will show how we can extend the use of ML classifiers to distributions parameterized by physical quantities like masses and couplings as well as nuisance parameters associated to systematic uncertainties. This allows for one to approximate the likelihood ratio while still using a high dimensional feature vector for the data. Both the MEM and ABC approaches mentioned above aim to provide inference on model parameters (like cross-sections, masses, couplings, etc.). ABC is fundamentally tied Bayesian inference and focuses on the “likelihood free” setting where only a simulator is available and one cannot directly compute the likelihood for the dat...
An Approximate Method for Analysis of Solitary Waves in Nonlinear Elastic Materials
Rushchitsky, J. J.; Yurchuk, V. N.
2016-05-01
Two types of solitary elastic waves are considered: a longitudinal plane displacement wave (longitudinal displacements along the abscissa axis of a Cartesian coordinate system) and a radial cylindrical displacement wave (displacements in the radial direction of a cylindrical coordinate system). The basic innovation is the use of nonlinear wave equations similar in form to describe these waves and the use of the same approximate method to analyze these equations. The distortion of the wave profile described by Whittaker (plane wave) or Macdonald (cylindrical wave) functions is described theoretically
On the Born-Oppenheimer approximation of diatomic molecular resonances
Energy Technology Data Exchange (ETDEWEB)
Martinez, André, E-mail: andre.martinez@unibo.it; Sordoni, Vania, E-mail: vania.sordoni@unibo.it [Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato, 40127 Bologna (Italy)
2015-10-15
We give a new reduction of a general diatomic molecular Hamiltonian, without modifying it near the collision set of nuclei. The resulting effective Hamiltonian is the sum of a smooth semiclassical pseudodifferential operator (the semiclassical parameter being the inverse of the square-root of the nuclear mass) and a semibounded operator localised in the elliptic region corresponding to the nuclear collision set. We also study its behaviour on exponential weights and give several applications where molecular resonances appear and can be well located.
Born-Oppenheimer approximation in EFT and quarkonium hybrids
Directory of Open Access Journals (Sweden)
Castellà Jaume Tarrús
2017-01-01
Full Text Available We report on the results of [1] for the calculations of quarkonium hybrids. We have developed and Effective Field Theory (EFT for quarkonium hybrids that systematically incorporates an expansion with respect to the adiabatic limit. We matched the potentials in our EFT to the static energies computed on the lattice. We discuss our results and compare them with direct lattice calculations and possible experimental candidates.
Mora, P J; Woodard, R P
2013-01-01
We use the Hartree approximation to the Einstein equation on de Sitter background to solve for the one loop correction to the graviton mode function. This should give a reasonable approximation to how the ensemble of inflationary gravitons affects a single external graviton. At late times we find that the one loop correction to the plane wave mode function $u(\\eta,k)$ goes like $G H^2 \\ln(a)/a^2$, where $a$ is the inflationary scale factor. One consequence is that the one loop corrections to the "electric" components of the linearized Weyl tensor grow compared to the tree order result.
Background: The awareness of food borne illness has shifted over the years as international agribusiness and transportation have steadily increased. At least 30 food borne agents have been identified, with one-third emerging in the last 3 decades. Despite an increased emphasis on control measures, t...
DEFF Research Database (Denmark)
Kraus, Sascha; Brem, Alexander; Muench, Miriam
2017-01-01
Internationalization is a hot topic in innovation management, whereby the phenomenon of “Born Globals” is still limited to research in the domains of Entrepreneurship and International Management. As business model design plays a key role for Born Globals, we link these two concepts. For this, we...
Chen, Bingxin; Wang, Jiamin; Qi, Hongxin; Zhang, Jie; Chen, Shude; Wang, Xianghui
2017-03-01
As electromagnetic exposure experiments can only be performed on small animals, usually rats, research on the characteristics of specific absorption rate (SAR) distribution in the rat has received increasing interest. A series of calculations, which simulated the SAR in a male rat anatomical model exposed to electromagnetic plane waves ranging from 0.05 to 5 GHz with different incidence and polarization, were conducted. The whole-body-averaged SAR (SARwb) and the tissue-averaged SAR (SARavg) in 20 major tissues were determined. Results revealed that incidence has great impact on SAR in the rat at higher frequencies owing to the skin effect and the effect on SARavg in tissues is much more apparent than that on SARwb; while polarization plays an important role under lower frequencies. Not only the incidence, but also the polarization in the rat keeps changing when the rat is in free movement. Thus, this article discussed a convenient way to obtain relatively accurate SARwb in a free-moving rat.
Institute of Scientific and Technical Information of China (English)
李兴财; 王虎
2014-01-01
The intensity of scattering field and the wave absorption properties of particle is determined by the internal electromagnetic field of particle.Based on the equivalent radius of the micro-surface for ellipsoid and the Mie scattering theory,we discuss the electromagnetic field distribution for a partially charged spheroid which illuminated by a plane wave,and make a comparison with uncharged particle.The numerical simulation results show that the surface charges have a significant effect on the internal and the external electromagnetic field distribution for particle, and hence influence its electromagnetic wave attenuation properties.%颗粒内部场强决定了粒子散射场强度及其对入射电磁波的吸收作用。借助椭球面的等效球面微元半径及带电球体粒子的 Mie 散射理论讨论了平面波入射下局部带电椭球体内外场强分布，并与不带电椭球粒子的结果进行了比较。数值结果表明：颗粒表面电荷显著改变了颗粒内外电磁场的分布规律及其强度，从而影响粒子的电磁散射性质。
Energy Technology Data Exchange (ETDEWEB)
Wesolowski, David J [ORNL; Bandura, Andrei V. [St. Petersburg State University, St. Petersburg, Russia; Sofo, Jorge O. [Pennsylvania State University; Kubicki, James D. [Pennsylvania State University
2006-01-01
Plane-wave density functional theory (DFT-PW) calculations were performed on bulk SnO{sub 2} (cassiterite) and the (100), (110), (001), and (101) surfaces with and without H{sub 2}O present. A classical interatomic force field has been developed to describe bulk SnO{sub 2} and SnO{sub 2}-H{sub 2}O surface interactions. Periodic density functional theory calculations using the program VASP (Kresse et al., 1996) and molecular cluster calculations using Gaussian 03 (Frisch et al., 2003) were used to derive the parametrization of the force field. The program GULP (Gale, 1997) was used to optimize parameters to reproduce experimental and ab initio results. The experimental crystal structure and elastic constants of SnO{sub 2} are reproduced reasonably well with the force field. Furthermore, surface atom relaxations and structures of adsorbed H{sub 2}O molecules agree well between the ab initio and force field predictions. H{sub 2}O addition above that required to form a monolayer results in consistent structures between the DFT-PW and classical force field results as well.
Energy Technology Data Exchange (ETDEWEB)
Ulian, Gianfranco; Valdrè, Giovanni, E-mail: giovanni.valdre@unibo.it [Dipartimento di Scienze Biologiche e Geologico-Ambientali, Centro di Ricerca Interdisciplinare di Biomineralogia, Cristallografia e Biomateriali, Università di Bologna “Alma Mater Studiorum” Piazza di Porta San Donato 1, 40126 Bologna (Italy); Tosoni, Sergio [Departament de Química Física and Institut de Química Teòrica i Computacional (IQTCUB), Universitat de Barcelona, C/ Martí i Franquès 1, E-08028 Barcelona (Spain)
2013-11-28
The quantum chemical characterization of solid state systems is conducted with many different approaches, among which the adoption of periodic boundary conditions to deal with three-dimensional infinite condensed systems. This method, coupled to the Density Functional Theory (DFT), has been proved successful in simulating a huge variety of solids. Only in relatively recent years this ab initio quantum-mechanic approach has been used for the investigation of layer silicate structures and minerals. In the present work, a systematic comparison of different DFT functionals (GGA-PBEsol and hybrid B3LYP) and basis sets (plane waves and all-electron Gaussian-type orbitals) on the geometry, energy, and phonon properties of a model layer silicate, talc [Mg{sub 3}Si{sub 4}O{sub 10}(OH){sub 2}], is presented. Long range dispersion is taken into account by DFT+D method. Results are in agreement with experimental data reported in literature, with minimal deviation given by the GTO/B3LYP-D* method regarding both axial lattice parameters and interaction energy and by PW/PBE-D for the unit-cell volume and angular values. All the considered methods adequately describe the experimental talc infrared spectrum.
Institute of Scientific and Technical Information of China (English)
张立民; 贾昌春; 王琦; 陈长进
2014-01-01
在共面双对称几何条件下，利用一阶扭曲波Born近似计算了中低能电子碰撞Ar原子(3p壳层电子)单电离的三重微分截面，并与最近的实验数据做了比较。结果表明，对于Ar原子，当入射电子能量比电离阈高40 eV以上，随着入射能量的增加， binary和recoil碰撞机理逐渐占据支配地位；在近阈能量范围，上述碰撞机理不再处于支配地位，扭曲效应明显。要完备地描述中低能入射条件下Ar原子的电子碰撞电离过程，理论模型必须同时考虑多种散射机理。%The first-order distorted wave Born approximation (DWBA) has been performed for single ionization of Ar(3p) by electron impact in coplanar doubly symmetric geometry from near threshold to intermediate energies. Theoretical triple differential cross sections (TDCS) are compared with the latest experimental data. It is found that when the incident electron energies are 40 eV higher than the ionization threshold, for argon, the binary and recoil collision mechanism will dominat as the energies increase, but not in the near threshold energy regime, where the distortion effects are of great significance. In order to completely describe the electron impact ionization of argon, it is imperative that more scattering mechanisms should be considered in the theoretical models.
DEFF Research Database (Denmark)
Kraus, Sascha; Brem, Alexander; Muench, Miriam
2017-01-01
Internationalization is a hot topic in innovation management, whereby the phenomenon of “Born Globals” is still limited to research in the domains of Entrepreneurship and International Management. As business model design plays a key role for Born Globals, we link these two concepts. For this, we...... propose hypotheses about the influence of efficiency-centered and novelty-entered business model design on international firm performance. To test these hypotheses, we performed a quantitative survey with 252 founders of international companies in Germany, Switzerland and Liechtenstein. Additionally, we...... gained further insights through a case study analysis of 11 Born Globals. The results show that business model design matters to international firm performance and the business model design of Born Globals tends to be more efficiency-centered. Based on a multiple case study, we analyzed business models...
Plane wave fast color flow mode imaging
DEFF Research Database (Denmark)
Bolic, Ibrahim; Udesen, Jesper; Gran, Fredrik
2006-01-01
degrees and 75 degrees. Compared to the conventional ultrasound imaging the frame rate is similar to 30 - 60 times higher. The bias, B-est of the velocity profile estimate, based on 8 pulse-echo emissions, is between 3.3% and 6.1% for beam to flow angles between 45 degrees and 75 degrees, and the standard...... deviation, sigma(est) of the velocity profile estimate is around 2% for beam to flow angles between 45 degrees and 75 degrees relative to the peak velocity, when the flow angle is known in advance. A study is performed to investigate how different parameters influence the blood velocity estimation....... The results confirmed expectations for beam to flow angles between 45 degrees and 75 degrees. The parameter study shows that the PWM using Directional velocity estimation gives the best results using spatial sampling interval = 10A, and number of directional signals >= 6...
Optics in a nonlinear gravitational plane wave
Harte, Abraham I.
2015-09-01
Gravitational waves can act like gravitational lenses, affecting the observed positions, brightnesses, and redshifts of distant objects. Exact expressions for such effects are derived here in general relativity, allowing for arbitrarily-moving sources and observers in the presence of plane-symmetric gravitational waves. At least for freely falling sources and observers, it is shown that the commonly-used predictions of linear perturbation theory can be generically overshadowed by nonlinear effects; even for very weak gravitational waves, higher-order perturbative corrections involve secularly-growing terms which cannot necessarily be neglected when considering observations of sufficiently distant sources. Even on more moderate scales where linear effects remain at least marginally dominant, nonlinear corrections are qualitatively different from their linear counterparts. There is a sense in which they can, for example, mimic the existence of a third type of gravitational wave polarization.
Coherent potential approximation of random nearly isostatic kagome lattice.
Mao, Xiaoming; Lubensky, T C
2011-01-01
The kagome lattice has coordination number 4, and it is mechanically isostatic when nearest-neighbor sites are connected by central-force springs. A lattice of N sites has O(√N) zero-frequency floppy modes that convert to finite-frequency anomalous modes when next-nearest-neighbor (NNN) springs are added. We use the coherent potential approximation to study the mode structure and mechanical properties of the kagome lattice in which NNN springs with spring constant κ are added with probability P=Δz/4, where Δz=z-4 and z is the average coordination number. The effective medium static NNN spring constant κ(m) scales as P(2) for P≪κ and as P for P≫κ, yielding a frequency scale ω*~Δz and a length scale l*~(Δz)(-1). To a very good approximation at small nonzero frequency, κ(m)(P,ω)/κ(m)(P,0) is a scaling function of ω/ω*. The Ioffe-Regel limit beyond which plane-wave states become ill-defined is reached at a frequency of order ω*.
Optical parametric amplification beyond the slowly varying amplitude approximation
Indian Academy of Sciences (India)
M Hosseini Farzad
2007-09-01
The coupled-wave equations describing optical parametric amplification (OPA) are usually solved in the slowly varying amplitude (SVA) approximation regime, in which the second-order derivatives of the signal and idler amplitudes are ignored and in fact the electromagnetic effects due to exit face of the medium is not involved. Here, an analytical plane-wave solution of these coupled-wave equations in a non-absorbing medium is presented. The solutions are derived beyond the SVA approximation up to order of = (coupling constant over the wave number). The intensity distributions of the signal and the idler waves show a periodic behavior about their corresponding distributions of SVA-adapted solution. This behavior can be explained by the interference of the forward propagating signal (idler) wave and the corresponding backward one resulted from the reflection by the end face of the medium. Furthermore, this interference pattern in the medium can in turn serve as a periodic source for the next generations of the signal and idler waves. Therefore, the superposition of the waves, generated from different points of this periodic source, at the exit face of the medium shows an oscillatory behavior of the transmitted signal (idler) wave in terms of normalized coupling constant, . This study also shows that this effect is more considerable for high intensity pump beam, high relative refractive index and short length of the nonlinear medium.
Diophantine approximation and badly approximable sets
DEFF Research Database (Denmark)
Kristensen, S.; Thorn, R.; Velani, S.
2006-01-01
Let (X,d) be a metric space and (Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Omega. Loosely speaking, these consist of points in Omega which `stay clear' of some given set of points in X. The clas......Let (X,d) be a metric space and (Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Omega. Loosely speaking, these consist of points in Omega which `stay clear' of some given set of points in X....... The classical set Bad of `badly approximable' numbers in the theory of Diophantine approximation falls within our framework as do the sets Bad(i,j) of simultaneously badly approximable numbers. Under various natural conditions we prove that the badly approximable subsets of Omega have full Hausdorff dimension...
... Health Topics Tick-Borne Disease Hazards to Outdoor Workers Physical Hazards Heat Stress Cold Stress Sun Exposure Noise Biological Hazards Insects ... No Longer Available Lyme Disease Hazards to Outdoor Workers Physical Hazards Heat Stress Cold Stress Sun Exposure Noise Biological Hazards Insects ...
Centers for Disease Control (CDC) Podcasts
2011-04-18
This podcast discusses emerging vector-borne pathogens, their role as prominent contributors to emerging infectious diseases, how they're spread, and the ineffectiveness of mosquito control methods. Created: 4/18/2011 by National Center for Emerging Zoonotic and Infectious Diseases (NCEZID). Date Released: 4/27/2011.
Leike, Reimar H
2016-01-01
In Bayesian statistics probability distributions express beliefs. However, for many problems the beliefs cannot be computed analytically and approximations of beliefs are needed. We seek a ranking function that quantifies how "embarrassing" it is to communicate a given approximation. We show that there is only one ranking under the requirements that (1) the best ranked approximation is the non-approximated belief and (2) that the ranking judges approximations only by their predictions for actual outcomes. We find that this ranking is equivalent to the Kullback-Leibler divergence that is frequently used in the literature. However, there seems to be confusion about the correct order in which its functional arguments, the approximated and non-approximated beliefs, should be used. We hope that our elementary derivation settles the apparent confusion. We show for example that when approximating beliefs with Gaussian distributions the optimal approximation is given by moment matching. This is in contrast to many su...
... Search The CDC Cancel Submit Search The CDC Tick-borne Encephalitis (TBE) Note: Javascript is disabled or ... CDC.gov . Recommend on Facebook Tweet Share Compartir Tick-borne encephalitis, or TBE, is a human viral ...
Turko, B.
1980-01-01
The Space Borne Event Timer is a part of the NASA laser ranging system that is intended to operate aboard the Space Shuttle orbiting over California. The object is to measure, by laser ranging, the earth movement along the San Andreas fault and possibly forecast future earthquakes. A number of cube reflector targets will be placed along both sides of the fault. The ranging system aboard the Space Shuttle will fire a burst of laser pulses at each target and detect the reflected light. Time differences between pulses from the two sides of the fault will indicate earth displacements. The Space Borne Event Timer is a CAMAC compatible system that provides extremely accurate timing data and controls the operation of the ranging system. For each event the time is given in 19.53 increments from the instant of firing the laser to the instant the reflected light is received back, within a range of 130 days.
Nakamura, Yuko; Sawada, Mikio; Ikeguchi, Kunihiko; Nakano, Imaharu
2012-08-01
Botulism is a neuroparalytic disease caused by neurotoxins produced by Clostridium botulinum, and classically presents as palsies of cranial nerves and acute descending flaccid paralysis. Food-borne botulism is the most common form of botulism, and caused by preformed neurotoxins produced by Clostridium botulinum. Electrophysiological studies play an important role in the early diagnosis. Confirmation of the diagnosis is based on the detection of botulinum toxins in the patient's serum or stool. In Japan, decades ago, botulism type E occurred, though only sporadically, almost every year, but in recent years, has dramatically decreased in frequency. Botulism is a curable disease when treated early and adequately. Differential diagnosis of cranial nerves and limb muscle palsies with rapid exacerbation should include food-borne botulism.
Rašin, Andrija
1994-01-01
We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed.
On Element SDD Approximability
Avron, Haim; Toledo, Sivan
2009-01-01
This short communication shows that in some cases scalar elliptic finite element matrices cannot be approximated well by an SDD matrix. We also give a theoretical analysis of a simple heuristic method for approximating an element by an SDD matrix.
Approximate iterative algorithms
Almudevar, Anthony Louis
2014-01-01
Iterative algorithms often rely on approximate evaluation techniques, which may include statistical estimation, computer simulation or functional approximation. This volume presents methods for the study of approximate iterative algorithms, providing tools for the derivation of error bounds and convergence rates, and for the optimal design of such algorithms. Techniques of functional analysis are used to derive analytical relationships between approximation methods and convergence properties for general classes of algorithms. This work provides the necessary background in functional analysis a
Where was Joseph Babinski born?
Directory of Open Access Journals (Sweden)
H A G Teive
2011-01-01
Full Text Available There is controversy in the neurological literature about where Joseph Babinski was born, including a myth propounded by various important authors that he was born in Lima, Peru. However, according to the most consistent biographical data, he was in fact born in Paris, France, and became a medical celebrity there and in Poland as well as around the world.
Where was Joseph Babinski born?
Teive, Hélio A G; Munhoz, Renato P; de Souza, Leonardo Cruz
2011-01-01
There is controversy in the neurological literature about where Joseph Babinski was born, including a myth propounded by various important authors that he was born in Lima, Peru. However, according to the most consistent biographical data, he was in fact born in Paris, France, and became a medical celebrity there and in Poland as well as around the world.
Approximation of distributed delays
Lu, Hao; Eberard, Damien; Simon, Jean-Pierre
2010-01-01
We address in this paper the approximation problem of distributed delays. Such elements are convolution operators with kernel having bounded support, and appear in the control of time-delay systems. From the rich literature on this topic, we propose a general methodology to achieve such an approximation. For this, we enclose the approximation problem in the graph topology, and work with the norm defined over the convolution Banach algebra. The class of rational approximates is described, and a constructive approximation is proposed. Analysis in time and frequency domains is provided. This methodology is illustrated on the stabilization control problem, for which simulations results show the effectiveness of the proposed methodology.
Diophantine approximation and badly approximable sets
DEFF Research Database (Denmark)
Kristensen, S.; Thorn, R.; Velani, S.
2006-01-01
Let (X,d) be a metric space and (Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Omega. Loosely speaking, these consist of points in Omega which `stay clear' of some given set of points in X. The clas......Let (X,d) be a metric space and (Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Omega. Loosely speaking, these consist of points in Omega which `stay clear' of some given set of points in X...
Sparse approximation with bases
2015-01-01
This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications. The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and do...
Institute of Scientific and Technical Information of China (English)
贾伟乐; 曹宗雁; 王龙; 迟学斌; 高卫国; 汪林望
2014-01-01
基于平面波的第一原理计算方法是目前材料科学中最常用的方法，但传统的CPU并行计算遇到可扩展性瓶颈，无法改善其求解的绝对速度。系统地介绍了利用图形处理器（graphic processing unit，GPU）加速技术开发的大规模第一原理材料计算软件：Ultra-Mat。该软件对第一原理平面波算法进行了系统的算法设计和软件实现：（1）通过采用并行方案，实现了快速傅里叶变换（fast Fourier transform，FFT）的GPU局部操作；（2）设计了基于数据压缩的混合精度算法，显著减少了电子结构计算部分的MPI（message passing interface）通信；（3）完成了逾90%代码的GPU实现，目的是最大限度地减少中间流程，以避免CPU-GPU切换引发的数据传输，这是GPU应用中公认的性能瓶颈。测试结果显示Ultra-Mat具有很好的计算性能，对于512原子的GaAs系统，在电子结构计算部分，使用256 GPU卡相比4096 CPU核心有18倍的加速。%First principle calculation based on plane wave is the most popular method in material science simulation. However, traditional CPU parallelization has encountered the scalability bottleneck. Thus the absolute computing time cannot be reduced by using more CPU cores. This paper presents a first principle calculation software on large scale GPU (graphic processing unit) cluster:Ultra-Mat. It also redesigns and implements the algorithm:(1) Utilize a hybrid parallelization scheme to do FFT (fast Fourier transform) in single GPU card. (2) Design and implement a mix preci-sion algorithm to avoid CPU-GPU memory copy and MPI (message passing interface) communication. (3) Imple-ment more than 90%of the codes using CUDA. This step reduces the CPU-GPU memory copy operation, which is an accepted bottleneck in the heterogonous supercomputer. For a 512 atom GaAs system, the testing results show that, the method of using 256 GPU cards has 18 times speedup in the
DEFF Research Database (Denmark)
More, Simon J.; Bicout, Dominique; Bøtner, Anette
2017-01-01
After a request from the Europea n Commission, EFSA’s Panel on Animal Health and Welfaresummarised the main characteristics of 36 vector-borne disease s (VBDs) in 36 web-based storymaps.The risk of introduction in the EU through movement of livestock or pets was assessed for eac h of the36 VBDs...... new information becomesavailable. Since this risk assessment was carried out for large regions in the EU for many VBD-agents,it should be considered as a ﬁrst screening. If a more detailed risk assessment for a speciﬁcVBDiswished for on a national or subnational level, the EFSA...
García-Salcedo, R; Garcia-Salcedo, Ricardo; Breton, Nora
2000-01-01
We present a model for an inhomogeneous and anisotropic early universe filled with a nonlinear electromagnetic field of Born-Infeld (BI) type. The effects of the BI field are compared with the linear case (Maxwell). Since the curvature invaria nts are well behaved then we conjecture that our model does not present an initial big bang singularity. The existence of the BI field modifies the curvature invariants at t=0 as well as sets bounds on the amplitude of the conformal metric function
Approximation techniques for engineers
Komzsik, Louis
2006-01-01
Presenting numerous examples, algorithms, and industrial applications, Approximation Techniques for Engineers is your complete guide to the major techniques used in modern engineering practice. Whether you need approximations for discrete data of continuous functions, or you''re looking for approximate solutions to engineering problems, everything you need is nestled between the covers of this book. Now you can benefit from Louis Komzsik''s years of industrial experience to gain a working knowledge of a vast array of approximation techniques through this complete and self-contained resource.
Achieser, N I
2004-01-01
A pioneer of many modern developments in approximation theory, N. I. Achieser designed this graduate-level text from the standpoint of functional analysis. The first two chapters address approximation problems in linear normalized spaces and the ideas of P. L. Tchebysheff. Chapter III examines the elements of harmonic analysis, and Chapter IV, integral transcendental functions of the exponential type. The final two chapters explore the best harmonic approximation of functions and Wiener's theorem on approximation. Professor Achieser concludes this exemplary text with an extensive section of pr
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...
Scalar geons in Born-Infeld gravity
Afonso, V. I.; Olmo, Gonzalo J.; Rubiera-Garcia, D.
2017-08-01
The existence of static, spherically symmetric, self-gravitating scalar field solutions in the context of Born-Infeld gravity is explored. Upon a combination of analytical approximations and numerical methods, the equations for a free scalar field (without a potential term) are solved, verifying that the solutions recover the predictions of General Relativity far from the center but finding important new effects in the central regions. We find two classes of objects depending on the ratio between the Schwarzschild radius and a length scale associated to the Born-Infeld theory: massive solutions have a wormhole structure, with their throat at r≈ 2M, while for the lighter configurations the topology is Euclidean. The total energy density of these solutions exhibits a solitonic profile with a maximum peaked away from the center, and located at the throat whenever a wormhole exists. The geodesic structure and curvature invariants are analyzed for the various configurations considered.
Makarenko, Andrey N; Olmo, Gonzalo J
2014-01-01
We work out a gravity theory that combines the Born-Infeld gravity Lagrangian with an $f(R)$ piece. The theory is formulated within the Palatini approach. This construction provides more freedom to address a number of important questions such as the dynamics of the early universe and the cosmic accelerated expansion, among others. In particular, we consider the effect that adding an $f(R)=a R^2$ term has on the early-time cosmology. We find that bouncing solutions are robust against these modifications of the Lagrangian whereas the solutions with loitering behavior of the original Born-Infeld theory are very sensitive to the $R^2$ term. In fact, these solutions are modified in such a way that a plateau in the $H^2$ function may arise yielding a period of (approximately) de Sitter inflationary expansion. This inflationary behavior may be found even in a radiation dominated universe.
Ordered cones and approximation
Keimel, Klaus
1992-01-01
This book presents a unified approach to Korovkin-type approximation theorems. It includes classical material on the approximation of real-valuedfunctions as well as recent and new results on set-valued functions and stochastic processes, and on weighted approximation. The results are notonly of qualitative nature, but include quantitative bounds on the order of approximation. The book is addressed to researchers in functional analysis and approximation theory as well as to those that want to applythese methods in other fields. It is largely self- contained, but the readershould have a solid background in abstract functional analysis. The unified approach is based on a new notion of locally convex ordered cones that are not embeddable in vector spaces but allow Hahn-Banach type separation and extension theorems. This concept seems to be of independent interest.
Approximate Modified Policy Iteration
Scherrer, Bruno; Ghavamzadeh, Mohammad; Geist, Matthieu
2012-01-01
Modified policy iteration (MPI) is a dynamic programming (DP) algorithm that contains the two celebrated policy and value iteration methods. Despite its generality, MPI has not been thoroughly studied, especially its approximation form which is used when the state and/or action spaces are large or infinite. In this paper, we propose three approximate MPI (AMPI) algorithms that are extensions of the well-known approximate DP algorithms: fitted-value iteration, fitted-Q iteration, and classification-based policy iteration. We provide an error propagation analysis for AMPI that unifies those for approximate policy and value iteration. We also provide a finite-sample analysis for the classification-based implementation of AMPI (CBMPI), which is more general (and somehow contains) than the analysis of the other presented AMPI algorithms. An interesting observation is that the MPI's parameter allows us to control the balance of errors (in value function approximation and in estimating the greedy policy) in the fina...
Directory of Open Access Journals (Sweden)
Terry Anderson, Canada Research Chair in Distance Education
2004-11-01
Full Text Available With significant male trepidation, I want to share a birth story with IRRODL readers. This month, after a seemingly endless gestation, the Canadian Institute for Distance Education Research (CIDER was born. Like most births, this new presence began with a blissful consummation, when I accepted the Canada Research Chair in Distance education at Athabasca University. After a very short honeymoon, a couple of miscarriages, and a few lover's spats that marked the relationship between the Center for Distance Education and myself, we struggled to determine the type of protégée we wanted to birth. The within the womb (in house development of the visible image and website took shape, which like all gestations, was marked by some lower backache, punctuated by a few graphic images that turned out to be false labour.
Approximate calculation of integrals
Krylov, V I
2006-01-01
A systematic introduction to the principal ideas and results of the contemporary theory of approximate integration, this volume approaches its subject from the viewpoint of functional analysis. In addition, it offers a useful reference for practical computations. Its primary focus lies in the problem of approximate integration of functions of a single variable, rather than the more difficult problem of approximate integration of functions of more than one variable.The three-part treatment begins with concepts and theorems encountered in the theory of quadrature. The second part is devoted to t
Approximate and renormgroup symmetries
Energy Technology Data Exchange (ETDEWEB)
Ibragimov, Nail H. [Blekinge Institute of Technology, Karlskrona (Sweden). Dept. of Mathematics Science; Kovalev, Vladimir F. [Russian Academy of Sciences, Moscow (Russian Federation). Inst. of Mathematical Modeling
2009-07-01
''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)
Approximating Stationary Statistical Properties
Institute of Scientific and Technical Information of China (English)
Xiaoming WANG
2009-01-01
It is well-known that physical laws for large chaotic dynamical systems are revealed statistically. Many times these statistical properties of the system must be approximated numerically. The main contribution of this manuscript is to provide simple and natural criterions on numerical methods (temporal and spatial discretization) that are able to capture the stationary statistical properties of the underlying dissipative chaotic dynamical systems asymptotically. The result on temporal approximation is a recent finding of the author, and the result on spatial approximation is a new one. Applications to the infinite Prandtl number model for convection and the barotropic quasi-geostrophic model are also discussed.
Directory of Open Access Journals (Sweden)
Malvina Baica
1985-01-01
Full Text Available The author uses a new modification of Jacobi-Perron Algorithm which holds for complex fields of any degree (abbr. ACF, and defines it as Generalized Euclidean Algorithm (abbr. GEA to approximate irrationals.
Approximations in Inspection Planning
DEFF Research Database (Denmark)
Engelund, S.; Sørensen, John Dalsgaard; Faber, M. H.
2000-01-01
Planning of inspections of civil engineering structures may be performed within the framework of Bayesian decision analysis. The effort involved in a full Bayesian decision analysis is relatively large. Therefore, the actual inspection planning is usually performed using a number of approximations....... One of the more important of these approximations is the assumption that all inspections will reveal no defects. Using this approximation the optimal inspection plan may be determined on the basis of conditional probabilities, i.e. the probability of failure given no defects have been found...... by the inspection. In this paper the quality of this approximation is investigated. The inspection planning is formulated both as a full Bayesian decision problem and on the basis of the assumption that the inspection will reveal no defects....
The Karlqvist approximation revisited
Tannous, C
2015-01-01
The Karlqvist approximation signaling the historical beginning of magnetic recording head theory is reviewed and compared to various approaches progressing from Green, Fourier, Conformal mapping that obeys the Sommerfeld edge condition at angular points and leads to exact results.
Approximations in Inspection Planning
DEFF Research Database (Denmark)
Engelund, S.; Sørensen, John Dalsgaard; Faber, M. H.
2000-01-01
Planning of inspections of civil engineering structures may be performed within the framework of Bayesian decision analysis. The effort involved in a full Bayesian decision analysis is relatively large. Therefore, the actual inspection planning is usually performed using a number of approximations....... One of the more important of these approximations is the assumption that all inspections will reveal no defects. Using this approximation the optimal inspection plan may be determined on the basis of conditional probabilities, i.e. the probability of failure given no defects have been found...... by the inspection. In this paper the quality of this approximation is investigated. The inspection planning is formulated both as a full Bayesian decision problem and on the basis of the assumption that the inspection will reveal no defects....
Institute of Scientific and Technical Information of China (English)
李祥震; 韩香娥
2011-01-01
On the basis of geometrical optics approximation (GOA) of light scattering by spheres, GOA method of forward scattering by a GI-POF for normally incident plane wave was presented. The convergence factor and the phase shift caused by focal line were deduced in GOA. The nondimensional form of scattering intensity formula of forward scattering by a GI-POF for normally incident plane wave was obtained. Based on the above work, the scattering intensity distribution and calculation speed calculated by GOA was compared with the result calculated by Mie theory. The comparison result shows that GOA can be used to calculate the forward scattering intensity of a GI-POF with normally incident plane wave exactly. And the calculation speed of GOA is higher than that of Mie theory, the GOA method is suitable for the real-time measurement of particle-sizing.%基于球粒子光散射的几何光学近似方法,推导了平面波垂直入射梯度折射率光纤(GI-POF)前向散射的几何光学近似.详细推导了几何光学近似方法中的收敛因子和焦线引起的相位变化,得到了平面波垂直入射到GI-POF时无量纲散射强度公式.在此基础上,将几何光学近似方法计算出的前向散射强度分布和算法的运行速度与Mie理论进行了对比,结果表明:几何光学近似方法可以快速而准确地计算出粒子前向散射分布,适用于粒度的在线测量.
Gautschi, Walter; Rassias, Themistocles M
2011-01-01
Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanovia, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational alg
Approximation Behooves Calibration
DEFF Research Database (Denmark)
da Silva Ribeiro, André Manuel; Poulsen, Rolf
2013-01-01
Calibration based on an expansion approximation for option prices in the Heston stochastic volatility model gives stable, accurate, and fast results for S&P500-index option data over the period 2005–2009.......Calibration based on an expansion approximation for option prices in the Heston stochastic volatility model gives stable, accurate, and fast results for S&P500-index option data over the period 2005–2009....
Approximate kernel competitive learning.
Wu, Jian-Sheng; Zheng, Wei-Shi; Lai, Jian-Huang
2015-03-01
Kernel competitive learning has been successfully used to achieve robust clustering. However, kernel competitive learning (KCL) is not scalable for large scale data processing, because (1) it has to calculate and store the full kernel matrix that is too large to be calculated and kept in the memory and (2) it cannot be computed in parallel. In this paper we develop a framework of approximate kernel competitive learning for processing large scale dataset. The proposed framework consists of two parts. First, it derives an approximate kernel competitive learning (AKCL), which learns kernel competitive learning in a subspace via sampling. We provide solid theoretical analysis on why the proposed approximation modelling would work for kernel competitive learning, and furthermore, we show that the computational complexity of AKCL is largely reduced. Second, we propose a pseudo-parallelled approximate kernel competitive learning (PAKCL) based on a set-based kernel competitive learning strategy, which overcomes the obstacle of using parallel programming in kernel competitive learning and significantly accelerates the approximate kernel competitive learning for large scale clustering. The empirical evaluation on publicly available datasets shows that the proposed AKCL and PAKCL can perform comparably as KCL, with a large reduction on computational cost. Also, the proposed methods achieve more effective clustering performance in terms of clustering precision against related approximate clustering approaches.
Directory of Open Access Journals (Sweden)
Maksim Duškin
2015-11-01
Full Text Available Approximation and supposition This article compares exponents of approximation (expressions like Russian около, примерно, приблизительно, более, свыше and the words expressing supposition (for example Russian скорее всего, наверное, возможно. These words are often confused in research, in particular researchers often mention exponents of supposition in case of exponents of approximation. Such approach arouses some objections. The author intends to demonstrate in this article a notional difference between approximation and supposition, therefore the difference between exponents of these two notions. This difference could be described by specifying different attitude of approximation and supposition to the notion of knowledge. Supposition implies speaker’s ignorance of the exact number, while approximation does not mean such ignorance. The article offers examples proving this point of view.
Covariant approximation averaging
Shintani, Eigo; Blum, Thomas; Izubuchi, Taku; Jung, Chulwoo; Lehner, Christoph
2014-01-01
We present a new class of statistical error reduction techniques for Monte-Carlo simulations. Using covariant symmetries, we show that correlation functions can be constructed from inexpensive approximations without introducing any systematic bias in the final result. We introduce a new class of covariant approximation averaging techniques, known as all-mode averaging (AMA), in which the approximation takes account of contributions of all eigenmodes through the inverse of the Dirac operator computed from the conjugate gradient method with a relaxed stopping condition. In this paper we compare the performance and computational cost of our new method with traditional methods using correlation functions and masses of the pion, nucleon, and vector meson in $N_f=2+1$ lattice QCD using domain-wall fermions. This comparison indicates that AMA significantly reduces statistical errors in Monte-Carlo calculations over conventional methods for the same cost.
Diophantine approximations on fractals
Einsiedler, Manfred; Shapira, Uri
2009-01-01
We exploit dynamical properties of diagonal actions to derive results in Diophantine approximations. In particular, we prove that the continued fraction expansion of almost any point on the middle third Cantor set (with respect to the natural measure) contains all finite patterns (hence is well approximable). Similarly, we show that for a variety of fractals in [0,1]^2, possessing some symmetry, almost any point is not Dirichlet improvable (hence is well approximable) and has property C (after Cassels). We then settle by similar methods a conjecture of M. Boshernitzan saying that there are no irrational numbers x in the unit interval such that the continued fraction expansions of {nx mod1 : n is a natural number} are uniformly eventually bounded.
Monotone Boolean approximation
Energy Technology Data Exchange (ETDEWEB)
Hulme, B.L.
1982-12-01
This report presents a theory of approximation of arbitrary Boolean functions by simpler, monotone functions. Monotone increasing functions can be expressed without the use of complements. Nonconstant monotone increasing functions are important in their own right since they model a special class of systems known as coherent systems. It is shown here that when Boolean expressions for noncoherent systems become too large to treat exactly, then monotone approximations are easily defined. The algorithms proposed here not only provide simpler formulas but also produce best possible upper and lower monotone bounds for any Boolean function. This theory has practical application for the analysis of noncoherent fault trees and event tree sequences.
Early Recollections of First-Borns.
Fakouri, M. Ebrahim; Hafner, James L.
1984-01-01
Compared the early recollections of 50 first-borns and 98 later-borns. The first-borns mentioned significantly more nonfamily members, illness/injury, hospital/doctor's office. Later-borns mentioned significantly more siblings than did first-borns. Findings were discussed in the context of Adler's personality theory. (JAC)
Prestack wavefield approximations
Alkhalifah, Tariq
2013-09-01
The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.
On Convex Quadratic Approximation
den Hertog, D.; de Klerk, E.; Roos, J.
2000-01-01
In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of
Norton, Andrew H.
1991-01-01
Local spline approximants offer a means for constructing finite difference formulae for numerical solution of PDEs. These formulae seem particularly well suited to situations in which the use of conventional formulae leads to non-linear computational instability of the time integration. This is explained in terms of frequency responses of the FDF.
On Convex Quadratic Approximation
den Hertog, D.; de Klerk, E.; Roos, J.
2000-01-01
In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of
Approximation by Cylinder Surfaces
DEFF Research Database (Denmark)
Randrup, Thomas
1997-01-01
We present a new method for approximation of a given surface by a cylinder surface. It is a constructive geometric method, leading to a monorail representation of the cylinder surface. By use of a weighted Gaussian image of the given surface, we determine a projection plane. In the orthogonal...
Born : vastutustundlikud tulevikus edukad / Kerstin Born ; interv. Kristo Kiviorg
Born, Kerstin
2007-01-01
Vastutustundliku ettevõtluse Euroopa organisatsiooni CSR Europe'i juht Kerstin Born vastab küsimustele ettevõtete vastutustundlikkuse kohta ühiskonnas. Vt. samas: Käivitus vastutustundliku ettevõtluse indeks
Born-Infeld cosmology with scalar Born-Infeld matter
Jana, Soumya
2016-01-01
Cosmology in Eddington-inspired Born-Infeld gravity is investigated using a scalar Born-Infeld field (eg. tachyon condensate) as matter. In this way, both in the gravity and matter sectors we have Born-Infeld-like structures characterised by their actions and via two separate constants, $\\kappa$ and $\\alpha_T^2$ respectively. With a particular choice of the form of $\\dot{\\phi}$ (time derivative of the Born-Infeld scalar), analytical cosmological solutions are found. Thereafter, we explore some of the unique features of the corresponding cosmological spacetimes. For $\\kappa>0$, our solution has a de Sitter-like expansion both at early and late times, with an intermediate deceleration sandwiched between the accelerating phases. On the other hand, when $\\kappa0$ solution, are as good as in $\\Lambda$CDM cosmology. However, the $\\kappa<0$ solution has to be discarded due to the occurrence of a bounce at an unacceptably low redshift.
Born-Infeld cosmology with scalar Born-Infeld matter
Jana, Soumya; Kar, Sayan
2016-09-01
Cosmology in Eddington-inspired Born-Infeld gravity is investigated using a scalar Born-Infeld field (e.g. tachyon condensate) as matter. In this way, both in the gravity and matter sectors we have Born-Infeld-like structures characterized by their actions and via two separate constants, κ and αT2 , respectively. With a particular choice of the form of ϕ ˙ (the time derivative of the Born-Infeld scalar), analytical cosmological solutions are found. Thereafter, we explore some of the unique features of the corresponding cosmological spacetimes. For κ >0 , our solution has a de Sitter-like expansion both at early and late times, with an intermediate deceleration sandwiched between the accelerating phases. On the other hand, when κ 0 solution are as good as in Λ CDM cosmology. However, the κ <0 solution has to be discarded due to the occurrence of a bounce at an unacceptably low redshift.
Born : vastutustundlikud tulevikus edukad / Kerstin Born ; interv. Kristo Kiviorg
Born, Kerstin
2007-01-01
Vastutustundliku ettevõtluse Euroopa organisatsiooni CSR Europe'i juht Kerstin Born vastab küsimustele ettevõtete vastutustundlikkuse kohta ühiskonnas. Vt. samas: Käivitus vastutustundliku ettevõtluse indeks
Topology, calculus and approximation
Komornik, Vilmos
2017-01-01
Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér, Stieltjes, and Turán. The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdős and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Carathéodory's definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations. Students of both pure an...
Prestack traveltime approximations
Alkhalifah, Tariq Ali
2011-01-01
Most prestack traveltime relations we tend work with are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multi-focusing or double square-root (DSR) and the common reflection stack (CRS) equations. Using the DSR equation, I analyze the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I derive expansion based solutions of this eikonal based on polynomial expansions in terms of the reflection and dip angles in a generally inhomogenous background medium. These approximate solutions are free of singularities and can be used to estimate travetimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. A Marmousi example demonstrates the usefulness of the approach. © 2011 Society of Exploration Geophysicists.
Optimization and approximation
Pedregal, Pablo
2017-01-01
This book provides a basic, initial resource, introducing science and engineering students to the field of optimization. It covers three main areas: mathematical programming, calculus of variations and optimal control, highlighting the ideas and concepts and offering insights into the importance of optimality conditions in each area. It also systematically presents affordable approximation methods. Exercises at various levels have been included to support the learning process.
Appearance of gauge fields and forces beyond the adiabatic approximation
Energy Technology Data Exchange (ETDEWEB)
Gosselin, Pierre [Institut Fourier, UMR 5582 CNRS-UJF, UFR de Mathematiques, Universite Grenoble I, BP74, 38402 Saint Martin d' Heres, Cedex (France); Mohrbach, Herve, E-mail: mohrbach@univ-metz.f [Laboratoire de Physique Moleculaire et des Collisions, ICPMB-FR CNRS 2843, Universite Paul Verlaine-Metz, 57078 Metz Cedex 3 (France)
2010-09-03
We investigate the origin of quantum geometric phases, gauge fields and forces beyond the adiabatic regime. In particular, we extend the notions of geometric magnetic and electric forces discovered in studies of the Born-Oppenheimer approximation to arbitrary quantum systems described by matrix-valued quantum Hamiltonians. The results are illustrated by several physical relevant examples.
Topics in Metric Approximation
Leeb, William Edward
This thesis develops effective approximations of certain metrics that occur frequently in pure and applied mathematics. We show that distances that often arise in applications, such as the Earth Mover's Distance between two probability measures, can be approximated by easily computed formulas for a wide variety of ground distances. We develop simple and easily computed characterizations both of norms measuring a function's regularity -- such as the Lipschitz norm -- and of their duals. We are particularly concerned with the tensor product of metric spaces, where the natural notion of regularity is not the Lipschitz condition but the mixed Lipschitz condition. A theme that runs throughout this thesis is that snowflake metrics (metrics raised to a power less than 1) are often better-behaved than ordinary metrics. For example, we show that snowflake metrics on finite spaces can be approximated by the average of tree metrics with a distortion bounded by intrinsic geometric characteristics of the space and not the number of points. Many of the metrics for which we characterize the Lipschitz space and its dual are snowflake metrics. We also present applications of the characterization of certain regularity norms to the problem of recovering a matrix that has been corrupted by noise. We are able to achieve an optimal rate of recovery for certain families of matrices by exploiting the relationship between mixed-variable regularity conditions and the decay of a function's coefficients in a certain orthonormal basis.
Dempsey, Allison G.; Keller-Margulis, Milena; Mire, Sarah; Abrahamson, Catherine; Dutt, Sonia; Llorens, Ashlie; Payan, Anita
2015-01-01
Children born preterm are at risk for developmental deficits across multiple functional domains. As the rate of survival for preterm infants increases due to medical advancements, a greater understanding is needed for how to meet the needs of this growing population in schools. Because approximately 50-70% of children born preterm require…
Dempsey, Allison G.; Keller-Margulis, Milena; Mire, Sarah; Abrahamson, Catherine; Dutt, Sonia; Llorens, Ashlie; Payan, Anita
2015-01-01
Children born preterm are at risk for developmental deficits across multiple functional domains. As the rate of survival for preterm infants increases due to medical advancements, a greater understanding is needed for how to meet the needs of this growing population in schools. Because approximately 50-70% of children born preterm require…
Accurate and efficient computation of nonlocal potentials based on Gaussian-sum approximation
Exl, Lukas; Mauser, Norbert J.; Zhang, Yong
2016-12-01
We introduce an accurate and efficient method for the numerical evaluation of nonlocal potentials, including the 3D/2D Coulomb, 2D Poisson and 3D dipole-dipole potentials. Our method is based on a Gaussian-sum approximation of the singular convolution kernel combined with a Taylor expansion of the density. Starting from the convolution formulation of the nonlocal potential, for smooth and fast decaying densities, we make a full use of the Fourier pseudospectral (plane wave) approximation of the density and a separable Gaussian-sum approximation of the kernel in an interval where the singularity (the origin) is excluded. The potential is separated into a regular integral and a near-field singular correction integral. The first is computed with the Fourier pseudospectral method, while the latter is well resolved utilizing a low-order Taylor expansion of the density. Both parts are accelerated by fast Fourier transforms (FFT). The method is accurate (14-16 digits), efficient (O (Nlog N) complexity), low in storage, easily adaptable to other different kernels, applicable for anisotropic densities and highly parallelizable.
Accurate and efficient computation of nonlocal potentials based on Gaussian-sum approximation
Exl, Lukas; Zhang, Yong
2015-01-01
We introduce an accurate and efficient method for a class of nonlocal potential evaluations with free boundary condition, including the 3D/2D Coulomb, 2D Poisson and 3D dipolar potentials. Our method is based on a Gaussian-sum approximation of the singular convolution kernel and Taylor expansion of the density. Starting from the convolution formulation, for smooth and fast decaying densities, we make a full use of the Fourier pseudospectral (plane wave) approximation of the density and a separable Gaussian-sum approximation of the kernel in an interval where the singularity (the origin) is excluded. Hence, the potential is separated into a regular integral and a near-field singular correction integral, where the first integral is computed with the Fourier pseudospectral method and the latter singular one can be well resolved utilizing a low-order Taylor expansion of the density. Both evaluations can be accelerated by fast Fourier transforms (FFT). The new method is accurate (14-16 digits), efficient ($O(N \\lo...
Energy Technology Data Exchange (ETDEWEB)
Chalasani, P.; Saias, I. [Los Alamos National Lab., NM (United States); Jha, S. [Carnegie Mellon Univ., Pittsburgh, PA (United States)
1996-04-08
As increasingly large volumes of sophisticated options (called derivative securities) are traded in world financial markets, determining a fair price for these options has become an important and difficult computational problem. Many valuation codes use the binomial pricing model, in which the stock price is driven by a random walk. In this model, the value of an n-period option on a stock is the expected time-discounted value of the future cash flow on an n-period stock price path. Path-dependent options are particularly difficult to value since the future cash flow depends on the entire stock price path rather than on just the final stock price. Currently such options are approximately priced by Monte carlo methods with error bounds that hold only with high probability and which are reduced by increasing the number of simulation runs. In this paper the authors show that pricing an arbitrary path-dependent option is {number_sign}-P hard. They show that certain types f path-dependent options can be valued exactly in polynomial time. Asian options are path-dependent options that are particularly hard to price, and for these they design deterministic polynomial-time approximate algorithms. They show that the value of a perpetual American put option (which can be computed in constant time) is in many cases a good approximation to the value of an otherwise identical n-period American put option. In contrast to Monte Carlo methods, the algorithms have guaranteed error bounds that are polynormally small (and in some cases exponentially small) in the maturity n. For the error analysis they derive large-deviation results for random walks that may be of independent interest.
Finite elements and approximation
Zienkiewicz, O C
2006-01-01
A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o
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.
Born-Infeld gravity coupled to Born-Infeld electrodynamics
Jana, Soumya
2015-01-01
We investigate spherically symmetric, static spacetimes in Eddington-inspired Born-Infeld gravity coupled to Born-Infeld electrodynamics. The two constants, $b^2$ and $\\kappa$ which parametrise the Born-Infeld structures in the electrodynamics (matter) and gravity sectors, characterise the features of our analytical solutions. Black holes or naked singularities are found to arise, depending on the values of $b^2$ and $\\kappa$, as well as charge and mass. Several such solutions are classified and understood through the analysis of the associated metric functions. Interestingly, for a particular relation between these two parameters, $b^2=1/{4\\kappa},\\, \\kappa >0$, we obtain a solution resembling the well-known Reissner-Nordstr\\" om line element, albeit some modifications. We study null geodesics and gravitational lensing using this particular solution. Among interesting features we note $(i)$ a decrease in the radius of the photon sphere with increasing $\\kappa$ and $(ii)$ a net negative contribution in the le...
Roy, Swapnoneel; Thakur, Ashok Kumar
2008-01-01
Genome rearrangements have been modelled by a variety of primitives such as reversals, transpositions, block moves and block interchanges. We consider such a genome rearrangement primitive Strip Exchanges. Given a permutation, the challenge is to sort it by using minimum number of strip exchanges. A strip exchanging move interchanges the positions of two chosen strips so that they merge with other strips. The strip exchange problem is to sort a permutation using minimum number of strip exchanges. We present here the first non-trivial 2-approximation algorithm to this problem. We also observe that sorting by strip-exchanges is fixed-parameter-tractable. Lastly we discuss the application of strip exchanges in a different area Optical Character Recognition (OCR) with an example.
Approximation by Cylinder Surfaces
DEFF Research Database (Denmark)
Randrup, Thomas
1997-01-01
We present a new method for approximation of a given surface by a cylinder surface. It is a constructive geometric method, leading to a monorail representation of the cylinder surface. By use of a weighted Gaussian image of the given surface, we determine a projection plane. In the orthogonal...... projection of the surface onto this plane, a reference curve is determined by use of methods for thinning of binary images. Finally, the cylinder surface is constructed as follows: the directrix of the cylinder surface is determined by a least squares method minimizing the distance to the points...... in the projection within a tolerance given by the reference curve, and the rulings are lines perpendicular to the projection plane. Application of the method in ship design is given....
S-Approximation: A New Approach to Algebraic Approximation
Directory of Open Access Journals (Sweden)
M. R. Hooshmandasl
2014-01-01
Full Text Available We intend to study a new class of algebraic approximations, called S-approximations, and their properties. We have shown that S-approximations can be used for applied problems which cannot be modeled by inclusion based approximations. Also, in this work, we studied a subclass of S-approximations, called Sℳ-approximations, and showed that this subclass preserves most of the properties of inclusion based approximations but is not necessarily inclusionbased. The paper concludes by studying some basic operations on S-approximations and counting the number of S-min functions.
Energy Technology Data Exchange (ETDEWEB)
Lestrange, Patrick J.; Egidi, Franco; Li, Xiaosong, E-mail: xsli@uw.edu [Department of Chemistry, University of Washington, Seattle, Washington 98195 (United States)
2015-12-21
The interaction between a quantum mechanical system and plane wave light is usually modeled within the electric dipole approximation. This assumes that the intensity of the incident field is constant over the length of the system and transition probabilities are described in terms of the electric dipole transition moment. For short wavelength spectroscopies, such as X-ray absorption, the electric dipole approximation often breaks down. Higher order multipoles are then included to describe transition probabilities. The square of the magnetic dipole and electric quadrupole are often included, but this results in an origin-dependent expression for the oscillator strength. The oscillator strength can be made origin-independent if all terms through the same order in the wave vector are retained. We will show the consequences and potential pitfalls of using either of these two expressions. It is shown that the origin-dependent expression may violate the Thomas-Reiche-Kuhn sum rule and the origin-independent expression can result in negative transition probabilities.
Prestack traveltime approximations
Alkhalifah, Tariq Ali
2012-05-01
Many of the explicit prestack traveltime relations used in practice are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multifocusing, based on the double square-root (DSR) equation, and the common reflection stack (CRS) approaches. Using the DSR equation, I constructed the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I recasted the eikonal in terms of the reflection angle, and thus, derived expansion based solutions of this eikonal in terms of the difference between the source and receiver velocities in a generally inhomogenous background medium. The zero-order term solution, corresponding to ignoring the lateral velocity variation in estimating the prestack part, is free of singularities and can be used to estimate traveltimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. The higher-order terms include limitations for horizontally traveling waves, however, we can readily enforce stability constraints to avoid such singularities. In fact, another expansion over reflection angle can help us avoid these singularities by requiring the source and receiver velocities to be different. On the other hand, expansions in terms of reflection angles result in singularity free equations. For a homogenous background medium, as a test, the solutions are reasonably accurate to large reflection and dip angles. A Marmousi example demonstrated the usefulness and versatility of the formulation. © 2012 Society of Exploration Geophysicists.
Treecode-Based Generalized Born Method
Energy Technology Data Exchange (ETDEWEB)
Xu, Zhenli [Shanghai Jiao Tong University, Shanghai; Cheng, Xiaolin [ORNL; Yang, Shihui [ORNL
2011-01-01
We have developed a treecode-based O(Nlog N) algorithm for the generalized Born (GB) implicit solvation model. Our treecode-based GB (tGB) is based on the GBr6 [J. Phys. Chem. B 111, 3055 (2007)], an analytical GB method with a pairwise descreening approximation for the R6 volume integral expression. The algorithm is composed of a cutoff scheme for the effective Born radii calculation, and a treecode implementation of the GB charge charge pair interactions. Test results demonstrate that the tGB algorithm can reproduce the vdW surface based Poisson solvation energy with an average relative error less than 0.6% while providing an almost linear-scaling calculation for a representative set of 25 proteins with different sizes (from 2815 atoms to 65456 atoms). For a typical system of 10k atoms, the tGB calculation is three times faster than the direct summation as implemented in the original GBr6 model. Thus, our tGB method provides an efficient way for performing implicit solvent GB simulations of larger biomolecular systems at longer time scales.
Effects on PP waves and Rayleigh waves of water column approximation
Zhou, Y.; Ni, S.
2015-12-01
Spectral-element method (SEM) combines the flexibility of the finite-element method and the accuracy of the pseudo-spectral method. It can handle the complexity of the 3-D earth model, such as heterogeneity of velocity and density, anisotropy, anelasticity, sharp velocity and density contrasts, topography. And with water column approximation, it can also deal with oceans. Because of its powerful ability, there are a wide range of application of SEM in studies of PP waves and Rayleigh waves. PP wave and its precursors have been used in measuring topography of 410 km or 660 km. Rayleigh waves are the most recognizable part of the seismograms and have been broadly applied in crustal and uppermost mantle tomography. In global SEM simulation, oceans are usually assumed to be incompressible, which means that the entire water column moves as a whole as a result of the normal displacement of the seafloor. It is necessary to investigate the accuracy of water column approximation when thickness of ocean approaches wavelength of the wave in the ocean water. In this paper, based on plane wave assumption, we study both the accurate form and water column approximate form of effective boundary condition. The reflection coefficient equation of PP waves with effective boundary of water was derived. Accurate and approximate PP reflection coefficient with oceans in different depth is demonstrated. The formula of Rayleigh wave phase velocity dispersion with effective water boundary is also investigated. It is shown that water column approximation in global SEM simulation is not sufficient for some parts of the ocean.
Operators of Approximations and Approximate Power Set Spaces
Institute of Scientific and Technical Information of China (English)
ZHANG Xian-yong; MO Zhi-wen; SHU Lan
2004-01-01
Boundary inner and outer operators are introduced; and union, intersection, complement operators of approximations are redefined. The approximation operators have a good property of maintaining union, intersection, complement operators, so the rough set theory has been enriched from the operator-oriented and set-oriented views. Approximate power set spaces are defined, and it is proved that the approximation operators are epimorphisms from power set space to approximate power set spaces. Some basic properties of approximate power set space are got by epimorphisms in contrast to power set space.
International Conference Approximation Theory XV
Schumaker, Larry
2017-01-01
These proceedings are based on papers presented at the international conference Approximation Theory XV, which was held May 22–25, 2016 in San Antonio, Texas. The conference was the fifteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 146 participants. The book contains longer survey papers by some of the invited speakers covering topics such as compressive sensing, isogeometric analysis, and scaling limits of polynomials and entire functions of exponential type. The book also includes papers on a variety of current topics in Approximation Theory drawn from areas such as advances in kernel approximation with applications, approximation theory and algebraic geometry, multivariate splines for applications, practical function approximation, approximation of PDEs, wavelets and framelets with applications, approximation theory in signal processing, compressive sensing, rational interpolation, spline approximation in isogeometric analysis, a...
Emerging food-borne parasites.
Dorny, P; Praet, N; Deckers, N; Gabriel, S
2009-08-07
Parasitic food-borne diseases are generally underrecognised, however they are becoming more common. Globalization of the food supply, increased international travel, increase of the population of highly susceptible persons, change in culinary habits, but also improved diagnostic tools and communication are some factors associated with the increased diagnosis of food-borne parasitic diseases worldwide. This paper reviews the most important emerging food-borne parasites, with emphasis on transmission routes. In a first part, waterborne parasites transmitted by contaminated food such as Cyclospora cayetanensis, Cryptosporidium and Giardia are discussed. Also human fasciolosis, of which the importance has only been recognised in the last decades, with total numbers of reported cases increasing from less than 3000 to 17 million, is looked at. Furthermore, fasciolopsiosis, an intestinal trematode of humans and pigs belongs to the waterborne parasites as well. A few parasites that may be transmitted through faecal contamination of foods and that have received renewed attention, such as Toxoplasma gondii, or that are (re-)emerging, such as Trypanosoma cruzi and Echinococcus spp., are briefly reviewed. In a second part, meat-borne parasite infections are reviewed. Humans get infected by eating raw or undercooked meat infected with cyst stages of these parasites. Meat inspection is the principal method applied in the control of Taenia spp. and Trichinella spp. However, it is often not very sensitive, frequently not practised, and not done for T. gondii and Sarcocystis spp. Meat of reptiles, amphibians and fish can be infected with a variety of parasites, including trematodes (Opisthorchis spp., Clonorchis sinensis, minute intestinal flukes), cestodes (Diphyllobothrium spp., Spirometra), nematodes (Gnathostoma, spp., anisakine parasites), and pentastomids that can cause zoonotic infections in humans when consumed raw or not properly cooked. Another important zoonotic food-borne
Hierarchical low-rank approximation for high dimensional approximation
Nouy, Anthony
2016-01-07
Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.
Born Reciprocity and Cosmic Accelerations
Bolognesi, S
2015-01-01
The trans-Planckian theory is a model that realizes concretely the Born reciprocity idea, which is the postulate of absolute equivalence between coordinate $x$ and momenta $p$. This model is intrinsically global, and thus it is naturally implemented in a cosmological setting. Cosmology and Born reciprocity are made for each other. Inflation provides the essential mechanism to suppress the terms coming from the dual part of the action. The trans-Planckian theory, on the other hand, provides an explanation for the accelerated periods of the universe scale factor, both the inflationary period and the present period dominated by dark energy. All of this is possible just considering a simple model that contains gravity, one gauge field plus one matter field (to be identified with dark matter) together with the reciprocity principle.
Nonlinear Approximation Using Gaussian Kernels
Hangelbroek, Thomas
2009-01-01
It is well-known that non-linear approximation has an advantage over linear schemes in the sense that it provides comparable approximation rates to those of the linear schemes, but to a larger class of approximands. This was established for spline approximations and for wavelet approximations, and more recently for homogeneous radial basis function (surface spline) approximations. However, no such results are known for the Gaussian function. The crux of the difficulty lies in the necessity to vary the tension parameter in the Gaussian function spatially according to local information about the approximand: error analysis of Gaussian approximation schemes with varying tension are, by and large, an elusive target for approximators. We introduce and analyze in this paper a new algorithm for approximating functions using translates of Gaussian functions with varying tension parameters. Our scheme is sophisticated to a degree that it employs even locally Gaussians with varying tensions, and that it resolves local ...
Brand Building of Born Globals
Cederäng, Jesper; Norberg, Markus
2008-01-01
Abstract The purpose of this thesis was to increase the understanding of two early internationalizing firms (Born Globals) brand building efforts. By performing case studies on these companies we wished to discover similarities and differences in their marketing efforts. The companies that we studied were CTEK Sweden AB, a battery charger manufacturer and POC Sweden AB, who designs advanced protective gear for the alpine ski market. The theoretical framework was divided according to the four ...
Institute of Scientific and Technical Information of China (English)
Fang Hong; Lou Shu-Qin; Guo Tie-Ying; Yao Lei; Li nong-Lei; Jian ShuiSheng
2008-01-01
A simple model for approximate bandgap structure caculation of all-solid photonic bandgap fibre based on an array of rings is proposed.In this model calculated are only the potential modes of a unit cell,which is a high-index ring in the low-index background for this fibre,rather than the whole cladding periodic structure based on Bloch's theorem to find the bandgap.Its accuracy is proved by comparing its results with the results obtained by using the accurate full-vector plane-wave method.High speed in computation is its great advantage over the other exact methods,because it only needs to find the roots of one-dimensional analytical expressions.And the results of this model,mode plots,offer an ideal environment to explore the basic properties of photonic bandgap clearly.
Forms of Approximate Radiation Transport
Brunner, G
2002-01-01
Photon radiation transport is described by the Boltzmann equation. Because this equation is difficult to solve, many different approximate forms have been implemented in computer codes. Several of the most common approximations are reviewed, and test problems illustrate the characteristics of each of the approximations. This document is designed as a tutorial so that code users can make an educated choice about which form of approximate radiation transport to use for their particular simulation.
Approximation by Multivariate Singular Integrals
Anastassiou, George A
2011-01-01
Approximation by Multivariate Singular Integrals is the first monograph to illustrate the approximation of multivariate singular integrals to the identity-unit operator. The basic approximation properties of the general multivariate singular integral operators is presented quantitatively, particularly special cases such as the multivariate Picard, Gauss-Weierstrass, Poisson-Cauchy and trigonometric singular integral operators are examined thoroughly. This book studies the rate of convergence of these operators to the unit operator as well as the related simultaneous approximation. The last cha
Approximations of fractional Brownian motion
Li, Yuqiang; 10.3150/10-BEJ319
2012-01-01
Approximations of fractional Brownian motion using Poisson processes whose parameter sets have the same dimensions as the approximated processes have been studied in the literature. In this paper, a special approximation to the one-parameter fractional Brownian motion is constructed using a two-parameter Poisson process. The proof involves the tightness and identification of finite-dimensional distributions.
Approximation by planar elastic curves
DEFF Research Database (Denmark)
Brander, David; Gravesen, Jens; Nørbjerg, Toke Bjerge
2016-01-01
We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good initial guess for the approximating curve. A gradient......-driven optimization is then used to find the approximating elastic curve....
A Quasiclassical Approximation in the Theory of the Landau-Pomeranchuk Effect
Tarasov, A V; Voskresenskaya, O O
2012-01-01
With the use of revised within the quasiclassical approximation the values of parameters of the Moliere multiple scattering theory it is shown that the best agreement of the Migdal theory of the LPM-effect with experiment achieved if to describe the electron-atomic scattering the quasiclassical approximation is used instead of the traditionally used Born one.
The born approximation and Calderón's method for reconstruction of conductivities in 3-D
DEFF Research Database (Denmark)
Knudsen, Kim; Mueller, Jennifer L.
2011-01-01
Two algorithms for the direct reconstruction of conductivities in a bounded domain in [\\mathbb{R}^3] from surface measurements of the solutions to the conductivity equation are presented. The algorithms are based on complex geometrical optics solutions and a nonlinear scattering transform. We test...... the algorithms on three numerically simulated examples, including an example with a complex coefficient. The spatial resolution and amplitude of the examples are well-reconstructed....
Radiative recombination of twisted electrons with bare nuclei: going beyond the Born approximation
Zaytsev, V A; Shabaev, V M
2016-01-01
We present a fully relativistic investigation of the radiative recombination of a twisted electron with a bare heavy nucleus. The twisted electron is described by the wave function which accounts for the interaction with the nucleus in all orders in $\\alpha Z$. We use this wave function to derive the probability of the radiative recombination with a single ion being shifted from the twisted electron propagation direction. We also consider more realistic experimental scenarios where the target is either localized (mesoscopic) or infinitely wide (macroscopic). The situation when the incident electron is a coherent superposition of two vortex states is considered as well. For the nonrelativistic case we present analytical expressions which support our numerical calculations. We study in details the influence of the electron twistedness on the polarization and angular distribution of the emitted photon. It is found that these properties of the outgoing photon might be very sensitive to the total angular momentum ...
A Priori Estimation of the Resolvent on Approximation of Born-Oppenheimer
Directory of Open Access Journals (Sweden)
Sabria B. Mentri
2007-01-01
Full Text Available In this study, we estimate the resolvent of the two bodies Shrodinger operator perturbed by a potential of Coulombian type on Hilbert space when h tends to zero. Using the Feschbach method, we first distorted it and then reduced it to a diagonal matrix. We considered a case where two energy levels cross in the classical forbidden region. Under the assumption that the second energy level admits a non degenerate point well and virial conditions on the others levels, a good estimate of the resolvent were observed.
THz-Imaging Through-the-Wall Using the Born and Rytov Approximation
2008-12-01
matter. Then we started with Maxwell’s equations to derive a model for the transmission of Green’s functions and used a Lippman- Schwinger integral...in matter. Then we started with Maxwell’s equations to derive a model for the transmission of Green’s functions and used a Lippman- Schwinger ...the inverse problem. The very first equation we need is a Lippman- Schwinger equation [9]. 3( ) ( , ) ( )( ( ) ( ))scatt k inc scattDx G x x x x x d xψ
Modeling and Inversion in the Ocean Waveguide Using Born and Rytov Approximation
1989-09-30
Ph.D. programs at the School of Mines. Last of all, I thank my parents who always believed in me and my husband, Russell, for enduring my manic...G ( r I~ e. = - f 0T0J4 )Jr kr dk, (B.3) Using the relationship between Bessel and Hankel functions T-3790 135 Jo(krro)Jo(krr) = "[ HIjo )(krro) + II
Andrei, R.M.; Smith, C.S.; Fraanje, P.R.; Verhaegen, M.; Korkiakoski, V.A.; Keller, C.U.; Doelman, N.J.
2012-01-01
In this paper we give a new wavefront estimation technique that overcomes the main disadvantages of the phase diversity (PD) algorithms, namely the large computational complexity and the fact that the solutions can get stuck in a local minima. Our approach gives a good starting point for an iterativ
International Conference Approximation Theory XIV
Schumaker, Larry
2014-01-01
This volume developed from papers presented at the international conference Approximation Theory XIV, held April 7–10, 2013 in San Antonio, Texas. The proceedings contains surveys by invited speakers, covering topics such as splines on non-tensor-product meshes, Wachspress and mean value coordinates, curvelets and shearlets, barycentric interpolation, and polynomial approximation on spheres and balls. Other contributed papers address a variety of current topics in approximation theory, including eigenvalue sequences of positive integral operators, image registration, and support vector machines. This book will be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related approximation areas.
Exact constants in approximation theory
Korneichuk, N
1991-01-01
This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base
Generalized eikonal approximation for strong-field ionization
Vélez, F Cajiao; Kamiński, J Z
2015-01-01
We develop the eikonal perturbation theory to describe the strong-field ionization by finite laser pulses. This approach in the first order with respect to the binding potential (the so-called generalized eikonal approximation) avoids a singularity at the potential center. Thus, in contrast to the ordinary eikonal approximation, it allows to treat rescattering phenomena in terms of quantum trajectories. We demonstrate how the first Born approximation and its domain of validity follow from eikonal perturbation theory. Using this approach, we study the coherent diffraction patterns in photoelectron energy spectra and their modifications induced by the interaction of photoelectrons with the atomic potential. Along with these first results, we discuss the prospects of using the generalized eikonal approximation to study strong-field ionization from multi-centered atomic systems and to study other strong-field phenomena.
Genetic Characterization of the Tick-Borne Orbiviruses
Directory of Open Access Journals (Sweden)
Manjunatha N. Belaganahalli
2015-04-01
Full Text Available The International Committee for Taxonomy of Viruses (ICTV recognizes four species of tick-borne orbiviruses (TBOs: Chenuda virus, Chobar Gorge virus, Wad Medani virus and Great Island virus (genus Orbivirus, family Reoviridae. Nucleotide (nt and amino acid (aa sequence comparisons provide a basis for orbivirus detection and classification, however full genome sequence data were only available for the Great Island virus species. We report representative genome-sequences for the three other TBO species (virus isolates: Chenuda virus (CNUV; Chobar Gorge virus (CGV and Wad Medani virus (WMV. Phylogenetic comparisons show that TBOs cluster separately from insect-borne orbiviruses (IBOs. CNUV, CGV, WMV and GIV share low level aa/nt identities with other orbiviruses, in ‘conserved’ Pol, T2 and T13 proteins/genes, identifying them as four distinct virus-species. The TBO genome segment encoding cell attachment, outer capsid protein 1 (OC1, is approximately half the size of the equivalent segment from insect-borne orbiviruses, helping to explain why tick-borne orbiviruses have a ~1 kb smaller genome.
Relativistic electronic dressing in laser-assisted ionization of atomic hydrogen by electron impact
Attaourti, Y
2004-01-01
Within the framework of the coplanar binary geometry where it is justified to use plane wave solutions for the study of the $(e,2e)$ reaction and in the presence of a circularly polarized laser field, we introduce as a first step the DVRPWBA1 (Dirac-Volkov Plane Wave Born Approximation1) where we take into account only the relativistic dressing of the incident and scattered electrons. Then, we introduce the DVRPWBA2 (Dirac-Volkov Plane Wave Born Approximation2) where we take totally into account the relativistic dressing of the incident, scattered and ejected electrons. We then compare the corresponding triple differential cross sections for laser-assisted ionization of atomic hydrogen by electron impact both for the non relativistic and the relativistic regime.
Detection of Water Borne Protozoa
DEFF Research Database (Denmark)
Al-Sabi, Mohammad Nafi Solaiman; Enemark, Heidi L.; Kurtzhals, J.A.L.
Protozoa of several species play a key role in water borne outbreaks of diarrhea worldwide. Identification of such protozoa depends mainly on parasite detection. However, water contains several hundreds of thousands of microorganisms belonging to different taxa. The exact identification...... of pathogenic protozoa relies on selective isolation and detection that is conducted by experienced technicians. Advanced techniques such as immuno-fluorescent dyes, polymerase chain reaction, and many other techniques, may be used for species-specific identification of pathogenic protozoa. Each diagnostic...... parasitic protozoa from other organisms in the aquatic environment....
Institute of Scientific and Technical Information of China (English)
1997-01-01
WITH 38 years of history, the Beijing Maternity Hospital gained fame as the birthplace of one-fifth of all Beijingers in the 1960s. Today, some 5,000 babies are born here each year. As Beijing’s oldest hospital specializing in gynaecology and obstetrics treatment and research, the Beijing Maternity Hospital ranks top among all maternity hospitals in China. Chen Wenshan. 52. oversees 272 nurses working at BMH. A vigorous and extremely strict woman. Chen is both respected and feared by the nurses on her staff. As the director of the Nursing
Detection of Water Borne Protozoa
DEFF Research Database (Denmark)
Al-Sabi, Mohammad Nafi Solaiman; Enemark, Heidi L.; Kurtzhals, J.A.L.
Protozoa of several species play a key role in water borne outbreaks of diarrhea worldwide. Identification of such protozoa depends mainly on parasite detection. However, water contains several hundreds of thousands of microorganisms belonging to different taxa. The exact identification...... of pathogenic protozoa relies on selective isolation and detection that is conducted by experienced technicians. Advanced techniques such as immuno-fluorescent dyes, polymerase chain reaction, and many other techniques, may be used for species-specific identification of pathogenic protozoa. Each diagnostic...... parasitic protozoa from other organisms in the aquatic environment....
BDD Minimization for Approximate Computing
Soeken, Mathias; Grosse, Daniel; Chandrasekharan, Arun; Drechsler, Rolf
2016-01-01
We present Approximate BDD Minimization (ABM) as a problem that has application in approximate computing. Given a BDD representation of a multi-output Boolean function, ABM asks whether there exists another function that has a smaller BDD representation but meets a threshold w.r.t. an error metric. We present operators to derive approximated functions and present algorithms to exactly compute the error metrics directly on the BDD representation. An experimental evaluation demonstrates the app...
Parallel Multi-Focusing Using Plane Wave Decomposition
DEFF Research Database (Denmark)
Misaridis, Thanassis; Munk, Peter; Jensen, Jørgen Arendt
2003-01-01
of the transmitted pulses is based on the directivity spectrum method, a generalization of the angular spectrum method, a generalization of the angular spectrum method, containing no evanescent waves. The underlying theory is based on the Fourier slice theorem, and field reconstruction from projections. First a set...... waves result in one time function per element. The numerical solution is presented and discussed. It contains pulses with a variation in central frequency and time-varying apodization across the aperture (dynamic apodization). The RMS difference between the transmitted field using the calculated pulse......In conventional phased-array imaging, identical short single-carrier pulses are emitted from the entire aperture, and focusing is done in one direction at a time by applying simple geometric delays. This is a sequential and not optimal transmission scheme, which limits the frame rate and makes 3D...
Characteristics of Plane Wave Propagation in Biaxially Anisotropic Gyrotropic Media
Institute of Scientific and Technical Information of China (English)
PAN Wei-Tao; LIU Song-Hua; QIU Zhi-Liang
2012-01-01
Propagation characteristics of electromagnetic waves at the interface between an isotropic regular medium and a biaxially anisotropic gyrotropic medium are investigated.The results indicate that the reflection and refract ionproperties of electromagnetic waves are closely dependent on the dispersion relation of the gyrotropic media,and that anomalous total reflection and negative refraction may occur.The existence conditions of total transmission are also considered.It is found that total transmission arises when the TE-polarized incident waves are normal to the interface and the physical parameters of the two media are chosen properly,which are quite different from the existence conditions of total transmission at the anisotropic left-handed material interface.Numerical resul tsare given to validate our theoretical analysis.
Plane-wave decomposition by spherical-convolution microphone array
Rafaely, Boaz; Park, Munhum
2001-05-01
Reverberant sound fields are widely studied, as they have a significant influence on the acoustic performance of enclosures in a variety of applications. For example, the intelligibility of speech in lecture rooms, the quality of music in auditoria, the noise level in offices, and the production of 3D sound in living rooms are all affected by the enclosed sound field. These sound fields are typically studied through frequency response measurements or statistical measures such as reverberation time, which do not provide detailed spatial information. The aim of the work presented in this seminar is the detailed analysis of reverberant sound fields. A measurement and analysis system based on acoustic theory and signal processing, designed around a spherical microphone array, is presented. Detailed analysis is achieved by decomposition of the sound field into waves, using spherical Fourier transform and spherical convolution. The presentation will include theoretical review, simulation studies, and initial experimental results.
A pulsed electron gun for the Plane Wave Transformer Linac
Mahadevan, S; Nandedkar, R V
2003-01-01
A pulsed diode electron gun delivering 500 mA current at 40 kV is described. The gun geometry is optimized using the Electron Trajectory Program EGUN at higher scaling factors by choosing the closest converging starting surface. The effect of an annular gap between cathode and focusing electrode on beam behaviour is compensated by using a suitable focusing electrode. The estimated perveance is 0.065 mu perv and the normalized emittance is within 5 pi mm mrad. The variation in current density at the cathode has been limited to within 10% across the face of the cathode. Salient features of the pulsed power supply and an insight of its interconnection with the gun are presented. The current measured at the Faraday cup is in agreement with the designed perveance.
Propagation of plane waves in poroviscoelastic anisotropic media
Institute of Scientific and Technical Information of China (English)
A.K.Vashishth,M.D.Sharma
2008-01-01
This study discusses wave propagation in perhaps the most general model of a poroelastic medium.The medium is considered as a viscoelastic,anisotropic and porous solid frame such that its pores of anisotropic permeability are filled with a viscous fluid.The anisotropy considered is of general type,and the attenuating waves in the medium are treated as the inhomogeneous waves.The complex slowness vector is resolved to define the phase velocity,homogeneous attenuation,inhomogeneous attenuation,and angle of attenuation for each of the four attenuating waves in the medium.A non-dimensional parameter measures the deviation of an inhomogeneous wave from its homogeneous version.An numerical model of a North-Sea sandstone is used to analyze the effects of the propagation direction,inhomogeneity parameter,frequency regime,anisotropy symmetry,anelasticity of the frame,and viscosity of the pore-fluid on the propagation characteristics of waves in such a medium.
Inverse problems and inverse scattering of plane waves
Ghosh Roy, Dilip N
2001-01-01
The purpose of this text is to present the theory and mathematics of inverse scattering, in a simple way, to the many researchers and professionals who use it in their everyday research. While applications range across a broad spectrum of disciplines, examples in this text will focus primarly, but not exclusively, on acoustics. The text will be especially valuable for those applied workers who would like to delve more deeply into the fundamentally mathematical character of the subject matter.Practitioners in this field comprise applied physicists, engineers, and technologists, whereas the theory is almost entirely in the domain of abstract mathematics. This gulf between the two, if bridged, can only lead to improvement in the level of scholarship in this highly important discipline. This is the book''s primary focus.
Plane-wave decomposition by spherical-convolution microphone array
Rafaely, Boaz; Park, Munhum
2004-05-01
Reverberant sound fields are widely studied, as they have a significant influence on the acoustic performance of enclosures in a variety of applications. For example, the intelligibility of speech in lecture rooms, the quality of music in auditoria, the noise level in offices, and the production of 3D sound in living rooms are all affected by the enclosed sound field. These sound fields are typically studied through frequency response measurements or statistical measures such as reverberation time, which do not provide detailed spatial information. The aim of the work presented in this seminar is the detailed analysis of reverberant sound fields. A measurement and analysis system based on acoustic theory and signal processing, designed around a spherical microphone array, is presented. Detailed analysis is achieved by decomposition of the sound field into waves, using spherical Fourier transform and spherical convolution. The presentation will include theoretical review, simulation studies, and initial experimental results.
Causality and conjugate points in general plane waves
Energy Technology Data Exchange (ETDEWEB)
Flores, J L; Sanchez, M [Departamento de Geometria y Topologia, Facultad de Ciencias, Universidad de Granada, Avenida Fuentenueva s/n, 18071 Granada (Spain)
2003-06-07
Let M = M{sub 0} x R{sup 2} be a pp-wave-type spacetime endowed with the metric ({center_dot}, {center_dot}){sub z} = ({center_dot}, {center_dot}){sub x} + 2 du dv + H(x, u) du{sup 2}, where (M{sub 0}, ({center_dot}, {center_dot}){sub x}) is any Riemannian manifold and H(x, u) is an arbitrary function. We show that the behaviour of H(x, u) at spatial infinity determines the causality of M, say: (a) if -H(x, u) behaves subquadratically (i.e, essentially -H(x, u) {<=} R{sub 1}(u)|x|{sup 2-{epsilon}} for some {epsilon} > 0 and large distance |x| to a fixed point) and the spatial part (M{sub 0}, ({center_dot}, {center_dot}){sub x}) is complete, then the spacetime M is globally hyperbolic, (b) if -H(x, u) grows at most quadratically (i.e, -H(x, u) {<=} R{sub 1}(u)|x|{sup 2} for large |x|) then it is strongly causal and (c) M is always causal, but there are non-distinguishing examples (and thus, not strongly causal), even when -H(x, u) {<=} R{sub 1}(u)|x|{sup 2+{epsilon}}, for small {epsilon} > 0. Therefore, the classical model M{sub 0} = R{sup 2}, H(x, u) = {sigma}{sub i,j} h{sub ij}(u)x{sub i}x{sub j} {ne} 0), which is known to be strongly causal but not globally hyperbolic, lies in the critical quadratic situation with complete M{sub 0}. This must be taken into account for realistic applications. In fact, we argue that -H will be subquadratic (and the spacetime globally hyperbolic) if M is asymptotically flat. The relation of these results with the notion of astigmatic conjugacy and the existence of conjugate points is also discussed.
Acoustic plane wave reflection from a composite laminate: normal incidence
Bagchi, A.; Bose, S.K.
1994-01-01
In using ultrasonic non-destructive evaluation methods for composite laminates, some features appear which are essentially due to the heterogeneity of the material. In performing backscattering phenomena, one such feature is the seemingly random backscattered amplitude with change of position in a c
Tree wavelet approximations with applications
Institute of Scientific and Technical Information of China (English)
XU Yuesheng; ZOU Qingsong
2005-01-01
We construct a tree wavelet approximation by using a constructive greedy scheme(CGS). We define a function class which contains the functions whose piecewise polynomial approximations generated by the CGS have a prescribed global convergence rate and establish embedding properties of this class. We provide sufficient conditions on a tree index set and on bi-orthogonal wavelet bases which ensure optimal order of convergence for the wavelet approximations encoded on the tree index set using the bi-orthogonal wavelet bases. We then show that if we use the tree index set associated with the partition generated by the CGS to encode a wavelet approximation, it gives optimal order of convergence.
We have "born digital" - now what about "born semantic"?
Leadbetter, Adam; Fredericks, Janet
2014-05-01
The phrase "born-digital" refers to those materials which originate in a digital form. In Earth and Space Sciences, this is now very much the norm for data: analogue to digital converters sit on instrument boards and produce a digital record of the observed environment. While much effort has been put in to creating and curating these digital data, there has been little work on using semantic mark up of data from the point of collection - what we term 'born semantic'. In this presentation we report on two efforts to expand this area: Qartod-to-OGC (Q2O) and SenseOCEAN. These projects have taken a common approach to 'born semantic': create or reuse appropriate controlled vocabularies, published to World Wide Web Commission (W3C) standards use standards from the Open Geospatial Consortium's Sensor Web Enablement (SWE) initiative to describe instrument setup, deployment and/or outputs using terms from those controlled vocabularies embed URLs from the controlled vocabularies within the SWE documents in a "Linked Data" conformant approach Q2O developed best practices examples of SensorML descriptions of Original Equipment Manufacturers' metadata (model characteristics, capabilities, manufacturer contact, etc ...) set-up and deployment SensorML files; and data centre process-lineage using registered vocabularies to describe terms (including input, output, processes, parameters, quality control flags) One Q2O use case, the Martha's Vineyard Coastal Observatory ADCP Waves instance, uses SensorML and registered vocabularies to fully describe the process of computing wave parameters from sensed properties, including quality control tests and associated results. The European Commission Framework Programme 7 project SenseOCEAN draws together world leading marine sensor developers to create a highly integrated multifunction and cost-effective in situ marine biogeochemical sensor system. This project will provide a quantum leap in the ability to measure crucial biogeochemical
Diophantine approximation and automorphic spectrum
Ghosh, Anish; Nevo, Amos
2010-01-01
The present paper establishes qunatitative estimates on the rate of diophantine approximation in homogeneous varieties of semisimple algebraic groups. The estimates established generalize and improve previous ones, and are sharp in a number of cases. We show that the rate of diophantine approximation is controlled by the spectrum of the automorphic representation, and is thus subject to the generalised Ramanujan conjectures.
Some results in Diophantine approximation
DEFF Research Database (Denmark)
the basic concepts on which the papers build. Among other it introduces metric Diophantine approximation, Mahler’s approach on algebraic approximation, the Hausdorff measure, and properties of the formal Laurent series over Fq. The introduction ends with a discussion on Mahler’s problem when considered...
Beyond the random phase approximation
DEFF Research Database (Denmark)
Olsen, Thomas; Thygesen, Kristian S.
2013-01-01
We assess the performance of a recently proposed renormalized adiabatic local density approximation (rALDA) for ab initio calculations of electronic correlation energies in solids and molecules. The method is an extension of the random phase approximation (RPA) derived from time-dependent density...
Uniform approximation by (quantum) polynomials
Drucker, A.; de Wolf, R.
2011-01-01
We show that quantum algorithms can be used to re-prove a classical theorem in approximation theory, Jackson's Theorem, which gives a nearly-optimal quantitative version of Weierstrass's Theorem on uniform approximation of continuous functions by polynomials. We provide two proofs, based respectivel
Global approximation of convex functions
Azagra, D
2011-01-01
We show that for every (not necessarily bounded) open convex subset $U$ of $\\R^n$, every (not necessarily Lipschitz or strongly) convex function $f:U\\to\\R$ can be approximated by real analytic convex functions, uniformly on all of $U$. In doing so we provide a technique which transfers results on uniform approximation on bounded sets to results on uniform approximation on unbounded sets, in such a way that not only convexity and $C^k$ smoothness, but also local Lipschitz constants, minimizers, order, and strict or strong convexity, are preserved. This transfer method is quite general and it can also be used to obtain new results on approximation of convex functions defined on Riemannian manifolds or Banach spaces. We also provide a characterization of the class of convex functions which can be uniformly approximated on $\\R^n$ by strongly convex functions.
Approximate circuits for increased reliability
Energy Technology Data Exchange (ETDEWEB)
Hamlet, Jason R.; Mayo, Jackson R.
2015-08-18
Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.
Approximate circuits for increased reliability
Energy Technology Data Exchange (ETDEWEB)
Hamlet, Jason R.; Mayo, Jackson R.
2015-12-22
Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.
Dirac-Born-Infeld Field Trapped in the Braneworld
Garcia-Salcedo, Ricardo; Gonzalez, Tame; Moreno, Claudia; Quiros, Israel
2009-01-01
We apply the dynamical systems tools to study the (linear) cosmic dynamics of a Dirac-Born-Infeld-type field trapped in the braneworld. We focus, exclusively, in Randall-Sundrum and in Dvali-Gabadadze-Porrati brane models. We analyze the existence and stability of asymptotic solutions for the AdS throat and the quadratic potential. It is demonstrated, in particular, that in the ultra-relativistic approximation matter-scaling and scalar field-dominated solutions always arise. In the first scenario the empty universe is the past attractor, while in the second model the past attractor is the matter-dominated phase. Chaotic behaviour of the probe trajectories in the phase space -- originated by the non-linear effects of the Dirac-Born-Infeld field -- is appreciable at late times. These non-linear effects conspire against infra-red modifications of the late-time cosmic dynamics.
Freeman, Simon E; D'Spain, Gerald L; Lynch, Stephen D; Stephen, Ralph A; Heaney, Kevin D; Murray, James J; Baggeroer, Arthur B; Worcester, Peter F; Dzieciuch, Matthew A; Mercer, James A
2013-10-01
Conventional and adaptive plane-wave beamforming with simultaneous recordings by large-aperture horizontal and vertical line arrays during the 2009 Philippine Sea Engineering Test (PhilSea09) reveal the rate of occurrence and the two-dimensional arrival structure of seismic phases that couple into the deep ocean. A ship-deployed, controlled acoustic source was used to evaluate performance of the horizontal array for a range of beamformer adaptiveness levels. Ninety T-phases from unique azimuths were recorded between Yeardays 107 to 119. T-phase azimuth and S-minus-P-phase time-of-arrival range estimates were validated using United States Geological Survey seismic monitoring network data. Analysis of phases from a seismic event that occurred on Yearday 112 near the east coast of Taiwan approximately 450 km from the arrays revealed a 22° clockwise evolution of T-phase azimuth over 90 s. Two hypotheses to explain such evolution-body wave excitation of multiple sources or in-water scattering-are presented based on T-phase origin sites at the intersection of azimuthal great circle paths and ridge/coastal bathymetry. Propagation timing between the source, scattering region, and array position suggests the mechanism behind the evolution involved scattering of the T-phase from the Ryukyu Ridge and a T-phase formation/scattering location estimation error of approximately 3.2 km.
Institute of Scientific and Technical Information of China (English)
张健; 黄雅妮; 龙春光; 邵毅敏; 彭平; 周惦武
2011-01-01
采用基于密度泛函理论的第一性原理赝势平面波方法.考察了Mg空位缺陷对MgH体系解氢性能的影响及微观机理.结果表明:Mg空位缺陷的出现使MgH晶胞发生收缩,晶格产生畸变,且极大地降低了体系的结构稳定性,显著提高了体系的解氢动力学;电子结构分析表明:Mg空位缺陷改善MgH体系解氢性能的微观机理在于体系在费米能级以下成键电子数的减少以及费米能级附近能隙的变窄.%Using the first-principles pseudopotential plane-wave method based on density functional theory, the influences and micro-mechanisms of Mg atom vacancy defect on the dehydrogenation properties of MgH2 system were investigated. The results show that the appearance of Mg atom vacancy results in the shrinkage of crystal cell and distortion of MgH2 lattice, which significantly decreases the structural stability and remarkably improves the dehydrogenation kinetics of this system. Further analysis on electronic structures shows that the mico-mechanisms for Mg atom vacancy improving the dehydrogenation properties of MgH2 attribute to the decreasing bonding electrons number below Fermi energy level and the narrowing energy gap near Fermi energy level of MgH2 system with Mg atom vacancy.
Validity of the nuclear Born-Oppenheimer method
Energy Technology Data Exchange (ETDEWEB)
Zettili, N.; Villars, F.M.H.
1987-07-20
The validity of the adiabatic nuclear Born-Oppenheimer (NBO) approximation method is investigated by means of an analytically solvable model. The NBO equation of collective motion derived, when this method is applied to the model, is shown to have the structure of a Schroedinger equation. The NBO energy spectrum is then obtained by numerical integration of this equation and compared with the analytic energy spectrum. We show that the NBO approximation is very accurate in the description of the system's eigenstates. The time-dependent Hartree-Fock (TDHF) results, obtained in a previous publication for the solvable model, are compared with their NBO counterparts. We find that, although both methods describe the system's states very well, the NBO approximation is more accurate in the adiabatic domain.
Validity of the nuclear Born-Oppenheimer method
Zettili, Nouredine; Villars, Felix M. H.
1987-07-01
The validity of the adiabatic nuclear Born-Oppenheimer (NBO) approximation method is investigated by means of an analytically solvable model. The NBO equation of collective motion derived, when this method is applied to the model, is shown to have the structure of a Schrödinger equation. The NBO energy spectrum is then obtained by numerical integration of this equation and compared with the analytic energy spectrum. We show that the NBO approximation is very accurate in the description of the system's eigenstates. The time-dependent Hartree-Fock (TDHF) results, obtained in a previous publication for the solvable model, are compared with their NBO counterparts. We find that, although both methods describe the system's states very well, the NBO approximation is more accurate in the adiabatic domain.
Born series for the Robin boundary condition
Machida, Manabu; Nakamura, Gen
2017-01-01
We solve the diffusion equation by constructing the Born series for the Robin boundary condition. We develop a general theory for arbitrary domains with smooth enough boundaries and explore the convergence. The proposed Born series is validated by numerical calculation in the three-dimensional half space. We show that in this case the Born series converges regardless the value of the impedance term in the Robin boundary condition. We point out that the solution from the so-called extrapolated...
Conceptualizing Innovation in Born Global Firms
DEFF Research Database (Denmark)
Zijdemans, Erik; Tanev, Stoyan
2014-01-01
This research provides insights from recent literature on innovativeness in the environment of born globals. This article will be relevant to researchers interested in born globals and their business environments and, more specifically, the role that innovation plays in their foundation...... and development. After discussing the internationalization of born globals as an innovation itself and the positive effect that innovation and internationalization have on each other, this article elaborates on the effect of innovativeness on the development of the company and, more in depth, the role...... of knowledge acquisition, networking capabilities and the lean startup approach in born global innovation. Finally, the article addresses the issue of quantifying and measuring innovativeness....
Rytov approximation in electron scattering
Krehl, Jonas; Lubk, Axel
2017-06-01
In this work we introduce the Rytov approximation in the scope of high-energy electron scattering with the motivation of developing better linear models for electron scattering. Such linear models play an important role in tomography and similar reconstruction techniques. Conventional linear models, such as the phase grating approximation, have reached their limits in current and foreseeable applications, most importantly in achieving three-dimensional atomic resolution using electron holographic tomography. The Rytov approximation incorporates propagation effects which are the most pressing limitation of conventional models. While predominately used in the weak-scattering regime of light microscopy, we show that the Rytov approximation can give reasonable results in the inherently strong-scattering regime of transmission electron microscopy.
Rollout sampling approximate policy iteration
Dimitrakakis, C.; Lagoudakis, M.G.
2008-01-01
Several researchers have recently investigated the connection between reinforcement learning and classification. We are motivated by proposals of approximate policy iteration schemes without value functions, which focus on policy representation using classifiers and address policy learning as a
Approximate common divisors via lattices
Cohn, Henry
2011-01-01
We analyze the multivariate generalization of Howgrave-Graham's algorithm for the approximate common divisor problem. In the m-variable case with modulus N and approximate common divisor of size N^beta, this improves the size of the error tolerated from N^(beta^2) to N^(beta^((m+1)/m)), under a commonly used heuristic assumption. This gives a more detailed analysis of the hardness assumption underlying the recent fully homomorphic cryptosystem of van Dijk, Gentry, Halevi, and Vaikuntanathan. While these results do not challenge the suggested parameters, a 2^sqrt(n) approximation algorithm for lattice basis reduction in n dimensions could be used to break these parameters. We have implemented our algorithm, and it performs better in practice than the theoretical analysis suggests. Our results fit into a broader context of analogies between cryptanalysis and coding theory. The multivariate approximate common divisor problem is the number-theoretic analogue of noisy multivariate polynomial interpolation, and we ...
Approximate Implicitization Using Linear Algebra
Directory of Open Access Journals (Sweden)
Oliver J. D. Barrowclough
2012-01-01
Full Text Available We consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore well suited to floating-point implementation in computer-aided geometric design (CAGD systems. We unify the approaches under the names of commonly known polynomial basis functions and consider various theoretical and practical aspects of the algorithms. We offer new methods for a least squares approach to approximate implicitization using orthogonal polynomials, which tend to be faster and more numerically stable than some existing algorithms. We propose several simple propositions relating the properties of the polynomial bases to their implicit approximation properties.
Binary nucleation beyond capillarity approximation
Kalikmanov, V.I.
2010-01-01
Large discrepancies between binary classical nucleation theory (BCNT) and experiments result from adsorption effects and inability of BCNT, based on the phenomenological capillarity approximation, to treat small clusters. We propose a model aimed at eliminating both of these deficiencies. Adsorption
Weighted approximation with varying weight
Totik, Vilmos
1994-01-01
A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.
Nonlinear approximation with redundant dictionaries
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, M.; Gribonval, R.
2005-01-01
In this paper we study nonlinear approximation and data representation with redundant function dictionaries. In particular, approximation with redundant wavelet bi-frame systems is studied in detail. Several results for orthonormal wavelets are generalized to the redundant case. In general......, for a wavelet bi-frame system the approximation properties are limited by the number of vanishing moments of the system. In some cases this can be overcome by oversampling, but at a price of replacing the canonical expansion by another linear expansion. Moreover, for special non-oversampled wavelet bi-frames we...... can obtain good approximation properties not restricted by the number of vanishing moments, but again without using the canonical expansion....
Mathematical algorithms for approximate reasoning
Murphy, John H.; Chay, Seung C.; Downs, Mary M.
1988-01-01
Most state of the art expert system environments contain a single and often ad hoc strategy for approximate reasoning. Some environments provide facilities to program the approximate reasoning algorithms. However, the next generation of expert systems should have an environment which contain a choice of several mathematical algorithms for approximate reasoning. To meet the need for validatable and verifiable coding, the expert system environment must no longer depend upon ad hoc reasoning techniques but instead must include mathematically rigorous techniques for approximate reasoning. Popular approximate reasoning techniques are reviewed, including: certainty factors, belief measures, Bayesian probabilities, fuzzy logic, and Shafer-Dempster techniques for reasoning. A group of mathematically rigorous algorithms for approximate reasoning are focused on that could form the basis of a next generation expert system environment. These algorithms are based upon the axioms of set theory and probability theory. To separate these algorithms for approximate reasoning various conditions of mutual exclusivity and independence are imposed upon the assertions. Approximate reasoning algorithms presented include: reasoning with statistically independent assertions, reasoning with mutually exclusive assertions, reasoning with assertions that exhibit minimum overlay within the state space, reasoning with assertions that exhibit maximum overlay within the state space (i.e. fuzzy logic), pessimistic reasoning (i.e. worst case analysis), optimistic reasoning (i.e. best case analysis), and reasoning with assertions with absolutely no knowledge of the possible dependency among the assertions. A robust environment for expert system construction should include the two modes of inference: modus ponens and modus tollens. Modus ponens inference is based upon reasoning towards the conclusion in a statement of logical implication, whereas modus tollens inference is based upon reasoning away
On the approximations of the distribution function of fusion alpha particles
Energy Technology Data Exchange (ETDEWEB)
Bilato, R., E-mail: roberto.bilato@ipp.mpg.de; Brambilla, M.; Poli, E. [Max Planck Institute for Plasma Physics, EURATOM Association, Boltzmannstr. 2, 85748 Garching (Germany)
2014-10-15
The solution of the drift-kinetic equation for fusion-born alpha particles is derived in the limit of dominant parallel streaming, and it is related to the usual slowing-down distribution function. The typical approximations of the fast tail of fusion-born alpha particles are briefly compared and discussed. In particular, approximating the distribution function of fast-alpha particles with an “equivalent” Maxwellian is inaccurate to describe absorption of radio-frequency waves in the ion-cyclotron range of frequencies.
Twisted inhomogeneous Diophantine approximation and badly approximable sets
Harrap, Stephen
2010-01-01
For any real pair i, j geq 0 with i+j=1 let Bad(i, j) denote the set of (i, j)-badly approximable pairs. That is, Bad(i, j) consists of irrational vectors x:=(x_1, x_2) in R^2 for which there exists a positive constant c(x) such that max {||qx_1||^(-i), ||qx_2||^(-j)} > c(x)/q for all q in N. Building on a result of Kurzweil, a new characterization of the set Bad(i, j) in terms of `well-approximable' vectors in the area of `twisted' inhomogeneous Diophantine approximation is established. In addition, it is shown that Bad^x(i, j), the `twisted' inhomogeneous analogue of Bad(i, j), has full Hausdorff dimension 2 when x is chosen from the set Bad(i, j).
Impact of cloud-borne aerosol representation on aerosol direct and indirect effects
Directory of Open Access Journals (Sweden)
S. J. Ghan
2006-01-01
Full Text Available Aerosol particles attached to cloud droplets are much more likely to be removed from the atmosphere and are much less efficient at scattering sunlight than if unattached. Models used to estimate direct and indirect effects of aerosols employ a variety of representations of such cloud-borne particles. Here we use a global aerosol model with a relatively complete treatment of cloud-borne particles to estimate the sensitivity of simulated aerosol, cloud and radiation fields to various approximations to the representation of cloud-borne particles. We find that neglecting transport of cloud-borne particles introduces little error, but that diagnosing cloud-borne particles produces global mean biases of 20% and local errors of up to 40% for aerosol, droplet number, and direct and indirect radiative forcing. Aerosol number, aerosol optical depth and droplet number are significantly underestimated in regions and seasons where and when wet removal is primarily by stratiform rather than convective clouds (polar regions during winter, but direct and indirect effects are less biased because of the limited sunlight there and then. A treatment that predicts the total mass concentration of cloud-borne particles for each mode yields smaller errors and runs 20% faster than the complete treatment. The errors are much smaller than current estimates of uncertainty in direct and indirect effects of aerosols, which suggests that the treatment of cloud-borne aerosol is not a significant source of uncertainty in estimates of direct and indirect effects.
Food-borne parasitic zoonoses in China: perspective for control.
Zhou, Peng; Chen, Ning; Zhang, Ren-Li; Lin, Rui-Qing; Zhu, Xing-Quan
2008-04-01
Food-borne parasitic zoonoses (FBPZs) cause death and serious diseases in humans and animals worldwide, and are of both public health significance and socioeconomic importance. The FBPZ problem is severe in mainland China, where approximately 150 million people are suffering from FBPZs and more people are at risk. Here, the current status of the FBPZ problem in mainland China is reviewed and strategies and measures for effective control of FBPZs are proposed. Major parasitic zoonoses transmitted through consumption of infected or contaminated meat, fish, plants and/or water will be discussed.
3D Born-Infeld gravity and supersymmetry
Bergshoeff, Eric; Ozkan, Mehmet
2014-08-01
We construct the most general parity-even higher-derivative = 1 off-shell supergravity model in three dimensions with a maximum of six derivatives. Excluding terms quadratic in the curvature tensor with two explicit derivatives and requiring the absence of ghosts in a linearized approximation around an AdS3 background, we find that there is a unique supersymmetric invariant which we call supersymmetric `cubic extended' New Massive Gravity. The purely gravitational part of this invariant is in agreement with an earlier analysis based upon the holographic c-theorem and coincides with an expansion of Born-Infeld gravity to the required order.
A Recursive Born Approach to Nonlinear Inverse Scattering
Kamilov, Ulugbek S; Mansour, Hassan; Boufounos, Petros T
2016-01-01
The Iterative Born Approximation (IBA) is a well-known method for describing waves scattered by semi-transparent objects. In this paper, we present a novel nonlinear inverse scattering method that combines IBA with an edge-preserving total variation (TV) regularizer. The proposed method is obtained by relating iterations of IBA to layers of a feedforward neural network and developing a corresponding error backpropagation algorithm for efficiently estimating the permittivity of the object. Simulations illustrate that, by accounting for multiple scattering, the method successfully recovers the permittivity distribution where the traditional linear inverse scattering fails.
Non-abelian Born-Infeld revisited
Roo, M. de
2002-01-01
We discuss the non-abelian Born-Infeld action, including fermions, as a series in Î±'. We review recent work establishing the complete result to Î±'2, and its impact on our earlier attempts to derive the Born-Infeld action using Îº-symmetry.
Thermodynamics of Born-Infeld black holes
Chemissany, Wissam A.; de Roo, Mees; Panda, Sudhakar
2008-01-01
We discuss the horizon structure for Born-Infeld black holes in the context of Einstein-Born-Infeld gravity. We show that the entropy function formalism agrees with a direct calculation of the entropy. With the entropy function formalism we also obtain the entropy when an axion-dilaton system as wel
Literacy Skills of Children Born Preterm
Holm, Alison; Crosbie, Sharon
2010-01-01
Most children born preterm are considered neurologically normal and free of disability. However in follow-up studies at school age, preterm children, born without major impairment, have been shown to have lower cognitive abilities and associated academic, social and behavioural difficulties. This study investigated the literacy, phonological…
Literacy Skills of Children Born Preterm
Holm, Alison; Crosbie, Sharon
2010-01-01
Most children born preterm are considered neurologically normal and free of disability. However in follow-up studies at school age, preterm children, born without major impairment, have been shown to have lower cognitive abilities and associated academic, social and behavioural difficulties. This study investigated the literacy, phonological…
PEOPLE BORN IN AUTUMN LIVE LONGER
Institute of Scientific and Technical Information of China (English)
张梦华
2004-01-01
People born in the autumn live longer an those born in the spring and are less likely to fall chronically ill when they are older,according to an Austrian scientist.Using census data for more than one million people in Austria,Denmark and Australia,scien-
MANAGEMENT OF ENDOCRINE DISEASE: Growth and growth hormone therapy in short children born preterm.
Boguszewski, Margaret Cristina da Silva; Cardoso-Demartini, Adriane de Andre
2017-03-01
Approximately 15 million babies are born preterm across the world every year, with less than 37 completed weeks of gestation. Survival rates increased during the last decades with the improvement of neonatal care. With premature birth, babies are deprived of the intense intrauterine growth phase, and postnatal growth failure might occur. Some children born prematurely will remain short at later ages and adult life. The risk of short stature increases if the child is also born small for gestational age. In this review, the effects of being born preterm on childhood growth and adult height and the hormonal abnormalities possibly associated with growth restriction are discussed, followed by a review of current information on growth hormone treatment for those who remain with short stature during infancy and childhood.
Reinforcement Learning via AIXI Approximation
Veness, Joel; Hutter, Marcus; Silver, David
2010-01-01
This paper introduces a principled approach for the design of a scalable general reinforcement learning agent. This approach is based on a direct approximation of AIXI, a Bayesian optimality notion for general reinforcement learning agents. Previously, it has been unclear whether the theory of AIXI could motivate the design of practical algorithms. We answer this hitherto open question in the affirmative, by providing the first computationally feasible approximation to the AIXI agent. To develop our approximation, we introduce a Monte Carlo Tree Search algorithm along with an agent-specific extension of the Context Tree Weighting algorithm. Empirically, we present a set of encouraging results on a number of stochastic, unknown, and partially observable domains.
Approximate Matching of Hierarchial Data
DEFF Research Database (Denmark)
Augsten, Nikolaus
The goal of this thesis is to design, develop, and evaluate new methods for the approximate matching of hierarchical data represented as labeled trees. In approximate matching scenarios two items should be matched if they are similar. Computing the similarity between labeled trees is hard...... as in addition to the data values also the structure must be considered. A well-known measure for comparing trees is the tree edit distance. It is computationally expensive and leads to a prohibitively high run time. Our solution for the approximate matching of hierarchical data are pq-grams. The pq...... formally proof that the pq-gram index can be incrementally updated based on the log of edit operations without reconstructing intermediate tree versions. The incremental update is independent of the data size and scales to a large number of changes in the data. We introduce windowed pq...
Concept Approximation between Fuzzy Ontologies
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Fuzzy ontologies are efficient tools to handle fuzzy and uncertain knowledge on the semantic web; but there are heterogeneity problems when gaining interoperability among different fuzzy ontologies. This paper uses concept approximation between fuzzy ontologies based on instances to solve the heterogeneity problems. It firstly proposes an instance selection technology based on instance clustering and weighting to unify the fuzzy interpretation of different ontologies and reduce the number of instances to increase the efficiency. Then the paper resolves the problem of computing the approximations of concepts into the problem of computing the least upper approximations of atom concepts. It optimizes the search strategies by extending atom concept sets and defining the least upper bounds of concepts to reduce the searching space of the problem. An efficient algorithm for searching the least upper bounds of concept is given.
Approximating Graphic TSP by Matchings
Mömke, Tobias
2011-01-01
We present a framework for approximating the metric TSP based on a novel use of matchings. Traditionally, matchings have been used to add edges in order to make a given graph Eulerian, whereas our approach also allows for the removal of certain edges leading to a decreased cost. For the TSP on graphic metrics (graph-TSP), the approach yields a 1.461-approximation algorithm with respect to the Held-Karp lower bound. For graph-TSP restricted to a class of graphs that contains degree three bounded and claw-free graphs, we show that the integrality gap of the Held-Karp relaxation matches the conjectured ratio 4/3. The framework allows for generalizations in a natural way and also leads to a 1.586-approximation algorithm for the traveling salesman path problem on graphic metrics where the start and end vertices are prespecified.
Diophantine approximation and Dirichlet series
Queffélec, Hervé
2013-01-01
This self-contained book will benefit beginners as well as researchers. It is devoted to Diophantine approximation, the analytic theory of Dirichlet series, and some connections between these two domains, which often occur through the Kronecker approximation theorem. Accordingly, the book is divided into seven chapters, the first three of which present tools from commutative harmonic analysis, including a sharp form of the uncertainty principle, ergodic theory and Diophantine approximation to be used in the sequel. A presentation of continued fraction expansions, including the mixing property of the Gauss map, is given. Chapters four and five present the general theory of Dirichlet series, with classes of examples connected to continued fractions, the famous Bohr point of view, and then the use of random Dirichlet series to produce non-trivial extremal examples, including sharp forms of the Bohnenblust-Hille theorem. Chapter six deals with Hardy-Dirichlet spaces, which are new and useful Banach spaces of anal...
Approximation methods in probability theory
Čekanavičius, Vydas
2016-01-01
This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function. Emphasising the correct usage of the methods presented, each step required for the proofs is examined in detail. As a result, this textbook provides valuable tools for proving approximation theorems. While Approximation Methods in Probability Theory will appeal to everyone interested in limit theorems of probability theory, the book is particularly aimed at graduate students who have completed a standard intermediate course in probability theory. Furthermore, experienced researchers wanting to enlarge their toolkit will also find this book useful.
Approximate Sparse Regularized Hyperspectral Unmixing
Directory of Open Access Journals (Sweden)
Chengzhi Deng
2014-01-01
Full Text Available Sparse regression based unmixing has been recently proposed to estimate the abundance of materials present in hyperspectral image pixel. In this paper, a novel sparse unmixing optimization model based on approximate sparsity, namely, approximate sparse unmixing (ASU, is firstly proposed to perform the unmixing task for hyperspectral remote sensing imagery. And then, a variable splitting and augmented Lagrangian algorithm is introduced to tackle the optimization problem. In ASU, approximate sparsity is used as a regularizer for sparse unmixing, which is sparser than l1 regularizer and much easier to be solved than l0 regularizer. Three simulated and one real hyperspectral images were used to evaluate the performance of the proposed algorithm in comparison to l1 regularizer. Experimental results demonstrate that the proposed algorithm is more effective and accurate for hyperspectral unmixing than state-of-the-art l1 regularizer.
Transfinite Approximation of Hindman's Theorem
Beiglböck, Mathias
2010-01-01
Hindman's Theorem states that in any finite coloring of the integers, there is an infinite set all of whose finite sums belong to the same color. This is much stronger than the corresponding finite form, stating that in any finite coloring of the integers there are arbitrarily long finite sets with the same property. We extend the finite form of Hindman's Theorem to a "transfinite" version for each countable ordinal, and show that Hindman's Theorem is equivalent to the appropriate transfinite approximation holding for every countable ordinal. We then give a proof of Hindman's Theorem by directly proving these transfinite approximations.
Tree wavelet approximations with applications
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
[1]Baraniuk, R. G., DeVore, R. A., Kyriazis, G., Yu, X. M., Near best tree approximation, Adv. Comput. Math.,2002, 16: 357-373.[2]Cohen, A., Dahmen, W., Daubechies, I., DeVore, R., Tree approximation and optimal encoding, Appl. Comput.Harmonic Anal., 2001, 11: 192-226.[3]Dahmen, W., Schneider, R., Xu, Y., Nonlinear functionals of wavelet expansions-adaptive reconstruction and fast evaluation, Numer. Math., 2000, 86: 49-101.[4]DeVore, R. A., Nonlinear approximation, Acta Numer., 1998, 7: 51-150.[5]Davis, G., Mallat, S., Avellaneda, M., Adaptive greedy approximations, Const. Approx., 1997, 13: 57-98.[6]DeVore, R. A., Temlyakov, V. N., Some remarks on greedy algorithms, Adv. Comput. Math., 1996, 5: 173-187.[7]Kashin, B. S., Temlyakov, V. N., Best m-term approximations and the entropy of sets in the space L1, Mat.Zametki (in Russian), 1994, 56: 57-86.[8]Temlyakov, V. N., The best m-term approximation and greedy algorithms, Adv. Comput. Math., 1998, 8:249-265.[9]Temlyakov, V. N., Greedy algorithm and m-term trigonometric approximation, Constr. Approx., 1998, 14:569-587.[10]Hutchinson, J. E., Fractals and self similarity, Indiana. Univ. Math. J., 1981, 30: 713-747.[11]Binev, P., Dahmen, W., DeVore, R. A., Petruchev, P., Approximation classes for adaptive methods, Serdica Math.J., 2002, 28: 1001-1026.[12]Gilbarg, D., Trudinger, N. S., Elliptic Partial Differential Equations of Second Order, Berlin: Springer-Verlag,1983.[13]Ciarlet, P. G., The Finite Element Method for Elliptic Problems, New York: North Holland, 1978.[14]Birman, M. S., Solomiak, M. Z., Piecewise polynomial approximation of functions of the class Wαp, Math. Sb.,1967, 73: 295-317.[15]DeVore, R. A., Lorentz, G. G., Constructive Approximation, New York: Springer-Verlag, 1993.[16]DeVore, R. A., Popov, V., Interpolation of Besov spaces, Trans. Amer. Math. Soc., 1988, 305: 397-414.[17]Devore, R., Jawerth, B., Popov, V., Compression of wavelet decompositions, Amer. J. Math., 1992, 114: 737-785.[18]Storozhenko, E
Adiabatic electronic flux density: a Born-Oppenheimer Broken Symmetry ansatz
Pohl, Vincent
2016-01-01
The Born-Oppenheimer approximation leads to the counterintuitive result of a vanishing electronic flux density upon vibrational dynamics in the electronic ground state. To circumvent this long known issue, we propose using pairwise anti-symmetrically translated vibronic densities to generate a symmetric electronic density that can be forced to satisfy the continuity equation approximately. The so-called Born-Oppenheimer broken symmetry ansatz yields all components of the flux density simultaneously while requiring only knowledge about the nuclear quantum dynamics on the electronic adiabatic ground state potential energy surface. The underlying minimization procedure is transparent and computationally inexpensive, and the solution can be computed from the standard output of any quantum chemistry program. Taylor series expansion reveals that the implicit electron dynamics originates from non-adiabatic coupling to the explicit Born-Oppenheimer nuclear dynamics. The new approach is applied to the ${\\rm H}_2^+$ mo...
WKB Approximation in Noncommutative Gravity
Directory of Open Access Journals (Sweden)
Maja Buric
2007-12-01
Full Text Available We consider the quasi-commutative approximation to a noncommutative geometry defined as a generalization of the moving frame formalism. The relation which exists between noncommutativity and geometry is used to study the properties of the high-frequency waves on the flat background.
Approximation properties of haplotype tagging
Directory of Open Access Journals (Sweden)
Dreiseitl Stephan
2006-01-01
Full Text Available Abstract Background Single nucleotide polymorphisms (SNPs are locations at which the genomic sequences of population members differ. Since these differences are known to follow patterns, disease association studies are facilitated by identifying SNPs that allow the unique identification of such patterns. This process, known as haplotype tagging, is formulated as a combinatorial optimization problem and analyzed in terms of complexity and approximation properties. Results It is shown that the tagging problem is NP-hard but approximable within 1 + ln((n2 - n/2 for n haplotypes but not approximable within (1 - ε ln(n/2 for any ε > 0 unless NP ⊂ DTIME(nlog log n. A simple, very easily implementable algorithm that exhibits the above upper bound on solution quality is presented. This algorithm has running time O((2m - p + 1 ≤ O(m(n2 - n/2 where p ≤ min(n, m for n haplotypes of size m. As we show that the approximation bound is asymptotically tight, the algorithm presented is optimal with respect to this asymptotic bound. Conclusion The haplotype tagging problem is hard, but approachable with a fast, practical, and surprisingly simple algorithm that cannot be significantly improved upon on a single processor machine. Hence, significant improvement in computatational efforts expended can only be expected if the computational effort is distributed and done in parallel.
Truthful approximations to range voting
DEFF Research Database (Denmark)
Filos-Ratsika, Aris; Miltersen, Peter Bro
We consider the fundamental mechanism design problem of approximate social welfare maximization under general cardinal preferences on a finite number of alternatives and without money. The well-known range voting scheme can be thought of as a non-truthful mechanism for exact social welfare...
Approximate Reasoning with Fuzzy Booleans
Broek, van den P.M.; Noppen, J.A.R.
2004-01-01
This paper introduces, in analogy to the concept of fuzzy numbers, the concept of fuzzy booleans, and examines approximate reasoning with the compositional rule of inference using fuzzy booleans. It is shown that each set of fuzzy rules is equivalent to a set of fuzzy rules with singleton crisp ante
Ultrafast Approximation for Phylogenetic Bootstrap
Bui Quang Minh, [No Value; Nguyen, Thi; von Haeseler, Arndt
2013-01-01
Nonparametric bootstrap has been a widely used tool in phylogenetic analysis to assess the clade support of phylogenetic trees. However, with the rapidly growing amount of data, this task remains a computational bottleneck. Recently, approximation methods such as the RAxML rapid bootstrap (RBS) and
On badly approximable complex numbers
DEFF Research Database (Denmark)
Esdahl-Schou, Rune; Kristensen, S.
We show that the set of complex numbers which are badly approximable by ratios of elements of , where has maximal Hausdorff dimension. In addition, the intersection of these sets is shown to have maximal dimension. The results remain true when the sets in question are intersected with a suitably...