Analytical approximations for the amplitude and period of a relaxation oscillator

Directory of Open Access Journals (Sweden)

Golkhou Vahid

2009-01-01

Full Text Available Abstract Background Analysis and design of complex systems benefit from mathematically tractable models, which are often derived by approximating a nonlinear system with an effective equivalent linear system. Biological oscillators with coupled positive and negative feedback loops, termed hysteresis or relaxation oscillators, are an important class of nonlinear systems and have been the subject of comprehensive computational studies. Analytical approximations have identified criteria for sustained oscillations, but have not linked the observed period and phase to compact formulas involving underlying molecular parameters. Results We present, to our knowledge, the first analytical expressions for the period and amplitude of a classic model for the animal circadian clock oscillator. These compact expressions are in good agreement with numerical solutions of corresponding continuous ODEs and for stochastic simulations executed at literature parameter values. The formulas are shown to be useful by permitting quick comparisons relative to a negative-feedback represillator oscillator for noise (10× less sensitive to protein decay rates, efficiency (2× more efficient, and dynamic range (30 to 60 decibel increase. The dynamic range is enhanced at its lower end by a new concentration scale defined by the crossing point of the activator and repressor, rather than from a steady-state expression level. Conclusion Analytical expressions for oscillator dynamics provide a physical understanding for the observations from numerical simulations and suggest additional properties not readily apparent or as yet unexplored. The methods described here may be applied to other nonlinear oscillator designs and biological circuits.

One-loop triple collinear splitting amplitudes in QCD

Energy Technology Data Exchange (ETDEWEB)

Badger, Simon; Buciuni, Francesco; Peraro, Tiziano [Higgs Centre for Theoretical Physics, School of Physics and Astronomy, University of Edinburgh,Edinburgh EH9 3JZ, Scotland (United Kingdom)

2015-09-28

We study the factorisation properties of one-loop scattering amplitudes in the triple collinear limit and extract the universal splitting amplitudes for processes initiated by a gluon. The splitting amplitudes are derived from the analytic Higgs plus four partons amplitudes. We present compact results for primitive helicity splitting amplitudes making use of super-symmetric decompositions. The universality of the collinear factorisation is checked numerically against the full colour six parton squared matrix elements.

Local analyticity properties of the n particle scattering amplitude

CERN Document Server

Bros, J; Glaser, Vladimir Jurko

1972-01-01

The connected part F/sub /c(p) of the scattering amplitude (p/sub 1 /...p/sub /r mod S-1 mod p/sub r+1/,..., p/sub n/) defined on the mass shell p/sub i//sup 2/=m/sub i//sup 2/ and deduced from a local field theory involving only (stable) particles with strictly positive masses can be represented in a suitable neighbourhood of any physical point p as a finite sum f/sub /c(p)= Sigma /sub 1//sup N/F/sub i/(p) of partial amplitudes', each F/sub i/(k) analytic in a certain domain F /sub i/ of the complex mass shell k/sub i//sup 2/=m/sub i//sup 2/. The mentioned real neighbourhood lies on the boundary of each F/sub i/. The above decomposition may fail to hold only at points p where any two incoming or any two outgoing four-momenta become parallel (thresholds). The number N as well as the shape of the domains F/sub i / depend on the number n and on the real neighbourhood considered. For a generic configuration p the intersection of the domains F/sub i/ is empty. When this does not happen, F/sub i/(p) is the boundar...

Full amplitude models of 15 day Cepheids

International Nuclear Information System (INIS)

Cogan, B.C.; Cox, A.N.; King, D.S.

1980-01-01

Numerical models of Cepheids have been computed with a range of effective temperatures and compositions. The amplitudes increase if the helium abundance increases or if the effective temperature decreases. The latter effect is contrary to observational data. The models also exhibit velocity amplitudes which are much lower than those observed

Full colour for loop amplitudes in Yang-Mills theory

Energy Technology Data Exchange (ETDEWEB)

Ochirov, Alexander [Higgs Centre for Theoretical Physics, School of Physics and Astronomy,The University of Edinburgh,Edinburgh EH9 3JZ, Scotland (United Kingdom); Page, Ben [Albert-Ludwigs-Universität Freiburg, Physikalisches Institut,D-79104 Freiburg (Germany)

2017-02-20

We present a general method to account for full colour dependence Yang-Mills amplitudes at loop level. The method fits most naturally into the framework of multi-loop integrand reduction and in a nutshell amounts to consistently retaining the colour structures of the unitarity cuts from which the integrand is gradually constructed. This technique has already been used in the recent calculation of the two-loop five-gluon amplitude in pure Yang-Mills theory with all positive helicities, (DOI: 10.1007/JHEP10(2015)064). In this note, we give a careful exposition of the method and discuss its connection to loop-level Kleiss-Kuijf relations. We also explore its implications for cancellation of nontrivial symmetry factors at two loops. As an example of its generality, we show how it applies to the three-loop case in supersymmetric Yang-Mills case.

Analytic expressions of amplitudes by the cross-ratio identity method

International Nuclear Information System (INIS)

Zhou, Kang

2017-01-01

In order to obtain the analytic expression of an amplitude from a generic CHY-integrand, a new algorithm based on the so-called cross-ratio identities has been proposed recently. In this paper, we apply this new approach to a variety of theories including the non-linear sigma model, special Galileon theory, pure Yang-Mills theory, pure gravity, Born-Infeld theory, Dirac-Born-Infeld theory and its extension, Yang-Mills-scalar theory, and Einstein-Maxwell and Einstein-Yang-Mills theory. CHY-integrands of these theories which contain higher-order poles can be calculated conveniently by using the cross-ratio identity method, and all results above have been verified numerically. (orig.)

Analytic expressions of amplitudes by the cross-ratio identity method

Energy Technology Data Exchange (ETDEWEB)

Zhou, Kang [Zhejiang University, Zhejiang Institute of Modern Physics, Hangzhou (China)

2017-06-15

In order to obtain the analytic expression of an amplitude from a generic CHY-integrand, a new algorithm based on the so-called cross-ratio identities has been proposed recently. In this paper, we apply this new approach to a variety of theories including the non-linear sigma model, special Galileon theory, pure Yang-Mills theory, pure gravity, Born-Infeld theory, Dirac-Born-Infeld theory and its extension, Yang-Mills-scalar theory, and Einstein-Maxwell and Einstein-Yang-Mills theory. CHY-integrands of these theories which contain higher-order poles can be calculated conveniently by using the cross-ratio identity method, and all results above have been verified numerically. (orig.)

Unified treatment: analyticity, Regge trajectories, Veneziano amplitude, fundamental regions and Moebius transformations

International Nuclear Information System (INIS)

Choudhary, A.R.

2003-01-01

In this paper we present a unified treatment that combines the analyticity properties of the scattering amplitudes, the threshold and asymptotic behaviors, the invariance group of Moebius transformations, the automorphic functions defined over this invariance group, the fundamental region in (Poincare) geometry, and the generators of the invariance group as they relate to the fundamental region. Using these concepts and techniques, we provide a theoretical basis for Veneziano type amplitudes with the ghost elimination condition built in, related the Regge trajectory functions to the generators of the invariance group, constrained the values of the Regge trajectories to take only inverse integer values at the threshold, used the threshold behavior in the forward direction to deduce the Pomeranchuk trajectory as well as other relations. The enabling tool for this unified treatment came from the multi-sheet conformal mapping techniques that map the physical sheet to a fundamental region which in turn defines a Riemann surface on which a global uniformization variable for the scattering amplitude is calculated via an automorphic function, which in turn can be constructed as a quotient of two automorphic forms of the same dimension. (orig.)

Off-shell amplitudes as boundary integrals of analytically continued Wilson line slope

International Nuclear Information System (INIS)

Kotko, P.; Serino, M.; Staśto, A.M.

2016-01-01

One of the methods to calculate tree-level multi-gluon scattering amplitudes is to use the Berends-Giele recursion relation involving off-shell currents or off-shell amplitudes, if working in the light cone gauge. As shown in recent works using the light-front perturbation theory, solutions to these recursions naturally collapse into gauge invariant and gauge-dependent components, at least for some helicity configurations. In this work, we show that such structure is helicity independent and emerges from analytic properties of matrix elements of Wilson line operators, where the slope of the straight gauge path is shifted in a certain complex direction. This is similar to the procedure leading to the Britto-Cachazo-Feng-Witten (BCFW) recursion, however we apply a complex shift to the Wilson line slope instead of the external momenta. While in the original BCFW procedure the boundary integrals over the complex shift vanish for certain deformations, here they are non-zero and are equal to the off-shell amplitudes. The main result can thus be summarized as follows: we derive a decomposition of a helicity-fixed off-shell current into gauge invariant component given by a matrix element of a straight Wilson line plus a reminder given by a sum of products of gauge invariant and gauge dependent quantities. We give several examples realizing this relation, including the five-point next-to-MHV helicity configuration.

Direct Calculation of the Scattering Amplitude Without Partial Wave Analysis

Science.gov (United States)

Shertzer, J.; Temkin, A.; Fisher, Richard R. (Technical Monitor)

2001-01-01

Two new developments in scattering theory are reported. We show, in a practical way, how one can calculate the full scattering amplitude without invoking a partial wave expansion. First, the integral expression for the scattering amplitude f(theta) is simplified by an analytic integration over the azimuthal angle. Second, the full scattering wavefunction which appears in the integral expression for f(theta) is obtained by solving the Schrodinger equation with the finite element method (FEM). As an example, we calculate electron scattering from the Hartree potential. With minimal computational effort, we obtain accurate and stable results for the scattering amplitude.

The Analytic Structure of Scattering Amplitudes in N = 4 Super-Yang-Mills Theory

Science.gov (United States)

Litsey, Sean Christopher

We begin the dissertation in Chapter 1 with a discussion of tree-level amplitudes in Yang-. Mills theories. The DDM and BCJ decompositions of the amplitudes are described and. related to one another by the introduction of a transformation matrix. This is related to the. Kleiss-Kuijf and BCJ amplitude identities, and we conjecture a connection to the existence. of a BCJ representation via a condition on the generalized inverse of that matrix. Under. two widely-believed assumptions, this relationship is proved. Switching gears somewhat, we introduce the RSVW formulation of the amplitude, and the extension of BCJ-like features to residues of the RSVW integrand is proposed. Using the previously proven connection of BCJ representations to the generalized inverse condition, this extension is validated, including a version of gravitational double copy. The remainder of the dissertation involves an analysis of the analytic properties of loop. amplitudes in N = 4 super-Yang-Mills theory. Chapter 2 contains a review of the planar case, including an exposition of dual variables and momentum twistors, dual conformal symmetry, and their implications for the amplitude. After defining the integrand and on-shell diagrams, we explain the crucial properties that the amplitude has no poles at infinite momentum and that its leading singularities are dual-conformally-invariant cross ratios, and can therefore be normalized to unity. We define the concept of a dlog form, and show that it is a feature of the planar integrand as well. This leads to the definition of a pure integrand basis. The proceeding setup is connected to the amplituhedron formulation, and we put forward the hypothesis that the amplitude is determined by zero conditions. Chapter 3 contains the primary computations of the dissertation. This chapter treats. amplitudes in fully nonplanar N = 4 super-Yang-Mills, analyzing the conjecture that they. follow the pattern of having no poles at infinity, can be written in dlog

Amplitude inversion of the 2D analytic signal of magnetic anomalies through the differential evolution algorithm

Science.gov (United States)

Ekinci, Yunus Levent; Özyalın, Şenol; Sındırgı, Petek; Balkaya, Çağlayan; Göktürkler, Gökhan

2017-12-01

In this work, analytic signal amplitude (ASA) inversion of total field magnetic anomalies has been achieved by differential evolution (DE) which is a population-based evolutionary metaheuristic algorithm. Using an elitist strategy, the applicability and effectiveness of the proposed inversion algorithm have been evaluated through the anomalies due to both hypothetical model bodies and real isolated geological structures. Some parameter tuning studies relying mainly on choosing the optimum control parameters of the algorithm have also been performed to enhance the performance of the proposed metaheuristic. Since ASAs of magnetic anomalies are independent of both ambient field direction and the direction of magnetization of the causative sources in a two-dimensional (2D) case, inversions of synthetic noise-free and noisy single model anomalies have produced satisfactory solutions showing the practical applicability of the algorithm. Moreover, hypothetical studies using multiple model bodies have clearly showed that the DE algorithm is able to cope with complicated anomalies and some interferences from neighbouring sources. The proposed algorithm has then been used to invert small- (120 m) and large-scale (40 km) magnetic profile anomalies of an iron deposit (Kesikköprü-Bala, Turkey) and a deep-seated magnetized structure (Sea of Marmara, Turkey), respectively to determine depths, geometries and exact origins of the source bodies. Inversion studies have yielded geologically reasonable solutions which are also in good accordance with the results of normalized full gradient and Euler deconvolution techniques. Thus, we propose the use of DE not only for the amplitude inversion of 2D analytical signals of magnetic profile anomalies having induced or remanent magnetization effects but also the low-dimensional data inversions in geophysics. A part of this paper was presented as an abstract at the 2nd International Conference on Civil and Environmental Engineering, 8

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition II

Science.gov (United States)

Shertzer, J.; Temkin, A.

2003-01-01

As is well known, the full scattering amplitude can be expressed as an integral involving the complete scattering wave function. We have shown that the integral can be simplified and used in a practical way. Initial application to electron-hydrogen scattering without exchange was highly successful. The Schrodinger equation (SE) can be reduced to a 2d partial differential equation (pde), and was solved using the finite element method. We have now included exchange by solving the resultant SE, in the static exchange approximation. The resultant equation can be reduced to a pair of coupled pde's, to which the finite element method can still be applied. The resultant scattering amplitudes, both singlet and triplet, as a function of angle can be calculated for various energies. The results are in excellent agreement with converged partial wave results.

Analyticity properties of two-body helicity amplitudes; Proprietes d'analyticite des amplitudes d'helicite a deux corps

Energy Technology Data Exchange (ETDEWEB)

Navelet-Noualhier, H [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1967-06-15

Helicity amplitudes are expressed via the spinor amplitudes in terms of the Joos invariant which have been shown by Williams to be free from kinematical singularities. This procedure allows to analyze the kinematical singularities of helicity amplitudes and separate them out, which results into the definition of regularized helicity amplitudes. A crossing matrix for helicity amplitudes, is written down, corresponding to the continuation path used to cross spinor amplitudes. We verify explicitly that the corresponding crossing matrix for regularized helicity amplitudes is uniform as it should be. Kinematical constraints which generalize, to the case of arbitrary spins and masses, relations which must hold between helicity amplitudes at some values of the energy variable in {pi}N {yields} {pi}N, {pi}{pi} {yields} NN-bar and NN-bar {yields} NN-bar reactions, appear as a consequence of the existence of poles in the crossing matrix between regularized helicity amplitudes. An english version of this work has been written with G. Cohen-Tannoudji and A. Morel and submitted for publication to Annals of Physics. (author) [French] Les amplitudes d'helicite pour une reaction a deux corps sont exprimees, par l'intermediaire des amplitudes spinorielles, en fonction d'amplitudes invariantes de Joos qui sont, comme l'a montre Williams, sans singularites cinematiques. Ce procede nous permet d'analyser puis d'eliminer les singularites cinematiques des amplitudes d'helicite. Ceci nous conduit a la definition d'amplitudes d'helicite 'regularisees'. Une relation de 'croisement' entre amplitudes d'helicite est ecrite; elle realise leur prolongement analytique le long du chemin utilise pour 'croiser' les amplitudes spinorielles. Nous verifions que les elements de la matrice de croisement entre amplitudes d'helicite 'regularisees' sont bien uniformes. Les contraintes cinematiques qui generalisent, au cas de masses et de spins arbitraires, les relations obtenues dans les reactions {pi

r-particle irreducible kernels, asymptotic completeness and analyticity properties of several particle collision amplitudes

International Nuclear Information System (INIS)

Bros, J.

1984-01-01

An account is given of the present status of many-particle structure analysis in the general framework of massive quantum field theory. Two main questions are discussed, namely: i) the equivalence between the asymptotic completeness of a field and the r-particle irreducibility of associated Bether-Salpeter type kernels; ii) the derivation of extended analyticity properties of the Green functions and multiparticle collision amplitudes around the corresponding physical regions. Substantial results concerning the 3→3 particle processes are described. An analogous multiparticle version of these results yields a partial understanding of the general case

Analytic properties of the partial amplitudes in the three-body problem

International Nuclear Information System (INIS)

Blokhintsev, L.D.; Simonov, Yu.A.

1978-01-01

The singularities of the partial waves for a multiple scattering series of a system of three nonrelativistic particles with arbitrary masses are studied. Both on-shell and off-shell diagrams are considered for binary processes (2→2), break-up processes (2→3) and also three-particle scattering (3→3). For any diagram there are obtained: 1) simple analytic expressions for the loci of the nonpotential singularities of the partial amplitudes, i.e. for the singularities independent of the form of interaction between particles; 2) necessary and sufficient conditions of an existence of these singularities on the physical sheet; 3) a character of the singularities. A criterium is found for the kinematic possibility of a process of N subsequent pair collisions in a classical system of three point like masses with the contact interaction the maximal number Nsub(max) of these collisions is deduced

Analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation

Directory of Open Access Journals (Sweden)

G. H. Gudmundsson

2008-07-01

Full Text Available New analytical solutions describing the effects of small-amplitude perturbations in boundary data on flow in the shallow-ice-stream approximation are presented. These solutions are valid for a non-linear Weertman-type sliding law and for Newtonian ice rheology. Comparison is made with corresponding solutions of the shallow-ice-sheet approximation, and with solutions of the full Stokes equations. The shallow-ice-stream approximation is commonly used to describe large-scale ice stream flow over a weak bed, while the shallow-ice-sheet approximation forms the basis of most current large-scale ice sheet models. It is found that the shallow-ice-stream approximation overestimates the effects of bed topography perturbations on surface profile for wavelengths less than about 5 to 10 ice thicknesses, the exact number depending on values of surface slope and slip ratio. For high slip ratios, the shallow-ice-stream approximation gives a very simple description of the relationship between bed and surface topography, with the corresponding transfer amplitudes being close to unity for any given wavelength. The shallow-ice-stream estimates for the timescales that govern the transient response of ice streams to external perturbations are considerably more accurate than those based on the shallow-ice-sheet approximation. In particular, in contrast to the shallow-ice-sheet approximation, the shallow-ice-stream approximation correctly reproduces the short-wavelength limit of the kinematic phase speed given by solving a linearised version of the full Stokes system. In accordance with the full Stokes solutions, the shallow-ice-sheet approximation predicts surface fields to react weakly to spatial variations in basal slipperiness with wavelengths less than about 10 to 20 ice thicknesses.

Discontinuity formulas for multiparticle amplitudes

International Nuclear Information System (INIS)

Stapp, H.P.

1976-03-01

It is shown how discontinuity formulas for multiparticle scattering amplitudes are derived from unitarity and analyticity. The assumed analyticity property is the normal analytic structure, which was shown to be equivalent to the space-time macrocausality condition. The discontinuity formulas to be derived are the basis of multi-particle fixed-t dispersion relations

Analytic computations of massive one-loop amplitudes

International Nuclear Information System (INIS)

Badger, Simon; Yundin, Valery; Sattler, Ralf

2010-06-01

We show some new applications of on-shell methods to calculate compact helicity amplitudes for t anti t production through gluon fusion. The rational and mass renormalisation contributions are extracted from two independent Feynman diagram based approaches. (orig.)

Exact solution to the Coulomb wave using the linearized phase-amplitude method

Directory of Open Access Journals (Sweden)

Shuji Kiyokawa

2015-08-01

Full Text Available The author shows that the amplitude equation from the phase-amplitude method of calculating continuum wave functions can be linearized into a 3rd-order differential equation. Using this linearized equation, in the case of the Coulomb potential, the author also shows that the amplitude function has an analytically exact solution represented by means of an irregular confluent hypergeometric function. Furthermore, it is shown that the exact solution for the Coulomb potential reproduces the wave function for free space expressed by the spherical Bessel function. The amplitude equation for the large component of the Dirac spinor is also shown to be the linearized 3rd-order differential equation.

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition II: Inclusion of Exchange

Science.gov (United States)

Shertzer, Janine; Temkin, A.

2003-01-01

As is well known, the full scattering amplitude can be expressed as an integral involving the complete scattering wave function. We have shown that the integral can be simplified and used in a practical way. Initial application to electron-hydrogen scattering without exchange was highly successful. The Schrodinger equation (SE), which can be reduced to a 2d partial differential equation (pde), was solved using the finite element method. We have now included exchange by solving the resultant SE, in the static exchange approximation, which is reducible to a pair of coupled pde's. The resultant scattering amplitudes, both singlet and triplet, calculated as a function of energy are in excellent agreement with converged partial wave results.

Determination of backward pion nucleon scattering amplitudes

International Nuclear Information System (INIS)

Pietarinen, E.

1978-04-01

Backward C(sup(+-))πN amplitudes are determined from πN→Nπ and NantiN→2π differential cross sections in such a way that they are consistent with the analyticity properties and information of the unphysical ππ→NantiN amplitudes. Combining the result with forward C(sup(+-)) amplitudes positive and negative parity resonances are extracted. An error analysis of the amplitudes is performed. (author)

Analytical approximations for stick-slip vibration amplitudes

DEFF Research Database (Denmark)

Thomsen, Jon Juel; Fidlin, A.

2003-01-01

, the amplitudes, and the base frequencies of friction-induced stick¿slip and pure-slip oscillations. For stick¿slip oscillations, this is accomplished by using perturbation analysis for the finite time interval of the stick phase, which is linked to the subsequent slip phase through conditions of continuity...

Scattering amplitudes in four- and six-dimensional gauge theories

International Nuclear Information System (INIS)

Schuster, Theodor

2014-01-01

We study scattering amplitudes in quantum chromodynamics (QCD), N=4 super Yang-Mills (SYM) theory and the six-dimensional N=(1,1) SYM theory, focusing on the symmetries of and relations between the tree-level scattering amplitudes in these three gauge theories. We derive the tree level and one-loop color decomposition of an arbitrary QCD amplitude into primitive amplitudes. Furthermore, we derive identities spanning the null space among the primitive amplitudes. We prove that every color ordered tree amplitude of massless QCD can be obtained from gluon-gluino amplitudes of N=4 SYM theory. Furthermore, we derive analytical formulae for all gluon-gluino amplitudes relevant for QCD. We compare the numerical efficiency and accuracy of evaluating these closed analytic formulae for color ordered QCD tree amplitudes to a numerically efficient implementation of the Berends-Giele recursion. We derive the symmetries of massive tree amplitudes on the coulomb branch of N=4 SYM theory, which in turn can be obtained from N=(1,1) SYM theory by dimensional reduction. Furthermore, we investigate the tree amplitudes of N=(1, 1) SYM theory and explain how analytical formulae can be obtained from a numerical implementation of the supersymmetric BCFW recursion relation and investigate a potential uplift of the massless tree amplitudes of N=4 SYM theory. Finally we study an alternative to dimensional regularization of N=4 SYM theory. The infrared divergences are regulated by masses obtained from a Higgs mechanism. The corresponding string theory set-up suggests that the amplitudes have an exact dual conformal symmetry. We confirm this expectation and illustrate the calculational advantages of the massive regulator by explicit calculations.

Analytic structure of the n=7 scattering amplitude in N=4 SYM theory in multi-Regge kinematics. Conformal Regge cut contribution

International Nuclear Information System (INIS)

Bartels, Jochen; Kormilitzin, Andrey; Oxford Univ.; Lipatov, Lev N.; Oxford Univ.; St. Petersburg State Univ.

2014-11-01

In this second part of our investigation of the analytic structure of the 2→5 scattering amplitude in the planar limit of N=4 SYM in multi-Regge kinematics we compute, in all kinematic regions, the Regge cut contributions in leading order. The results are infrared finite and conformally invariant.

Analytic structure of the n=7 scattering amplitude in N=4 SYM theory at multi-Regge kinematics. Conformal Regge pole contribution

Energy Technology Data Exchange (ETDEWEB)

Bartels, Jochen; Kormilitzin, Andrey [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik; Lipatov, Lev [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik; St. Petersburg Nuclear Physics Institute, St. Petersburg (Russian Federation)

2013-11-15

We investigate the analytic structure of the 2 {yields} 5 scattering amplitude in the planar limit of N=4 SYM in multi-Regge kinematics in all physical regions. We demonstrate the close connection between Regge pole and Regge cut contributions: in a selected class of kinematic regions (Mandelstam regions) the usual factorizing Regge pole formula develops unphysical singularities which have to be absorbed and compensated by Regge cut contributions. This leads, in the corrections to the BDS formula, to conformal invariant 'renormalized' Regge pole expressions in the remainder function. We compute these renormalized Regge poles for the 2 {yields} 5 scattering amplitude.

Differential equations, associators, and recurrences for amplitudes

Directory of Open Access Journals (Sweden)

Georg Puhlfürst

2016-01-01

Full Text Available We provide new methods to straightforwardly obtain compact and analytic expressions for ϵ-expansions of functions appearing in both field and string theory amplitudes. An algebraic method is presented to explicitly solve for recurrence relations connecting different ϵ-orders of a power series solution in ϵ of a differential equation. This strategy generalizes the usual iteration by Picard's method. Our tools are demonstrated for generalized hypergeometric functions. Furthermore, we match the ϵ-expansion of specific generalized hypergeometric functions with the underlying Drinfeld associator with proper Lie algebra and monodromy representations. We also apply our tools for computing ϵ-expansions for solutions to generic first-order Fuchsian equations (Schlesinger system. Finally, we set up our methods to systematically get compact and explicit α′-expansions of tree-level superstring amplitudes to any order in α′.

Normal stress differences from Oldroyd 8-constant framework: Exact analytical solution for large-amplitude oscillatory shear flow

Science.gov (United States)

Saengow, C.; Giacomin, A. J.

2017-12-01

The Oldroyd 8-constant framework for continuum constitutive theory contains a rich diversity of popular special cases for polymeric liquids. In this paper, we use part of our exact solution for shear stress to arrive at unique exact analytical solutions for the normal stress difference responses to large-amplitude oscillatory shear (LAOS) flow. The nonlinearity of the polymeric liquids, triggered by LAOS, causes these responses at even multiples of the test frequency. We call responses at a frequency higher than twice the test frequency higher harmonics. We find the new exact analytical solutions to be compact and intrinsically beautiful. These solutions reduce to those of our previous work on the special case of the corotational Maxwell fluid. Our solutions also agree with our new truncated Goddard integral expansion for the special case of the corotational Jeffreys fluid. The limiting behaviors of these exact solutions also yield new explicit expressions. Finally, we use our exact solutions to see how η∞ affects the normal stress differences in LAOS.

Analytical modeling of large amplitude free vibration of non-uniform beams carrying a both transversely and axially eccentric tip mass

Science.gov (United States)

Malaeke, Hasan; Moeenfard, Hamid

2016-03-01

The objective of this paper is to study large amplitude flexural-extensional free vibration of non-uniform cantilever beams carrying a both transversely and axially eccentric tip mass. The effects of variable axial force is also taken into account. Hamilton's principle is utilized to obtain the partial differential equations governing the nonlinear vibration of the system as well as the corresponding boundary conditions. A numerical finite difference scheme is proposed to find the natural frequencies and mode shapes of the system which is validated specifically for a beam with linearly varying cross section. Using a single mode approximation in conjunction with the Lagrange method, the governing equations are reduced to a set of two nonlinear ordinary differential equations in terms of end displacement components of the beam which are coupled due to the presence of the transverse eccentricity. These temporal coupled equations are then solved analytically using the multiple time scales perturbation technique. The obtained analytical results are compared with the numerical ones and excellent agreement is observed. The qualitative and quantitative knowledge resulting from this research is expected to enable the study of the effects of eccentric tip mass and non-uniformity on the large amplitude flexural-extensional vibration of beams for improved dynamic performance.

A two-loop four-gluon helicity amplitude in QCD

Energy Technology Data Exchange (ETDEWEB)

Dixon, L.

2000-01-06

The authors present the two-loop pure gauge contribution to the gluon-gluon scattering amplitude with maximal helicity violation. The construction of the amplitude does not rely directly on Feynman diagrams, but instead uses its analytic properties 4--2{epsilon} dimensions. The authors evaluate the loop integrals appearing in the amplitude through order({epsilon}{sup 0})in terms of polylogarithms.

Improved pion pion scattering amplitude from dispersion relation formalism

International Nuclear Information System (INIS)

Cavalcante, I.P.; Coutinho, Y.A.; Borges, J. Sa

2005-01-01

Pion-pion scattering amplitude is obtained from Chiral Perturbation Theory at one- and two-loop approximations. Dispersion relation formalism provides a more economic method, which was proved to reproduce the analytical structure of that amplitude at both approximation levels. This work extends the use of the formalism in order to compute further unitarity corrections to partial waves, including the D-wave amplitude. (author)

Scattering amplitudes in gauge theories

CERN Document Server

Henn, Johannes M

2014-01-01

At the fundamental level, the interactions of elementary particles are described by quantum gauge field theory. The quantitative implications of these interactions are captured by scattering amplitudes, traditionally computed using Feynman diagrams. In the past decade tremendous progress has been made in our understanding of and computational abilities with regard to scattering amplitudes in gauge theories, going beyond the traditional textbook approach. These advances build upon on-shell methods that focus on the analytic structure of the amplitudes, as well as on their recently discovered hidden symmetries. In fact, when expressed in suitable variables the amplitudes are much simpler than anticipated and hidden patterns emerge.   These modern methods are of increasing importance in phenomenological applications arising from the need for high-precision predictions for the experiments carried out at the Large Hadron Collider, as well as in foundational mathematical physics studies on the S-matrix in quantum ...

Analytical fits to Fink's electron scattering amplitudes, 1

International Nuclear Information System (INIS)

Hayashi, Shigeo

1984-01-01

Numerical data of the direct and spin-flip amplitudes for elastic electron scattering, calculated previously by Fink and co-workers, were expressed in the form Σc 1 exp(-c 2 x+ic 3 +ic 4 ), where x=1-cos theta,theta being a scattering angle. The adjustable c-parameters were determined by the use of a simplex method. Results are reported for carbon at incident electron energies of 25-1000eV. (author)

The amplitude of quantum field theory

International Nuclear Information System (INIS)

Medvedev, B.V.; Pavlov, V.P.; Polivanov, M.K.; Sukhanov, A.D.

1989-01-01

General properties of the transition amplitude in axiomatic quantum field theory are discussed. Bogolyubov's axiomatic method is chosen as the variant of the theory. The axioms of this method are analyzed. In particular, the significance of the off-shell extension and of the various forms of the causality condition are examined. A complete proof is given of the existence of a single analytic function whose boundary values are the amplitudes of all channels of a process with given particle number

Renormalization Scale-Fixing for Complex Scattering Amplitudes

Energy Technology Data Exchange (ETDEWEB)

Brodsky, Stanley J.; /SLAC; Llanes-Estrada, Felipe J.; /Madrid U.

2005-12-21

We show how to fix the renormalization scale for hard-scattering exclusive processes such as deeply virtual meson electroproduction by applying the BLM prescription to the imaginary part of the scattering amplitude and employing a fixed-t dispersion relation to obtain the scale-fixed real part. In this way we resolve the ambiguity in BLM renormalization scale-setting for complex scattering amplitudes. We illustrate this by computing the H generalized parton distribution at leading twist in an analytic quark-diquark model for the parton-proton scattering amplitude which can incorporate Regge exchange contributions characteristic of the deep inelastic structure functions.

Properties of the scattering amplitude for electron-atom collisions

International Nuclear Information System (INIS)

Combes, J.M.; Tip, A.

1983-02-01

For the scattering of an electron by an atom finiteness of the amplitude at non threshold energies is proved in the framework of the N-body Schroedinger equation. It is also shown that both the direct and exchange amplitudes have analytic continuations for complex values of incident momentum, with pole or cut singularities on the imaginary axis

Scattering Amplitudes via Algebraic Geometry Methods

CERN Document Server

Søgaard, Mads; Damgaard, Poul Henrik

This thesis describes recent progress in the understanding of the mathematical structure of scattering amplitudes in quantum field theory. The primary purpose is to develop an enhanced analytic framework for computing multiloop scattering amplitudes in generic gauge theories including QCD without Feynman diagrams. The study of multiloop scattering amplitudes is crucial for the new era of precision phenomenology at the Large Hadron Collider (LHC) at CERN. Loop-level scattering amplitudes can be reduced to a basis of linearly independent integrals whose coefficients are extracted from generalized unitarity cuts. We take advantage of principles from algebraic geometry in order to extend the notion of maximal cuts to a large class of two- and three-loop integrals. This allows us to derive unique and surprisingly compact formulae for the coefficients of the basis integrals. Our results are expressed in terms of certain linear combinations of multivariate residues and elliptic integrals computed from products of ...

Analytic amplitudes for hadronic forward scattering and the Heisenberg ln{sup 2} s behaviour of total cross sections

Energy Technology Data Exchange (ETDEWEB)

Nicolescu, Basarab [LPNHE, Unite de Recherche des Universites Paris 6 et Paris 7, associee au CNRS, Theory Group, Universite Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05 (France)

2004-07-01

We consider several classes of analytic parametrizations of hadronic scattering amplitudes (the COMPETE analysis), and compare their predictions to all available forward data (pp, {pi}p, Kp, {gamma}p, {gamma}{gamma}, {sigma}p). Although these parametrizations are very close for {radical}s {>=} 9 GeV, it turns out that they differ markedly at low energy, where a universal Pomeron term {approx} ln{sup 2} s enables one to extend the fit down to {radical}s = 4 GeV. We present predictions on the total cross sections and on the ratio of the real part to the imaginary part of the elastic amplitude ({rho} parameter) for present and future pp colliders, and on total cross sections for {gamma}p {yields} hadrons at cosmic-ray energies and for it{gamma}{gamma} {yields} hadrons up to {radical}s = 1 TeV. The ln{sup 2} s behaviour of total cross sections, first obtained by Heisenberg 50 years ago, receives now increased interest both on phenomenological and theoretical levels. We present a modification of the Heisenberg's model in connection with the presence of glueballs and we show that it leads to a realistic description of all existing hadron total cross-sections data, in agreement with the COMPETE analysis.

Modelling and mitigation of wheel squeal noise amplitude

Science.gov (United States)

Meehan, Paul A.; Liu, Xiaogang

2018-01-01

The prediction of vibration amplitude and sound pressure level of wheel squeal noise is investigated using a concise mathematical model that is verified with measurements from both a rolling contact two disk test rig and a field case study. The model is used to perform an energy-based analysis to determine a closed form solution to the steady state limit cycle amplitude of creep and vibration oscillations during squealing. The analytical solution compares well with a numerical solution using an experimentally tuned creep curve with full nonlinear shape. The predicted squeal sound level trend also compares well with that recorded at various crabbing velocities (proportional to angle of attack) for the test rig at different rolling speeds. In addition, further verification is performed against many field recordings of wheel squeal on a sharp curve of 300 m. A comparison with a simplified modified result from Rudd [1] is also provided and highlights the accuracy and advantages of the present efficient model. The analytical solution provides insight into why the sound pressure level of squeal noise increases with crabbing velocity (or angle of attack) as well as how the amplitude is affected by the critical squeal parameters including a detailed investigation of modal damping. Finally, the efficient model is used to perform a parametric investigation into means of achieving a 6 dB decrease in squeal noise. The results highlight the primary importance of crabbing velocity (and angle of attack) as well as the creep curve parameters that may be controlled using third body control (ie friction modifiers). The results concur with experimental and field observations and provide important theoretical insight into the useful mechanisms of mitigating wheel squeal and quantifying their relative merits.

The threshold expansion of the 2-loop sunrise self-mass master amplitudes

International Nuclear Information System (INIS)

Caffo, M.; Czyz, H.; Remiddi, E.

2001-01-01

The threshold behavior of the master amplitudes for two loop sunrise self-mass graph is studied by solving the system of differential equations, which they satisfy. The expansion at the threshold of the master amplitudes is obtained analytically for arbitrary masses

3D elastic full-waveform inversion for OBC data using the P-wave excitation amplitude

KAUST Repository

Oh, Juwon

2017-08-17

We suggest a fast and efficient 3D elastic full waveform inversion (FWI) algorithm based on the excitation amplitude (maximum energy arrival) of the P-wave in the source wavefield. It evaluates the gradient direction significantly faster than its conventional counterpart. In addition, it removes the long-wavelength artifacts from the gradient, which are often originated from SS correlation process. From these advantages, the excitation approach offers faster convergence not only for the S wave velocity, but also for the entire process of multi-parameter inversion, compared to the conventional FWI. The feasibility of the proposed method is demonstrated through the synthetic Marmousi and a real OBC data from North Sea.

3D elastic full-waveform inversion for OBC data using the P-wave excitation amplitude

KAUST Repository

Oh, Juwon; Kalita, Mahesh; Alkhalifah, Tariq Ali

2017-01-01

We suggest a fast and efficient 3D elastic full waveform inversion (FWI) algorithm based on the excitation amplitude (maximum energy arrival) of the P-wave in the source wavefield. It evaluates the gradient direction significantly faster than its conventional counterpart. In addition, it removes the long-wavelength artifacts from the gradient, which are often originated from SS correlation process. From these advantages, the excitation approach offers faster convergence not only for the S wave velocity, but also for the entire process of multi-parameter inversion, compared to the conventional FWI. The feasibility of the proposed method is demonstrated through the synthetic Marmousi and a real OBC data from North Sea.

Amplitude-integrated Electroencephalography in Full-term Newborns without Severe Hypoxic-ischemic Encephalopathy: Case Series

OpenAIRE

Osredkar, Damjan; Derganc, Metka; Paro-Panjan, Darja; Neubauer, David

2006-01-01

Aim: To assess the diagnostic value of amplitude-integrated electroencephalography (EEG) in comparison to standard EEG in newborns without severe hypoxic-ischemic encephalopathy who were at risk for seizures. Methods: The study included a consecutive series of 18 term newborns without severe hypoxic-ischemic encephalopathy, but with clinical signs suspicious of epileptic seizures, history of loss of social contact, disturbance of muscle tone, hyperirritability, and/or jitteriness. Amplitud...

Cosmological constraints on the amplitude of relic gravitational waves

International Nuclear Information System (INIS)

Novosyadlij, B.; Apunevich, S.

2005-01-01

The evolution of the amplitude of relic gravitational waves (RGW) generated in early Universe has been analyzed. The analytical approximation is presented for angular power spectrum of cosmic microwave background anisotropies caused by gravitational waves through Sachs-Wolfe effect. The estimate of the most probable value for this amplitude was obtained on the basis of observation data on cosmic microwave background anisotropies from COBE, WMAP and BOOMERanG experiments along with large-scale structure observations

Scaling of saturation amplitudes in baroclinic instability

International Nuclear Information System (INIS)

Shepherd, T.G.

1994-01-01

By using finite-amplitude conservation laws for pseudomomentum and pseudoenergy, rigorous upper bounds have been derived on the saturation amplitudes in baroclinic instability for layered and continuously-stratified quasi-geostrophic models. Bounds have been obtained for both the eddy energy and the eddy potential enstrophy. The bounds apply to conservative (inviscid, unforced) flow, as well as to forced-dissipative flow when the dissipation is proportional to the potential vorticity. This approach provides an efficient way of extracting an analytical estimate of the dynamical scalings of the saturation amplitudes in terms of crucial non-dimensional parameters. A possible use is in constructing eddy parameterization schemes for zonally-averaged climate models. The scaling dependences are summarized, and compared with those derived from weakly-nonlinear theory and from baroclinic-adjustment estimates

Semiclassical approach to fidelity amplitude

International Nuclear Information System (INIS)

García-Mata, Ignacio; Vallejos, Raúl O; Wisniacki, Diego A

2011-01-01

The fidelity amplitude (FA) is a quantity of paramount importance in echo-type experiments. We use semiclassical theory to study the average FA for quantum chaotic systems under external perturbation. We explain analytically two extreme cases: the random dynamics limit - attained approximately by strongly chaotic systems - and the random perturbation limit, which shows a Lyapunov decay. Numerical simulations help us to bridge the gap between both the extreme cases. (paper)

Analytic multi-Regge theory and the pomeron in QCD. 1

International Nuclear Information System (INIS)

White, A.R.

1991-01-01

This paper reports on the formalism of analytic multi-Regge theory developed as a basis for the study of abstract critical and super-critical pomeron high-energy behavior and for related studies of the Regge behavior of spontaneously broken gauge theories and the pomeron in QCD. Asymptotic domains of analyticity for multiparticle amplitudes are shown to follow from properties of field theory and S-matrix theory. General asymptotic dispersion relations are then derived for such amplitudes in which the spectral components are described by the graphical formalism of hexagraphs. Further consequences are distinct Sommerfeld-Watson representations for each hexagraph spectral component, together with a complete set of angular momentum plane unitarity equations which control the form of all multi-Regge amplitudes. Because of this constraint of reggeon unitarity the critical pomeron solution of the reggeon field theory gives the only known non-trivial unitary high-energy S-matrix. By exploiting the full structure of multi-Regge amplitudes as the pomeron becomes super-critical, one can study the simultaneous modification of hadrons and the pomeron. The result is a completely consistent description of the super-critical pomeron appearing in hadron scattering. Reggeon unitarity is satisfied in the super-critical phase by the appearance of a massive gluon (Reggeized vector particle) coupling pair-wise to the pomeron

Emergence of amplitude death scenario in a network of oscillators under repulsive delay interaction

Energy Technology Data Exchange (ETDEWEB)

Bera, Bidesh K., E-mail: bideshbera18@gmail.com [Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108 (India); Hens, Chittaranjan, E-mail: chittaranjanhens@gmail.com [Department of Mathematics, Bar-Ilan University, Ramat Gan 52900 (Israel); Ghosh, Dibakar, E-mail: dibakar@isical.ac.in [Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108 (India)

2016-07-15

Highlights: • Amplitude death is observed using repulsive mean coupling. • Analytical conditions for amplitude death are derived. • Effect of asymmetry time delay coupling for death is discussed. - Abstract: We report the existence of amplitude death in a network of identical oscillators under repulsive mean coupling. Amplitude death appears in a globally coupled network of identical oscillators with instantaneous repulsive mean coupling only when the number of oscillators is more than two. We further investigate that, amplitude death may emerge even in two coupled oscillators as well as network of oscillators if we introduce delay time in the repulsive mean coupling. We have analytically derived the region of amplitude death island and find out how strength of delay controls the death regime in two coupled or a large network of coupled oscillators. We have verified our results on network of delayed Mackey–Glass systems where parameters are set in hyperchaotic regime. We have also tested our coupling approach in two paradigmatic limit cycle oscillators: Stuart–Landau and Van der Pol oscillators.

Emergence of amplitude death scenario in a network of oscillators under repulsive delay interaction

International Nuclear Information System (INIS)

Bera, Bidesh K.; Hens, Chittaranjan; Ghosh, Dibakar

2016-01-01

Highlights: • Amplitude death is observed using repulsive mean coupling. • Analytical conditions for amplitude death are derived. • Effect of asymmetry time delay coupling for death is discussed. - Abstract: We report the existence of amplitude death in a network of identical oscillators under repulsive mean coupling. Amplitude death appears in a globally coupled network of identical oscillators with instantaneous repulsive mean coupling only when the number of oscillators is more than two. We further investigate that, amplitude death may emerge even in two coupled oscillators as well as network of oscillators if we introduce delay time in the repulsive mean coupling. We have analytically derived the region of amplitude death island and find out how strength of delay controls the death regime in two coupled or a large network of coupled oscillators. We have verified our results on network of delayed Mackey–Glass systems where parameters are set in hyperchaotic regime. We have also tested our coupling approach in two paradigmatic limit cycle oscillators: Stuart–Landau and Van der Pol oscillators.

Numerical calculation of spin echo amplitude in pulsed NMR: effects of quadrupole interaction

International Nuclear Information System (INIS)

Sobral, R.R.

1986-01-01

The spin echo obtained by nuclear magnetic resonance, in systems which atomic nuclei interact with magnetic fields and electric field gradients, present oscillations in function of the time interval between two excitations pulses. Using the density matrix formalism, the amplitudes of these echo is calculated, analytically. In this work, echo amplitudes obtained under different excitation conditions for nuclei of different nuclear spin values are calculated. The numerical results are compared with disposable analytical solutions. Applications of this method to the case of electric field gradient without axial symmetry were studied. Within the used approximation limits, an expression for attnuation of oscillatory behaviour of echo amplitude in function of the time interval between experimentally observed pulses was obtained. (M.C.K.) [pt

The prognostic value of amplitude-integrated EEG in full-term neonates with seizures.

Directory of Open Access Journals (Sweden)

Dandan Zhang

Full Text Available Neonatal seizures pose a high risk for adverse outcome in survived infants. While the prognostic value of amplitude-integrated electroencephalogram (aEEG is well established in neonates with encephalopathy and asphyxia, neonatal seizure studies focusing on the direct correlation between early aEEG measurement and subsequent neurologic outcome are scarce. In this study, the prognostic value of aEEG features was systematically analyzed in 143 full-term neonates to identify prognostic indicators of neurodevelopmental outcome. Neonatal aEEG features of background pattern, cyclicity, and seizure activity, as well as the etiology of neonatal seizures, were significantly associated with neurodevelopmental outcome at one year of age. aEEG background pattern was highly associated with neurologic outcomes (χ² = 116.9, followed by aEEG cyclicity (χ² = 87.2 and seizure etiology (χ² = 79.3. Multiple linear regression showed that the four predictors explained 71.2% of the variation in neurological outcome, with standardized β coefficients of 0.44, 0.24, 0.22, and 0.14 for the predictors of aEEG background pattern, cyclicity, etiology, and aEEG seizure activity, respectively. This clinically applicable scoring system based on etiology and three aEEG indices would allow pediatricians to assess the risk for neurodevelopmental impairment and facilitate an early intervention in newborns developing seizures.

Compact QED tree-level amplitudes from dressed BCFW recursion relations

International Nuclear Information System (INIS)

Badger, Simon D.; Henn, Johannes M.

2010-05-01

We construct a modified on-shell BCFW recursion relation to derive compact analytic representations of tree-level amplitudes in QED. As an application, we study the amplitudes of a fermion pair coupling to an arbitrary number of photons and give compact formulae for the NMHV and N 2 MHV case. We demonstrate that the new recursion relation reduces the growth in complexity with additional photons to be exponential rather than factorial. (orig.)

Compact QED tree-level amplitudes from dressed BCFW recursion relations

Energy Technology Data Exchange (ETDEWEB)

Badger, Simon D. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Henn, Johannes M. [Humboldt Univ., Berlin (Germany). Inst. fuer Physik

2010-05-15

We construct a modified on-shell BCFW recursion relation to derive compact analytic representations of tree-level amplitudes in QED. As an application, we study the amplitudes of a fermion pair coupling to an arbitrary number of photons and give compact formulae for the NMHV and N{sup 2}MHV case. We demonstrate that the new recursion relation reduces the growth in complexity with additional photons to be exponential rather than factorial. (orig.)

Laser beam complex amplitude measurement by phase diversity.

Science.gov (United States)

Védrenne, Nicolas; Mugnier, Laurent M; Michau, Vincent; Velluet, Marie-Thérèse; Bierent, Rudolph

2014-02-24

The control of the optical quality of a laser beam requires a complex amplitude measurement able to deal with strong modulus variations and potentially highly perturbed wavefronts. The method proposed here consists in an extension of phase diversity to complex amplitude measurements that is effective for highly perturbed beams. Named camelot for Complex Amplitude MEasurement by a Likelihood Optimization Tool, it relies on the acquisition and processing of few images of the beam section taken along the optical path. The complex amplitude of the beam is retrieved from the images by the minimization of a Maximum a Posteriori error metric between the images and a model of the beam propagation. The analytical formalism of the method and its experimental validation are presented. The modulus of the beam is compared to a measurement of the beam profile, the phase of the beam is compared to a conventional phase diversity estimate. The precision of the experimental measurements is investigated by numerical simulations.

Constraints on low energy Compton scattering amplitudes

International Nuclear Information System (INIS)

Raszillier, I.

1979-04-01

We derive the constraints and correlations of fairly general type for Compton scattering amplitudes at energies below photoproduction threshold and fixed momentum transfer, following from (an upper bound on) the corresponding differential cross section above photoproduction threshold. The derivation involves the solution of an extremal problem in a certain space of vector - valued analytic functions. (author)

Scattering amplitudes in gauge theories

Energy Technology Data Exchange (ETDEWEB)

Henn, Johannes M. [Institute for Advanced Study, Princeton, NJ (United States). School of Natural Sciences; Plefka, Jan C. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik

2014-03-01

First monographical text on this fundamental topic. Course-tested, pedagogical and self-contained exposition. Includes exercises and solutions. At the fundamental level, the interactions of elementary particles are described by quantum gauge field theory. The quantitative implications of these interactions are captured by scattering amplitudes, traditionally computed using Feynman diagrams. In the past decade tremendous progress has been made in our understanding of and computational abilities with regard to scattering amplitudes in gauge theories, going beyond the traditional textbook approach. These advances build upon on-shell methods that focus on the analytic structure of the amplitudes, as well as on their recently discovered hidden symmetries. In fact, when expressed in suitable variables the amplitudes are much simpler than anticipated and hidden patterns emerge. These modern methods are of increasing importance in phenomenological applications arising from the need for high-precision predictions for the experiments carried out at the Large Hadron Collider, as well as in foundational mathematical physics studies on the S-matrix in quantum field theory. Bridging the gap between introductory courses on quantum field theory and state-of-the-art research, these concise yet self-contained and course-tested lecture notes are well-suited for a one-semester graduate level course or as a self-study guide for anyone interested in fundamental aspects of quantum field theory and its applications. The numerous exercises and solutions included will help readers to embrace and apply the material presented in the main text.

Scattering amplitudes in gauge theories

International Nuclear Information System (INIS)

Henn, Johannes M.; Plefka, Jan C.

2014-01-01

First monographical text on this fundamental topic. Course-tested, pedagogical and self-contained exposition. Includes exercises and solutions. At the fundamental level, the interactions of elementary particles are described by quantum gauge field theory. The quantitative implications of these interactions are captured by scattering amplitudes, traditionally computed using Feynman diagrams. In the past decade tremendous progress has been made in our understanding of and computational abilities with regard to scattering amplitudes in gauge theories, going beyond the traditional textbook approach. These advances build upon on-shell methods that focus on the analytic structure of the amplitudes, as well as on their recently discovered hidden symmetries. In fact, when expressed in suitable variables the amplitudes are much simpler than anticipated and hidden patterns emerge. These modern methods are of increasing importance in phenomenological applications arising from the need for high-precision predictions for the experiments carried out at the Large Hadron Collider, as well as in foundational mathematical physics studies on the S-matrix in quantum field theory. Bridging the gap between introductory courses on quantum field theory and state-of-the-art research, these concise yet self-contained and course-tested lecture notes are well-suited for a one-semester graduate level course or as a self-study guide for anyone interested in fundamental aspects of quantum field theory and its applications. The numerous exercises and solutions included will help readers to embrace and apply the material presented in the main text.

Local integrands for two-loop all-plus Yang-Mills amplitudes

International Nuclear Information System (INIS)

Badger, Simon; Mogull, Gustav; Peraro, Tiziano

2016-01-01

We express the planar five- and six-gluon two-loop Yang-Mills amplitudes with all positive helicities in compact analytic form using D-dimensional local integrands that are free of spurious singularities. The integrand is fixed from on-shell tree amplitudes in six dimensions using D-dimensional generalised unitarity cuts. The resulting expressions are shown to have manifest infrared behaviour at the integrand level. We also find simple representations of the rational terms obtained after integration in 4−2ϵ dimensions.

Local integrands for two-loop all-plus Yang-Mills amplitudes

Energy Technology Data Exchange (ETDEWEB)

Badger, Simon; Mogull, Gustav; Peraro, Tiziano [Higgs Centre for Theoretical Physics, School of Physics and Astronomy,The University of Edinburgh, James Clerk Maxwell Building,Peter Guthrie Tait Road, Edinburgh EH9 3FD (United Kingdom)

2016-08-09

We express the planar five- and six-gluon two-loop Yang-Mills amplitudes with all positive helicities in compact analytic form using D-dimensional local integrands that are free of spurious singularities. The integrand is fixed from on-shell tree amplitudes in six dimensions using D-dimensional generalised unitarity cuts. The resulting expressions are shown to have manifest infrared behaviour at the integrand level. We also find simple representations of the rational terms obtained after integration in 4−2ϵ dimensions.

SOLUTION OF SIGNAL UNCERTAINTY PROBLEM AT ANALYTICAL DESIGN OF CONSECUTIVE COMPENSATOR IN PIEZO ACTUATOR CONTROL

Directory of Open Access Journals (Sweden)

S.V. Bystrov

2016-05-01

Full Text Available Subject of Research.We present research results for the signal uncertainty problem that naturally arises for the developers of servomechanisms, including analytical design of serial compensators, delivering the required quality indexes for servomechanisms. Method. The problem was solved with the use of Besekerskiy engineering approach, formulated in 1958. This gave the possibility to reduce requirements for input signal composition of servomechanisms by using only two of their quantitative characteristics, such as maximum speed and acceleration. Information about input signal maximum speed and acceleration allows entering into consideration the equivalent harmonic input signal with calculated amplitude and frequency. In combination with requirements for maximum tracking error, the amplitude and frequency of the equivalent harmonic effects make it possible to estimate analytically the value of the amplitude characteristics of the system by error and then convert it to amplitude characteristic of open-loop system transfer function. While previously Besekerskiy approach was mainly used in relation to the apparatus of logarithmic characteristics, we use this approach for analytical synthesis of consecutive compensators. Main Results. Proposed technique is used to create analytical representation of "input–output" and "error–output" polynomial dynamic models of the designed system. In turn, the desired model of the designed system in the "error–output" form of analytical representation of transfer functions is the basis for the design of consecutive compensator, that delivers the desired placement of state matrix eigenvalues and, consequently, the necessary set of dynamic indexes for the designed system. The given procedure of consecutive compensator analytical design on the basis of Besekerskiy engineering approach under conditions of signal uncertainty is illustrated by an example. Practical Relevance. The obtained theoretical results are

A novel amplitude modulated triangular carrier gain linearization technique for SPWM inverter

Directory of Open Access Journals (Sweden)

Ramkumar Subburam

2009-01-01

Full Text Available This paper presents a new method to extend the linearity of the sinusoidal pulse width modulation (SPWM to full range of the pulse dropping region. The proposed amplitude modulated triangular carrier PWM method (AMTCPWM increases the dynamic range of the SPWM control and eliminates the need of nonlinear modulation in the pulse dropping region to reach the square wave boundary. The novel method combines the spectral quality of SPWM with the efficient single-mode linear control. A simple analytical characterization of the exact method is presented and its effectiveness is demonstrated using simulation for the basic single-phase H-bridge inverter circuit. The hardware results of the designed prototype inverter are presented to validate the betterment of the novel scheme. .

COEFICIENTES DE TRANSMISSÃO E REFLEXÃO PELO MÉTODO DA AMPLITUDE VARIÁVEL

Directory of Open Access Journals (Sweden)

Éderson D'M. Costa

Full Text Available In this work, a simple derivation of the variable amplitude method using the variation of parameters to solve a differential equation is presented. The variable amplitude method was originally devised by Tikochinsky in 1977, using the quantum theory of scattering. The method is applied to two model potentials, the rectangular potential barrier and the Eckart potential, both with analytical solutions for the reflection coefficient. Numerical results will be compared with the exact values for several energies. The problem of calculating the reflection coefficient, usually involving extensive algebra as described in several textbooks, is reduced to solving a first order differential equation with initial condition. The method is very simple to apply, representing an attractive tool for teaching introductory quantum mechanics. A simple computer code is available from which reflection coefficients for the Eckart potential can be calculated.

An analytical model for the description of the full-polarimetric sea surface Doppler signature

NARCIS (Netherlands)

Fois, F.; Hoogeboom, P.; Le Chevalier, F.; Stoffelen, A.

2015-01-01

This paper describes an analytical model of the full-polarimetric sea surface scattering and Doppler signature. The model combines the small-slope-approximation theory (at the second order) with a weak nonlinear sea surface representation. Such a model is used to examine the variation of the Doppler

Unitarity and amplitudes for high energies

International Nuclear Information System (INIS)

Efimov, G.V.

1997-01-01

It is shown that in the quantum field theory of scalar particles with mass m the following inequalities for the upper bound for the amplitude of elastic scattering Μ(s,t) |Μ(s,t)| 0 )s, (|t|≥|t 0 |>0) and for the total cross section of scalar particles σ tot (s)≤C|d/dt ln Im Μ(s,t)| t=0 , (s → ∞) are valid. This result is based on the unitarity of the S-matrix on the mass shell and on a natural assumption that the imaginary part of the elastic scattering Im Μ(s,t) is a differentiable and convex down function in some vicinity of t=0. The locality of the theory and the analyticity of the elastic amplitude in the Martin-Lehmann ellipse are not used in proving these inequalities

Higher order modes excitation of electrostatically actuated clamped–clamped microbeams: experimental and analytical investigation

KAUST Repository

Jaber, Nizar

2016-01-06

© 2016 IOP Publishing Ltd. In this study, we demonstrate analytically and experimentally the excitations of the higher order modes of vibrations in electrostatically actuated clamped-clamped microbeam resonators. The concept is based on using partial electrodes with shapes that induce strong excitation of the mode of interest. The devices are fabricated using polyimide as a structural layer coated with nickel from the top and chrome and gold layers from the bottom. Experimentally, frequency sweeps with different electro-dynamical loading conditions are shown to demonstrate the excitation of the higher order modes of vibration. Using a half electrode, the second mode is excited with high amplitude of vibration compared with almost zero response using the full electrode. Also, using a two-third electrode configuration is shown to amplify the third mode resonance amplitude compared with the full electrode under the same electrical loading conditions. An analytical model is developed based on the Euler-Bernollui beam model and the Galerkin method to simulate the device response. Good agreement between the simulation results and the experimental data is reported.

The dispersion relation for the forward elastic electron-atom scattering amplitude

International Nuclear Information System (INIS)

Amusia, M.Y.

1978-01-01

The analytical properties of forward elastic electron-atom scattering amplitude are discussed. It is noted that the occurrence of exchange between the incoming and atomic electrons leads to the appearance of a number of singularities on the negative real axis in the complex energy plane. The conclusion is drawn that the dispersion relation for the forward electron-atom scattering amplitude should also include an integration over the negative energy from - I to - infinity, where I is the ionization potential. (author)

Equality of some integrals from real and imaginary parts of a scattering amplitude

International Nuclear Information System (INIS)

Vernov, Yu.S.; Konovalov, A.V.; Mnatsakanova, M.N.

1984-01-01

Relation between the behaviour of real and imaginary parts of a forward elastic scattering amplitude is investigated on the basis of analyticity and crossing symmetry. Possibility for the generalization of this equality also for symmetric amplitude resulted from dispersion relations was considered. It is noted that the investigation performed is true for any function complying with the dispersion relation, for example, for polarization operator

New strings for old Veneziano amplitudes. II. Group-theoretic treatment

Science.gov (United States)

Kholodenko, A. L.

2006-09-01

In this part of our four parts work we use theory of polynomial invariants of finite pseudo-reflection groups in order to reconstruct both the Veneziano and Veneziano-like (tachyon-free) amplitudes and the generating function reproducing these amplitudes. We demonstrate that such generating function and amplitudes associated with it can be recovered with help of finite dimensional exactly solvableN=2 supersymmetric quantum mechanical model known earlier from works of Witten, Stone and others. Using the Lefschetz isomorphism theorem we replace traditional supersymmetric calculations by the group-theoretic thus solving the Veneziano model exactly using standard methods of representation theory. Mathematical correctness of our arguments relies on important theorems by Shepard and Todd, Serre and Solomon proven respectively in the early 50s and 60s and documented in the monograph by Bourbaki. Based on these theorems, we explain why the developed formalism leaves all known results of conformal field theories unchanged. We also explain why these theorems impose stringent requirements connecting analytical properties of scattering amplitudes with symmetries of space-time in which such amplitudes act.

Analysis of Peak-to-Peak Current Ripple Amplitude in Seven-Phase PWM Voltage Source Inverters

Directory of Open Access Journals (Sweden)

Gabriele Grandi

2013-08-01

Full Text Available Multiphase systems are nowadays considered for various industrial applications. Numerous pulse width modulation (PWM schemes for multiphase voltage source inverters with sinusoidal outputs have been developed, but no detailed analysis of the impact of these modulation schemes on the output peak-to-peak current ripple amplitude has been reported. Determination of current ripple in multiphase PWM voltage source inverters is important for both design and control purposes. This paper gives the complete analysis of the peak-to-peak current ripple distribution over a fundamental period for multiphase inverters, with particular reference to seven-phase VSIs. In particular, peak-to-peak current ripple amplitude is analytically determined as a function of the modulation index, and a simplified expression to get its maximum value is carried out. Although reference is made to the centered symmetrical PWM, being the most simple and effective solution to maximize the DC bus utilization, leading to a nearly-optimal modulation to minimize the RMS of the current ripple, the analysis can be readily extended to either discontinuous or asymmetrical modulations, both carrier-based and space vector PWM. A similar approach can be usefully applied to any phase number. The analytical developments for all different sub-cases are verified by numerical simulations.

Iterative structure within the five-particle two-loop amplitude

International Nuclear Information System (INIS)

Cachazo, Freddy; Spradlin, Marcus; Volovich, Anastasia

2006-01-01

We find an unexpected iterative structure within the two-loop five-gluon amplitude in N=4 supersymmetric Yang-Mills theory. Specifically, we show that a subset of diagrams contributing to the full amplitude, including a two-loop pentagon-box integral with nontrivial dependence on five kinematical variables, satisfies an iterative relation in terms of one-loop scalar box diagrams. The implications of this result for the possible iterative structure of the full two-loop amplitude are discussed

Parametric validations of analytical lifetime estimates for radiation belt electron diffusion by whistler waves

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A. V. Artemyev

2013-04-01

Full Text Available The lifetimes of electrons trapped in Earth's radiation belts can be calculated from quasi-linear pitch-angle diffusion by whistler-mode waves, provided that their frequency spectrum is broad enough and/or their average amplitude is not too large. Extensive comparisons between improved analytical lifetime estimates and full numerical calculations have been performed in a broad parameter range representative of a large part of the magnetosphere from L ~ 2 to 6. The effects of observed very oblique whistler waves are taken into account in both numerical and analytical calculations. Analytical lifetimes (and pitch-angle diffusion coefficients are found to be in good agreement with full numerical calculations based on CRRES and Cluster hiss and lightning-generated wave measurements inside the plasmasphere and Cluster lower-band chorus waves measurements in the outer belt for electron energies ranging from 100 keV to 5 MeV. Comparisons with lifetimes recently obtained from electron flux measurements on SAMPEX, SCATHA, SAC-C and DEMETER also show reasonable agreement.

Separation of musical instruments based on amplitude and frequency comodulation

Science.gov (United States)

Jacobson, Barry D.; Cauwenberghs, Gert; Quatieri, Thomas F.

2002-05-01

In previous work, amplitude comodulation was investigated as a basis for monaural source separation. Amplitude comodulation refers to similarities in amplitude envelopes of individual spectral components emitted by particular types of sources. In many types of musical instruments, amplitudes of all resonant modes rise/fall, and start/stop together during the course of normal playing. We found that under certain well-defined conditions, a mixture of constant frequency, amplitude comodulated sources can unambiguously be decomposed into its constituents on the basis of these similarities. In this work, system performance was improved by relaxing the constant frequency requirement. String instruments, for example, which are normally played with vibrato, are both amplitude and frequency comodulated sources, and could not be properly tracked under the constant frequency assumption upon which our original algorithm was based. Frequency comodulation refers to similarities in frequency variations of individual harmonics emitted by these types of sources. The analytical difficulty is in defining a representation of the source which properly tracks frequency varying components. A simple, fixed filter bank can only track an individual spectral component for the duration in which it is within the passband of one of the filters. Alternatives are therefore explored which are amenable to real-time implementation.

High Frequency Amplitude Detector for GMI Magnetic Sensors

Directory of Open Access Journals (Sweden)

Aktham Asfour

2014-12-01

Full Text Available A new concept of a high-frequency amplitude detector and demodulator for Giant-Magneto-Impedance (GMI sensors is presented. This concept combines a half wave rectifier, with outstanding capabilities and high speed, and a feedback approach that ensures the amplitude detection with easily adjustable gain. The developed detector is capable of measuring high-frequency and very low amplitude signals without the use of diode-based active rectifiers or analog multipliers. The performances of this detector are addressed throughout the paper. The full circuitry of the design is given, together with a comprehensive theoretical study of the concept and experimental validation. The detector has been used for the amplitude measurement of both single frequency and pulsed signals and for the demodulation of amplitude-modulated signals. It has also been successfully integrated in a GMI sensor prototype. Magnetic field and electrical current measurements in open- and closed-loop of this sensor have also been conducted.

Amplitudes and observables in pp elastic scattering at {radical}(s)=7 TeV

Energy Technology Data Exchange (ETDEWEB)

Kohara, A.K.; Ferreira, E. [Universidade Federal do Rio de Janeiro, Instituto de Fisica, C.P. 68528, Rio de Janeiro, RJ (Brazil); Kodama, T. [Universidade Federal do Rio de Janeiro, Instituto de Fisica, C.P. 68528, Rio de Janeiro, RJ (Brazil); EMMI at FIAS-Frankfurt Institute for Advanced Study, Frankfurt am Main (Germany)

2013-02-15

A precise analysis of the pp elastic scattering data at 7 TeV in terms of its amplitudes is performed as an extension of previous studies for lower energies. Slopes B{sub R} and B{sub I} of the real and imaginary amplitudes are independent quantities, and a proper expression for the Coulomb phase is used. The real and imaginary amplitudes are fully disentangled, consistently with forward dispersion relations for amplitudes and for slopes. We present analytic expressions for the amplitudes that cover all t range completely, while values of total cross section {sigma}, ratio {rho}, B{sub I}, and B{sub R} enter consistently to describe forward scattering. It is stressed that the identification of the amplitudes is an essential step for the description of elastic scattering, and pointed out the importance of the experimental investigation of the transition range from non-perturbative to perturbative dynamics, which may confirm the three gluon exchange mechanism observed at lower energies. (orig.)

Dispersion relation for elastic electron-hydrogen atom forward scattering amplitude

International Nuclear Information System (INIS)

Kuchiev, M.Yu.; Amusia, M.Ya.

1978-01-01

The elastic e+H forward scattering amplitude is an analytical function in the complex energy E plane and has two cuts on the real axis: 0 < E < infinity and -infinity < E < -B, B being the hydrogen ionization potential. The e+H dispersion relation contains two integrals over the right and left cuts. (Auth.)

One-loop helicity amplitudes for t anti t production at hadron colliders

International Nuclear Information System (INIS)

Badger, Simon; Yundin, Valery

2011-01-01

We present compact analytic expressions for all one-loop helicity amplitudes contributing to t anti t production at hadron colliders. Using recently developed generalised unitarity methods and a traditional Feynman based approach we produce a fast and flexible implementation. (ORIG.)

One-loop helicity amplitudes for t anti t production at hadron colliders

Energy Technology Data Exchange (ETDEWEB)

Badger, Simon [The Niels Bohr International Academy and Discovery Center, Copenhagen (Denmark). Niels Bohr Inst.; Sattler, Ralf [Humboldt Univ. Berlin (Germany). Inst. fuer Physik; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Yundin, Valery [Silesia Univ., Katowice (Poland). Inst. of Physics; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

2011-01-15

We present compact analytic expressions for all one-loop helicity amplitudes contributing to t anti t production at hadron colliders. Using recently developed generalised unitarity methods and a traditional Feynman based approach we produce a fast and flexible implementation. (ORIG.)

Parametric resonances in the amplitude-modulated probe-field absorption spectrum of a two-level atom driven by a resonance amplitude- and phase-modulated pumping field

International Nuclear Information System (INIS)

Sushilov, N.V.; Kholodkevich, E.D.

1995-01-01

An analytical expression is derived for the polarization induced by a weak probe field with periodically modulated amplitude in a two-level medium saturated by a strong amplitude-and phase-modulated resonance field. It is shown that the absorption spectrum of the probe field includes parametric resonances, the maxima corresponding to the condition δ= 2nΓ-Ω w and the minima to that of δ= (2n + 1)Γ- w , where δ is the probe-field detuning front the resonance frequency, Ω w is the modulation frequency of the probe-field amplitude, and Γ is the transition line width, n = 1, 2, 3, hor-ellipsis. At the specific modulation parameters, a substantial region of negative values (i.e., the region of amplification without the population inversion) exists in the absorption spectrum of the probe field

A new analytical approximation to the Duffing-harmonic oscillator

International Nuclear Information System (INIS)

Fesanghary, M.; Pirbodaghi, T.; Asghari, M.; Sojoudi, H.

2009-01-01

In this paper, a novel analytical approximation to the nonlinear Duffing-harmonic oscillator is presented. The variational iteration method (VIM) is used to obtain some accurate analytical results for frequency. The accuracy of the results is excellent in the whole range of oscillation amplitude variations.

Nth-powered amplitude squeezing in fan-states

CERN Document Server

Duc, T M

2002-01-01

Squeezing properties of the Hillery-type N-powered amplitude are investigated in the fan-state vertical bar xi; 2k, f> sub F which is linearly superposed by 2k 2k-quantum nonlinear coherent states in the phase-locked manner. The general expression of squeezing is derived analytically for arbitrary xi, k, N and f showing a multi-directional character of squeezing. For a given k, squeezing may appear to the even power N=2k if f ident to 1 and N>=2k if f not =1 and the number of directions along with the Nth-powered amplitude is squeezed is exactly equal to N, for both f ident to 1 (the light field) and f not =1 (the vibrational motion of the trapped ion). Discussions are also given elucidating the qualitative difference between the cases of f ident to 1 and f not =1.

NOTE ON TRAVEL TIME SHIFTS DUE TO AMPLITUDE MODULATION IN TIME-DISTANCE HELIOSEISMOLOGY MEASUREMENTS

International Nuclear Information System (INIS)

Nigam, R.; Kosovichev, A. G.

2010-01-01

Correct interpretation of acoustic travel times measured by time-distance helioseismology is essential to get an accurate understanding of the solar properties that are inferred from them. It has long been observed that sunspots suppress p-mode amplitude, but its implications on travel times have not been fully investigated so far. It has been found in test measurements using a 'masking' procedure, in which the solar Doppler signal in a localized quiet region of the Sun is artificially suppressed by a spatial function, and using numerical simulations that the amplitude modulations in combination with the phase-speed filtering may cause systematic shifts of acoustic travel times. To understand the properties of this procedure, we derive an analytical expression for the cross-covariance of a signal that has been modulated locally by a spatial function that has azimuthal symmetry and then filtered by a phase-speed filter typically used in time-distance helioseismology. Comparing this expression to the Gabor wavelet fitting formula without this effect, we find that there is a shift in the travel times that is introduced by the amplitude modulation. The analytical model presented in this paper can be useful also for interpretation of travel time measurements for the non-uniform distribution of oscillation amplitude due to observational effects.

Nonsinglet pentagons and NMHV amplitudes

Directory of Open Access Journals (Sweden)

A.V. Belitsky

2015-07-01

Full Text Available Scattering amplitudes in maximally supersymmetric gauge theory receive a dual description in terms of the expectation value of the super Wilson loop stretched on a null polygonal contour. This makes the analysis amenable to nonperturbative techniques. Presently, we elaborate on a refined form of the operator product expansion in terms of pentagon transitions to compute twist-two contributions to NMHV amplitudes. To start with, we provide a novel derivation of scattering matrices starting from Baxter equations for flux-tube excitations propagating on magnon background. We propose bootstrap equations obeyed by pentagon form factors with nonsinglet quantum numbers with respect to the R-symmetry group and provide solutions to them to all orders in 't Hooft coupling. These are then successfully confronted against available perturbative calculations for NMHV amplitudes to four-loop order.

Finite amplitude effects on drop levitation for material properties measurement

Science.gov (United States)

Ansari Hosseinzadeh, Vahideh; Holt, R. Glynn

2017-05-01

The method of exciting shape oscillation of drops to extract material properties has a long history, which is most often coupled with the technique of acoustic levitation to achieve non-contact manipulation of the drop sample. We revisit this method with application to the inference of bulk shear viscosity and surface tension. The literature is replete with references to a "10% oscillation amplitude" as a sufficient condition for the application of Lamb's analytical expressions for the shape oscillations of viscous liquids. Our results show that even a 10% oscillation amplitude leads to dynamic effects which render Lamb's results inapplicable. By comparison with samples of known viscosity and surface tension, we illustrate the complicating finite-amplitude effects (mode-splitting and excess dissipation associated with vorticity) that can occur and then show that sufficiently small oscillations allow us to recover the correct material properties using Lamb's formula.

Parametric characterization of a mesomechanic kinematic caused by ondulation in fabric reinforced composites: analytical and numerical investigations

Directory of Open Access Journals (Sweden)

Marco Romano

2017-01-01

Full Text Available A parametric characterization of a mesomechanic kinematic caused by ondulation in fabric reinforced composites is investigated by analytical and numerical investigations. Due to the definition of plain representative sequences of balanced plain-weave fabric reinforced single layers based on sines the variable geometric parameters are the amplitude and the length of the ondulation. The mesomechanic kinematic can be observed in both the analytic model and the FE-analyses. The analytic model yields hyperbolic correlations due to the strongly simplifying presumptions that neglect elasticity. In contrast the FE-analyses yield linear correlations in much smaller amounts due to the consideration of elastic parts, yet distinctly.

Multichannel scattering amplitudes of microparticles in a quantum well with two-dimensional -potential

International Nuclear Information System (INIS)

Sedrakian, D.M.; Badalyan, D.H.; Sedrakian, L.R.

2015-01-01

Quasi-one-dimensional quantum particle scattering on two-dimensional δ-potential is considered. Analytical expressions for the amplitudes of the multi-channel transmission and reflection are given. The problem for the case when the number of channels is finite and equal N, and the particle falls on the potential moving through the channel l is solved. The case of a three channel scattering is studied in details. It is shown that under conditions k 2 → 0 and k 3 → 0 'overpopulation' of particles on the second and third channels occurs. The points of δ-potential location which provide a full 'overpopulation' of particles is also found

Phases and amplitudes for a modified repulsive Coulomb field

International Nuclear Information System (INIS)

Chidichimo, M.C.; Davison, T.S.

1990-01-01

The asymptotic form of the radial wave function for positive-energy states is calculated for the case of a repulsive Coulomb field. The cases of a pure Coulomb potential and a modified Coulomb potential are considered. Second-order analytic solutions for the amplitudes and phases are obtained when the modifications to the pure Coulombic potential take the form αr -2 +βr -3 +γr -4 , using the Jeffreys or WKB method. For the case of a pure Coulomb field, numerical results obtained from this method were compared with ''exact'' numerical results that were obtained using the analytic properties of the Coulomb wave functions. Tables are presented to show the conditions under which the method is accurate

Theoretical treatment of high-frequency, large-amplitude ac voltammetry applied to ideal surface-confined redox systems

International Nuclear Information System (INIS)

Bell, Christopher G.; Anastassiou, Costas A.; O’Hare, Danny; Parker, Kim H.; Siggers, Jennifer H.

2012-01-01

Highlights: ► Theory of ac voltammetry on ideal surface-confined redox systems. ► Analytical description of the harmonics and transient of the current response. ► Solution valid for high frequency, large-amplitude sinusoidal input voltage. ► Protocol for determining system parameters from experimental current responses. - Abstract: Large-amplitude ac voltammetry, where the applied voltage is a large-amplitude sinusoidal waveform superimposed onto a dc ramp, is a powerful method for investigating the reaction kinetics of surface-confined redox species. Here we consider the large-amplitude ac voltammetric current response of a quasi-reversible, ideal, surface-confined redox system, for which the redox reaction is described by Butler–Volmer theory. We derive an approximate analytical solution, which is valid whenever the angular frequency of the sine-wave is much larger than the rate of the dc ramp and the standard kinetic rate constant of the redox reaction. We demonstrate how the third harmonic and the initial transient of the current response can be used to estimate parameters of the electrochemical system, namely the kinetic rate constant, the electron transfer coefficient, the adsorption formal potential, the initial proportion of oxidised molecules and the linear double-layer capacitance.

Multi-parton loop amplitudes and next-to-leading order jet cross-sections

International Nuclear Information System (INIS)

Bern, Z.; Dixon, L.; Kosower, D.A.; Signer, A.

1998-02-01

The authors review recent developments in the calculation of QCD loop amplitudes with several external legs, and their application to next-to-leading order jet production cross-sections. When a number of calculational tools are combined together--helicity, color and supersymmetry decompositions, plus unitarity and factorization properties--it becomes possible to compute multi-parton one-loop QCD amplitudes without ever evaluating analytically standard one-loop Feynman diagrams. One-loop helicity amplitudes are now available for processes with five external partons (ggggg, q anti qggg and q anti qq anti q' g), and for an intermediate vector boson V ≡ γ * , Z, W plus four external partons (V q anti q and V q anti qq'anti q'). Using these amplitudes, numerical programs have been constructed for the next-to-leading order corrections to the processes p anti p → 3 jets (ignoring quark contributions so far) and e + e - → 4 jets

The two Josephson junction flux qubit with large tunneling amplitude

International Nuclear Information System (INIS)

Shnurkov, V.I.; Soroka, A.A.; Mel'nik, S.I.

2008-01-01

In this paper we discuss solid-state nanoelectronic realizations of Josephson flux qubits with large tunneling amplitude between the two macroscopic states. The latter can be controlled via the height and form of the potential barrier, which is determined by quantum-state engineering of the flux qubit circuit. The simplest circuit of the flux qubit is a superconducting loop interrupted by a Josephson nanoscale tunnel junction. The tunneling amplitude between two macroscopically different states can be increased substantially by engineering of the qubit circuit if the tunnel junction is replaced by a ScS contact. However, only Josephson tunnel junctions are particularly suitable for large-scale integration circuits and quantum detectors with present-day technology. To overcome this difficulty we consider here a flux qubit with high energy-level separation between the 'ground' and 'excited' states, consisting of a superconducting loop with two low-capacitance Josephson tunnel junctions in series. We demonstrate that for real parameters of resonant superposition between the two macroscopic states the tunneling amplitude can reach values greater than 1 K. Analytical results for the tunneling amplitude obtained within the semiclassical approximation by the instanton technique show good correlation with a numerical solution

Full and semi-analytic analyses of two-pump parametric amplification with pump depletion

DEFF Research Database (Denmark)

Steffensen, Henrik; Ott, Johan Raunkjær; Rottwitt, Karsten

2011-01-01

This paper solves the four coupled equations describing non-degenerate four-wave mixing, with the focus on amplifying a signal in a fiber optical parametric amplifier (FOPA). Based on the full analytic solution, a simple approximate solution describing the gain is developed. The advantage...... of this new approximation is that it includes the depletion of the pumps, which is lacking in the usual quasi-linearized approximation. With the proposed model it is thus simple to predict the gain of a FOPA, which we demonstrate with a highly nonlinear fiber to show that an undepleted FOPA can produce a flat...

3D elastic full waveform inversion using P-wave excitation amplitude: Application to OBC field data

KAUST Repository

Oh, Juwon; Kalita, Mahesh; Alkhalifah, Tariq Ali

2017-01-01

We propose an efficient elastic full waveform inversion (FWI) based on the P-wave excitation amplitude (maximum energy arrival) approximation in the source wavefields. Because, based on the P-wave excitation approximation (ExA), the gradient direction is approximated by the cross-correlation of source and receiver wavefields at only excitation time, it estimates the gradient direction faster than its conventional counterpart. In addition to this computational speedup, the P-wave excitation approximation automatically ignores SP and SS correlations in the approximated gradient direction. In elastic FWI for ocean bottom cable (OBC) data, the descent direction for the S-wave velocity is often degraded by undesired long-wavelength features from the SS correlation. For this reason, the P-wave excitation approach increases the convergence rate of multi-parameter FWI compared to the conventional approach. The modified 2D Marmousi model with OBC acquisition is used to verify the differences between the conventional method and ExA. Finally, the feasibility of the proposed method is demonstrated on a real OBC data from North Sea.

3D elastic full waveform inversion using P-wave excitation amplitude: Application to OBC field data

KAUST Repository

Oh, Juwon

2017-12-05

We propose an efficient elastic full waveform inversion (FWI) based on the P-wave excitation amplitude (maximum energy arrival) approximation in the source wavefields. Because, based on the P-wave excitation approximation (ExA), the gradient direction is approximated by the cross-correlation of source and receiver wavefields at only excitation time, it estimates the gradient direction faster than its conventional counterpart. In addition to this computational speedup, the P-wave excitation approximation automatically ignores SP and SS correlations in the approximated gradient direction. In elastic FWI for ocean bottom cable (OBC) data, the descent direction for the S-wave velocity is often degraded by undesired long-wavelength features from the SS correlation. For this reason, the P-wave excitation approach increases the convergence rate of multi-parameter FWI compared to the conventional approach. The modified 2D Marmousi model with OBC acquisition is used to verify the differences between the conventional method and ExA. Finally, the feasibility of the proposed method is demonstrated on a real OBC data from North Sea.

Dispersion relation for the 3. -->. 3 forward scattering amplitude and the generalized optical theorem. [Crossing properties, dispersion relations

Energy Technology Data Exchange (ETDEWEB)

Logunov, A A; Medvedev, B V; Mestvirishvili, M A; Pavlov, V P; Polivanov, M K; Sukhanov, A D [Gosudarstvennyj Komitet po Ispol' zovaniyu Atomnoj Ehnergii SSSR, Serpukhov. Inst. Fiziki Vysokikh Ehnergij

1977-11-01

Investigation of analytical structure of the three-particle forward scattering amplitude with respect to energy variable of one of particles is performed. The results obtained make it possible to draw the conclusions on crossing properties of the amplitude and to derive the generalized optical theorem relating the discontinuity of the amplitude to the distribution function of an inclusive process. For a special case when two of three particles are of zero mass, a dispersion relation is proved.

Scattering amplitudes over finite fields and multivariate functional reconstruction

Energy Technology Data Exchange (ETDEWEB)

Peraro, Tiziano [Higgs Centre for Theoretical Physics,School of Physics and Astronomy, The University of Edinburgh,James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD (United Kingdom)

2016-12-07

Several problems in computer algebra can be efficiently solved by reducing them to calculations over finite fields. In this paper, we describe an algorithm for the reconstruction of multivariate polynomials and rational functions from their evaluation over finite fields. Calculations over finite fields can in turn be efficiently performed using machine-size integers in statically-typed languages. We then discuss the application of the algorithm to several techniques related to the computation of scattering amplitudes, such as the four- and six-dimensional spinor-helicity formalism, tree-level recursion relations, and multi-loop integrand reduction via generalized unitarity. The method has good efficiency and scales well with the number of variables and the complexity of the problem. As an example combining these techniques, we present the calculation of full analytic expressions for the two-loop five-point on-shell integrands of the maximal cuts of the planar penta-box and the non-planar double-pentagon topologies in Yang-Mills theory, for a complete set of independent helicity configurations.

Scattering amplitudes over finite fields and multivariate functional reconstruction

International Nuclear Information System (INIS)

Peraro, Tiziano

2016-01-01

Several problems in computer algebra can be efficiently solved by reducing them to calculations over finite fields. In this paper, we describe an algorithm for the reconstruction of multivariate polynomials and rational functions from their evaluation over finite fields. Calculations over finite fields can in turn be efficiently performed using machine-size integers in statically-typed languages. We then discuss the application of the algorithm to several techniques related to the computation of scattering amplitudes, such as the four- and six-dimensional spinor-helicity formalism, tree-level recursion relations, and multi-loop integrand reduction via generalized unitarity. The method has good efficiency and scales well with the number of variables and the complexity of the problem. As an example combining these techniques, we present the calculation of full analytic expressions for the two-loop five-point on-shell integrands of the maximal cuts of the planar penta-box and the non-planar double-pentagon topologies in Yang-Mills theory, for a complete set of independent helicity configurations.

Amplitude modulation control of escape from a potential well

International Nuclear Information System (INIS)

Chacón, R.; Martínez García-Hoz, A.; Miralles, J.J.; Martínez, P.J.

2014-01-01

We demonstrate the effectiveness of periodic amplitude modulations in controlling (suppressing and enhancing) escape from a potential well through the universal model of a damped Helmholtz oscillator subjected to an external periodic excitation (the escape-inducing excitation) whose amplitude is periodically modulated (the escape-controlling excitation). Analytical and numerical results show that this multiplicative control works reliably for different subharmonic resonances between the two periodic excitations involved, and that its effectiveness is comparable to those of different methods of additive control. Additionally, we demonstrate the robustness of the multiplicative control against the presence of low-intensity Gaussian noise. -- Highlights: •Multiplicative control of escape from a potential well has been demonstrated. •Theoretical predictions are obtained from a Melnikov analysis. •It has been shown the robustness of the multiplicative control against noise.

Analytic observables in nuclear physics

International Nuclear Information System (INIS)

Borbely, I.

1980-05-01

The analytical dependence of quantum mechanical observables on their variables is discussed by using the assumption that the corresponding probability amplitudes are analytic functions. The properties of the cross section in the energy plane for spinless particles as well as the properties of the most general polarization observables in the cosdelta plane are considered in detail. In particular, the strength of the transfer pole for polarization observables is given. The practical possibilities to extract the different orbital momentum components of nuclei by extrapolation techniques are briefly outlined. (author)

Amplitude damping of vortex modes

CSIR Research Space (South Africa)

Dudley, Angela L

2010-09-01

Full Text Available An interferometer, mimicking an amplitude damping channel for vortex modes, is presented. Experimentally the action of the channel is in good agreement with that predicted theoretically. Since we can characterize the action of the channel on orbital...

Real-Time Amplitude and Phase Imaging of Optically Opaque Objects by Combining Full-Field Off-Axis Terahertz Digital Holography with Angular Spectrum Reconstruction

Science.gov (United States)

Yamagiwa, Masatomo; Ogawa, Takayuki; Minamikawa, Takeo; Abdelsalam, Dahi Ghareab; Okabe, Kyosuke; Tsurumachi, Noriaki; Mizutani, Yasuhiro; Iwata, Testuo; Yamamoto, Hirotsugu; Yasui, Takeshi

2018-06-01

Terahertz digital holography (THz-DH) has the potential to be used for non-destructive inspection of visibly opaque soft materials due to its good immunity to optical scattering and absorption. Although previous research on full-field off-axis THz-DH has usually been performed using Fresnel diffraction reconstruction, its minimum reconstruction distance occasionally prevents a sample from being placed near a THz imager to increase the signal-to-noise ratio in the hologram. In this article, we apply the angular spectrum method (ASM) for wavefront reconstruction in full-filed off-axis THz-DH because ASM is more accurate at short reconstruction distances. We demonstrate real-time phase imaging of a visibly opaque plastic sample with a phase resolution power of λ/49 at a frame rate of 3.5 Hz in addition to real-time amplitude imaging. We also perform digital focusing of the amplitude image for the same object with a depth selectivity of 447 μm. Furthermore, 3D imaging of visibly opaque silicon objects was achieved with a depth precision of 1.7 μm. The demonstrated results indicate the high potential of the proposed method for in-line or in-process non-destructive inspection of soft materials.

Real-Time Amplitude and Phase Imaging of Optically Opaque Objects by Combining Full-Field Off-Axis Terahertz Digital Holography with Angular Spectrum Reconstruction

Science.gov (United States)

Yamagiwa, Masatomo; Ogawa, Takayuki; Minamikawa, Takeo; Abdelsalam, Dahi Ghareab; Okabe, Kyosuke; Tsurumachi, Noriaki; Mizutani, Yasuhiro; Iwata, Testuo; Yamamoto, Hirotsugu; Yasui, Takeshi

2018-04-01

Terahertz digital holography (THz-DH) has the potential to be used for non-destructive inspection of visibly opaque soft materials due to its good immunity to optical scattering and absorption. Although previous research on full-field off-axis THz-DH has usually been performed using Fresnel diffraction reconstruction, its minimum reconstruction distance occasionally prevents a sample from being placed near a THz imager to increase the signal-to-noise ratio in the hologram. In this article, we apply the angular spectrum method (ASM) for wavefront reconstruction in full-filed off-axis THz-DH because ASM is more accurate at short reconstruction distances. We demonstrate real-time phase imaging of a visibly opaque plastic sample with a phase resolution power of λ/49 at a frame rate of 3.5 Hz in addition to real-time amplitude imaging. We also perform digital focusing of the amplitude image for the same object with a depth selectivity of 447 μm. Furthermore, 3D imaging of visibly opaque silicon objects was achieved with a depth precision of 1.7 μm. The demonstrated results indicate the high potential of the proposed method for in-line or in-process non-destructive inspection of soft materials.

Application of modified homotopy perturbation method and amplitude frequency formulation to strongly nonlinear oscillators

Directory of Open Access Journals (Sweden)

seyd ghasem enayati

2017-01-01

Full Text Available In this paper, two powerful analytical methods known as modified homotopy perturbation method and Amplitude Frequency Formulation called respectively MHPM and AFF, are introduced to derive approximate solutions of a system of ordinary differential equations appear in mechanical applications. These methods convert a difficult problem into a simple one, which can be easily handled. The obtained solutions are compared with numerical fourth order runge-kutta method to show the applicability and accuracy of both MHPM and AFF in solving this sample problem. The results attained in this paper confirm the idea that MHPM and AFF are powerful mathematical tools and they can be applied to linear and nonlinear problems.

Ambitwistor strings and reggeon amplitudes in N=4 SYM

Directory of Open Access Journals (Sweden)

L.V. Bork

2017-11-01

Full Text Available We consider the description of reggeon amplitudes (Wilson lines form factors in N=4 SYM within the framework of four dimensional ambitwistor string theory. The latter is used to derive scattering equations representation for reggeon amplitudes with multiple reggeized gluons present. It is shown, that corresponding tree-level string correlation function correctly reproduces previously obtained Grassmannian integral representation of reggeon amplitudes in N=4 SYM.

ANALYTICAL EXPRESSION FOR THE ELECTRIC FIELD OF THE SINGLE MODE LASER HOMOGENEOUS BROADENING IN THE PULSE REGIME

Directory of Open Access Journals (Sweden)

S. Ayadi

2015-07-01

Full Text Available The simplest model of the laser is that of a single mode system homogenously broadened. The dynamical behavior of this laser is described by three differential equations, called Haken-Lorenz equations[1],  similar to the Lorenz model [1] already known to predict deterministic chaos. In previous recent work [5-7] we have proposed a simple harmonic expansion method to obtain a series of harmonics terms that yield analytical solutions to the laser equations. ¶This method allows us to derive an analytical expression of the laser field amplitude  when this last  undergoes a  periodic oscillations around zero mean value. We also obtain an analytical expression of the pulsing frequency.

Analytic solution for a quartic electron mirror

Energy Technology Data Exchange (ETDEWEB)

Straton, Jack C., E-mail: straton@pdx.edu

2015-01-15

A converging electron mirror can be used to compensate for spherical and chromatic aberrations in an electron microscope. This paper presents an analytical solution to a diode (two-electrode) electrostatic mirror including the next term beyond the known hyperbolic shape. The latter is a solution of the Laplace equation to second order in the variables perpendicular to and along the mirror's radius (z{sup 2}−r{sup 2}/2) to which we add a quartic term (kλz{sup 4}). The analytical solution is found in terms of Jacobi cosine-amplitude functions. We find that a mirror less concave than the hyperbolic profile is more sensitive to changes in mirror voltages and the contrary holds for the mirror more concave than the hyperbolic profile. - Highlights: • We find the analytical solution for electron mirrors whose curvature has z4 dependence added to the usual z{sup 2} – r{sup 2}/2 terms. • The resulting Jacobi cosine-amplitude function reduces to the well-known cosh solution in the limit where the new term is 0. • This quartic term gives a mirror designer additional flexibility for eliminating spherical and chromatic aberrations. • The possibility of using these analytical results to approximately model spherical tetrode mirrors close to axis is noted.

On the analytic continuation of functions defined by Legendre series

International Nuclear Information System (INIS)

Grinstein, F.F.

1981-07-01

An infinite diagonal sequence of Punctual Pade Approximants is considered for the approximate analytical continuation of a function defined by a formal Legendre series. The technique is tested in the case of two series with exactly known analytical sum: the generating function for Legendre polynomials and the Coulombian scattering amplitude. (author)

Propagation of Finite Amplitude Sound in Multiple Waveguide Modes.

Science.gov (United States)

van Doren, Thomas Walter

1993-01-01

This dissertation describes a theoretical and experimental investigation of the propagation of finite amplitude sound in multiple waveguide modes. Quasilinear analytical solutions of the full second order nonlinear wave equation, the Westervelt equation, and the KZK parabolic wave equation are obtained for the fundamental and second harmonic sound fields in a rectangular rigid-wall waveguide. It is shown that the Westervelt equation is an acceptable approximation of the full nonlinear wave equation for describing guided sound waves of finite amplitude. A system of first order equations based on both a modal and harmonic expansion of the Westervelt equation is developed for waveguides with locally reactive wall impedances. Fully nonlinear numerical solutions of the system of coupled equations are presented for waveguides formed by two parallel planes which are either both rigid, or one rigid and one pressure release. These numerical solutions are compared to finite -difference solutions of the KZK equation, and it is shown that solutions of the KZK equation are valid only at frequencies which are high compared to the cutoff frequencies of the most important modes of propagation (i.e., for which sound propagates at small grazing angles). Numerical solutions of both the Westervelt and KZK equations are compared to experiments performed in an air-filled, rigid-wall, rectangular waveguide. Solutions of the Westervelt equation are in good agreement with experiment for low source frequencies, at which sound propagates at large grazing angles, whereas solutions of the KZK equation are not valid for these cases. At higher frequencies, at which sound propagates at small grazing angles, agreement between numerical solutions of the Westervelt and KZK equations and experiment is only fair, because of problems in specifying the experimental source condition with sufficient accuracy.

Fringe image analysis based on the amplitude modulation method.

Science.gov (United States)

Gai, Shaoyan; Da, Feipeng

2010-05-10

A novel phase-analysis method is proposed. To get the fringe order of a fringe image, the amplitude-modulation fringe pattern is carried out, which is combined with the phase-shift method. The primary phase value is obtained by a phase-shift algorithm, and the fringe-order information is encoded in the amplitude-modulation fringe pattern. Different from other methods, the amplitude-modulation fringe identifies the fringe order by the amplitude of the fringe pattern. In an amplitude-modulation fringe pattern, each fringe has its own amplitude; thus, the order information is integrated in one fringe pattern, and the absolute fringe phase can be calculated correctly and quickly with the amplitude-modulation fringe image. The detailed algorithm is given, and the error analysis of this method is also discussed. Experimental results are presented by a full-field shape measurement system where the data has been processed using the proposed algorithm. (c) 2010 Optical Society of America.

Causality and analyticity in quantum fields theory

International Nuclear Information System (INIS)

Iagolnitzer, D.

1992-01-01

This is a presentation of results on the causal and analytical structure of Green functions and on the collision amplitudes in fields theories, for massive particles of one type, with a positive mass and a zero spin value. (A.B.)

Effective gluon interactions from superstring disk amplitudes

International Nuclear Information System (INIS)

Oprisa, D.

2006-05-01

In this thesis an efficient method for the calculation of the N-point tree-level string amplitudes is presented. Furthermore it is shown that the six-gluon open-superstring disk amplitude can be expressed by a basis of six triple hypergeometric functions, which encode the full α' dependence. In this connection material for obtaining the α' expansion of these functions is derived. Hereby many Euler-Zagier sums are calculated including multiple harmonic series. (HSI)

A Big Data Analytics Pipeline for the Analysis of TESS Full Frame Images

Science.gov (United States)

Wampler-Doty, Matthew; Pierce Doty, John

2015-12-01

We present a novel method for producing a catalogue of extra-solar planets and transients using the full frame image data from TESS. Our method involves (1) creating a fast Monte Carlo simulation of the TESS science instruments, (2) using the simulation to create a labeled dataset consisting of exoplanets with various orbital durations as well as transients (such as tidal disruption events), (3) using supervised machine learning to find optimal matched filters, Support Vector Machines (SVMs) and statistical classifiers (i.e. naïve Bayes and Markov Random Fields) to detect astronomical objects of interest and (4) “Big Data” analysis to produce a catalogue based on the TESS data. We will apply the resulting methods to all stars in the full frame images. We hope that by providing libraries that conform to industry standards of Free Open Source Software we may invite researchers from the astronomical community as well as the wider data-analytics community to contribute to our effort.

Amplitude-Integrated EEG in the Newborn

Directory of Open Access Journals (Sweden)

J Gordon Millichap

2008-11-01

Full Text Available Th value of amplitude-integrated electroencephalography (aEEG in the newborn is explored by researchers at Washington University, St Louis; Wilhelmina Children’s Hospital, Utrecht, Netherlands; and Uppsala University Hospital, Sweden.

Properties of partial-wave amplitudes in conformal invariant field theories

CERN Document Server

Ferrara, Sergio; Grillo, A F

1975-01-01

Analyticity properties of partial-wave amplitudes of the conformal group O/sub D,2/ (D not necessarily integer) in configuration space are investigated. The presence of Euclidean singularities in the Wilson expansion in conformal invariant field theories is discussed, especially in connection with the program of formulating dynamical bootstrap conditions coming from the requirement of causality. The exceptional case of D-2 is discussed in detail. (18 refs).

True amplitude wave equation migration arising from true amplitude one-way wave equations

Science.gov (United States)

Zhang, Yu; Zhang, Guanquan; Bleistein, Norman

2003-10-01

One-way wave operators are powerful tools for use in forward modelling and inversion. Their implementation, however, involves introduction of the square root of an operator as a pseudo-differential operator. Furthermore, a simple factoring of the wave operator produces one-way wave equations that yield the same travel times as the full wave equation, but do not yield accurate amplitudes except for homogeneous media and for almost all points in heterogeneous media. Here, we present augmented one-way wave equations. We show that these equations yield solutions for which the leading order asymptotic amplitude as well as the travel time satisfy the same differential equations as the corresponding functions for the full wave equation. Exact representations of the square-root operator appearing in these differential equations are elusive, except in cases in which the heterogeneity of the medium is independent of the transverse spatial variables. Here, we address the fully heterogeneous case. Singling out depth as the preferred direction of propagation, we introduce a representation of the square-root operator as an integral in which a rational function of the transverse Laplacian appears in the integrand. This allows us to carry out explicit asymptotic analysis of the resulting one-way wave equations. To do this, we introduce an auxiliary function that satisfies a lower dimensional wave equation in transverse spatial variables only. We prove that ray theory for these one-way wave equations leads to one-way eikonal equations and the correct leading order transport equation for the full wave equation. We then introduce appropriate boundary conditions at z = 0 to generate waves at depth whose quotient leads to a reflector map and an estimate of the ray theoretical reflection coefficient on the reflector. Thus, these true amplitude one-way wave equations lead to a 'true amplitude wave equation migration' (WEM) method. In fact, we prove that applying the WEM imaging condition

Full-Color Plasmonic Metasurface Holograms.

Science.gov (United States)

Wan, Weiwei; Gao, Jie; Yang, Xiaodong

2016-12-27

Holography is one of the most attractive approaches for reconstructing optical images, due to its capability of recording both the amplitude and phase information on light scattered from objects. Recently, optical metasurfaces for manipulating the wavefront of light with well-controlled amplitude, phase, and polarization have been utilized to reproduce computer-generated holograms. However, the currently available metasurface holograms have only been designed to achieve limited colors and record either amplitude or phase information. This fact significantly limits the performance of metasurface holograms to reconstruct full-color images with low noise and high quality. Here, we report the design and realization of ultrathin plasmonic metasurface holograms made of subwavelength nanoslits for reconstructing both two- and three-dimensional full-color holographic images. The wavelength-multiplexed metasurface holograms with both amplitude and phase modulations at subwavelength scale can faithfully produce not only three primary colors but also their secondary colors. Our results will advance various holographic applications.

Effective gluon interactions from superstring disk amplitudes

Energy Technology Data Exchange (ETDEWEB)

Oprisa, D.

2006-05-15

In this thesis an efficient method for the calculation of the N-point tree-level string amplitudes is presented. Furthermore it is shown that the six-gluon open-superstring disk amplitude can be expressed by a basis of six triple hypergeometric functions, which encode the full {alpha}' dependence. In this connection material for obtaining the {alpha}' expansion of these functions is derived. Hereby many Euler-Zagier sums are calculated including multiple harmonic series. (HSI)

Padé approximant for normal stress differences in large-amplitude oscillatory shear flow

Science.gov (United States)

Poungthong, P.; Saengow, C.; Giacomin, A. J.; Kolitawong, C.; Merger, D.; Wilhelm, M.

2018-04-01

Analytical solutions for the normal stress differences in large-amplitude oscillatory shear flow (LAOS), for continuum or molecular models, normally take the inexact form of the first few terms of a series expansion in the shear rate amplitude. Here, we improve the accuracy of these truncated expansions by replacing them with rational functions called Padé approximants. The recent advent of exact solutions in LAOS presents an opportunity to identify accurate and useful Padé approximants. For this identification, we replace the truncated expansion for the corotational Jeffreys fluid with its Padé approximants for the normal stress differences. We uncover the most accurate and useful approximant, the [3,4] approximant, and then test its accuracy against the exact solution [C. Saengow and A. J. Giacomin, "Normal stress differences from Oldroyd 8-constant framework: Exact analytical solution for large-amplitude oscillatory shear flow," Phys. Fluids 29, 121601 (2017)]. We use Ewoldt grids to show the stunning accuracy of our [3,4] approximant in LAOS. We quantify this accuracy with an objective function and then map it onto the Pipkin space. Our two applications illustrate how to use our new approximant reliably. For this, we use the Spriggs relations to generalize our best approximant to multimode, and then, we compare with measurements on molten high-density polyethylene and on dissolved polyisobutylene in isobutylene oligomer.

Optical asymmetric cryptography based on amplitude reconstruction of elliptically polarized light

Science.gov (United States)

Cai, Jianjun; Shen, Xueju; Lei, Ming

2017-11-01

We propose a novel optical asymmetric image encryption method based on amplitude reconstruction of elliptically polarized light, which is free from silhouette problem. The original image is analytically separated into two phase-only masks firstly, and then the two masks are encoded into amplitudes of the orthogonal polarization components of an elliptically polarized light. Finally, the elliptically polarized light propagates through a linear polarizer, and the output intensity distribution is recorded by a CCD camera to obtain the ciphertext. The whole encryption procedure could be implemented by using commonly used optical elements, and it combines diffusion process and confusion process. As a result, the proposed method achieves high robustness against iterative-algorithm-based attacks. Simulation results are presented to prove the validity of the proposed cryptography.

Scattering amplitudes in gauge theories with and without supersymmetry

International Nuclear Information System (INIS)

Ochirov, Alexander

2014-01-01

This thesis aims at providing better understanding of the perturbative expansion of gauge theories with and without supersymmetry. At tree level, the BCFW recursion relations are analyzed with respect to their validity for general off-shell objects in Yang-Mills theory, which is a significant step away from their established zone of applicability. Unphysical poles constitute a new potential problem in addition to the boundary behavior issue, common to the on-shell case as well. For an infinite family of massive fermion currents, both obstacles are shown to be avoided under the certain conditions, which provides a natural recursion relation. At one loop, scattering amplitudes can be calculated from unitarity cuts through their expansion into known scalar integrals with free coefficients. A powerful method to obtain these coefficients, namely spinor integration, is discussed and rederived in a somewhat novel form. It is then used to compute analytically the infinite series of one-loop gluon amplitudes in N = 1 super-Yang-Mills theory with exactly three negative helicities. The final part of this thesis concerns the intriguing relationship between gluon and graviton scattering amplitudes, which involves a beautiful duality between the color and kinematic content of gauge theories. This BCJ duality is extended to include particles in the fundamental representation of the gauge group, which is shown to relieve the restriction of the BCJ construction to factorizable gravities and thus give access to amplitudes in generic (super-)gravity theories. (author) [fr

Stora's fine notion of divergent amplitudes

Directory of Open Access Journals (Sweden)

Joseph C. Várilly

2016-11-01

Full Text Available Stora and coworkers refined the notion of divergent quantum amplitude, somewhat upsetting the standard power-counting recipe. This unexpectedly clears the way to new prototypes for free and interacting field theories of bosons of any mass and spin.

Analytical model for vibration prediction of two parallel tunnels in a full-space

Science.gov (United States)

He, Chao; Zhou, Shunhua; Guo, Peijun; Di, Honggui; Zhang, Xiaohui

2018-06-01

This paper presents a three-dimensional analytical model for the prediction of ground vibrations from two parallel tunnels embedded in a full-space. The two tunnels are modelled as cylindrical shells of infinite length, and the surrounding soil is modelled as a full-space with two cylindrical cavities. A virtual interface is introduced to divide the soil into the right layer and the left layer. By transforming the cylindrical waves into the plane waves, the solution of wave propagation in the full-space with two cylindrical cavities is obtained. The transformations from the plane waves to cylindrical waves are then used to satisfy the boundary conditions on the tunnel-soil interfaces. The proposed model provides a highly efficient tool to predict the ground vibration induced by the underground railway, which accounts for the dynamic interaction between neighbouring tunnels. Analysis of the vibration fields produced over a range of frequencies and soil properties is conducted. When the distance between the two tunnels is smaller than three times the tunnel diameter, the interaction between neighbouring tunnels is highly significant, at times in the order of 20 dB. It is necessary to consider the interaction between neighbouring tunnels for the prediction of ground vibrations induced underground railways.

Analytic nuclear forces and molecular properties from full configuration interaction quantum Monte Carlo

International Nuclear Information System (INIS)

Thomas, Robert E.; Overy, Catherine; Opalka, Daniel; Alavi, Ali; Knowles, Peter J.; Booth, George H.

2015-01-01

Unbiased stochastic sampling of the one- and two-body reduced density matrices is achieved in full configuration interaction quantum Monte Carlo with the introduction of a second, “replica” ensemble of walkers, whose population evolves in imaginary time independently from the first and which entails only modest additional computational overheads. The matrices obtained from this approach are shown to be representative of full configuration-interaction quality and hence provide a realistic opportunity to achieve high-quality results for a range of properties whose operators do not necessarily commute with the Hamiltonian. A density-matrix formulated quasi-variational energy estimator having been already proposed and investigated, the present work extends the scope of the theory to take in studies of analytic nuclear forces, molecular dipole moments, and polarisabilities, with extensive comparison to exact results where possible. These new results confirm the suitability of the sampling technique and, where sufficiently large basis sets are available, achieve close agreement with experimental values, expanding the scope of the method to new areas of investigation

Singularity Structure of Maximally Supersymmetric Scattering Amplitudes

DEFF Research Database (Denmark)

Arkani-Hamed, Nima; Bourjaily, Jacob L.; Cachazo, Freddy

2014-01-01

We present evidence that loop amplitudes in maximally supersymmetric (N=4) Yang-Mills theory (SYM) beyond the planar limit share some of the remarkable structures of the planar theory. In particular, we show that through two loops, the four-particle amplitude in full N=4 SYM has only logarithmic ...... singularities and is free of any poles at infinity—properties closely related to uniform transcendentality and the UV finiteness of the theory. We also briefly comment on implications for maximal (N=8) supergravity theory (SUGRA)....

Heptagon amplitude in the multi-Regge regime

International Nuclear Information System (INIS)

Bartels, J.

2014-05-01

As we have shown in previous work, the high energy limit of scattering amplitudes in N=4 supersymmetric Yang-Mills theory corresponds to the infrared limit of the 1-dimensional quantum integrable system that solves minimal area problems in AdS 5 . This insight can be developed into a systematic algorithm to compute the strong coupling limit of amplitudes in the multi-Regge regime through the solution of auxiliary Bethe Ansatz equations. We apply this procedure to compute the scattering amplitude for n=7 external gluons in different multi-Regge regions at infinite 't Hooft coupling. Our formulas are remarkably consistent with the expected form of 7-gluon Regge cut contributions in perturbative gauge theory. A full description of the general algorithm and a derivation of results is given in a forthcoming paper.

A complete two-loop, five-gluon helicity amplitude in Yang-Mills theory

International Nuclear Information System (INIS)

Badger, Simon; Mogull, Gustav; Ochirov, Alexander; O’Connell, Donal

2015-01-01

We compute the integrand of the full-colour, two-loop, five-gluon scattering amplitude in pure Yang-Mills theory with all helicities positive, using generalized unitarity cuts. Tree-level BCJ relations, satisfied by amplitudes appearing in the cuts, allow us to deduce all the necessary non-planar information for the full-colour amplitude from known planar data. We present our result in terms of irreducible numerators, with colour factors derived from the multi-peripheral colour decomposition. Finally, the leading soft divergences are checked to reproduce the expected infrared behaviour.

A complete two-loop, five-gluon helicity amplitude in Yang-Mills theory

Energy Technology Data Exchange (ETDEWEB)

Badger, Simon; Mogull, Gustav; Ochirov, Alexander [Higgs Centre for Theoretical Physics, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3JZ, Scotland (United Kingdom); O’Connell, Donal [Higgs Centre for Theoretical Physics, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3JZ, Scotland (United Kingdom); Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106-4030 (United States)

2015-10-09

We compute the integrand of the full-colour, two-loop, five-gluon scattering amplitude in pure Yang-Mills theory with all helicities positive, using generalized unitarity cuts. Tree-level BCJ relations, satisfied by amplitudes appearing in the cuts, allow us to deduce all the necessary non-planar information for the full-colour amplitude from known planar data. We present our result in terms of irreducible numerators, with colour factors derived from the multi-peripheral colour decomposition. Finally, the leading soft divergences are checked to reproduce the expected infrared behaviour.

Color guided amplitudes

Energy Technology Data Exchange (ETDEWEB)

Broedel, Johannes [Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, CA (United States); Dixon, Lance J. [SLAC National Accelerator Laboratory, Stanford University, Stanford, CA (United States)

2012-07-01

Amplitudes in gauge thoeries obtain contributions from color and kinematics. While these two parts of the amplitude seem to exhibit different symmetry structures, it turns out that they can be reorganized in a way to behave equally, which leads to the so-called color-kinematic dual representations of amplitudes. Astonishingly, the existence of those representations allows squaring to related gravitational theories right away. Contrary to the Kawaii-Levellen-Tye relations, which have been used to relate gauge theories and gravity previously, this method is applicable not only to tree amplitudes but also at loop level. In this talk, the basic technique is introduced followed by a discussion of the existence of color-kinematic dual representations for amplitudes derived from gauge theory actions which are deformed by higher-operator insertions. In addition, it is commented on the implications for deformed gravitational theories.

Full energy peak efficiency of NaI(Tl) gamma detectors and its analytical and semi-empirical representations

International Nuclear Information System (INIS)

Sudarshan, M.; Joseph, J.; Singh, R.

1992-01-01

The validity of various analytical functions and semi-empirical formulae proposed for representing the full energy peak efficiency (FEPE) curves of Ge(Li) and HPGe detectors has been tested for the FEPE of 7.6 cm x 7.6 cm and 5 cm x 5 cm Nal(Tl) detectors in the gamma energy range from 59.5 to 1408.03 keV. The functions proposed by East, and McNelles and Campbell provide by far the best representations of the present data. The semi-empirical formula of Mowatt describes the present data very well. The present investigation shows that some of the analytical functions and semi-empirical formulae, which represent the FEPE of the Ge(Li) and HPGe detectors very well, can be quite fruitfully used for Nal(Tl) detectors. (Author)

Amplitude Modulation in the δ Sct star KIC 7106205

Directory of Open Access Journals (Sweden)

Bowman Dominic. M.

2015-01-01

Full Text Available The δ Sct star KIC 7106205 showed amplitude modulation in a single p mode, whilst all other p and g modes remained stable in amplitude and phase over 1470 d of the Kepler dataset. The data were divided into 30 time bins of equal length and a series of consecutive Fourier transforms was calculated. A fixed frequency, calculated from a least-squares fit of all data, allowed amplitude and phase for every mode in each time bin to be tracked. The missing p mode energy was not transferred to any other visible modes.

Simulation of channeling and radiation of 855 MeV electrons and positrons in a small-amplitude short-period bent crystal

Energy Technology Data Exchange (ETDEWEB)

Korol, Andrei V., E-mail: korol@mbnexplorer.com [MBN Research Center, Altenhöferallee 3, 60438 Frankfurt am Main (Germany); Bezchastnov, Victor G. [A.F. Ioffe Physical-Technical Institute, Politechnicheskaya Str. 26, 194021 St. Petersburg (Russian Federation); Peter the Great St. Petersburg Polytechnic University, Politechnicheskaya 29, 195251 St. Petersburg (Russian Federation); Sushko, Gennady B.; Solov’yov, Andrey V. [MBN Research Center, Altenhöferallee 3, 60438 Frankfurt am Main (Germany)

2016-11-15

Channeling and radiation are studied for the relativistic electrons and positrons passing through a Si crystal periodically bent with a small amplitude and a short period. Comprehensive analysis of the channeling process for various bending amplitudes is presented on the grounds of numerical simulations. The features of the channeling are highlighted and elucidated within an analytically developed continuous potential approximation. The radiation spectra are computed and discussed.

Source-Space Cross-Frequency Amplitude-Amplitude Coupling in Tinnitus

Directory of Open Access Journals (Sweden)

Oliver Zobay

2015-01-01

Full Text Available The thalamocortical dysrhythmia (TCD model has been influential in the development of theoretical explanations for the neurological mechanisms of tinnitus. It asserts that thalamocortical oscillations lock a region in the auditory cortex into an ectopic slow-wave theta rhythm (4–8 Hz. The cortical area surrounding this region is hypothesized to generate abnormal gamma (>30 Hz oscillations (“edge effect” giving rise to the tinnitus percept. Consequently, the model predicts enhanced cross-frequency coherence in a broad range between theta and gamma. In this magnetoencephalography study involving tinnitus and control cohorts, we investigated this prediction. Using beamforming, cross-frequency amplitude-amplitude coupling (AAC was computed within the auditory cortices for frequencies (f1,f2 between 2 and 80 Hz. We find the AAC signal to decompose into two distinct components at low (f1,f230 Hz frequencies, respectively. Studying the correlation of AAC with several key covariates (age, hearing level (HL, tinnitus handicap and duration, and HL at tinnitus frequency, we observe a statistically significant association between age and low-frequency AAC. Contrary to the TCD predictions, however, we do not find any indication of statistical differences in AAC between tinnitus and controls and thus no evidence for the predicted enhancement of cross-frequency coupling in tinnitus.

Classical gluon production amplitude for nucleus-nucleus collisions:First saturation correction in the projectile

International Nuclear Information System (INIS)

Chirilli, Giovanni A.; Kovchegov, Yuri V.; Wertepny, Douglas E.

2015-01-01

We calculate the classical single-gluon production amplitude in nucleus-nucleus collisions including the first saturation correction in one of the nuclei (the projectile) while keeping multiple-rescattering (saturation) corrections to all orders in the other nucleus (the target). In our approximation only two nucleons interact in the projectile nucleus: the single-gluon production amplitude we calculate is order-g"3 and is leading-order in the atomic number of the projectile, while resumming all order-one saturation corrections in the target nucleus. Our result is the first step towards obtaining an analytic expression for the first projectile saturation correction to the gluon production cross section in nucleus-nucleus collisions.

Modeling and experimental characterization of a new piezoelectric sensor for low-amplitude vibration measurement

International Nuclear Information System (INIS)

Hou, X Y; Koh, C G; Kuang, K S C; Lee, W H

2017-01-01

This paper investigates the capability of a novel piezoelectric sensor for low-frequency and low-amplitude vibration measurement. The proposed design effectively amplifies the input acceleration via two amplifying mechanisms and thus eliminates the use of the external charge amplifier or conditioning amplifier typically employed for measurement system. The sensor is also self-powered, i.e. no external power unit is required. Consequently, wiring and electrical insulation for on-site measurement are considerably simpler. In addition, the design also greatly reduces the interference from rotational motion which often accompanies the translational acceleration to be measured. An analytical model is developed based on a set of piezoelectric constitutive equations and beam theory. Closed-form expression is derived to correlate sensor geometry and material properties with its dynamic performance. Experimental calibration is then carried out to validate the analytical model. After calibration, experiments are carried out to check the feasibility of the new sensor in structural vibration detection. From experimental results, it is concluded that the proposed sensor is suitable for measuring low-frequency and low-amplitude vibrations. (paper)

Bessel–Gauss resonator with internal amplitude filter

CSIR Research Space (South Africa)

Litvin, IA

2008-05-01

Full Text Available The authors investigate a conventional resonator configuration, using only spherical curvature optical elements, for the generation of Bessel–Gauss beams. This is achieved through the deployment of a suitable amplitude filter at a Fourier plane...

On the loop-loop scattering amplitudes in Abelian and non-Abelian gauge theories

International Nuclear Information System (INIS)

Meggiolaro, Enrico

2005-01-01

The high-energy elastic scattering amplitude of two colour-singlet qq-bar pairs is governed by the correlation function of two Wilson loops, which follow the classical straight lines for quark (antiquark) trajectories. This quantity is expected to be free of IR divergences, differently from what happens for the parton-parton elastic scattering amplitude, described, in the high-energy limit, by the expectation value of two Wilson lines. We shall explicitly test this IR finiteness by a direct non-perturbative computation of the loop-loop scattering amplitudes in the (pedagogic, but surely physically interesting) case of quenched QED. The results obtained for the Abelian case will be generalized to the case of a non-Abelian gauge theory with Nc colours, but stopping to the order O(g4) in perturbation theory. In connection with the above-mentioned IR finiteness, we shall also discuss some analytic properties of the loop-loop scattering amplitudes in both Abelian and non-Abelian gauge theories, when going from Minkowskian to Euclidean theory, which can be relevant to the still unsolved problem of the s-dependence of hadron-hadron total cross-sections

Modeling of large amplitude plasma blobs in three-dimensions

Energy Technology Data Exchange (ETDEWEB)

Angus, Justin R. [Naval Research Laboratory, 4555 Overlook Avenue, Washington, DC 20375 (United States); Umansky, Maxim V. [Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94550 (United States)

2014-01-15

Fluctuations in fusion boundary and similar plasmas often have the form of filamentary structures, or blobs, that convectively propagate radially. This may lead to the degradation of plasma facing components as well as plasma confinement. Theoretical analysis of plasma blobs usually takes advantage of the so-called Boussinesq approximation of the potential vorticity equation, which greatly simplifies the treatment analytically and numerically. This approximation is only strictly justified when the blob density amplitude is small with respect to that of the background plasma. However, this is not the case for typical plasma blobs in the far scrape-off layer region, where the background density is small compared to that of the blob, and results obtained based on the Boussinesq approximation are questionable. In this report, the solution of the full vorticity equation, without the usual Boussinesq approximation, is proposed via a novel numerical approach. The method is used to solve for the evolution of 2D and 3D plasma blobs in a regime where the Boussinesq approximation is not valid. The Boussinesq solution under predicts the cross field transport in 2D. However, in 3D, for parameters typical of current tokamaks, the disparity between the radial cross field transport from the Boussinesq approximation and full solution is virtually non-existent due to the effects of the drift wave instability.

Modeling of large amplitude plasma blobs in three-dimensions

International Nuclear Information System (INIS)

Angus, Justin R.; Umansky, Maxim V.

2014-01-01

Fluctuations in fusion boundary and similar plasmas often have the form of filamentary structures, or blobs, that convectively propagate radially. This may lead to the degradation of plasma facing components as well as plasma confinement. Theoretical analysis of plasma blobs usually takes advantage of the so-called Boussinesq approximation of the potential vorticity equation, which greatly simplifies the treatment analytically and numerically. This approximation is only strictly justified when the blob density amplitude is small with respect to that of the background plasma. However, this is not the case for typical plasma blobs in the far scrape-off layer region, where the background density is small compared to that of the blob, and results obtained based on the Boussinesq approximation are questionable. In this report, the solution of the full vorticity equation, without the usual Boussinesq approximation, is proposed via a novel numerical approach. The method is used to solve for the evolution of 2D and 3D plasma blobs in a regime where the Boussinesq approximation is not valid. The Boussinesq solution under predicts the cross field transport in 2D. However, in 3D, for parameters typical of current tokamaks, the disparity between the radial cross field transport from the Boussinesq approximation and full solution is virtually non-existent due to the effects of the drift wave instability

Validity of Miles Equation in Predicting Propellant Slosh Damping in Baffled Tanks at Variable Slosh Amplitude

Science.gov (United States)

Yang, H. Q.; West, Jeff

2018-01-01

Determination of slosh damping is a very challenging task as there is no analytical solution. The damping physics involves the vorticity dissipation which requires the full solution of the nonlinear Navier-Stokes equations. As a result, previous investigations were mainly carried out by extensive experiments. A systematical study is needed to understand the damping physics of baffled tanks, to identify the difference between the empirical Miles equation and experimental measurements, and to develop new semi-empirical relations to better represent the real damping physics. The approach of this study is to use Computational Fluid Dynamics (CFD) technology to shed light on the damping mechanisms of a baffled tank. First, a 1-D Navier-Stokes equation representing different length scales and time scales in the baffle damping physics is developed and analyzed. Loci-STREAM-VOF, a well validated CFD solver developed at NASA MSFC, is applied to study the vorticity field around a baffle and around the fluid-gas interface to highlight the dissipation mechanisms at different slosh amplitudes. Previous measurement data is then used to validate the CFD damping results. The study found several critical parameters controlling fluid damping from a baffle: local slosh amplitude to baffle thickness (A/t), surface liquid depth to tank radius (d/R), local slosh amplitude to baffle width (A/W); and non-dimensional slosh frequency. The simulation highlights three significant damping regimes where different mechanisms dominate. The study proves that the previously found discrepancies between Miles equation and experimental measurement are not due to the measurement scatter, but rather due to different damping mechanisms at various slosh amplitudes. The limitations on the use of Miles equation are discussed based on the flow regime.

Multi-loop positivity of the planar N=4 SYM six-point amplitude

Energy Technology Data Exchange (ETDEWEB)

Dixon, Lance J. [SLAC National Accelerator Laboratory,Stanford University, Stanford, CA 94309 (United States); Hippel, Matt von [Perimeter Institute for Theoretical Physics,Waterloo, Ontario N2L 2Y5 (Canada); McLeod, Andrew J. [SLAC National Accelerator Laboratory,Stanford University, Stanford, CA 94309 (United States); Trnka, Jaroslav [Center for Quantum Mathematics and Physics (QMAP),Department of Physics, University of California, Davis, CA 95616 (United States)

2017-02-22

We study the six-point NMHV ratio function in planar N=4 SYM theory in the context of positive geometry. The Amplituhedron construction of the integrand for the amplitudes provides a kinematical region in which the integrand was observed to be positive. It is natural to conjecture that this property survives integration, i.e. that the final result for the ratio function is also positive in this region. Establishing such a result would imply that preserving positivity is a surprising property of the Minkowski contour of integration and it might indicate some deeper underlying structure. We find that the ratio function is positive everywhere we have tested it, including analytic results for special kinematical regions at one and two loops, as well as robust numerical evidence through five loops. There is also evidence for not just positivity, but monotonicity in a “radial” direction. We also investigate positivity of the MHV six-gluon amplitude. While the remainder function ceases to be positive at four loops, the BDS-like normalized MHV amplitude appears to be positive through five loops.

Large-amplitude dust acoustic shocklets in non-Maxwellian dusty plasmas

Science.gov (United States)

Ali, S.; Naeem, Ismat; Mirza, Arshad M.

2017-10-01

The formation and propagation of fully nonlinear dust-acoustic (DA) waves and shocks are studied in a non-Maxwellian thermal dusty plasma which is composed of Maxwellian electrons and nonthermal energetic ions with a neutralizing background of negatively charged dust grains. For this purpose, we have solved dust dynamical equations along with quasineutrality equation by using a diagonalization matrix technique. A set of two characteristic wave equations is obtained, which admits both analytical and numerical solutions. Taylor expansion in the small-amplitude limit ( Φ ≪ 1 ) leads to nonlinear effective phase and shock speeds accounting for nonthermal energetic ions. It is numerically shown that DA pulses can be developed into DA shocklets involving the negative electrostatic potential, dust fluid velocity, and dust number density. These structures are significantly influenced by the ion-nonthermality, dust thermal correction, and temporal variations. However, the amplitudes of solitary and shock waves are found smaller in case of Cairns-distributed ions as compared to Kappa-distributed ions due to smaller linear and nonlinear effective phase speeds that cause smaller nonlinearity effects. The present results should be useful for understanding the nonlinear characteristics of large-amplitude DA excitations and nonstationary shocklets in a laboratory non-Maxwellian dusty plasma, where nonthermal energetic ions are present in addition to Maxwellian electrons.

Damage accumulation of bovine bone under variable amplitude loads

Directory of Open Access Journals (Sweden)

Abbey M. Campbell

2016-12-01

Full Text Available Stress fractures, a painful injury, are caused by excessive fatigue in bone. This study on damage accumulation in bone sought to determine if the Palmgren-Miner rule (PMR, a well-known linear damage accumulation hypothesis, is predictive of fatigue failure in bone. An electromagnetic shaker apparatus was constructed to conduct cyclic and variable amplitude tests on bovine bone specimens. Three distinct damage regimes were observed following fracture. Fractures due to a low cyclic amplitude loading appeared ductile (4000 μϵ, brittle due to high cyclic amplitude loading (>9000 μϵ, and a combination of ductile and brittle from mid-range cyclic amplitude loading (6500 –6750 μϵ. Brittle and ductile fracture mechanisms were isolated and mixed, in a controlled way, into variable amplitude loading tests. PMR predictions of cycles to failure consistently over-predicted fatigue life when mixing isolated fracture mechanisms. However, PMR was not proven ineffective when used with a single damage mechanism. Keywords: Bone fatigue, Bone fracture, Health system monitoring, Failure prediction

Two-Loop Splitting Amplitudes

International Nuclear Information System (INIS)

Bern, Z.

2004-01-01

Splitting amplitudes govern the behavior of scattering amplitudes at the momenta of external legs become collinear. In this talk we outline the calculation of two-loop splitting amplitudes via the unitarity sewing method. This method retains the simple factorization properties of light-cone gauge, but avoids the need for prescriptions such as the principal value or Mandelstam-Leibbrandt ones. The encountered loop momentum integrals are then evaluated using integration-by-parts and Lorentz invariance identities. We outline a variety of applications for these splitting amplitudes

Two-loop splitting amplitudes

International Nuclear Information System (INIS)

Bern, Z.; Dixon, L.J.; Kosower, D.A.

2004-01-01

Splitting amplitudes govern the behavior of scattering amplitudes at the momenta of external legs become collinear. In this talk we outline the calculation of two-loop splitting amplitudes via the unitarity sewing method. This method retains the simple factorization properties of light-cone gauge, but avoids the need for prescriptions such as the principal value or Mandelstam-Leibbrandt ones. The encountered loop momentum integrals are then evaluated using integration-by-parts and Lorentz invariance identities. We outline a variety of applications for these splitting amplitudes

Large amplitude parallel propagating electromagnetic oscillitons

International Nuclear Information System (INIS)

Cattaert, Tom; Verheest, Frank

2005-01-01

Earlier systematic nonlinear treatments of parallel propagating electromagnetic waves have been given within a fluid dynamic approach, in a frame where the nonlinear structures are stationary and various constraining first integrals can be obtained. This has lead to the concept of oscillitons that has found application in various space plasmas. The present paper differs in three main aspects from the previous studies: first, the invariants are derived in the plasma frame, as customary in the Sagdeev method, thus retaining in Maxwell's equations all possible effects. Second, a single differential equation is obtained for the parallel fluid velocity, in a form reminiscent of the Sagdeev integrals, hence allowing a fully nonlinear discussion of the oscilliton properties, at such amplitudes as the underlying Mach number restrictions allow. Third, the transition to weakly nonlinear whistler oscillitons is done in an analytical rather than a numerical fashion

Wilson loop OPE, analytic continuation and multi-Regge limit

International Nuclear Information System (INIS)

Hatsuda, Yasuyuki

2014-05-01

We explore a direct connection between the collinear limit and the multi-Regge limit for scattering amplitudes in the N=4 super Yang-Mills theory. Starting with the collinear expansion for the six-gluon amplitude in the Euclidean kinematic region, we perform an analytic continuation term by term to the so-called Mandelstam region. We find that the result coincides with the collinear expansion of the analytically continued amplitude. We then take the multi-Regge limit, and conjecture that the final result precisely reproduces the one from the BFKL approach. Combining this procedure with the OPE for null polygonal Wilson loops, we explicitly compute the leading contribution in the ''collinear-Regge'' limit up to five loops. Our results agree with all the known results up to four loops. At five-loop, our results up to the next-to-next-to-leading logarithmic approximation (NNLLA) also reproduce the known results, and for the N 3 LLA and the N 4 LLA give non-trivial predictions. We further present an all-loop prediction for the imaginary part of the next-to-double-leading logarithmic approximation. Our procedure has a possibility of an interpolation from weak to strong coupling in the multi-Regge limit with the help of the OPE.

Amplitudes, acquisition and imaging

Energy Technology Data Exchange (ETDEWEB)

Bloor, Robert

1998-12-31

Accurate seismic amplitude information is important for the successful evaluation of many prospects and the importance of such amplitude information is increasing with the advent of time lapse seismic techniques. It is now widely accepted that the proper treatment of amplitudes requires seismic imaging in the form of either time or depth migration. A key factor in seismic imaging is the spatial sampling of the data and its relationship to the imaging algorithms. This presentation demonstrates that acquisition caused spatial sampling irregularity can affect the seismic imaging and perturb amplitudes. Equalization helps to balance the amplitudes, and the dealing strategy improves the imaging further when there are azimuth variations. Equalization and dealiasing can also help with the acquisition irregularities caused by shot and receiver dislocation or missing traces. 2 refs., 2 figs.

Investigation of Damping Physics and CFD Tool Validation for Simulation of Baffled Tanks at Variable Slosh Amplitude

Science.gov (United States)

Yang, H. Q.; West, Jeff

2016-01-01

Determination of slosh damping is a very challenging task as there is no analytical solution. The damping physics involves the vorticity dissipation which requires the full solution of the nonlinear Navier-Stokes equations. As a result, previous investigations were mainly carried out by extensive experiments. A systematical study is needed to understand the damping physics of baffled tanks, to identify the difference between the empirical Miles equation and experimental measurements, and to develop new semi-empirical relations to better represent the real damping physics. The approach of this study is to use Computational Fluid Dynamics (CFD) technology to shed light on the damping mechanisms of a baffled tank. First, a 1-D Navier-Stokes equation representing different length scales and time scales in the baffle damping physics is developed and analyzed. Loci-STREAM-VOF, a well validated CFD solver developed at NASA MSFC, is applied to study the vorticity field around a baffle and around the fluid-gas interface to highlight the dissipation mechanisms at different slosh amplitudes. Previous measurement data is then used to validate the CFD damping results. The study found several critical parameters controlling fluid damping from a baffle: local slosh amplitude to baffle thickness (A/t), surface liquid depth to tank radius (d/R), local slosh amplitude to baffle width (A/W); and non-dimensional slosh frequency. The simulation highlights three significant damping regimes where different mechanisms dominate. The study proves that the previously found discrepancies between Miles equation and experimental measurement are not due to the measurement scatter, but rather due to different damping mechanisms at various slosh amplitudes. The limitations on the use of Miles equation are discussed based on the flow regime.

Monodromy relations in higher-loop string amplitudes

Directory of Open Access Journals (Sweden)

S. Hohenegger

2017-12-01

Full Text Available New monodromy relations of loop amplitudes are derived in open string theory. We particularly study N-point (planar and non-planar one-loop amplitudes described by a world-sheet cylinder and derive a set of relations between subamplitudes of different color orderings. Various consistency checks are performed by matching α′-expansions of planar and non-planar amplitudes involving elliptic iterated integrals with the resulting periods giving rise to two sets of multiple elliptic zeta values. The latter refer to the two homology cycles on the once-punctured complex elliptic curve and the monodromy equations provide relations between these two sets of multiple elliptic zeta values. Furthermore, our monodromy relations involve new objects for which we present a tentative interpretation in terms of open string scattering amplitudes in the presence of a non-trivial gauge field flux. Finally, we provide an outlook on how to generalize the new monodromy relations to the non-oriented case and beyond the one-loop level. Comparing a subset of our results with recent findings in the literature we find therein several serious issues related to the structure and significance of monodromy phases and the relevance of missed contributions from contour integrations.

N ≥ 4 Supergravity Amplitudes from Gauge Theory at Two Loops

International Nuclear Information System (INIS)

Boucher-Veronneau, Camille

2012-01-01

We present the full two-loop four-graviton amplitudes in N = 4, 5, 6 supergravity. These results were obtained using the double-copy structure of gravity, which follows from the recently conjectured color-kinematics duality in gauge theory. The two-loop four-gluon scattering amplitudes in N = 0, 1, 2 supersymmetric gauge theory are a second essential ingredient. The gravity amplitudes have the expected infrared behavior: the two-loop divergences are given in terms of the squares of the corresponding one-loop amplitudes. The finite remainders are presented in a compact form. The finite remainder for N = 8 supergravity is also presented, in a form that utilizes a pure function with a very simple symbol.

Relative amplitude preservation processing utilizing surface consistent amplitude correction. Part 4; Surface consistent amplitude correction wo mochiita sotai shinpuku hozon shori. 4

Energy Technology Data Exchange (ETDEWEB)

Saeki, T [Japan National Oil Corp., Tokyo (Japan). Technology Research Center

1997-10-22

Discussions were given on seismic exploration from the ground surface using the reflection method, for surface consistent amplitude correction from among effects imposed from the ground surface and a surface layer. Amplitude distribution on the reflection wave zone is complex. Therefore, items to be considered in making an analysis are multiple, such as estimation of spherical surface divergence effect and exponential attenuation effect, not only amplitude change through the surface layer. If all of these items are taken into consideration, burden of the work becomes excessive. As a method to solve this problem, utilization of amplitude in initial movement of a diffraction wave may be conceived. Distribution of the amplitude in initial movement of the diffraction wave shows a value relatively close to distribution of the vibration transmitting and receiving points. The reason for this is thought because characteristics of the vibration transmitting and receiving points related with waveline paths in the vicinity of the ground surface have no great difference both on the diffraction waves and on the reflection waves. The lecture described in this paper introduces an attempt of improving the efficiency of the surface consistent amplitude correction by utilizing the analysis of amplitude in initial movement of the diffraction wave. 4 refs., 2 figs.

2-vertex Lorentzian spin foam amplitudes for dipole transitions

Science.gov (United States)

Sarno, Giorgio; Speziale, Simone; Stagno, Gabriele V.

2018-04-01

We compute transition amplitudes between two spin networks with dipole graphs, using the Lorentzian EPRL model with up to two (non-simplicial) vertices. We find power-law decreasing amplitudes in the large spin limit, decreasing faster as the complexity of the foam increases. There are no oscillations nor asymptotic Regge actions at the order considered, nonetheless the amplitudes still induce non-trivial correlations. Spin correlations between the two dipoles appear only when one internal face is present in the foam. We compute them within a mini-superspace description, finding positive correlations, decreasing in value with the Immirzi parameter. The paper also provides an explicit guide to computing Lorentzian amplitudes using the factorisation property of SL(2,C) Clebsch-Gordan coefficients in terms of SU(2) ones. We discuss some of the difficulties of non-simplicial foams, and provide a specific criterion to partially limit the proliferation of diagrams. We systematically compare the results with the simplified EPRLs model, much faster to evaluate, to learn evidence on when it provides reliable approximations of the full amplitudes. Finally, we comment on implications of our results for the physics of non-simplicial spin foams and their resummation.

Direct amplitude detuning measurement with ac dipole

Directory of Open Access Journals (Sweden)

S. White

2013-07-01

Full Text Available In circular machines, nonlinear dynamics can impact parameters such as beam lifetime and could result in limitations on the performance reach of the accelerator. Assessing and understanding these effects in experiments is essential to confirm the accuracy of the magnetic model and improve the machine performance. A direct measurement of the machine nonlinearities can be obtained by characterizing the dependency of the tune as a function of the amplitude of oscillations (usually defined as amplitude detuning. The conventional technique is to excite the beam to large amplitudes with a single kick and derive the tune from turn-by-turn data acquired with beam position monitors. Although this provides a very precise tune measurement it has the significant disadvantage of being destructive. An alternative, nondestructive way of exciting large amplitude oscillations is to use an ac dipole. The perturbation Hamiltonian in the presence of an ac dipole excitation shows a distinct behavior compared to the free oscillations which should be correctly taken into account in the interpretation of experimental data. The use of an ac dipole for direct amplitude detuning measurement requires careful data processing allowing one to observe the natural tune of the machine; the feasibility of such a measurement is demonstrated using experimental data from the Large Hadron Collider. An experimental proof of the theoretical derivations based on measurements performed at injection energy is provided as well as an application of this technique at top energy using a large number of excitations on the same beam.

Light-cone distribution amplitudes of the baryon octet

International Nuclear Information System (INIS)

Bali, Gunnar S.; Braun, Vladimir M.; Göckeler, Meinulf; Gruber, Michael; Hutzler, Fabian; Schäfer, Andreas; Schiel, Rainer W.; Simeth, Jakob; Söldner, Wolfgang; Sternbeck, Andre; Wein, Philipp

2016-01-01

We present results of the first ab initio lattice QCD calculation of the normalization constants and first moments of the leading twist distribution amplitudes of the full baryon octet, corresponding to the small transverse distance limit of the associated S-wave light-cone wave functions. The P-wave (higher twist) normalization constants are evaluated as well. The calculation is done using N_f=2+1 flavors of dynamical (clover) fermions on lattices of different volumes and pion masses down to 222 MeV. Significant SU(3) flavor symmetry violation effects in the shape of the distribution amplitudes are observed.

Light-cone distribution amplitudes of the baryon octet

Energy Technology Data Exchange (ETDEWEB)

Bali, Gunnar S. [Institut für Theoretische Physik, Universität Regensburg,Universitätsstraße 31, D-93040 Regensburg (Germany); Department of Theoretical Physics, Tata Institute of Fundamental Research,Homi Bhabha Road, Mumbai 400005 (India); Braun, Vladimir M.; Göckeler, Meinulf; Gruber, Michael; Hutzler, Fabian; Schäfer, Andreas; Schiel, Rainer W.; Simeth, Jakob; Söldner, Wolfgang [Institut für Theoretische Physik, Universität Regensburg,Universitätsstraße 31, D-93040 Regensburg (Germany); Sternbeck, Andre [Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena,Max-Wien-Platz 1, D-07743 Jena (Germany); Wein, Philipp [Institut für Theoretische Physik, Universität Regensburg,Universitätsstraße 31, D-93040 Regensburg (Germany)

2016-02-10

We present results of the first ab initio lattice QCD calculation of the normalization constants and first moments of the leading twist distribution amplitudes of the full baryon octet, corresponding to the small transverse distance limit of the associated S-wave light-cone wave functions. The P-wave (higher twist) normalization constants are evaluated as well. The calculation is done using N{sub f}=2+1 flavors of dynamical (clover) fermions on lattices of different volumes and pion masses down to 222 MeV. Significant SU(3) flavor symmetry violation effects in the shape of the distribution amplitudes are observed.

Tune-shift with amplitude due to nonlinear kinematic effect

CERN Document Server

Wan, W

1999-01-01

Tracking studies of the Muon Collider 50 on 50 GeV collider ring show that the on-momentum dynamic aperture is limited to around 10 sigma even with the chromaticity sextupoles turned off. Numerical results from the normal form algorithm show that the tune-shift with amplitude is surprisingly large. Both analytical and numerical results are presented to show that nonlinear kinematic effect originated from the large angles of particles in the interaction region is responsible for the large tune-shift which in turn limits the dynamic aperture. A comparative study of the LHC collider ring is also presented to demonstrate the difference between the two machines. (14 refs).

High-Energy String Scattering Amplitudes and Signless Stirling Number Identity

Directory of Open Access Journals (Sweden)

Jen-Chi Lee

2012-07-01

Full Text Available We give a complete proof of a set of identities (7 proposed recently from calculation of high-energy string scattering amplitudes. These identities allow one to extract ratios among high-energy string scattering amplitudes in the fixed angle regime from high-energy amplitudes in the Regge regime. The proof is based on a signless Stirling number identity in combinatorial theory. The results are valid for arbitrary real values L rather than only for L=0,1 proved previously. The identities for non-integer real value L were recently shown to be realized in high-energy compactified string scattering amplitudes [He S., Lee J.C., Yang Y., arXiv:1012.3158]. The parameter L is related to the mass level of an excited string state and can take non-integer values for Kaluza-Klein modes.

Analytical calculation of heavy quarkonia production processes in computer

International Nuclear Information System (INIS)

Braguta, V V; Likhoded, A K; Luchinsky, A V; Poslavsky, S V

2014-01-01

This report is devoted to the analytical calculation of heavy quarkonia production processes in modern experiments such as LHC, B-factories and superB-factories in computer. Theoretical description of heavy quarkonia is based on the factorization theorem. This theorem leads to special structure of the production amplitudes which can be used to develop computer algorithm which calculates these amplitudes automatically. This report is devoted to the description of this algorithm. As an example of its application we present the results of the calculation of double charmonia production in bottomonia decays and inclusive the χ cJ mesons production in pp-collisions

Mimicking an amplitude damping channel for Laguerre Gaussian Modes

CSIR Research Space (South Africa)

Dudley, Angela L

2010-10-01

Full Text Available An amplitude damping channel for Laguerre-Gaussian (LG) modes is presented. Experimentally the action of the channel on LG modes is in good agreement with that predicted theoretically....

Analytical Analysis on Nonlinear Parametric Vibration of an Axially Moving String with Fractional Viscoelastic Damping

Directory of Open Access Journals (Sweden)

Ying Li

2017-01-01

Full Text Available The nonlinear parametric vibration of an axially moving string made by rubber-like materials is studied in the paper. The fractional viscoelastic model is used to describe the damping of the string. Then, a new nonlinear fractional mathematical model governing transverse motion of the string is derived based on Newton’s second law, the Euler beam theory, and the Lagrangian strain. Taking into consideration the fractional calculus law of Riemann-Liouville form, the principal parametric resonance is analytically investigated via applying the direct multiscale method. Numerical results are presented to show the influences of the fractional order, the stiffness constant, the viscosity coefficient, and the axial-speed fluctuation amplitude on steady-state responses. It is noticeable that the amplitudes and existing intervals of steady-state responses predicted by Kirchhoff’s fractional material model are much larger than those predicted by Mote’s fractional material model.

Geometric scaling behavior of the scattering amplitude for DIS with nuclei

Science.gov (United States)

Kormilitzin, Andrey; Levin, Eugene; Tapia, Sebastian

2011-12-01

The main question, that we answer in this paper, is whether the initial condition can influence on the geometric scaling behavior of the amplitude for DIS at high energy. We re-write the non-linear Balitsky-Kovchegov equation in the form which is useful for treating the interaction with nuclei. Using the simplified BFKL kernel, we find the analytical solution to this equation with the initial condition given by the McLerran-Venugopalan formula. This solution does not show the geometric scaling behavior of the amplitude deeply in the saturation region. On the other hand, the BFKL Pomeron calculus with the initial condition at x=1/mR given by the solution to Balitsky-Kovchegov equation, leads to the geometric scaling behavior. The McLerran-Venugopalan formula is the natural initial condition for the Color Glass Condensate (CGC) approach. Therefore, our result gives a possibility to check experimentally which approach: CGC or BFKL Pomeron calculus, is more satisfactory.

Geometric scaling behavior of the scattering amplitude for DIS with nuclei

International Nuclear Information System (INIS)

Kormilitzin, Andrey; Levin, Eugene; Tapia, Sebastian

2011-01-01

The main question, that we answer in this paper, is whether the initial condition can influence on the geometric scaling behavior of the amplitude for DIS at high energy. We re-write the non-linear Balitsky–Kovchegov equation in the form which is useful for treating the interaction with nuclei. Using the simplified BFKL kernel, we find the analytical solution to this equation with the initial condition given by the McLerran–Venugopalan formula. This solution does not show the geometric scaling behavior of the amplitude deeply in the saturation region. On the other hand, the BFKL Pomeron calculus with the initial condition at x A =1/mR A given by the solution to Balitsky–Kovchegov equation, leads to the geometric scaling behavior. The McLerran–Venugopalan formula is the natural initial condition for the Color Glass Condensate (CGC) approach. Therefore, our result gives a possibility to check experimentally which approach: CGC or BFKL Pomeron calculus, is more satisfactory.

Diphoton generalized distribution amplitudes

International Nuclear Information System (INIS)

El Beiyad, M.; Pire, B.; Szymanowski, L.; Wallon, S.

2008-01-01

We calculate the leading order diphoton generalized distribution amplitudes by calculating the amplitude of the process γ*γ→γγ in the low energy and high photon virtuality region at the Born order and in the leading logarithmic approximation. As in the case of the anomalous photon structure functions, the γγ generalized distribution amplitudes exhibit a characteristic lnQ 2 behavior and obey inhomogeneous QCD evolution equations.

Real topological string amplitudes

Energy Technology Data Exchange (ETDEWEB)

Narain, K.S. [The Abdus Salam International Centre for Theoretical Physics (ICTP),Strada Costiera 11, Trieste, 34151 (Italy); Piazzalunga, N. [Simons Center for Geometry and Physics, State University of New York,Stony Brook, NY, 11794-3636 (United States); International School for Advanced Studies (SISSA) and INFN, Sez. di Trieste,via Bonomea 265, Trieste, 34136 (Italy); Tanzini, A. [International School for Advanced Studies (SISSA) and INFN, Sez. di Trieste,via Bonomea 265, Trieste, 34136 (Italy)

2017-03-15

We discuss the physical superstring correlation functions in type I theory (or equivalently type II with orientifold) that compute real topological string amplitudes. We consider the correlator corresponding to holomorphic derivative of the real topological amplitude G{sub χ}, at fixed worldsheet Euler characteristic χ. This corresponds in the low-energy effective action to N=2 Weyl multiplet, appropriately reduced to the orientifold invariant part, and raised to the power g{sup ′}=−χ+1. We show that the physical string correlator gives precisely the holomorphic derivative of topological amplitude. Finally, we apply this method to the standard closed oriented case as well, and prove a similar statement for the topological amplitude F{sub g}.

Integrable spin chains and scattering amplitudes

Energy Technology Data Exchange (ETDEWEB)

Bartels, J.; Prygarin, A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Lipatov, L.N. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Petersburg Nuclear Physics Institute (Russian Federation); Sankt-Peterburgskij Univ., St. Petersburg (Russian Federation)

2011-04-15

In this review we show that the multi-particle scattering amplitudes in N=4 SYM at large N{sub c} and in the multi-Regge kinematics for some physical regions have the high energy behavior appearing from the contribution of the Mandelstam cuts in the complex angular momentum plane of the corresponding t-channel partial waves. These Mandelstam cuts or Regge cuts are resulting from gluon composite states in the adjoint representation of the gauge group SU(N{sub c}). In the leading logarithmic approximation (LLA) their contribution to the six point amplitude is in full agreement with the known two-loop result. The Hamiltonian for the Mandelstam states constructed from n gluons in LLA coincides with the local Hamiltonian of an integrable open spin chain. We construct the corresponding wave functions using the integrals of motion and the Baxter-Sklyanin approach. (orig.)

Unifying relations for scattering amplitudes

Science.gov (United States)

Cheung, Clifford; Shen, Chia-Hsien; Wen, Congkao

2018-02-01

We derive new amplitudes relations revealing a hidden unity among a wideranging variety of theories in arbitrary spacetime dimensions. Our results rely on a set of Lorentz invariant differential operators which transmute physical tree-level scattering amplitudes into new ones. By transmuting the amplitudes of gravity coupled to a dilaton and two-form, we generate all the amplitudes of Einstein-Yang-Mills theory, Dirac-Born-Infield theory, special Galileon, nonlinear sigma model, and biadjoint scalar theory. Transmutation also relates amplitudes in string theory and its variants. As a corollary, celebrated aspects of gluon and graviton scattering like color-kinematics duality, the KLT relations, and the CHY construction are inherited traits of the transmuted amplitudes. Transmutation recasts the Adler zero as a trivial consequence of the Weinberg soft theorem and implies new subleading soft theorems for certain scalar theories.

Accommodative Amplitude in School-Age Children

Directory of Open Access Journals (Sweden)

Ikaunieks Gatis

2017-10-01

Full Text Available In children, intensive near-work affects the accommodation system of the eye. Younger children, due to anatomical parameters, read at smaller distance than older children and we can expect that the accommodation system of younger can be affected more than that of older children. We wanted to test this hypothesis. Some authors showed that the norms of amplitude of accommodation (AA developed by Hofstetter (1950 not always could be applied for children. We also wanted to verify these results. A total of 106 (age 7-15 children participated in the study. Distance visual acuity was measured for all children and only data of children with good visual acuity 1.0 or more (dec. units were analysed (73 children. Accommodative amplitude was measured before and after lessons using subjective push-up technique (with RAF Near Point Ruler. The results showed that the amplitude of accommodation reduced significantly (p < 0.05 during the day and decrease of AA was similar in different age groups (about ~0.70 D. Additional measurements are needed to verify that the observed changes in AA were associated with fatigue effect. The results showed lower accommodation values compared to average values calculated according to the Hofstetter equation (p < 0.05.

Optical-wireless-optical full link for polarization multiplexing quadrature amplitude/phase modulation signal transmission.

Science.gov (United States)

Li, Xinying; Yu, Jianjun; Chi, Nan; Zhang, Junwen

2013-11-15

We propose and experimentally demonstrate an optical wireless integration system at the Q-band, in which up to 40 Gb/s polarization multiplexing multilevel quadrature amplitude/phase modulation (PM-QAM) signal can be first transmitted over 20 km single-mode fiber-28 (SMF-28), then delivered over a 2 m 2 × 2 multiple-input multiple-output wireless link, and finally transmitted over another 20 km SMF-28. The PM-QAM modulated wireless millimeter-wave (mm-wave) signal at 40 GHz is generated based on the remote heterodyning technique, and demodulated by the radio-frequency transparent photonic technique based on homodyne coherent detection and baseband digital signal processing. The classic constant modulus algorithm equalization is used at the receiver to realize polarization demultiplexing of the PM-QAM signal. For the first time, to the best of our knowledge, we realize the conversion of the PM-QAM modulated wireless mm-wave signal to the optical signal as well as 20 km fiber transmission of the converted optical signal.

Nonlinear ordinary differential equations analytical approximation and numerical methods

CERN Document Server

Hermann, Martin

2016-01-01

The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs. The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation, variational iteration method, homotopy perturbation method, iteration perturbation method, homotopy analysis method, simple and multiple shooting method, and the nonlinear stabilized march...

Pulse-amplitude multipliers using logarithmic amplitude-to-time conversion; Amplificateurs d'impulsions utilisant une conversion logarithmique temps-amplitude; Ob umnozhitelyakh amplitudy impul'sov s ispol'zovaniem logarifmicheskogo preobrazovaniya amplitudy vo vremya; Multiplicadores de amplitud de impulso usando una conversion logaritmica de amplitud en tiempo

Energy Technology Data Exchange (ETDEWEB)

Konrad, M [Institut Rudjer Boskovic, Zagreb, Yugoslavia (Croatia)

1962-04-15

The accuracy and limitations of multipliers based on logarithmic amplitude-to-time conversion using RC pulse stretchers are discussed with respect to their application for determining whether the amplitude product of two coincident pulses has a given value. Some possible circuits are given. (author) [French] L'auteur etudie la precision et les limitations des amplificateurs fondes sur la conversion logarithmique temps-amplitude et utilisant des allongeurs d'impulsions RC, afin d'etablir si ces appareils peuvent servir a determiner la valeur du produit des amplitudes de deux impulsions coincidentes. Il decrit en outre plusieurs circuits possibles. (author) [Spanish] La memoria discute la precision y limitaciones de los multiplicadores basados en la conversion logaritmica de amplitud en tiempo empleando circuitos alargadores de resistencia-capacidad en relacion con su aplicacion para determinar si el producto de las amplitudes de dos impulsos coincidentes tiene un valor determinado. Indica algunos circuitos posibles. (author) [Russian] Obsuzhdayutsya predel pogreshnosti i ogranicheniya umnozhitelej, osnovannykh na logarifmicheskom preobrazovanii amplitudy vo vremya, s ispol'zovaniem rasshiritelej impul'sov RC; ehto delaetsya v svyazi s ikh primeneniem dlya vyyasneniya voprosa o tom, imeet li opredelennuyu velichinu proizvedenie amplitud dvukh sovpadayushchikh impul'sov. Privodyatsya nekotorye vozmozhnye blok-skhemy. (author)

Time-amplitude converter; Convertisseur temps-amplitude

Energy Technology Data Exchange (ETDEWEB)

Banner, M [Commissariat a l' Energie Atomique, Saclay (France).Centre d' Etudes Nucleaires

1961-07-01

It is normal in high energy physics to measure the time of flight of a particle in order to determine its mass. This can be done by the method which consists in transforming the time measurement into an analysis of amplitude, which is easier; a time-amplitude converter has therefore been built for this purpose. The apparatus here described uses a double grid control tube 6 BN 6 whose resolution time, as measured with a pulse generator, is 5 x 10{sup -11} s. The analysis of the response of a particle counter, made up of a scintillator and a photomultiplier, indicates that a time of resolution of 5 x 10{sup -10} s. can be obtained. A time of this order of magnitude is obtained experimentally with the converter. This converter has been used in the study of the time of flight of particles in a secondary beam of the accelerator Saturne. It has thus been possible to measure the energy spectrum of {pi}-mesons, of protons, and of deutons emitted from a polyethylene target bombarded by 1,4 and 2 GeV protons. (author) [French] Pour determiner la masse d'une particule, il est courant, en physique des hautes energies, de mesurer le temps de vol de cette particule. Cela peut etre fait par la methode qui consiste a transformer la mesure d'un temps en une analyse d'amplitude, plus aisee; aussi a-t-on, a cet effet, cree un convertisseur temps-amplitude. L'appareillage decrit dans cet article utilise un tube a double grille de commande 6 BN 6 dont le temps de resolution mesure avec un generateur d'impulsion est de 5.10{sup -11} s. L'analyse de la reponse d'un compteur de particules, constitue par un scintillateur et un photomultiplicateur, indique qu'un temps de resolution de 5.10{sup -10} s peut etre obtenu. Un temps de cet ordre est atteint experimentalement avec le convertisseur. Ce convertisseur a servi a l'etude du temps de vol des particules dans un faisceau secondaire de l'accelerateur Saturne. On a mesure ainsi le spectre d'energie des mesons {pi}, des protons, des deutons

Plasma wave amplitude measurement created by guided laser wakefield

International Nuclear Information System (INIS)

Wojda, Franck

2010-01-01

The interaction of an intense laser pulse of short duration with a plasma produces a plasma wave with large amplitude in its wake, which is associated with a longitudinal electric field. It can be used to accelerate relativistic electrons injected into the wave to energies in the GeV range over distances of the order of a few centimeters, short compared to acceleration lengths in conventional accelerators. The control of the electron beam characteristics during the acceleration process is fundamental for achieving a usable laser-plasma acceleration stage. The main result of this thesis is the creation and characterization of a plasma wave in a weakly nonlinear regime over a length of several centimeters. Capillary tubes are used to guide the laser beam over these distances, while maintaining a large enough intensity (∼ 10 17 W/cm 2 ). The guided laser beam ionizes the gas in the tube and creates the plasma wave. A diagnostic based on the modification of the laser pulse spectrum was used to determine the amplitude of the plasma wave along the tube. The amplitude of the plasma wave was studied as a function of gas filling pressure, length of the capillary and laser energy. Experimental results are compared; they are in excellent agreement with analytical results and modeling. They show that the electric field associated with the plasma wave is between 1 and 10 GV/m over a length of up to 8 cm. This work has demonstrated the ability to create a controlled plasma wave in a weakly nonlinear regime. (author)

Two- and three-loop amplitudes in covariant loop calculus

International Nuclear Information System (INIS)

Roland, K.

1988-04-01

We study 2- and 3-loop vacuum-amplitudes for the closed bosonic string. We compare two sets of expressions for the corresponding density on moduli space: One, based on the covariant Reggeon loop calculus (where modular invariance is not manifest). The other, based on analytic geometry. We want to prove identity between the two sets of expressions. Quite apart from demonstrating modular invariance of the Reggeon results, this would in itself be a remarkable mathematical feature. Identity is established to 'high' order in some moduli and exactly in others. The expansions reveal an essentially number-theoretical structure. Agreement is found only by exploiting the connection between the 4 Jacobi θ-functions and number theory. (orig.)

Rectangular amplitudes, conformal blocks, and applications to loop models

Energy Technology Data Exchange (ETDEWEB)

Bondesan, Roberto, E-mail: roberto.bondesan@cea.fr [LPTENS, Ecole Normale Superieure, 24 rue Lhomond, 75231 Paris (France); Institute de Physique Theorique, CEA Saclay, F-91191 Gif-sur-Yvette (France); Jacobsen, Jesper L. [LPTENS, Ecole Normale Superieure, 24 rue Lhomond, 75231 Paris (France); Universite Pierre et Marie Curie, 4 place Jussieu, 75252 Paris (France); Saleur, Hubert [Institute de Physique Theorique, CEA Saclay, F-91191 Gif-sur-Yvette (France); Physics Department, USC, Los Angeles, CA 90089-0484 (United States)

2013-02-21

In this paper we continue the investigation of partition functions of critical systems on a rectangle initiated in [R. Bondesan, et al., Nucl. Phys. B 862 (2012) 553-575]. Here we develop a general formalism of rectangle boundary states using conformal field theory, adapted to describe geometries supporting different boundary conditions. We discuss the computation of rectangular amplitudes and their modular properties, presenting explicit results for the case of free theories. In a second part of the paper we focus on applications to loop models, discussing in details lattice discretizations using both numerical and analytical calculations. These results allow to interpret geometrically conformal blocks, and as an application we derive new probability formulas for self-avoiding walks.

Two- and three-loop amplitudes in covariant loop calculus

International Nuclear Information System (INIS)

Roland, K.

1989-01-01

We study two- and three-loop vacuum amplitudes for the closed bosonic string. We compare two sets of expressions for the corresponding density on moduli space. One is based on the covariant reggeon loop calculus (where modular invariance is not manifest). The other is based on analytic geometry. We want to prove identity between the two sets of expressions. Quite apart from demonstrating modular invariance of the reggeon results, this would in itself be a remarkable mathematical feature. Identity is established to ''high'' order in some moduli and exactly in others. The expansions reveal an essentially number-theoretic structure. Agreement is found only by exploiting the connection between the four Jacobi θ-functions and number theory. (orig.)

Growth of 2D and 3D plane cracks under thermo-mechanical loading with varying amplitudes

International Nuclear Information System (INIS)

Sbitti, Amine

2009-01-01

After a presentation of the phenomenon of thermal fatigue (in industrial applications and nuclear plants), this research thesis reports the investigation of the growth and arrest of a 2D crack under thermal fatigue (temperature and stress distribution over thickness, calculation of stress intensity factors, laws of fatigue crack growth, growth under varying amplitude), and the investigation of 3D crack growth under cyclic loading with varying amplitudes (analytic and numerical calculation of stress intensity factors, variational formulation in failure mechanics, 3D crack propagation under fatigue, use of the Aster code, use of the extended finite element method or X-FEM). The author discusses the origin and influence of the 3D crack network under thermal fatigue

Uncertainties in model-independent extractions of amplitudes from complete experiments

International Nuclear Information System (INIS)

Hoblit, S.; Sandorfi, A.M.; Kamano, H.; Lee, T.-S.H.

2012-01-01

A new generation of over-complete experiments is underway, with the goal of performing a high precision extraction of pseudoscalar meson photo-production amplitudes. Such experimentally determined amplitudes can be used both as a test to validate models and as a starting point for an analytic continuation in the complex plane to search for poles. Of crucial importance for both is the level of uncertainty in the extracted multipoles. We have probed these uncertainties by analyses of pseudo-data for KLambda photoproduction, first for the set of 8 observables that have been published for the K + Lambda channel and then for pseudo-data on a complete set of 16 observables with the uncertainties expected from analyses of ongoing CLAS experiments. In fitting multipoles, we have used a combined Monte Carlo sampling of the amplitude space, with gradient minimization, and have found a shallow X 2 valley pitted with a large number of local minima. This results in bands of solutions that are experimentally indistinguishable. All ongoing experiments will measure observables with limited statistics. We have found a dependence on the particular random choice of values of Gaussian distributed pseudo-data, due to the presence of multiple local minima. This results in actual uncertainties for reconstructed multipoles that are often considerable larger than those returned by gradient minimization routines such as Minuit which find a single local minimum. As intuitively expected, this additional level of uncertainty decreases as larger numbers of observables are included.

Analytic approach to nonlinear hydrodynamic instabilities driven by time-dependent accelerations

Energy Technology Data Exchange (ETDEWEB)

Mikaelian, K O

2009-09-28

We extend our earlier model for Rayleigh-Taylor and Richtmyer-Meshkov instabilities to the more general class of hydrodynamic instabilities driven by a time-dependent acceleration g(t) . Explicit analytic solutions for linear as well as nonlinear amplitudes are obtained for several g(t)'s by solving a Schroedinger-like equation d{sup 2}{eta}/dt{sup 2} - g(t)kA{eta} = 0 where A is the Atwood number and k is the wavenumber of the perturbation amplitude {eta}(t). In our model a simple transformation k {yields} k{sub L} and A {yields} A{sub L} connects the linear to the nonlinear amplitudes: {eta}{sup nonlinear} (k,A) {approx} (1/k{sub L})ln{eta}{sup linear} (k{sub L}, A{sub L}). The model is found to be in very good agreement with direct numerical simulations. Bubble amplitudes for a variety of accelerations are seen to scale with s defined by s = {integral} {radical}g(t)dt, while spike amplitudes prefer scaling with displacement {Delta}x = {integral}[{integral}g(t)dt]dt.

Nuclear-Mechanical Coupling: Small Amplitude Mechanical Vibrations and High Amplitude Power Oscillations in Nuclear Reactors

International Nuclear Information System (INIS)

Suarez Antola, R.

2008-11-01

The cores of nuclear reactors, including its structural parts and cooling fluids, are complex mechanical systems able to vibrate in a set of normal modes and frequencies, if suitable perturbed. The cyclic variations in the strain state of the core materials may produce changes in density. Changes in density modify the reactivity. Changes in reactivity modify thermal power. Modifications in thermal power produce variations in temperature fields. Variations in temperature produce variations in strain due to thermal-elastic effects. If the variation of the temperature field is fast enough and if the Doppler Effect and other stabilizing prompt effects in the fuel are weak enough, a fast oscillatory instability could be produced, coupled with mechanical vibrations of small amplitude. A recently constructed, simple mathematical model of nuclear reactor kinetics, that improves the one due to A.S. Thompson, is reviewed. It was constructed in order to study, in a first approximation, the stability of the reactor: a nonlinear nuclear-thermal oscillator (that corresponds to reactor point kinetics with thermal-elastic feedback and with frozen delayed neutron effects) is coupled nonlinearly with a linear mechanical-thermal oscillator (that corresponds to the first normal mode of mechanical vibrations excited by thermo-elastic effects). This mathematical model is studied here from the standpoint of mechanical vibrations. It is shown how, under certain conditions, a suitable mechanical perturbation could elicit fast and growing oscillatory instabilities in the reactor power. Applying the asymptotic method due to Krylov, Bogoliubov and Mitropolsky, analytical formulae that may be used in the calculation of the time varying amplitude and phase of the mechanical oscillations are given, as functions of the mechanical, thermal and nuclear parameters of the reactor. The consequences for the mechanical integrity of the reactor are assessed. Some conditions, mainly, but not exclusively

Hidden beauty in multiloop amplitudes

International Nuclear Information System (INIS)

Cachazo, Freddy; Spradlin, Marcus; Volovich, Anastasia

2006-01-01

Planar L-loop maximally helicity violating amplitudes in N = 4 supersymmetric Yang-Mills theory are believed to possess the remarkable property of satisfying iteration relations in L. We propose a simple new method for studying iteration relations for four-particle amplitudes which involves the use of certain linear differential operators and eliminates the need to fully evaluate any loop integrals. We carry out this procedure in explicit detail for the two-loop amplitude and prove that this method can be applied to any multiloop integral, allowing a conjectured iteration relation for any given amplitude to be tested up to polynomials in logarithms

Amplitude of Accommodation and its Relation to Refractive Errors

Directory of Open Access Journals (Sweden)

Abraham Lekha

2005-01-01

Full Text Available Aims: To evaluate the relationship between amplitude of accommodation and refractive errors in the peri-presbyopic age group. Materials and Methods: Three hundred and sixteen right eyes of 316 consecutive patients in the age group 35-50 years who attended our outpatient clinic were studied. Emmetropes, hypermetropes and myopes with best-corrected visual acuity of 6/6 J1 in both eyes were included. The amplitude of accommodation (AA was calculated by measuring the near point of accommodation (NPA. In patients with more than ± 2 diopter sphere correction for distance, the NPA was also measured using appropriate soft contact lenses. Results: There was a statistically significant difference in AA between myopes and hypermetropes ( P P P P P P >0.5. Conclusion: Our study showed higher amplitude of accommodation among myopes between 35 and 44 years compared to emmetropes and hypermetropes

Amplitude-independent flaw length determination using differential eddy current

Science.gov (United States)

Shell, E.

2013-01-01

Military engine component manufacturers typically specify the eddy current (EC) inspection requirements as a crack length or depth with the assumption that the cracks in both the test specimens and inspected component are of a similar fixed aspect ratio. However, differential EC response amplitude is dependent on the area of the crack face, not the length or depth. Additionally, due to complex stresses, in-service cracks do not always grow in the assumed manner. It would be advantageous to use more of the information contained in the EC data to better determine the full profile of cracks independent of the fixed aspect ratio amplitude response curve. A specimen with narrow width notches is used to mimic cracks of varying aspect ratios in a controllable manner. The specimen notches have aspect ratios that vary from 1:1 to 10:1. Analysis routines have been developed using the shape of the EC response signals that can determine the length of a surface flaw of common orientations without use of the amplitude of the signal or any supporting traditional probability of detection basis. Combined with the relationship between signal amplitude and area, the depth of the flaw can also be calculated.

Off-shell CHY amplitudes

Energy Technology Data Exchange (ETDEWEB)

Lam, C.S., E-mail: Lam@physics.mcgill.ca [Department of Physics, McGill University, Montreal, Q.C., H3A 2T8 (Canada); Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, V6T 1Z1 (Canada); Yao, York-Peng, E-mail: yyao@umich.edu [Department of Physics, The University of Michigan Ann Arbor, MI 48109 (United States)

2016-06-15

The Cachazo–He–Yuan (CHY) formula for on-shell scattering amplitudes is extended off-shell. The off-shell amplitudes (amputated Green's functions) are Möbius invariant, and have the same momentum poles as the on-shell amplitudes. The working principles which drive the modifications to the scattering equations are mainly Möbius covariance and energy momentum conservation in off-shell kinematics. The same technique is also used to obtain off-shell massive scalars. A simple off-shell extension of the CHY gauge formula which is Möbius invariant is proposed, but its true nature awaits further study.

Non-dissipative kinetic simulation and analytical solution of three-mode equations of ion temperature gradient instability

International Nuclear Information System (INIS)

Watanabe, T.-H.; Sugama, H.; Sato, T.

1999-12-01

A non-dissipative drift kinetic simulation scheme, which rigorously satisfies the time-reversibility, is applied to the three-mode coupling problem of the ion temperature gradient (ITG) instability. It is found from the simulation that the three-mode ITG system repeats growth and decay with a period which shows a logarithmic divergence for infinitesimal initial perturbations. Accordingly, time average of the mode amplitude vanishes, as the initial amplitude approaches to zero. An exact solution is analytically given for a class of initial conditions. An excellent agreement is confirmed between the analytical solution and numerical results. The results obtained here provide a useful reference for basic benchmarking of theories and simulation of the ITG modes. (author)

Resonant particle production during inflation: a full analytical study

Energy Technology Data Exchange (ETDEWEB)

Pearce, Lauren; Peloso, Marco [School of Physics and Astronomy, University of Minnesota, 116 Church Street S.E., Minneapolis, MN 55455 (United States); Sorbo, Lorenzo, E-mail: lpearce@physics.umn.edu, E-mail: peloso@physics.umn.edu, E-mail: sorbo@physics.umass.edu [Amherst Center for Fundamental Interactions, Department of Physics, University of Massachusetts, 1126 Lederle Graduate Research Tower (LGRT), Amherst, MA 01003 (United States)

2017-05-01

We revisit the study of the phenomenology associated to a burst of particle production of a field whose mass is controlled by the inflaton field and vanishes at one given instance during inflation. This generates a bump in the correlators of the primordial scalar curvature. We provide a unified formalism to compute various effects that have been obtained in the literature and confirm that the dominant effects are due to the rescattering of the produced particles on the inflaton condensate. We improve over existing results (based on numerical fits) by providing exact analytic expressions for the shape and height of the bump, both in the power spectrum and the equilateral bispectrum. We then study the regime of validity of the perturbative computations of this signature. Finally, we extend these computations to the case of a burst of particle production in a sector coupled only gravitationally to the inflaton.

Analytical model of the optical vortex microscope.

Science.gov (United States)

Płocinniczak, Łukasz; Popiołek-Masajada, Agnieszka; Masajada, Jan; Szatkowski, Mateusz

2016-04-20

This paper presents an analytical model of the optical vortex scanning microscope. In this microscope the Gaussian beam with an embedded optical vortex is focused into the sample plane. Additionally, the optical vortex can be moved inside the beam, which allows fine scanning of the sample. We provide an analytical solution of the whole path of the beam in the system (within paraxial approximation)-from the vortex lens to the observation plane situated on the CCD camera. The calculations are performed step by step from one optical element to the next. We show that at each step, the expression for light complex amplitude has the same form with only four coefficients modified. We also derive a simple expression for the vortex trajectory of small vortex displacements.

On the origin of amplitude reduction mechanism in tapping mode atomic force microscopy

Science.gov (United States)

Keyvani, Aliasghar; Sadeghian, Hamed; Goosen, Hans; van Keulen, Fred

2018-04-01

The origin of amplitude reduction in Tapping Mode Atomic Force Microscopy (TM-AFM) is typically attributed to the shift in resonance frequency of the cantilever due to the nonlinear tip-sample interactions. In this paper, we present a different insight into the same problem which, besides explaining the amplitude reduction mechanism, provides a simple reasoning for the relationship between tip-sample interactions and operation parameters (amplitude and frequency). The proposed formulation, which attributes the amplitude reduction to an interference between the tip-sample and dither force, only deals with the linear part of the system; however, it fully agrees with experimental results and numerical solutions of the full nonlinear model of TM-AFM.

Speech Enhancement by MAP Spectral Amplitude Estimation Using a Super-Gaussian Speech Model

Directory of Open Access Journals (Sweden)

Lotter Thomas

2005-01-01

Full Text Available This contribution presents two spectral amplitude estimators for acoustical background noise suppression based on maximum a posteriori estimation and super-Gaussian statistical modelling of the speech DFT amplitudes. The probability density function of the speech spectral amplitude is modelled with a simple parametric function, which allows a high approximation accuracy for Laplace- or Gamma-distributed real and imaginary parts of the speech DFT coefficients. Also, the statistical model can be adapted to optimally fit the distribution of the speech spectral amplitudes for a specific noise reduction system. Based on the super-Gaussian statistical model, computationally efficient maximum a posteriori speech estimators are derived, which outperform the commonly applied Ephraim-Malah algorithm.

School of Analytic Computing in Theoretical High-Energy Physics

CERN Document Server

2015-01-01

In recent years, a huge progress has been made on computing rates for production processes of direct relevance to experiments at the Large Hadron Collider (LHC). Crucial to that remarkable advance has been our understanding and ability to compute scattering amplitudes and cross sections. The aim of the School is to bring together young theorists working on the phenomenology of LHC physics with those working in more formal areas, and to provide them the analytic tools to compute amplitudes in gauge theories. The school is addressed to Ph.D. students and post-docs in Theoretical High-Energy Physics. 30 hours of lectures and 4 hours of tutorials will be delivered over the 6 days of the School.

Exact Analytical Solutions in Three-Body Problems and Model of Neutrino Generator

Directory of Open Access Journals (Sweden)

Takibayev N.Zh.

2010-04-01

Full Text Available Exact analytic solutions are obtained in three-body problem for the scattering of light particle on the subsystem of two fixed centers in the case when pair potentials have a separable form. Solutions show an appearance of new resonance states and dependence of resonance energy and width on distance between two fixed centers. The approach of exact analytical solutions is expanded to the cases when two-body scattering amplitudes have the Breit-Wigner’s form and employed for description of neutron resonance scattering on subsystem of two heavy nuclei fixed in nodes of crystalline lattice. It is shown that some resonance states have widths close to zero at the certain values of distance between two heavy scatterer centers, this gives the possibility of transitions between states. One of these transitions between three-body resonance states could be connected with process of electron capture by proton with formation of neutron and emission of neutrino. This exoenergic process leading to the cooling of star without nuclear reactions is discussed.

On the amplitude/Wilson loop duality in N=2 SCQCD

Directory of Open Access Journals (Sweden)

Marta Leoni

2015-07-01

Full Text Available We compute the four-point amplitude with external adjoint particles in N=2 SCQCD at two loops using N=1 superspace Feynman diagrams, extending the results of arXiv:1406.7283. We consider the diagrammatic difference with the corresponding process of N=4 SYM finding a non-vanishing result, which is a non-trivial function of the kinematic variables. This demonstrates that in N=2 SCQCD, even in the sector with external particles in the vector multiplet, the amplitude/Wilson loop duality is inevitably broken at two loops.

The open superstring 6-point amplitude with manifest symmetries

International Nuclear Information System (INIS)

Barreiro, Luiz Antonio; Medina, Ricardo; Stieberger, Stephan

2011-01-01

Full text: The general tree level amplitude for massless bosons states of open superstrings has been known for a long time ago. It is clear how to obtain this general formula using vertex operators in the Ramond-Neveu-Schwarz formalism. From the beginning of the eighties the explicit expression for this formula has been known in the case of 3 and 4-point amplitudes. In that decade an attempt (with partial success) was done, by Kitazawa, to obtain the corresponding 5-point amplitude. Only in 2002 a complete and correct expression for this amplitude was obtained. Its low energy expansion was compared to the corresponding one from the low energy effective Lagrangian of the open superstring, finding a perfect match. A few years later, in 2005, it was realized that the 5-point formula could be written in a very much compact form, as a sum of two terms: each of them consisting of a momentum factor and a kinematic expression. This constituted a generalization of the 4-point amplitude case, which had been known to be cast in only one momentum factor multiplied by one kinematic expression. For this simplification to happen, known symmetries of the (tree level) scattering amplitudes were implemented in a manifest form. These symmetries are (on-shell) gauge symmetry, cyclic symmetry and twisting symmetry (or world sheet parity). In the recent years it has been realized that the N-point amplitude can be written as a sum of (N - 3)! terms (where N > 3). This result not only agrees with the 3, 4 and 5-point results, but also with the 6-point result which had been obtained by 2005, written as a sum of six terms. The expression that up to now has been obtained for the 6-point amplitude is quite complicated and, besides knowing that it consists of six terms, is not very illuminating. In this work we report on the recent result of writing the 6-point amplitude with gauge, cyclic and twisting symmetries manifest. Not only because of the manifest symmetries this result is important

Mammalian cycles: internally defined periods and interaction-driven amplitudes

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LR Ginzburg

2015-08-01

Full Text Available The cause of mammalian cycles—the rise and fall of populations over a predictable period of time—has remained controversial since these patterns were first observed over a century ago. In spite of extensive work on observable mammalian cycles, the field has remained divided upon what the true cause is, with a majority of opinions attributing it to either predation or to intra-species mechanisms. Here we unite the eigenperiod hypothesis, which describes an internal, maternal effect-based mechanism to explain the cycles’ periods with a recent generalization explaining the amplitude of snowshoe hare cycles in northwestern North America based on initial predator abundance. By explaining the period and the amplitude of the cycle with separate mechanisms, a unified and consistent view of the causation of cycles is reached. Based on our suggested theory, we forecast the next snowshoe hare cycle (predicted peak in 2016 to be of extraordinarily low amplitude.

Analytical model of internally coupled ears

DEFF Research Database (Denmark)

Vossen, Christine; Christensen-Dalsgaard, Jakob; Leo van Hemmen, J

2010-01-01

Lizards and many birds possess a specialized hearing mechanism: internally coupled ears where the tympanic membranes connect through a large mouth cavity so that the vibrations of the tympanic membranes influence each other. This coupling enhances the phase differences and creates amplitude...... additionally provides the opportunity to incorporate the effect of the asymmetrically attached columella, which leads to the activation of higher membrane vibration modes. Incorporating this effect, the analytical model can explain measurements taken from the tympanic membrane of a living lizard, for example...

New relations for Einstein–Yang–Mills amplitudes

International Nuclear Information System (INIS)

Stieberger, Stephan; Taylor, Tomasz R.

2016-01-01

We obtain new relations between Einstein–Yang–Mills (EYM) amplitudes involving N gauge bosons plus a single graviton and pure Yang–Mills amplitudes involving N gauge bosons plus one additional vector boson inserted in a way typical for a gauge boson of a “spectator” group commuting with the group associated to original N gauge bosons. We show that such EYM amplitudes satisfy U(1) decoupling relations similar to Kleiss–Kuijf relations for Yang–Mills amplitudes. We consider a D-brane embedding of EYM amplitudes in the framework of disk amplitudes involving open and closed strings. A new set of monodromy relations is derived for mixed open–closed amplitudes with one closed string inserted on the disk world-sheet and a number of open strings at the boundary. These relations allow expressing the latter in terms of pure open string amplitudes and, in the field-theory limit, they yield the U(1) decoupling relations for EYM amplitudes.

Utilizing time-frequency amplitude and phase synchrony measure to assess feedback processing in a gambling task.

Science.gov (United States)

Watts, Adreanna T M; Tootell, Anne V; Fix, Spencer T; Aviyente, Selin; Bernat, Edward M

2018-04-29

The neurophysiological mechanisms involved in the evaluation of performance feedback have been widely studied in the ERP literature over the past twenty years, but understanding has been limited by the use of traditional time-domain amplitude analytic approaches. Gambling outcome valence has been identified as an important factor modulating event-related potential (ERP) components, most notably the feedback negativity (FN). Recent work employing time-frequency analysis has shown that processes indexed by the FN are confounded in the time-domain and can be better represented as separable feedback-related processes in the theta (3-7 Hz) and delta (0-3 Hz) frequency bands. In addition to time-frequency amplitude analysis, phase synchrony measures have begun to further our understanding of performance evaluation by revealing how feedback information is processed within and between various brain regions. The current study aimed to provide an integrative assessment of time-frequency amplitude, inter-trial phase synchrony, and inter-channel phase synchrony changes following monetary feedback in a gambling task. Results revealed that time-frequency amplitude activity explained separable loss and gain processes confounded in the time-domain. Furthermore, phase synchrony measures explained unique variance above and beyond amplitude measures and demonstrated enhanced functional integration between medial prefrontal and bilateral frontal, motor, and occipital regions for loss relative to gain feedback. These findings demonstrate the utility of assessing time-frequency amplitude, inter-trial phase synchrony, and inter-channel phase synchrony together to better elucidate the neurophysiology of feedback processing. Copyright © 2017. Published by Elsevier B.V.

Motivic amplitudes and cluster coordinates

International Nuclear Information System (INIS)

Golden, J.K.; Goncharov, A.B.; Spradlin, M.; Vergu, C.; Volovich, A.

2014-01-01

In this paper we study motivic amplitudes — objects which contain all of the essential mathematical content of scattering amplitudes in planar SYM theory in a completely canonical way, free from the ambiguities inherent in any attempt to choose particular functional representatives. We find that the cluster structure on the kinematic configuration space Conf n (ℙ 3 ) underlies the structure of motivic amplitudes. Specifically, we compute explicitly the coproduct of the two-loop seven-particle MHV motivic amplitude A 7,2 M and find that like the previously known six-particle amplitude, it depends only on certain preferred coordinates known in the mathematics literature as cluster X-coordinates on Conf n (ℙ 3 ). We also find intriguing relations between motivic amplitudes and the geometry of generalized associahedrons, to which cluster coordinates have a natural combinatoric connection. For example, the obstruction to A 7,2 M being expressible in terms of classical polylogarithms is most naturally represented by certain quadrilateral faces of the appropriate associahedron. We also find and prove the first known functional equation for the trilogarithm in which all 40 arguments are cluster X-coordinates of a single algebra. In this respect it is similar to Abel’s 5-term dilogarithm identity

A Note on Standing Internal Inertial Gravity Waves of Finite Amplitude

Science.gov (United States)

Thorpe, S. A.

2003-01-01

The effects of finite amplitude are examined in two-dimensional, standing, internal gravity waves in a rectangular container which rotates about a vertical axis at frequency f/2. Expressions are given for the velocity components, density fluctuations and isopycnal displacements to second order in the wave steepness in fluids with buoyancy frequency, N, of general form, and the effect of finite amplitude on wave frequency is given in an expansion to third order. The first order solutions, and the solutions to second order in the absence of rotation, are shown to conserve energy during a wave cycle. Analytical solutions are found to second order for the first two modes in a deep fluid with N proportional to sech(az), where z is the upward vertical coordinate and a is scaling factor. In the absence of rotation, results for the first mode in the latter stratification are found to be consistent with those for interfacial waves. An analytical solution to fourth order in a fluid with constant N is given and used to examine the effects of rotation on the development of static instability or of conditions in which shear instability may occur. As in progressive internal waves, an effect of rotation is to enhance the possibility of shear instability for waves with frequencies close to f. The analysis points to a significant difference between the dynamics of standing waves in containers of limited size and progressive internal waves in an unlimited fluid; the effect of boundaries on standing waves may inhibit the onset of instability. A possible application of the analysis is to transverse oscillations in long, narrow, steep-sided lakes such as Loch Ness, Scotland.

An analytic equation of state for Ising-like models

International Nuclear Information System (INIS)

O'Connor, Denjoe; Santiago, J A; Stephens, C R

2007-01-01

Using an environmentally friendly renormalization we derive, from an underlying field theory representation, a formal expression for the equation of state, y = f(x), that exhibits all desired asymptotic and analyticity properties in the three limits x → 0, x → ∞ and x → -1. The only necessary inputs are the Wilson functions γ λ , γ ψ and γ φ 2 , associated with a renormalization of the transverse vertex functions. These Wilson functions exhibit a crossover between the Wilson-Fisher fixed point and the fixed point that controls the coexistence curve. Restricting to the case N = 1, we derive a one-loop equation of state for 2 < d < 4 naturally parameterized by a ratio of nonlinear scaling fields. For d = 3 we show that a non-parameterized analytic form can be deduced. Various asymptotic amplitudes are calculated directly from the equation of state in all three asymptotic limits of interest and comparison made with known results. By positing a scaling form for the equation of state inspired by the one-loop result, but adjusted to fit the known values of the critical exponents, we obtain better agreement with known asymptotic amplitudes

QCD amplitudes with 2 initial spacelike legs via generalised BCFW recursion

Energy Technology Data Exchange (ETDEWEB)

Kutak, Krzysztof; Hameren, Andreas van; Serino, Mirko [The H. Niewodniczański Institute of Nuclear Physics, Polish Academy of Sciences, ul. Radzikowskiego 152, 31-342, Cracow (Poland)

2017-02-02

We complete the generalisation of the BCFW recursion relation to the off-shell case, allowing for the computation of tree level scattering amplitudes for full High Energy Factorisation (HEF), i.e. with both incoming partons having a non-vanishing transverse momentum. We provide explicit results for color-ordered amplitudes with two off-shell legs in massless QCD up to 4 point, continuing the program begun in two previous papers. For the 4-fermion amplitudes, which are not BCFW-recursible, we perform a diagrammatic computation, so as to offer a complete set of expressions. We explicitly show and discuss some plots of the squared 2→2 matrix elements as functions of the differences in rapidity and azimuthal angle of the final state particles.

Travelling-wave amplitudes as solutions of the phase-field crystal equation

Science.gov (United States)

Nizovtseva, I. G.; Galenko, P. K.

2018-01-01

The dynamics of the diffuse interface between liquid and solid states is analysed. The diffuse interface is considered as an envelope of atomic density amplitudes as predicted by the phase-field crystal model (Elder et al. 2004 Phys. Rev. E 70, 051605 (doi:10.1103/PhysRevE.70.051605); Elder et al. 2007 Phys. Rev. B 75, 064107 (doi:10.1103/PhysRevB.75.064107)). The propagation of crystalline amplitudes into metastable liquid is described by the hyperbolic equation of an extended Allen-Cahn type (Galenko & Jou 2005 Phys. Rev. E 71, 046125 (doi:10.1103/PhysRevE.71.046125)) for which the complete set of analytical travelling-wave solutions is obtained by the method (Malfliet & Hereman 1996 Phys. Scr. 15, 563-568 (doi:10.1088/0031-8949/54/6/003); Wazwaz 2004 Appl. Math. Comput. 154, 713-723 (doi:10.1016/S0096-3003(03)00745-8)). The general solution of travelling waves is based on the function of hyperbolic tangent. Together with its set of particular solutions, the general solution is analysed within an example of specific task about the crystal front invading metastable liquid (Galenko et al. 2015 Phys. D 308, 1-10 (doi:10.1016/j.physd.2015.06.002)). The influence of the driving force on the phase-field profile, amplitude velocity and correlation length is investigated for various relaxation times of the gradient flow. This article is part of the theme issue `From atomistic interfaces to dendritic patterns'.

Two Photon Distribution Amplitudes

International Nuclear Information System (INIS)

El Beiyad, M.; Pire, B.; Szymanowski, L.; Wallon, S.

2008-01-01

The factorization of the amplitude of the process γ*γ→γγ in the low energy and high photon virtuality region is demonstrated at the Born order and in the leading logarithmic approximation. The leading order two photon (generalized) distribution amplitudes exhibit a characteristic ln Q 2 behaviour and obey new inhomogeneous evolution equations

Flat-Cladding Fiber Bragg Grating Sensors for Large Strain Amplitude Fatigue Tests

Directory of Open Access Journals (Sweden)

Xijia Gu

2010-08-01

Full Text Available We have successfully developed a flat-cladding fiber Bragg grating sensor for large cyclic strain amplitude tests of up to ±8,000 με. The increased contact area between the flat-cladding fiber and substrate, together with the application of a new bonding process, has significantly increased the bonding strength. In the push-pull fatigue tests of an aluminum alloy, the plastic strain amplitudes measured by three optical fiber sensors differ only by 0.43% at a cyclic strain amplitude of ±7,000 με and 1.9% at a cyclic strain amplitude of ±8,000 με. We also applied the sensor on an extruded magnesium alloy for evaluating the peculiar asymmetric hysteresis loops. The results obtained were in good agreement with those measured from the extensometer, a further validation of the sensor.

Unitarity relations for the four-body scattering amplitude

International Nuclear Information System (INIS)

Matsui, Y.

1988-01-01

A formal derivation of the general unitarity relation for the four-particle transition operator is given by generalizing the three-body formalism of Karlson and Zeiger to the four-body case. From this operator relation the on-shell unitarity relations for the amplitudes that describe elastic/rearrangement, partial breakup, and full breakup scattering processes are obtained

Two-loop planar master integrals for Higgs →3 partons with full heavy-quark mass dependence

International Nuclear Information System (INIS)

Bonciani, Roberto; Duca, Vittorio Del; Frellesvig, Hjalte; Henn, Johannes M.; Moriello, Francesco; Smirnov, Vladimir A.

2016-01-01

We present the analytic computation of all the planar master integrals which contribute to the two-loop scattering amplitudes for Higgs→3 partons, with full heavy-quark mass dependence. These are relevant for the NNLO corrections to fully inclusive Higgs production and to the NLO corrections to Higgs production in association with a jet, in the full theory. The computation is performed using the differential equations method. Whenever possible, a basis of master integrals that are pure functions of uniform weight is used. The result is expressed in terms of one-fold integrals of polylogarithms and elementary functions up to transcendental weight four. Two integral sectors are expressed in terms of elliptic integrals. We show that by introducing a one-dimensional parametrization of the integrals the relevant second order differential equation can be readily solved, and the solution can be expressed to all orders of the dimensional regularization parameter in terms of iterated integrals over elliptic kernels. We express the result for the elliptic sectors in terms of two and three-fold iterated integrals, which we find suitable for numerical evaluations. This is the first time that four-point multiscale Feynman integrals have been computed in a fully analytic way in terms of elliptic integrals.

Two-loop planar master integrals for Higgs →3 partons with full heavy-quark mass dependence

Energy Technology Data Exchange (ETDEWEB)

Bonciani, Roberto [Dipartimento di Fisica, Sapienza - Università di Roma,Piazzale Aldo Moro 5, 00185, Rome (Italy); INFN Sezione di Roma, Piazzale Aldo Moro 2, 00185, Rome (Italy); Duca, Vittorio Del [ETH Zurich, Institut fur theoretische Physik, Wolfgang-Paulistr. 27, 8093, Zurich (Switzerland); INFN Laboratori Nazionali di Frascati, 00044 Frascati, Roma (Italy); Frellesvig, Hjalte [Institute of Nuclear and Particle Physics, NCSR Demokritos, Agia Paraskevi, 15310 (Greece); Henn, Johannes M. [PRISMA Cluster of Excellence, Johannes Gutenberg University, 55099 Mainz (Germany); Moriello, Francesco [Dipartimento di Fisica, Sapienza - Università di Roma,Piazzale Aldo Moro 5, 00185, Rome (Italy); INFN Sezione di Roma, Piazzale Aldo Moro 2, 00185, Rome (Italy); ETH Zurich, Institut fur theoretische Physik, Wolfgang-Paulistr. 27, 8093, Zurich (Switzerland); Smirnov, Vladimir A. [Skobeltsyn Institute of Nuclear Physics of Moscow State University, 119991 Moscow (Russian Federation)

2016-12-19

We present the analytic computation of all the planar master integrals which contribute to the two-loop scattering amplitudes for Higgs→3 partons, with full heavy-quark mass dependence. These are relevant for the NNLO corrections to fully inclusive Higgs production and to the NLO corrections to Higgs production in association with a jet, in the full theory. The computation is performed using the differential equations method. Whenever possible, a basis of master integrals that are pure functions of uniform weight is used. The result is expressed in terms of one-fold integrals of polylogarithms and elementary functions up to transcendental weight four. Two integral sectors are expressed in terms of elliptic integrals. We show that by introducing a one-dimensional parametrization of the integrals the relevant second order differential equation can be readily solved, and the solution can be expressed to all orders of the dimensional regularization parameter in terms of iterated integrals over elliptic kernels. We express the result for the elliptic sectors in terms of two and three-fold iterated integrals, which we find suitable for numerical evaluations. This is the first time that four-point multiscale Feynman integrals have been computed in a fully analytic way in terms of elliptic integrals.

Relative amplitude preservation processing utilizing surface consistent amplitude correction. Part 3; Surface consistent amplitude correction wo mochiita sotai shinpuku hozon shori. 3

Energy Technology Data Exchange (ETDEWEB)

Saeki, T [Japan National Oil Corporation, Tokyo (Japan). Technology Research Center

1996-10-01

For the seismic reflection method conducted on the ground surface, generator and geophone are set on the surface. The observed waveforms are affected by the ground surface and surface layer. Therefore, it is required for discussing physical properties of the deep underground to remove the influence of surface layer, preliminarily. For the surface consistent amplitude correction, properties of the generator and geophone were removed by assuming that the observed waveforms can be expressed by equations of convolution. This is a correction method to obtain records without affected by the surface conditions. In response to analysis and correction of waveforms, wavelet conversion was examined. Using the amplitude patterns after correction, the significant signal region, noise dominant region, and surface wave dominant region would be separated each other. Since the amplitude values after correction of values in the significant signal region have only small variation, a representative value can be given. This can be used for analyzing the surface consistent amplitude correction. Efficiency of the process can be enhanced by considering the change of frequency. 3 refs., 5 figs.

New relations for gauge-theory amplitudes

International Nuclear Information System (INIS)

Bern, Z.; Carrasco, J. J. M.; Johansson, H.

2008-01-01

We present an identity satisfied by the kinematic factors of diagrams describing the tree amplitudes of massless gauge theories. This identity is a kinematic analog of the Jacobi identity for color factors. Using this we find new relations between color-ordered partial amplitudes. We discuss applications to multiloop calculations via the unitarity method. In particular, we illustrate the relations between different contributions to a two-loop four-point QCD amplitude. We also use this identity to reorganize gravity tree amplitudes diagram by diagram, offering new insight into the structure of the Kawai-Lewellen-Tye (KLT) relations between gauge and gravity tree amplitudes. This insight leads to similar but novel relations. We expect this to be helpful in higher-loop studies of the ultraviolet properties of gravity theories.

Analytical prediction on the pump-induced pulsating pressure in a reactor coolant pipe

International Nuclear Information System (INIS)

Lee, K.B.; Im, I.Y.; Lee, S.K.

1992-01-01

An analytical method is presented for predicting the amplitudes of pump-induced fluctuating pressures in a reactor coolant pipe using a linear transformation technique which reduces a homogeneous differential equation with non-homogeneous boundary conditions into a nonhomogeneous differential equation with homogeneous boundary conditions. At the end of the pipe, three types of boundary conditions are considered-open, closed and piston-spring supported. Numerical examples are given for a typical reactor. Comparisons of measured pressure amplitudes in the pipe with model prediction are shown to be in good agreement for the forcing frequencies. (author)

Multiscalar production amplitudes beyond threshold

CERN Document Server

Argyres, E N; Kleiss, R H

1993-01-01

We present exact tree-order amplitudes for $H^* \\to n~H$, for final states containing one or two particles with non-zero three-momentum, for various interaction potentials. We show that there are potentials leading to tree amplitudes that satisfy unitarity, not only at threshold but also in the above kinematical configurations and probably beyond. As a by-product, we also calculate $2\\to n$ tree amplitudes at threshold and show that for the unbroken $\\phi^4$ theory they vanish for $n>4~$, for the Standard Model Higgs they vanish for $n\\ge 3~$ and for a model potential, respecting tree-order unitarity, for $n$ even and $n>4~$. Finally, we calculate the imaginary part of the one-loop $1\\to n$ amplitude in both symmetric and spontaneously broken $\\phi^4$ theory.

Subleading terms in the collinear limit of Yang–Mills amplitudes

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Stephan Stieberger

2015-11-01

Full Text Available For two massless particles i and j, the collinear limit is a special kinematic configuration in which the particles propagate with parallel four-momentum vectors, with the total momentum P distributed as pi=xP and pj=(1−xP, so that sij≡(pi+pj2=P2=0. In Yang–Mills theory, if i and j are among N gauge bosons participating in a scattering process, it is well known that the partial amplitudes associated to the (single trace group factors with adjacent i and j are singular in the collinear limit and factorize at the leading order into (N−1-particle amplitudes times the universal, x-dependent Altarelli–Parisi factors. We give a precise definition of the collinear limit and show that at the tree level, the subleading, non-singular terms are related to the amplitudes with a single graviton inserted instead of two collinear gauge bosons. To that end, we argue that in one-graviton Einstein–Yang–Mills amplitudes, the graviton with momentum P can be replaced by a pair of collinear gauge bosons carrying arbitrary momentum fractions xP and (1−xP.

Amplitude structure of off-shell processes

International Nuclear Information System (INIS)

Fearing, H.W.; Goldstein, G.R.; Moravcsik, M.J.

1984-01-01

The structure of M matrices, or scattering amplitudes, and of potentials for off-shell processes is discussed with the objective of determining how one can obtain information on off-shell amplitudes of a process in terms of the physical observables of a larger process in which the first process is embedded. The procedure found is inevitably model dependent, but within a particular model for embedding, a determination of the physically measurable amplitudes of the larger process is able to yield a determination of the off-shell amplitudes of the embedded process

Slow oscillation amplitudes and up-state lengths relate to memory improvement.

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Dominik P J Heib

Full Text Available There is growing evidence of the active involvement of sleep in memory consolidation. Besides hippocampal sharp wave-ripple complexes and sleep spindles, slow oscillations appear to play a key role in the process of sleep-associated memory consolidation. Furthermore, slow oscillation amplitude and spectral power increase during the night after learning declarative and procedural memory tasks. However, it is unresolved whether learning-induced changes specifically alter characteristics of individual slow oscillations, such as the slow oscillation up-state length and amplitude, which are believed to be important for neuronal replay. 24 subjects (12 men aged between 20 and 30 years participated in a randomized, within-subject, multicenter study. Subjects slept on three occasions for a whole night in the sleep laboratory with full polysomnography. Whereas the first night only served for adaptation purposes, the two remaining nights were preceded by a declarative word-pair task or by a non-learning control task. Slow oscillations were detected in non-rapid eye movement sleep over electrode Fz. Results indicate positive correlations between the length of the up-state as well as the amplitude of both slow oscillation phases and changes in memory performance from pre to post sleep. We speculate that the prolonged slow oscillation up-state length might extend the timeframe for the transfer of initial hippocampal to long-term cortical memory representations, whereas the increase in slow oscillation amplitudes possibly reflects changes in the net synaptic strength of cortical networks.

Algebraic and analyticity properties of the n-point function in quantum field theory

International Nuclear Information System (INIS)

Bros, Jacques

1970-01-01

The general theory of quantized fields (axiomatic approach) is investigated. A systematic study of the algebraic properties of all the Green functions of a local field, which generalize the ordinary retarded and advanced functions, is presented. The notion emerges of a primitive analyticity domain of the n-point function, and of the existence of auxiliary analytic functions into which the various Green functions can be decomposed. Certain processes of analytic completion are described, and then applied to enlarging the primitive domain, particularly for the case n = 4; among the results the crossing property for all scattering amplitudes which involve two incoming and two outgoing particles is proved. (author) [fr

Non-supersymmetric loop amplitudes and MHV vertices

International Nuclear Information System (INIS)

Bedford, James; Brandhuber, Andreas; Spence, Bill; Travaglini, Gabriele

2005-01-01

We show how the MHV diagram description of Yang-Mills theories can be used to study non-supersymmetric loop amplitudes. In particular, we derive a compact expression for the cut-constructible part of the general one-loop MHV multi-gluon scattering amplitude in pure Yang-Mills theory. We show that in special cases this expression reduces to known amplitudes-the amplitude with adjacent negative-helicity gluons, and the five gluon non-adjacent amplitude. Finally, we briefly discuss the twistor space interpretation of our result

The Construction of Spin Foam Vertex Amplitudes

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Eugenio Bianchi

2013-01-01

Full Text Available Spin foam vertex amplitudes are the key ingredient of spin foam models for quantum gravity. These fall into the realm of discretized path integral, and can be seen as generalized lattice gauge theories. They can be seen as an attempt at a 4-dimensional generalization of the Ponzano-Regge model for 3d quantum gravity. We motivate and review the construction of the vertex amplitudes of recent spin foam models, giving two different and complementary perspectives of this construction. The first proceeds by extracting geometric configurations from a topological theory of the BF type, and can be seen to be in the tradition of the work of Barrett, Crane, Freidel and Krasnov. The second keeps closer contact to the structure of Loop Quantum Gravity and tries to identify an appropriate set of constraints to define a Lorentz-invariant interaction of its quanta of space. This approach is in the tradition of the work of Smolin, Markopoulous, Engle, Pereira, Rovelli and Livine.

Use of analytical Born amplitude representation in studies of dispersion potentials and electron-atom scattering

International Nuclear Information System (INIS)

Carvalho, I.L. de.

1985-01-01

Two distinct problems have been studied using simplifield Born's Amplitude Analitical Expressions. The first problem deals with the dispersion energy between the constituent members of the systems He - Ne, - He and H 2 - H 2 . In the second problem second order Born Aproximation has been used for the Electron - Atom Inelastic Scattering for the transitions 1 1 S → 2 1 S and 1 1 S → 2 1 P of helium atom and 1 S → 1 s 2 ([3s' {1/2} sup(o) 1; M sub(j)>) of neon atom (in the case of neon we have used the coupling scheme proposed by Cowan and Andrew). The results obtained by us have been compared with the theoretical and experimental results available in the literature. (author) [pt

GRMHD Simulations of Visibility Amplitude Variability for Event Horizon Telescope Images of Sgr A*

Science.gov (United States)

Medeiros, Lia; Chan, Chi-kwan; Özel, Feryal; Psaltis, Dimitrios; Kim, Junhan; Marrone, Daniel P.; Sa¸dowski, Aleksander

2018-04-01

The Event Horizon Telescope will generate horizon scale images of the black hole in the center of the Milky Way, Sgr A*. Image reconstruction using interferometric visibilities rests on the assumption of a stationary image. We explore the limitations of this assumption using high-cadence disk- and jet-dominated GRMHD simulations of Sgr A*. We also employ analytic models that capture the basic characteristics of the images to understand the origin of the variability in the simulated visibility amplitudes. We find that, in all simulations, the visibility amplitudes for baselines oriented parallel and perpendicular to the spin axis of the black hole follow general trends that do not depend strongly on accretion-flow properties. This suggests that fitting Event Horizon Telescope observations with simple geometric models may lead to a reasonably accurate determination of the orientation of the black hole on the plane of the sky. However, in the disk-dominated models, the locations and depths of the minima in the visibility amplitudes are highly variable and are not related simply to the size of the black hole shadow. This suggests that using time-independent models to infer additional black hole parameters, such as the shadow size or the spin magnitude, will be severely affected by the variability of the accretion flow.

Enhanced brainstem and cortical evoked response amplitudes: single-trial covariance analysis.

Science.gov (United States)

Galbraith, G C

2001-06-01

The purpose of the present study was to develop analytic procedures that improve the definition of sensory evoked response components. Such procedures could benefit all recordings but would especially benefit difficult recordings where many trials are contaminated by muscle and movement artifacts. First, cross-correlation and latency adjustment analyses were applied to the human brainstem frequency-following response and cortical auditory evoked response recorded on the same trials. Lagged cross-correlation functions were computed, for each of 17 subjects, between single-trial data and templates consisting of the sinusoid stimulus waveform for the brainstem response and the subject's own smoothed averaged evoked response P2 component for the cortical response. Trials were considered in the analysis only if the maximum correlation-squared (r2) exceeded .5 (negatively correlated trials were thus included). Identical correlation coefficients may be based on signals with quite different amplitudes, but it is possible to assess amplitude by the nonnormalized covariance function. Next, an algorithm is applied in which each trial with negative covariance is matched to a trial with similar, but positive, covariance and these matched-trial pairs are deleted. When an evoked response signal is present in the data, the majority of trials positively correlate with the template. Thus, a residual of positively correlated trials remains after matched covariance trials are deleted. When these residual trials are averaged, the resulting brainstem and cortical responses show greatly enhanced amplitudes. This result supports the utility of this analysis technique in clarifying and assessing evoked response signals.

Microscopic theory of dynamical subspace for large amplitude collective motion

International Nuclear Information System (INIS)

Sakata, Fumihiko; Marumori, Toshio; Ogura, Masanori.

1986-01-01

A full quantum theory appropriate for describing large amplitude collective motion is proposed by exploiting the basic idea of the semi-classical theory so far developed within the time-depedent Hartree-Fock theory. A central problem of the quantum theory is how to determine an optimal representation called a dynamical representation specific for the collective subspace where the large amplitude collective motion is replicated as precisely as possible. As an extension of the semi-classical theory where the concept of an approximate integral surface played an important role, the collective subspace is properly characterized by introducing a concept of an approximate invariant subspace of the Hamiltonian. (author)

Evaluation of Analytical Modeling Functions for the Phonation Onset Process

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Simon Petermann

2016-01-01

Full Text Available The human voice originates from oscillations of the vocal folds in the larynx. The duration of the voice onset (VO, called the voice onset time (VOT, is currently under investigation as a clinical indicator for correct laryngeal functionality. Different analytical approaches for computing the VOT based on endoscopic imaging were compared to determine the most reliable method to quantify automatically the transient vocal fold oscillations during VO. Transnasal endoscopic imaging in combination with a high-speed camera (8000 fps was applied to visualize the phonation onset process. Two different definitions of VO interval were investigated. Six analytical functions were tested that approximate the envelope of the filtered or unfiltered glottal area waveform (GAW during phonation onset. A total of 126 recordings from nine healthy males and 210 recordings from 15 healthy females were evaluated. Three criteria were analyzed to determine the most appropriate computation approach: (1 reliability of the fit function for a correct approximation of VO; (2 consistency represented by the standard deviation of VOT; and (3 accuracy of the approximation of VO. The results suggest the computation of VOT by a fourth-order polynomial approximation in the interval between 32.2 and 67.8% of the saturation amplitude of the filtered GAW.

Business analytics a practitioner's guide

CERN Document Server

Saxena, Rahul

2013-01-01

This book provides a guide to businesses on how to use analytics to help drive from ideas to execution. Analytics used in this way provides "full lifecycle support" for business and helps during all stages of management decision-making and execution.The framework presented in the book enables the effective interplay of business, analytics, and information technology (business intelligence) both to leverage analytics for competitive advantage and to embed the use of business analytics into the business culture. It lays out an approach for analytics, describes the processes used, and provides gu

Scattering amplitude and bosonization duality in general Chern-Simons vector models

Science.gov (United States)

Yokoyama, Shuichi

2016-09-01

We present the exact large N calculus of four point functions in general Chern-Simons bosonic and fermionic vector models. Applying the LSZ formula to the four point function we determine the two body scattering amplitudes in these theories taking a special care for a non-analytic term to achieve unitarity in the singlet channel. We show that the S-matrix enjoys the bosonization duality, an unusual crossing relation and a non-relativistic reduction to Aharonov-Bohm scattering. We also argue that the S-matrix develops a pole in a certain range of coupling constants, which disappears in the range where the theory reduces to the Chern-Simons theory interacting with free fermions.

A trigonometric approximation for the tension in the string of a simple pendulum accurate for all amplitudes

International Nuclear Information System (INIS)

Lima, F M S

2009-01-01

In a previous work, O'Connell (Phys. Teach. 40, 24 (2002)) investigated the time dependence of the tension in the string of a simple pendulum oscillating within the small-angle regime. In spite of the approximation sin θ ∼ θ being accurate only for amplitudes below 7 deg., his experimental results are for a pendulum oscillating with an amplitude of about 18 deg., therefore beyond the small-angle regime. This lapse may also be found in some textbooks, laboratory manuals and internet. By noting that the exact analytical solution for this problem involves the so-called Jacobi elliptic functions, which are unknown to most students (even instructors), I take into account a sinusoidal approximate solution for the pendulum equation I introduced in a recent work (Eur. J. Phys. 29 1091 (2008)) for deriving a simple trigonometric approximation for the tension valid for all possible amplitudes. This approximation is compared to both the O'Connell and the exact results, revealing that it is accurate enough for analysing large-angle pendulum experiments. (letters and comments)

Scattering amplitudes in open superstring theory

Energy Technology Data Exchange (ETDEWEB)

Schlotterer, Oliver

2011-07-15

The present thesis deals with the theme field of the scattering amplitudes in theories of open superstrings. Especially two different formalisms for the handling of superstrings are introduced and applied for the calaculation of tree-level amplitudes - the Ramond- Neveu-Schwarz (RNS) and the Pure-Spinor (PS) formalism. The RNS approach is proved as flexible in order to describe compactification of the initially ten flat space-time dimensions to four dimensions. We solve the technical problems, which result from the interacting basing world-sheet theory with conformal symmetry. This is used to calculate phenomenologically relevant scattering amplitudes of gluons and quarks as well as production rates of massive harmonic vibrations, which were already identified as virtual exchange particles on the massless level. In the case of a low string mass scale in the range of some Tev the string-specific signatures in parton collisions can be observed in the near future in the LHC experiment at CERN and indicated as first experimental proof of the string theory. THose string effects occur universally for a wide class of string ground states respectively internal geometries and represent an elegant way to avoid the so-called landscape problem of the string theory. A further theme complex in this thesis is based on the PS formalism, which allows a manifestly supersymmetric treatment of scattering amplitudes in ten space-time dimension with sixteen supercharges. We introduce a family of superfields, which occur in massless amplitudes of the open string and can be naturally identified with diagrams of three-valued knots. Thereby we reach not only a compact superspace representation of the n-point field-theory amplitude but can also write the complete superstring n-point amplitude as minimal linear combination of partial amplitudes of the field theory as well as hypergeometric functions. The latter carry the string effects and are analyzed from different perspectives, above all

Scattering amplitudes in open superstring theory

International Nuclear Information System (INIS)

Schlotterer, Oliver

2011-01-01

The present thesis deals with the theme field of the scattering amplitudes in theories of open superstrings. Especially two different formalisms for the handling of superstrings are introduced and applied for the calaculation of tree-level amplitudes - the Ramond- Neveu-Schwarz (RNS) and the Pure-Spinor (PS) formalism. The RNS approach is proved as flexible in order to describe compactification of the initially ten flat space-time dimensions to four dimensions. We solve the technical problems, which result from the interacting basing world-sheet theory with conformal symmetry. This is used to calculate phenomenologically relevant scattering amplitudes of gluons and quarks as well as production rates of massive harmonic vibrations, which were already identified as virtual exchange particles on the massless level. In the case of a low string mass scale in the range of some Tev the string-specific signatures in parton collisions can be observed in the near future in the LHC experiment at CERN and indicated as first experimental proof of the string theory. THose string effects occur universally for a wide class of string ground states respectively internal geometries and represent an elegant way to avoid the so-called landscape problem of the string theory. A further theme complex in this thesis is based on the PS formalism, which allows a manifestly supersymmetric treatment of scattering amplitudes in ten space-time dimension with sixteen supercharges. We introduce a family of superfields, which occur in massless amplitudes of the open string and can be naturally identified with diagrams of three-valued knots. Thereby we reach not only a compact superspace representation of the n-point field-theory amplitude but can also write the complete superstring n-point amplitude as minimal linear combination of partial amplitudes of the field theory as well as hypergeometric functions. The latter carry the string effects and are analyzed from different perspectives, above all

Multiaxial Fatigue Properties of 2A12 Aluminum Alloy Under Different Stress Amplitude Ratio Loadings

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CHEN Ya-jun

2017-09-01

Full Text Available The multiaxial fatigue behavior of 2A12 aluminum alloy was studied with SDN100/1000 electro-hydraulic servo tension-torsion fatigue tester under different stress amplitude ratios, the fracture morphology and the fatigue loading curve were observed to study the failure mechanism. The results show that, under the one stage loading condition, the fatigue life prolongs with the stress amplitude ratio increasing. Under pure torsion loading, smooth and even area exists in the fracture surface. As the stress amplitude ratio increases, the number of scratch reduces, the fatigue striation and some special morphology such as the fishbone pattern, scale pattern and honeycomb pattern can be observed; under cumulative paths of different stress amplitude ratios, the variation of multiaxial fatigue life changes with first stage loading cycles; under cumulative paths of high-low stress amplitude ratio, the cycle hardening occurs obviously in the axial direction for the first stage high stress amplitude ratio loading and 2A12 alloy shows training effect.

AMPLITUDE AND TIME MEASUREMENT ASIC WITH ANALOG DERANDOMIZATION

International Nuclear Information System (INIS)

O CONNOR, P.; DE GERONIMO, G.; KANDASAMY, A.

2002-01-01

We describe a new ASIC for accurate and efficient processing of high-rate pulse signals from highly segmented detectors. In contrast to conventional approaches, this circuit affords a dramatic reduction in data volume through the use of analog techniques (precision peak detectors and time-to-amplitude converters) together with fast arbitration and sequencing logic to concentrate the data before digitization. In operation the circuit functions like a data-driven analog first-in, first-out (FIFO) memory between the preamplifiers and the ADC. Peak amplitudes of pulses arriving at any one of the 32 inputs are sampled, stored, and queued for readout and digitization through a single output port. Hit timing, pulse risetime, and channel address are also available at the output. Prototype chips have been fabricated in 0.35 micron CMOS and tested. First results indicate proper functionality for pulses down to 30 ns peaking time and input rates up to 1.6 MHz/channel. Amplitude accuracy of the peak detect and hold circuit is 0.3% (absolute). TAC accuracy is within 0.3% of full scale. Power consumption is less than 2 mW/channel. Compared with conventional techniques such as track-and-hold and analog memory, this new ASIC will enable efficient pulse height measurement at 20 to 300 times higher rates

The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM

CERN Document Server

Dixon, Lance J.; Henn, Johannes M.

2011-01-01

We provide an analytic formula for the (rescaled) one-loop scalar hexagon integral $\\tilde\\Phi_6$ with all external legs massless, in terms of classical polylogarithms. We show that this integral is closely connected to two integrals appearing in one- and two-loop amplitudes in planar $\\\\mathcal{N}=4$ super-Yang-Mills theory, $\\Omega^{(1)}$ and $\\Omega^{(2)}$. The derivative of $\\Omega^{(2)}$ with respect to one of the conformal invariants yields $\\tilde\\Phi_6$, while another first-order differential operator applied to $\\tilde\\Phi_6$ yields $\\Omega^{(1)}$. We also introduce some kinematic variables that rationalize the arguments of the polylogarithms, making it easy to verify the latter differential equation. We also give a further example of a six-dimensional integral relevant for amplitudes in $\\\\mathcal{N}=4$ super-Yang-Mills.

Fatigue Crack Propagation Under Variable Amplitude Loading Analyses Based on Plastic Energy Approach

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Sofiane Maachou

2014-04-01

Full Text Available Plasticity effects at the crack tip had been recognized as “motor” of crack propagation, the growth of cracks is related to the existence of a crack tip plastic zone, whose formation and intensification is accompanied by energy dissipation. In the actual state of knowledge fatigue crack propagation is modeled using crack closure concept. The fatigue crack growth behavior under constant amplitude and variable amplitude loading of the aluminum alloy 2024 T351 are analyzed using in terms energy parameters. In the case of VAL (variable amplitude loading tests, the evolution of the hysteretic energy dissipated per block is shown similar with that observed under constant amplitude loading. A linear relationship between the crack growth rate and the hysteretic energy dissipated per block is obtained at high growth rates. For lower growth rates values, the relationship between crack growth rate and hysteretic energy dissipated per block can represented by a power law. In this paper, an analysis of fatigue crack propagation under variable amplitude loading based on energetic approach is proposed.

eAnalytics: Dynamic Web-based Analytics for the Energy Industry

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Paul Govan

2016-11-01

Full Text Available eAnalytics is a web application built on top of R that provides dynamic data analytics to energy industry stakeholders. The application allows users to dynamically manipulate chart data and style through the Shiny package’s reactive framework. eAnalytics currently supports a number of features including interactive datatables, dynamic charting capabilities, and the ability to save, download, or export information for further use. Going forward, the goal for this project is that it will serve as a research hub for discovering new relationships in the data. The application is illustrated with a simple tutorial of the user interface design.

Color-Kinematics Duality for QCD Amplitudes

CERN Document Server

Johansson, Henrik

2016-01-01

We show that color-kinematics duality is present in tree-level amplitudes of quantum chromodynamics with massive flavored quarks. Starting with the color structure of QCD, we work out a new color decomposition for n-point tree amplitudes in a reduced basis of primitive amplitudes. These primitives, with k quark-antiquark pairs and (n-2k) gluons, are taken in the (n-2)!/k! Melia basis, and are independent under the color-algebra Kleiss-Kuijf relations. This generalizes the color decomposition of Del Duca, Dixon, and Maltoni to an arbitrary number of quarks. The color coefficients in the new decomposition are given by compact expressions valid for arbitrary gauge group and representation. Considering the kinematic structure, we show through explicit calculations that color-kinematics duality holds for amplitudes with general configurations of gluons and massive quarks. The new (massive) amplitude relations that follow from the duality can be mapped to a well-defined subset of the familiar BCJ relations for gluo...

Scaling of the polarization amplitude in quantum many-body systems in one dimension

Science.gov (United States)

Kobayashi, Ryohei; Nakagawa, Yuya O.; Fukusumi, Yoshiki; Oshikawa, Masaki

2018-04-01

Resta proposed a definition of the electric polarization in one-dimensional systems in terms of the ground-state expectation value of the large gauge transformation operator. Vanishing of the expectation value in the thermodynamic limit implies that the system is a conductor. We study Resta's polarization amplitude (expectation value) in the S =1 /2 XXZ chain and its several generalizations, in the gapless conducting Tomonaga-Luttinger liquid phase. We obtain an analytical expression in the lowest-order perturbation theory about the free fermion point (XY chain) and an exact result for the Haldane-Shastry model with long-range interactions. We also obtain numerical results, mostly using the exact diagonalization method. We find that the amplitude exhibits a power-law scaling in the system size (chain length) and vanishes in the thermodynamic limit. On the other hand, the exponent depends on the model even when the low-energy limit is described by the Tomonaga-Luttinger liquid with the same Luttinger parameter. We find that a change in the exponent occurs when the Umklapp term(s) are eliminated, suggesting the importance of the Umklapp terms.

Cascaded Amplitude Modulations in Sound Texture Perception

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Richard McWalter

2017-09-01

Full Text Available Sound textures, such as crackling fire or chirping crickets, represent a broad class of sounds defined by their homogeneous temporal structure. It has been suggested that the perception of texture is mediated by time-averaged summary statistics measured from early auditory representations. In this study, we investigated the perception of sound textures that contain rhythmic structure, specifically second-order amplitude modulations that arise from the interaction of different modulation rates, previously described as “beating” in the envelope-frequency domain. We developed an auditory texture model that utilizes a cascade of modulation filterbanks that capture the structure of simple rhythmic patterns. The model was examined in a series of psychophysical listening experiments using synthetic sound textures—stimuli generated using time-averaged statistics measured from real-world textures. In a texture identification task, our results indicated that second-order amplitude modulation sensitivity enhanced recognition. Next, we examined the contribution of the second-order modulation analysis in a preference task, where the proposed auditory texture model was preferred over a range of model deviants that lacked second-order modulation rate sensitivity. Lastly, the discriminability of textures that included second-order amplitude modulations appeared to be perceived using a time-averaging process. Overall, our results demonstrate that the inclusion of second-order modulation analysis generates improvements in the perceived quality of synthetic textures compared to the first-order modulation analysis considered in previous approaches.

New relations for graviton-matter amplitudes

CERN Multimedia

CERN. Geneva

2018-01-01

I report on recent progress in finding compact expressions for scattering amplitudes involving gravitons and gluons as well as massive scalar and fermionic matter particles. At tree level the single graviton emission amplitudes may be expressed as linear combination of purely non-gravitational ones. At the one-loop level recent results on all four point Einstein-Yang-Mills amplitudes with at most one opposite helicity state using unitarity methods are reported. 

Reflection and refraction of elastic waves at a corrugated interface in a bi-material transversely isotropic full-space

International Nuclear Information System (INIS)

Shad-Manamen, N.; Eskandari-Ghadi, M.

2008-01-01

The existing theory for wave propagation through a soil layer are not compatible with the real soil layers because in the theory the layers are flat and the sub-layers are parallel, while in real the soil layers are not flat and they may not be parallel. Thus, wave propagations through a corrugated interface are so important. In this paper, a two dimensional SH-wave propagation through a corrugated interface between two linear transversely isotropic half-spaces is assessed. In order to do this, Lord Rayleigh's method is accepted to express the non-flat surface by a Fourier series. In this way, the amplitude of the reflected and transmitted waves is analytically determined in terms of the incident SH-wave amplitude. It is shown that except for the regular reflected and refracted waves, some irregular reflected and refracted waves are exist, and the amplitudes of these waves vary in terms of the angle and frequency of incident wave, equation of surface, and the material properties of the domains. The numerical computations for some cases of different amplitude/wave-length ratio of the interface are done. This work is an extension of Asano's paper (1960) for a more complicated interface, where more non-zero coefficients are considered in expressing the equation of surface in the form of Fourier series. The analytical results for some simpler case of isotropic domain are collapsed on Asano's results (1960). In addition, the numerical evaluation is in good agreement with Asano's.

Dissociable neural response signatures for slow amplitude and frequency modulation in human auditory cortex.

Science.gov (United States)

Henry, Molly J; Obleser, Jonas

2013-01-01

Natural auditory stimuli are characterized by slow fluctuations in amplitude and frequency. However, the degree to which the neural responses to slow amplitude modulation (AM) and frequency modulation (FM) are capable of conveying independent time-varying information, particularly with respect to speech communication, is unclear. In the current electroencephalography (EEG) study, participants listened to amplitude- and frequency-modulated narrow-band noises with a 3-Hz modulation rate, and the resulting neural responses were compared. Spectral analyses revealed similar spectral amplitude peaks for AM and FM at the stimulation frequency (3 Hz), but amplitude at the second harmonic frequency (6 Hz) was much higher for FM than for AM. Moreover, the phase delay of neural responses with respect to the full-band stimulus envelope was shorter for FM than for AM. Finally, the critical analysis involved classification of single trials as being in response to either AM or FM based on either phase or amplitude information. Time-varying phase, but not amplitude, was sufficient to accurately classify AM and FM stimuli based on single-trial neural responses. Taken together, the current results support the dissociable nature of cortical signatures of slow AM and FM. These cortical signatures potentially provide an efficient means to dissect simultaneously communicated slow temporal and spectral information in acoustic communication signals.

Method of analytic continuation by duality in QCD: Beyond QCD sum rules

International Nuclear Information System (INIS)

Kremer, M.; Nasrallah, N.F.; Papadopoulos, N.A.; Schilcher, K.

1986-01-01

We present the method of analytic continuation by duality which allows the approximate continuation of QCD amplitudes to small values of the momentum variables where direct perturbative calculations are not possible. This allows a substantial extension of the domain of applications of hadronic QCD phenomenology. The method is illustrated by a simple example which shows its essential features

Analyticity in a phenomenology of electro-weak structure of hadrons

International Nuclear Information System (INIS)

Dubnicka, S.; Dubnickova, A. Z.

2010-01-01

The utility of an application of the analyticity in a phenomenology of electro-weak structure of hadrons is demonstrated in a number of obtained new and experimentally verifiable results. With this aim first the problem of an inconsistency of the asymptotic behavior of vector-meson-dominance model with the asymptotic behavior of form factors of baryons and nuclei is solved generally and a general approach for determination of the lowest normal and anomalous singularities of form factors from the corresponding Feynman diagrams is reviewed. Then many useful applications by making use of the analytic properties of electro-weak form factors and amplitudes of various electromagnetic processes of hadrons are carried out. (Author)

Analytic perturbation theory for screened Coulomb potential: full continuum wave function

International Nuclear Information System (INIS)

Bechler, A.; Ennan, Mc J.; Pratt, R.H.

1979-01-01

An analytic perturbation theory developed previously is used to find a continuum screened-Coulomb wave function characterized by definite asymptotic momentum. This wave function satisfies an inhomogeneous partial differential equation which is solved in parabolic coordinates; the solution depends on both parabolic variables. We calculate partial wave projections of this solution and show that we can choose to add a solution of the homogeneous equation such that the partial wave projections become equal to the normalized continuum radial function found previously. However, finding the unique solution with given asymptotic linear momentum will require either using boundary conditions to determine the unique needed solution of the homogeneous equation or equivalently specifying the screened-Coulomb phase-shifts. (author)

FEASIBILITY OF INVESTMENT IN BUSINESS ANALYTICS

Directory of Open Access Journals (Sweden)

Mladen Varga

2007-12-01

Full Text Available Trends in data processing for decision support show that business users need business analytics, i.e. analytical applications which incorporate a variety of business oriented data analysis techniques and task-specific knowledge. The paper discusses the feasibility of investment in two models of implementing business analytics: custom development and packed analytical applications. The consequences of both models are shown on two models of business analytics implementation in Croatia.

External Ear Resonant Amplitude and Frequency of 3-7 Year Old Children

Directory of Open Access Journals (Sweden)

Amir Hossein Zare

2004-06-01

Full Text Available Objective: To measure external ear resonant amplitude and frequency in children (3-7 years old and to compare with adult measures. Method and materials: The external ear resonance peak amplitude and frequency of 63 children 3-7 years old were recorded. All of the children had normal tympanogram and there was no cerumen in external auditory canal. 20 adult of 21-24 years old (10 male , 10 female were selected in order to compare with children that had normal tympanogram. The tests included : 1-otoscopy 2- tympanometry 3-microphone probe tube test. Results: The average of resonance peak frequency for children and adult is 4200 Hz and 3200 Hz , respectively. The resonance frequency of children had significantly diffrence with average of resonance frequency in adults. The average of resonance peak amplitude for children and adult is 17.70 dB and 17.17 dB , respectively. Conclusion: Resonant frequency and amplitude affect the hearing aid prescription and fitting process and calculating insertion gain; so, this measures seem should be considered in children hearing aid fitting.

Recursion relations for multi-gluon off-shell amplitudes on the light-front and Wilson lines

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C. Cruz-Santiago

2015-06-01

Full Text Available We analyze the off-shell scattering amplitudes in the framework of the light-front perturbation theory. It is shown that the previously derived recursion relation between tree level off-shell amplitudes in this formalism actually resums whole classes of graphs into a Wilson line. More precisely, we establish a correspondence between the light-front methods for the computation of the off-shell amplitudes and the approach which makes use of the matrix elements of straight infinite Wilson lines, which are manifestly gauge invariant objects. Furthermore, since it is needed to explicitly verify the gauge invariance of light-front amplitudes, it is demonstrated that the Ward identities in this framework need additional instantaneous terms in the light-front graphs.

Arnol'd tongues for a resonant injection-locked frequency divider: analytical and numerical results

DEFF Research Database (Denmark)

Bartuccelli, Michele; Deane, Jonathan H.B.; Gentile, Guido

2010-01-01

’d tongues in the frequency–amplitude plane. In particular, we provide exact analytical formulae for the widths of the tongues, which correspond to the plateaux of the devil’s staircase picture. The results account for numerical and experimental findings presented in the literature for special driving terms...

Generalized unitarity for N=4 super-amplitudes

Energy Technology Data Exchange (ETDEWEB)

Drummond, J.M.; Henn, J. [LAPTH, Université de Savoie, CNRS B.P. 110, F-74941 Annecy-le-Vieux Cedex (France); Korchemsky, G.P., E-mail: Gregory.Korchemsky@cea.fr [Institut de Physique Théorique, CEA Saclay, 91191 Gif-sur-Yvette Cedex (France); Sokatchev, E. [LAPTH, Université de Savoie, CNRS B.P. 110, F-74941 Annecy-le-Vieux Cedex (France)

2013-04-21

We develop a manifestly supersymmetric version of the generalized unitarity cut method for calculating scattering amplitudes in N=4 SYM theory. We illustrate the power of this method by computing the one-loop n-point NMHV super-amplitudes. The result confirms two conjectures which we made in Drummond, et al., [1]. Firstly, we derive the compact, manifestly dual superconformally covariant form of the NMHV tree amplitudes for arbitrary number and types of external particles. Secondly, we show that the ratio of the one-loop NMHV to the MHV amplitude is dual conformal invariant.

An analytical method for the investigation of instability of a collisionless plasma in strong magnetic fields

International Nuclear Information System (INIS)

Zakharov, V.U.

1993-01-01

An analytical method for the investigation of special types of dispersion relations is presented. In particular, analysis of the propagation of small-amplitude hydromagnetic waves in a collisionless plasma in a strong magnetic field leads to such dispersion relations. The fifth-degree dispersion relation corresponding to a particular case is considered. The necessary stability condition for a steady state and conditions for the degeneration of small-amplitude waves are derived. A comparison with other methods for the analysis of similar dispersion relations is also presented. (author)

Ratios of helicity amplitudes for exclusive ρ0 electroproduction on transversely polarized proton

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Manaenkov Serguei

2017-01-01

Full Text Available Exclusive ρ0-meson electroproduction is studied by the HERMES experiment, using the 27.6 GeV longitudinally polarized electron/positron beam of HERA and a transversely polarized hydrogen target, in the kinematic region 1.0 GeV2 < Q2 < 7.0 GeV2, 3.0 GeV < W < 6.3 GeV, and −t′ < 0.4 GeV2. Using an unbinned maximum-likelihood method, 25 parameters are extracted. They determine the real and imaginary parts of the ratios of certain helicity amplitudes describing ρ0-meson production by a virtual photon, where the denominator is the dominant amplitude F012012${F_{0{1 \\over 2}}}_{0{1 \\over 2}}$. The latter is the nucleon-helicity-non-flip amplitude, which describes the production of a longitudinal ρ0 meson by a longitudinal virtual photon. The transverse target polarization allows for the first time the extraction of ratios of a number of nucleon-helicity-flip amplitudes to F012012${F_{0{1 \\over 2}}}_{0{1 \\over 2}}$. The ratios of nucleon-helicity-non-flip amplitudes are found to be in good agreement with those from the previous HERMES analysis.

The generation of flat-top beams by complex amplitude modulation with a phase-only spatial light modulator

CSIR Research Space (South Africa)

Hendriks, A

2012-08-01

Full Text Available amplitude modulation of the light, i.e., in amplitude and phase. We outline the theoretical concept, and then illustrate its use with the example of the laser beam shaping of Gaussian beams into flat-top beams. We quantify the performance of this approach...

Mirror symmetry, toric branes and topological string amplitudes as polynomials

Energy Technology Data Exchange (ETDEWEB)

Alim, Murad

2009-07-13

The central theme of this thesis is the extension and application of mirror symmetry of topological string theory. The contribution of this work on the mathematical side is given by interpreting the calculated partition functions as generating functions for mathematical invariants which are extracted in various examples. Furthermore the extension of the variation of the vacuum bundle to include D-branes on compact geometries is studied. Based on previous work for non-compact geometries a system of differential equations is derived which allows to extend the mirror map to the deformation spaces of the D-Branes. Furthermore, these equations allow the computation of the full quantum corrected superpotentials which are induced by the D-branes. Based on the holomorphic anomaly equation, which describes the background dependence of topological string theory relating recursively loop amplitudes, this work generalizes a polynomial construction of the loop amplitudes, which was found for manifolds with a one dimensional space of deformations, to arbitrary target manifolds with arbitrary dimension of the deformation space. The polynomial generators are determined and it is proven that the higher loop amplitudes are polynomials of a certain degree in the generators. Furthermore, the polynomial construction is generalized to solve the extension of the holomorphic anomaly equation to D-branes without deformation space. This method is applied to calculate higher loop amplitudes in numerous examples and the mathematical invariants are extracted. (orig.)

Mirror symmetry, toric branes and topological string amplitudes as polynomials

International Nuclear Information System (INIS)

Alim, Murad

2009-01-01

The central theme of this thesis is the extension and application of mirror symmetry of topological string theory. The contribution of this work on the mathematical side is given by interpreting the calculated partition functions as generating functions for mathematical invariants which are extracted in various examples. Furthermore the extension of the variation of the vacuum bundle to include D-branes on compact geometries is studied. Based on previous work for non-compact geometries a system of differential equations is derived which allows to extend the mirror map to the deformation spaces of the D-Branes. Furthermore, these equations allow the computation of the full quantum corrected superpotentials which are induced by the D-branes. Based on the holomorphic anomaly equation, which describes the background dependence of topological string theory relating recursively loop amplitudes, this work generalizes a polynomial construction of the loop amplitudes, which was found for manifolds with a one dimensional space of deformations, to arbitrary target manifolds with arbitrary dimension of the deformation space. The polynomial generators are determined and it is proven that the higher loop amplitudes are polynomials of a certain degree in the generators. Furthermore, the polynomial construction is generalized to solve the extension of the holomorphic anomaly equation to D-branes without deformation space. This method is applied to calculate higher loop amplitudes in numerous examples and the mathematical invariants are extracted. (orig.)

Phonological awareness and sinusoidal amplitude modulation in phonological dislexia.

Science.gov (United States)

Peñaloza-López, Yolanda; Herrera-Rangel, Aline; Pérez-Ruiz, Santiago J; Poblano, Adrián

2016-04-01

Dyslexia is the difficulty of children in learning to read and write as results of neurological deficiencies. The objective was to test the Phonological awareness (PA) and Sinusoidal amplitude modulation (SAM) threshold in children with Phonological dyslexia (PD). We performed a case-control, analytic, cross sectional study. We studied 14 children with PD and 14 control children from 7 to 11 years of age, by means of PA measurement and by SAM test. The mean age of dyslexic children was 8.39 years and in the control group was 8.15. Children with PD exhibited inadequate skills in PA, and SAM. We found significant correlations between PA and SAM at 4 Hertz frequency, and calculated regression equations that predicts between one-fourth and one-third of variance of measurements. Alterations in PA and SAM found can help to explain basis of deficient language processing exhibited by children with PD.

Holographic corrections to meson scattering amplitudes

Energy Technology Data Exchange (ETDEWEB)

Armoni, Adi; Ireson, Edwin, E-mail: 746616@swansea.ac.uk

2017-06-15

We compute meson scattering amplitudes using the holographic duality between confining gauge theories and string theory, in order to consider holographic corrections to the Veneziano amplitude and associated higher-point functions. The generic nature of such computations is explained, thanks to the well-understood nature of confining string backgrounds, and two different examples of the calculation in given backgrounds are used to illustrate the details. The effect we discover, whilst only qualitative, is re-obtainable in many such examples, in four-point but also higher point amplitudes.

Metabolic and respiratory costs of increasing song amplitude in zebra finches.

Directory of Open Access Journals (Sweden)

Sue Anne Zollinger

Full Text Available Bird song is a widely used model in the study of animal communication and sexual selection, and several song features have been shown to reflect the quality of the singer. Recent studies have demonstrated that song amplitude may be an honest signal of current condition in males and that females prefer high amplitude songs. In addition, birds raise the amplitude of their songs to communicate in noisy environments. Although it is generally assumed that louder song should be more costly to produce, there has been little empirical evidence to support this assumption. We tested the assumption by measuring oxygen consumption and respiratory patterns in adult male zebra finches (Taeniopygia guttata singing at different amplitudes in different background noise conditions. As background noise levels increased, birds significantly increased the sound pressure level of their songs. We found that louder songs required significantly greater subsyringeal air sac pressure than quieter songs. Though increased pressure is probably achieved by increasing respiratory muscle activity, these increases did not correlate with measurable increases in oxygen consumption. In addition, we found that oxygen consumption increased in higher background noise, independent of singing behaviour. This observation supports previous research in mammals showing that high levels of environmental noise can induce physiological stress responses. While our study did not find that increasing vocal amplitude increased metabolic costs, further research is needed to determine whether there are other non-metabolic costs of singing louder or costs associated with chronic noise exposure.

Nonclassical thermal-state superpositions: Analytical evolution law and decoherence behavior

Science.gov (United States)

Meng, Xiang-guo; Goan, Hsi-Sheng; Wang, Ji-suo; Zhang, Ran

2018-03-01

Employing the integration technique within normal products of bosonic operators, we present normal product representations of thermal-state superpositions and investigate their nonclassical features, such as quadrature squeezing, sub-Poissonian distribution, and partial negativity of the Wigner function. We also analytically and numerically investigate their evolution law and decoherence characteristics in an amplitude-decay model via the variations of the probability distributions and the negative volumes of Wigner functions in phase space. The results indicate that the evolution formulas of two thermal component states for amplitude decay can be viewed as the same integral form as a displaced thermal state ρ(V , d) , but governed by the combined action of photon loss and thermal noise. In addition, the larger values of the displacement d and noise V lead to faster decoherence for thermal-state superpositions.

Leading Wave Amplitude of a Tsunami

Science.gov (United States)

Kanoglu, U.

2015-12-01

Okal and Synolakis (EGU General Assembly 2015, Geophysical Research Abstracts-Vol. 17-7622) recently discussed that why the maximum amplitude of a tsunami might not occur for the first wave. Okal and Synolakis list observations from 2011 Japan tsunami, which reached to Papeete, Tahiti with a fourth wave being largest and 72 min later after the first wave; 1960 Chilean tsunami reached Hilo, Hawaii with a maximum wave arriving 1 hour later with a height of 5m, first wave being only 1.2m. Largest later waves is a problem not only for local authorities both in terms of warning to the public and rescue efforts but also mislead the public thinking that it is safe to return shoreline or evacuated site after arrival of the first wave. Okal and Synolakis considered Hammack's (1972, Ph.D. Dissertation, Calif. Inst. Tech., 261 pp., Pasadena) linear dispersive analytical solution with a tsunami generation through an uplifting of a circular plug on the ocean floor. They performed parametric study for the radius of the plug and the depth of the ocean since these are the independent scaling lengths in the problem. They identified transition distance, as the second wave being larger, regarding the parameters of the problem. Here, we extend their analysis to an initial wave field with a finite crest length and, in addition, to a most common tsunami initial wave form of N-wave as presented by Tadepalli and Synolakis (1994, Proc. R. Soc. A: Math. Phys. Eng. Sci., 445, 99-112). We compare our results with non-dispersive linear shallow water wave results as presented by Kanoglu et al. (2013, Proc. R. Soc. A: Math. Phys. Eng. Sci., 469, 20130015), investigating focusing feature. We discuss the results both in terms of leading wave amplitude and tsunami focusing. Acknowledgment: The research leading to these results has received funding from the European Union's Seventh Framework Programme (FP7/2007-2013) under grant agreement no 603839 (Project ASTARTE - Assessment, Strategy and Risk

Event-related potentials during individual, cooperative, and competitive task performance differ in subjects with analytic vs. holistic thinking.

Science.gov (United States)

Apanovich, V V; Bezdenezhnykh, B N; Sams, M; Jääskeläinen, I P; Alexandrov, YuI

2018-01-01

It has been presented that Western cultures (USA, Western Europe) are mostly characterized by competitive forms of social interaction, whereas Eastern cultures (Japan, China, Russia) are mostly characterized by cooperative forms. It has also been stated that thinking in Eastern countries is predominantly holistic and in Western countries analytic. Based on this, we hypothesized that subjects with analytic vs. holistic thinking styles show differences in decision making in different types of social interaction conditions. We investigated behavioural and brain-activity differences between subjects with analytic and holistic thinking during a choice reaction time (ChRT) task, wherein the subjects either cooperated, competed (in pairs), or performed the task without interaction with other participants. Healthy Russian subjects (N=78) were divided into two groups based on having analytic or holistic thinking as determined with an established questionnaire. We measured reaction times as well as event-related brain potentials. There were significant differences between the interaction conditions in task performance between subjects with analytic and holistic thinking. Both behavioral performance and physiological measures exhibited higher variance in holistic than in analytic subjects. Differences in amplitude and P300 latency suggest that decision making was easier for the holistic subjects in the cooperation condition, in contrast to analytic subjects for whom decision making based on these measures seemed to be easier in the competition condition. The P300 amplitude was higher in the individual condition as compared with the collective conditions. Overall, our results support the notion that the brains of analytic and holistic subjects work differently in different types of social interaction conditions. Copyright © 2017 Elsevier B.V. All rights reserved.

Multi-leg one-loop gravity amplitudes from gauge theory

International Nuclear Information System (INIS)

Bern, Z.; Dixon, L.; Perelstein, M.; Rozowsky, J.S.

1999-01-01

By exploiting relations between gravity and gauge theories, we present two infinite sequences of one-loop n-graviton scattering amplitudes: the 'maximally helicity-violating' amplitudes in N = 8 supergravity, and the 'all-plus' helicity amplitudes in gravity with any minimally coupled massless matter content. The all-plus amplitudes correspond to self-dual field configurations and vanish in supersymmetric theories. We make use of the tree-level Kawai-Lewellen-Tye (KLT) relations between open and closed string theory amplitudes, which in the low-energy limit imply relations between gravity and gauge theory tree amplitudes. For n ≤ 6, we determine the all-plus amplitudes explicitly from their unitarity cuts. The KLT relations, applied to the cuts, allow us to extend to gravity a previously found 'dimension-shifting' relation between (the cuts of) the all-plus amplitudes in gauge theory and the maximally helicity-violating amplitudes in N = 4 super-Yang-Mills theory. The gravitational version of the relation lets us determine the n ≤ 6N = 8 supergravity amplitudes from the all-plus gravity amplitudes. We infer the two series of amplitudes for all n from their soft and collinear properties, which can also be derived from gauge theory using the KLT relations

Covariant amplitudes in Polyakov string theory

International Nuclear Information System (INIS)

Aoyama, H.; Dhar, A.; Namazie, M.A.

1986-01-01

A manifestly Lorentz-covariant and reparametrization-invariant procedure for computing string amplitudes using Polyakov's formulation is described. Both bosonic and superstring theories are dealt with. The computation of string amplitudes is greatly facilitated by this formalism. (orig.)

Complex amplitude reconstruction by iterative amplitude-phase retrieval algorithm with reference

Science.gov (United States)

Shen, Cheng; Guo, Cheng; Tan, Jiubin; Liu, Shutian; Liu, Zhengjun

2018-06-01

Multi-image iterative phase retrieval methods have been successfully applied in plenty of research fields due to their simple but efficient implementation. However, there is a mismatch between the measurement of the first long imaging distance and the sequential interval. In this paper, an amplitude-phase retrieval algorithm with reference is put forward without additional measurements or priori knowledge. It gets rid of measuring the first imaging distance. With a designed update formula, it significantly raises the convergence speed and the reconstruction fidelity, especially in phase retrieval. Its superiority over the original amplitude-phase retrieval (APR) method is validated by numerical analysis and experiments. Furthermore, it provides a conceptual design of a compact holographic image sensor, which can achieve numerical refocusing easily.

Amplitude and phase fluctuations of Van der Pol oscillator under external random forcing

Science.gov (United States)

Singh, Aman K.; Yadava, R. D. S.

2018-05-01

The paper presents an analytical study of noise in Van der Pol oscillator output subjected to an external force noise assumed to be characterized by delta function (white noise). The external fluctuations are assumed to be small in comparison to the average response of the noise free system. The autocorrelation function and power spectrum are calculated under the condition of weak nonlinearity. The latter ensures limit cycle oscillations. The total spectral power density is dominated by the contributions from the phase fluctuations. The amplitude fluctuations are at least two orders of magnitude smaller. The analysis is shown to be useful to interpretation microcantilever based biosensing data.

Is the effect of tinnitus on auditory steady-state response amplitude mediated by attention?

Directory of Open Access Journals (Sweden)

Eugen eDiesch

2012-05-01

Full Text Available Objectives: The amplitude of the auditory steady-state response (ASSR is enhanced in tinnitus. As ASSR ampli¬tude is also enhanced by attention, the effect of tinnitus on ASSR amplitude could be interpreted as an effect of attention mediated by tinnitus. As attention effects on the N1 are signi¬fi¬cantly larger than those on the ASSR, if the effect of tinnitus on ASSR amplitude were due to attention, there should be similar amplitude enhancement effects in tinnitus for the N1 component of the auditory evoked response. Methods: MEG recordings of auditory evoked responses which were previously examined for the ASSR (Diesch et al. 2010 were analysed with respect to the N1m component. Like the ASSR previously, the N1m was analysed in the source domain (source space projection. Stimuli were amplitude-modulated tones with one of three carrier fre¬quen¬cies matching the tinnitus frequency or a surrogate frequency 1½ octaves above the audio¬metric edge frequency in con¬trols, the audiometric edge frequency, and a frequency below the audio¬metric edgeResults: In the earlier ASSR study (Diesch et al., 2010, the ASSR amplitude in tinnitus patients, but not in controls, was significantly larger in the (surrogate tinnitus condition than in the edge condition. In the present study, both tinnitus patients and healthy controls show an N1m-amplitude profile identical to the one of ASSR amplitudes in healthy controls. N1m amplitudes elicited by tonal frequencies located at the audiometric edge and at the (surrogate tinnitus frequency are smaller than N1m amplitudes elicited by sub-edge tones and do not differ among each other.Conclusions: There is no N1-amplitude enhancement effect in tinnitus. The enhancement effect of tinnitus on ASSR amplitude cannot be accounted for in terms of attention induced by tinnitus.

The Correlation between Electroencephalography Amplitude and Interictal Abnormalities: Audit study

Directory of Open Access Journals (Sweden)

Sami F. Al-Rawas

2014-10-01

Full Text Available Objectives: The aim of this study was to establish the relationship between background amplitude and interictal abnormalities in routine electroencephalography (EEG. Methods: This retrospective audit was conducted between July 2006 and December 2009 at the Department of Clinical Physiology at Sultan Qaboos University Hospital (SQUH in Muscat, Oman. A total of 1,718 electroencephalograms (EEGs were reviewed. All EEGs were from patients who had been referred due to epilepsy, syncope or headaches. EEGs were divided into four groups based on their amplitude: group one ≤20 μV; group two 21–35 μV; group three 36–50 μV, and group four >50 μV. Interictal abnormalities were defined as epileptiform discharges with or without associated slow waves. Abnormalities were identified during periods of resting, hyperventilation and photic stimulation in each group. Results: The mean age ± standard deviation of the patients was 27 ± 12.5 years. Of the 1,718 EEGs, 542 (31.5% were abnormal. Interictal abnormalities increased with amplitude in all four categories and demonstrated a significant association (P <0.05. A total of 56 EEGs (3.3% had amplitudes that were ≤20 μV and none of these showed interictal epileptiform abnormalities. Conclusion: EEG amplitude is an important factor in determining the presence of interictal epileptiform abnormalities in routine EEGs. This should be taken into account when investigating patients for epilepsy. A strong argument is made for considering long-term EEG monitoring in order to identify unexplained seizures which may be secondary to epilepsy. It is recommended that all tertiary institutions provide EEG telemetry services.

DVCS amplitude with kinematical twist-3 terms

International Nuclear Information System (INIS)

Radyushkin, A.V.; Weiss, C.

2000-01-01

The authors compute the amplitude of deeply virtual Compton scattering (DVCS) using the calculus of QCD string operators in coordinate representation. To restore the electromagnetic gauge invariance (transversality) of the twist-2 amplitude they include the operators of twist-3 which appear as total derivatives of twist-2 operators. The results are equivalent to a Wandzura-Wilczek approximation for twist-3 skewed parton distributions. They find that this approximation gives a finite result for the amplitude of a longitudinally polarized virtual photon, while the amplitude for transverse polarization is divergent, i.e., factorization breaks down in this term

Amplitude-Mode Dynamics of Polariton Condensates

International Nuclear Information System (INIS)

Brierley, R. T.; Littlewood, P. B.; Eastham, P. R.

2011-01-01

We study the stability of collective amplitude excitations in nonequilibrium polariton condensates. These excitations correspond to renormalized upper polaritons and to the collective amplitude modes of atomic gases and superconductors. They would be present following a quantum quench or could be created directly by resonant excitation. We show that uniform amplitude excitations are unstable to the production of excitations at finite wave vectors, leading to the formation of density-modulated phases. The physical processes causing the instabilities can be understood by analogy to optical parametric oscillators and the atomic Bose supernova.

An Analytical Finite-Strain Parameterization for Texture Evolution in Deformed Olivine Polycrystals

Science.gov (United States)

Ribe, N. M.; Castelnau, O.

2017-12-01

Current methods for calculating the evolution of flow-induced seismic anisotropy in the upper mantle describe crystal preferred orientation (CPO) using ensembles of 103-104 individual grains, and are too computationally expensive to be used in three-dimensional time-dependent convection models. We propose a much faster method based on the hypothesis that CPO of olivine polycrystals is a unique function of the finite strain. Our goal is then to determine how the CPO depends on the ratios r12 and r23 of the axes of the finite strain ellipsoid and on the two independent ratios p12 and p23 of the strengths (critical resolved shear stresses) of the three independent slip systems of olivine. To do this, we introduce a new analytical representation of olivine CPO in terms of three `structured basis functions' (SBFs) Fs(g, r12, r23) (s = 1, 2, 3), where g is the set of three Eulerian angles that describe the orientation of a crystal lattice relative to an external reference frame. Each SBF represents the virtual CPO that would be produced by the action of only one of the slip systems of olivine, and can be determined analytically to within an unknown time-dependent amplitude. The amplitudes are then determined by fitting the SBFs to the predictions of the second-order self-consistent (SOSC) model of Ponte-Castaneda (2002). To implement the SBF representation, we express the orientation distribution function (ODF) f(g) of the polycrystal approximately as a linear superposition of SBFs with weighting coefficients Cs. Substituting the superposition into the general evolution equation for the ODF and minimizing the residual error, we find that the weighting coefficients Cs(t) satisfy coupled evolution equations of the form αisCs + βisCs + γs = 0 where the coefficients αis, βis and γs can be calculated in advance from the expressions for the SBFs. These equations are solved numerically for different values of p12 and p23, yielding numerical values of Cs(r12, r23, p12, p23

Effects of strength training on mechanomyographic amplitude

International Nuclear Information System (INIS)

DeFreitas, Jason M; Beck, Travis W; Stock, Matt S

2012-01-01

The aim of the present study was to determine if the patterns of mechanomyographic (MMG) amplitude across force would change with strength training. Twenty-two healthy men completed an 8-week strength training program. During three separate testing visits (pre-test, week 4, and week 8), the MMG signal was detected from the vastus lateralis as the subjects performed isometric step muscle actions of the leg extensors from 10–100% of maximal voluntary contraction (MVC). During pre-testing, the MMG amplitude increased linearly with force to 66% MVC and then plateaued. Conversely, weeks 4 and 8 demonstrated an increase in MMG amplitude up to ∼85% of the subject's original MVC before plateauing. Furthermore, seven of the ten force levels (30–60% and 80–100%) showed a significant decrease in mean MMG amplitude values after training, which consequently led to a decrease in the slope of the MMG amplitude/force relationship. The decreases in MMG amplitude at lower force levels are indicative of hypertrophy, since fewer motor units would be required to produce the same absolute force if the motor units increased in size. However, despite the clear changes in the mean values, analyses of individual subjects revealed that only 55% of the subjects demonstrated a significant decrease in the slope of the MMG amplitude/force relationship. (paper)

Organizational Models for Big Data and Analytics

Directory of Open Access Journals (Sweden)

Robert L. Grossman

2014-04-01

Full Text Available In this article, we introduce a framework for determining how analytics capability should be distributed within an organization. Our framework stresses the importance of building a critical mass of analytics staff, centralizing or decentralizing the analytics staff to support business processes, and establishing an analytics governance structure to ensure that analytics processes are supported by the organization as a whole.

Multivariable controller for discrete stochastic amplitude-constrained systems

Directory of Open Access Journals (Sweden)

Hannu T. Toivonen

1983-04-01

Full Text Available A sub-optimal multivariable controller for discrete stochastic amplitude-constrained systems is presented. In the approach the regulator structure is restricted to the class of linear saturated feedback laws. The stationary covariances of the controlled system are evaluated by approximating the stationary probability distribution of the state by a gaussian distribution. An algorithm for minimizing a quadratic loss function is given, and examples are presented to illustrate the performance of the sub-optimal controller.

Nonsinglet pentagons and NMHV amplitudes

Energy Technology Data Exchange (ETDEWEB)

Belitsky, A.V., E-mail: andrei.belitsky@asu.edu

2015-07-15

Scattering amplitudes in maximally supersymmetric gauge theory receive a dual description in terms of the expectation value of the super Wilson loop stretched on a null polygonal contour. This makes the analysis amenable to nonperturbative techniques. Presently, we elaborate on a refined form of the operator product expansion in terms of pentagon transitions to compute twist-two contributions to NMHV amplitudes. To start with, we provide a novel derivation of scattering matrices starting from Baxter equations for flux-tube excitations propagating on magnon background. We propose bootstrap equations obeyed by pentagon form factors with nonsinglet quantum numbers with respect to the R-symmetry group and provide solutions to them to all orders in 't Hooft coupling. These are then successfully confronted against available perturbative calculations for NMHV amplitudes to four-loop order.

Analytical theory of Doppler reflectometry in slab plasma model

Energy Technology Data Exchange (ETDEWEB)

Gusakov, E.Z.; Surkov, A.V. [Ioffe Institute, Politekhnicheskaya 26, St. Petersburg (Russian Federation)

2004-07-01

Doppler reflectometry is considered in slab plasma model in the frameworks of analytical theory. The diagnostics locality is analyzed for both regimes: linear and nonlinear in turbulence amplitude. The toroidal antenna focusing of probing beam to the cut-off is proposed and discussed as a method to increase diagnostics spatial resolution. It is shown that even in the case of nonlinear regime of multiple scattering, the diagnostics can be used for an estimation (with certain accuracy) of plasma poloidal rotation profile. (authors)

Amplitude ratios in ρ0 leptoproductions and GPDs

Directory of Open Access Journals (Sweden)

Goloskokov S.V.

2017-01-01

Using the model results we calculate the ratio of different helicity amplitudes for a transversely polarized proton target to the leading twist longitudinal amplitude. Our results are close to the amplitude ratios measured by HERMES.

Tree-level gluon amplitudes on the celestial sphere

Science.gov (United States)

Schreiber, Anders Ø.; Volovich, Anastasia; Zlotnikov, Michael

2018-06-01

Pasterski, Shao and Strominger have recently proposed that massless scattering amplitudes can be mapped to correlators on the celestial sphere at infinity via a Mellin transform. We apply this prescription to arbitrary n-point tree-level gluon amplitudes. The Mellin transforms of MHV amplitudes are given by generalized hypergeometric functions on the Grassmannian Gr (4 , n), while generic non-MHV amplitudes are given by more complicated Gelfand A-hypergeometric functions.

Correlations for reduced-width amplitudes in 49V

International Nuclear Information System (INIS)

Chou, B.H.; Mitchell, G.E.; Bilpuch, E.G.; Westerfeldt, C.R.

1980-01-01

Measurement of the relative sign of inelastic proton-channel amplitudes permits the determination of amplitude correlations. Data were obtained for 45 5/2 + resonances in 49 V. Although the reduced widths in each channel followed a Porter-Thomas distribution, large amplitude correlations were observed. The results are compared with the reduced-width--amplitude distribution of Krieger and Porter. This is the first direct test of the Krieger-Porter distribution

Tree-level amplitudes and dual superconformal symmetry

Energy Technology Data Exchange (ETDEWEB)

Drummond, J M, E-mail: drummond@lapp.in2p3.fr [PH-TH Division, CERN, CH-1211, Geneva 23 (Switzerland); LAPTH, Universite de Savoie, CNRS, B.P. 110, F-74941 Annecy-le-Vieux Cedex (France)

2011-11-11

We review the structure of gauge theory scattering amplitudes at tree level and describe how a compact expression can be found which encodes all the tree-level amplitudes in the maximally supersymmetric N=4 theory. The expressions for the amplitudes reveal a dual superconformal symmetry. We describe how these ideas can be extended to leading singularities and the loop integrand in the planar theory and discuss the appearance of dual conformal symmetry in higher-dimensional gauge theories. This paper is an invited review for a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Scattering amplitudes in gauge theories'. (review)

Scattering Amplitudes via Algebraic Geometry Methods

DEFF Research Database (Denmark)

Søgaard, Mads

Feynman diagrams. The study of multiloop scattering amplitudes is crucial for the new era of precision phenomenology at the Large Hadron Collider (LHC) at CERN. Loop-level scattering amplitudes can be reduced to a basis of linearly independent integrals whose coefficients are extracted from generalized...

The analytical evolution of NLS solitons due to the numerical discretization error

Science.gov (United States)

Hoseini, S. M.; Marchant, T. R.

2011-12-01

Soliton perturbation theory is used to obtain analytical solutions describing solitary wave tails or shelves, due to numerical discretization error, for soliton solutions of the nonlinear Schrödinger equation. Two important implicit numerical schemes for the nonlinear Schrödinger equation, with second-order temporal and spatial discretization errors, are considered. These are the Crank-Nicolson scheme and a scheme, due to Taha [1], based on the inverse scattering transform. The first-order correction for the solitary wave tail, or shelf, is in integral form and an explicit expression is found for large time. The shelf decays slowly, at a rate of t^{-{1\\over 2}}, which is characteristic of the nonlinear Schrödinger equation. Singularity theory, usually used for combustion problems, is applied to the explicit large-time expression for the solitary wave tail. Analytical results are then obtained, such as the parameter regions in which qualitatively different types of solitary wave tails occur, the location of zeros and the location and amplitude of peaks. It is found that three different types of tail occur for the Crank-Nicolson and Taha schemes and that the Taha scheme exhibits some unusual symmetry properties, as the tails for left and right moving solitary waves are different. Optimal choices of the discretization parameters for the numerical schemes are also found, which minimize the amplitude of the solitary wave tail. The analytical solutions are compared with numerical simulations, and an excellent comparison is found.

The analytical evolution of NLS solitons due to the numerical discretization error

International Nuclear Information System (INIS)

Hoseini, S M; Marchant, T R

2011-01-01

Soliton perturbation theory is used to obtain analytical solutions describing solitary wave tails or shelves, due to numerical discretization error, for soliton solutions of the nonlinear Schrödinger equation. Two important implicit numerical schemes for the nonlinear Schrödinger equation, with second-order temporal and spatial discretization errors, are considered. These are the Crank–Nicolson scheme and a scheme, due to Taha, based on the inverse scattering transform. The first-order correction for the solitary wave tail, or shelf, is in integral form and an explicit expression is found for large time. The shelf decays slowly, at a rate of t -1/2 , which is characteristic of the nonlinear Schrödinger equation. Singularity theory, usually used for combustion problems, is applied to the explicit large-time expression for the solitary wave tail. Analytical results are then obtained, such as the parameter regions in which qualitatively different types of solitary wave tails occur, the location of zeros and the location and amplitude of peaks. It is found that three different types of tail occur for the Crank–Nicolson and Taha schemes and that the Taha scheme exhibits some unusual symmetry properties, as the tails for left and right moving solitary waves are different. Optimal choices of the discretization parameters for the numerical schemes are also found, which minimize the amplitude of the solitary wave tail. The analytical solutions are compared with numerical simulations, and an excellent comparison is found. (paper)

Analytical and Numerical Studies of Sloshing in Tanks

Energy Technology Data Exchange (ETDEWEB)

Solaas, F

1996-12-31

For oil cargo ship tanks and liquid natural gas carriers, the dimensions of the tanks are often such that the highest resonant sloshing periods and the ship motions are in the same period range, which may cause violent resonant sloshing of the liquid. In this doctoral thesis, linear and non-linear analytical potential theory solutions of the sloshing problem are studied for a two-dimensional rectangular tank and a vertical circular cylindrical tank, using perturbation technique for the non-linear case. The tank is forced to oscillate harmonically with small amplitudes of sway with frequency in the vicinity of the lowest natural frequency of the fluid inside the tank. The method is extended to other tank shapes using a combined analytical and numerical method. A boundary element numerical method is used to determine the eigenfunctions and eigenvalues of the problem. These are used in the non-linear analytical free surface conditions, and the velocity potential and free surface elevation for each boundary value problem in the perturbation scheme are determined by the boundary element method. Both the analytical method and the combined analytical and numerical method are restricted to tanks with vertical walls in the free surface. The suitability of a commercial programme, FLOW-3D, to estimate sloshing is studied. It solves the Navier-Stokes equations by the finite difference method. The free surface as function of time is traced using the fractional volume of fluid method. 59 refs., 54 figs., 37 tabs.

Analytical and Numerical Studies of Sloshing in Tanks

Energy Technology Data Exchange (ETDEWEB)

Solaas, F.

1995-12-31

For oil cargo ship tanks and liquid natural gas carriers, the dimensions of the tanks are often such that the highest resonant sloshing periods and the ship motions are in the same period range, which may cause violent resonant sloshing of the liquid. In this doctoral thesis, linear and non-linear analytical potential theory solutions of the sloshing problem are studied for a two-dimensional rectangular tank and a vertical circular cylindrical tank, using perturbation technique for the non-linear case. The tank is forced to oscillate harmonically with small amplitudes of sway with frequency in the vicinity of the lowest natural frequency of the fluid inside the tank. The method is extended to other tank shapes using a combined analytical and numerical method. A boundary element numerical method is used to determine the eigenfunctions and eigenvalues of the problem. These are used in the non-linear analytical free surface conditions, and the velocity potential and free surface elevation for each boundary value problem in the perturbation scheme are determined by the boundary element method. Both the analytical method and the combined analytical and numerical method are restricted to tanks with vertical walls in the free surface. The suitability of a commercial programme, FLOW-3D, to estimate sloshing is studied. It solves the Navier-Stokes equations by the finite difference method. The free surface as function of time is traced using the fractional volume of fluid method. 59 refs., 54 figs., 37 tabs.

Expansion of all multitrace tree level EYM amplitudes

Science.gov (United States)

Du, Yi-Jian; Feng, Bo; Teng, Fei

2017-12-01

In this paper, we investigate the expansion of tree level multitrace Einstein-Yang-Mills (EYM) amplitudes. First, we propose two types of recursive expansions of tree level EYM amplitudes with an arbitrary number of gluons, gravitons and traces by those amplitudes with fewer traces or/and gravitons. Then we give many support evidence, including proofs using the Cachazo-He-Yuan (CHY) formula and Britto-Cachazo-Feng-Witten (BCFW) recursive relation. As a byproduct, two types of generalized BCJ relations for multitrace EYM are further proposed, which will be useful in the BCFW proof. After one applies the recursive expansions repeatedly, any multitrace EYM amplitudes can be given in the Kleiss-Kuijf (KK) basis of tree level color ordered Yang-Mills (YM) amplitudes. Thus the Bern-Carrasco-Johansson (BCJ) numerators, as the expansion coefficients, for all multitrace EYM amplitudes are naturally constructed.

Quantum theory of dynamical collective subspace for large-amplitude collective motion

International Nuclear Information System (INIS)

Sakata, Fumihiko; Marumori, Toshio; Ogura, Masanori.

1986-03-01

By placing emphasis on conceptual correspondence to the ''classical'' theory which has been developed within the framework of the time-dependent Hartree-Fock theory, a full quantum theory appropriate for describing large-amplitude collective motion is proposed. A central problem of the quantum theory is how to determine an optimal representation called a dynamical representation; the representation is specific for the collective subspace where the large-amplitude collective motion is replicated as satisfactorily as possible. As an extension of the classical theory where the concept of an approximate integral surface plays an important role, the dynamical representation is properly characterized by introducing a concept of an approximate invariant subspace of the Hamiltonian. (author)

Positivity of spin foam amplitudes

International Nuclear Information System (INIS)

Baez, John C; Christensen, J Daniel

2002-01-01

The amplitude for a spin foam in the Barrett-Crane model of Riemannian quantum gravity is given as a product over its vertices, edges and faces, with one factor of the Riemannian 10j symbols appearing for each vertex, and simpler factors for the edges and faces. We prove that these amplitudes are always nonnegative for closed spin foams. As a corollary, all open spin foams going between a fixed pair of spin networks have real amplitudes of the same sign. This means one can use the Metropolis algorithm to compute expectation values of observables in the Riemannian Barrett-Crane model, as in statistical mechanics, even though this theory is based on a real-time (e iS ) rather than imaginary-time e -S path integral. Our proof uses the fact that when the Riemannian 10j symbols are nonzero, their sign is positive or negative depending on whether the sum of the ten spins is an integer or half-integer. For the product of 10j symbols appearing in the amplitude for a closed spin foam, these signs cancel. We conclude with some numerical evidence suggesting that the Lorentzian 10j symbols are always nonnegative, which would imply similar results for the Lorentzian Barrett-Crane model

Employing helicity amplitudes for resummation

International Nuclear Information System (INIS)

Moult, Ian; Stewart, Iain W.; Tackmann, Frank J.; Waalewijn, Wouter J.; Amsterdam Univ.

2015-08-01

Many state-of-the-art QCD calculations for multileg processes use helicity amplitudes as their fundamental ingredients. We construct a simple and easy-to-use helicity operator basis in soft-collinear effective theory (SCET), for which the hard Wilson coefficients from matching QCD onto SCET are directly given in terms of color-ordered helicity amplitudes. Using this basis allows one to seamlessly combine fixed-order helicity amplitudes at any order they are known with a resummation of higher-order logarithmic corrections. In particular, the virtual loop amplitudes can be employed in factorization theorems to make predictions for exclusive jet cross sections without the use of numerical subtraction schemes to handle real-virtual infrared cancellations. We also discuss matching onto SCET in renormalization schemes with helicities in 4- and d-dimensions. To demonstrate that our helicity operator basis is easy to use, we provide an explicit construction of the operator basis, as well as results for the hard matching coefficients, for pp → H+0,1,2 jets, pp → W/Z/γ+0,1,2 jets, and pp → 2,3 jets. These operator bases are completely crossing symmetric, so the results can easily be applied to processes with e + e - and e - p collisions.

Bayesian extraction of the parton distribution amplitude from the Bethe–Salpeter wave function

Directory of Open Access Journals (Sweden)

Fei Gao

2017-07-01

Full Text Available We propose a new numerical method to compute the parton distribution amplitude (PDA from the Euclidean Bethe–Salpeter wave function. The essential step is to extract the weight function in the Nakanishi representation of the Bethe–Salpeter wave function in Euclidean space, which is an ill-posed inversion problem, via the maximum entropy method (MEM. The Nakanishi weight function as well as the corresponding light-front parton distribution amplitude (PDA can be well determined. We confirm prior work on PDA computations, which was based on different methods.

An analysis of beam parameters on proton-acoustic waves through an analytic approach.

Science.gov (United States)

Kipergil, Esra Aytac; Erkol, Hakan; Kaya, Serhat; Gulsen, Gultekin; Unlu, Mehmet Burcin

2017-06-21

It has been reported that acoustic waves are generated when a high-energy pulsed proton beam is deposited in a small volume within tissue. One possible application of proton-induced acoustics is to get real-time feedback for intra-treatment adjustments by monitoring such acoustic waves. A high spatial resolution in ultrasound imaging may reduce proton range uncertainty. Thus, it is crucial to understand the dependence of the acoustic waves on the proton beam characteristics. In this manuscript, firstly, an analytic solution for the proton-induced acoustic wave is presented to reveal the dependence of the signal on the beam parameters; then it is combined with an analytic approximation of the Bragg curve. The influence of the beam energy, pulse duration and beam diameter variation on the acoustic waveform are investigated. Further analysis is performed regarding the Fourier decomposition of the proton-acoustic signals. Our results show that the smaller spill time of the proton beam upsurges the amplitude of the acoustic wave for a constant number of protons, which is hence beneficial for dose monitoring. The increase in the energy of each individual proton in the beam leads to the spatial broadening of the Bragg curve, which also yields acoustic waves of greater amplitude. The pulse duration and the beam width of the proton beam do not affect the central frequency of the acoustic wave, but they change the amplitude of the spectral components.

Superposed epoch analysis applied to large-amplitude travelling convection vortices

Directory of Open Access Journals (Sweden)

H. Lühr

1998-07-01

Full Text Available For the six months from 1 October 1993 to 1 April 1994 the recordings of the IMAGE magnetometer network have been surveyed in a search for large-amplitude travelling convection vortices (TCVs. The restriction to large amplitudes (>100 nT was chosen to ensure a proper detection of evens also during times of high activity. Readings of all stations of the northern half of the IMAGE network were employed to check the consistency of the ground signature with the notation of a dual-vortex structure moving in an azimuthal direction. Applying these stringent selection criteria we detected a total of 19 clear TCV events. The statistical properties of our selection resemble the expected characteristics of large-amplitude TCVs. New and unexpected results emerged from the superposed epoch analysis. TCVs tend to form during quiet intervals embedded in moderately active periods. The occurrence of events is not randomly distributed but rather shows a clustering around a few days. These clusters recur once or twice every 27 days. Within a storm cycle they show up five to seven days after the commencement. With regard to solar wind conditions, we see the events occurring in the middle of the IMF sector structure. Large-amplitude TCVs seem to require certain conditions to make solar wind transients 'geoeffective', which have the tendency to recur with the solar rotation period.Key words. Ionosphere (Aural ionosphere; Ionosphere- magnetosphere interactions · Magnetospheric Physics (current system

Fatigue life prediction of rotor blade composites: Validation of constant amplitude formulations with variable amplitude experiments

International Nuclear Information System (INIS)

Westphal, T; Nijssen, R P L

2014-01-01

The effect of Constant Life Diagram (CLD) formulation on the fatigue life prediction under variable amplitude (VA) loading was investigated based on variable amplitude tests using three different load spectra representative for wind turbine loading. Next to the Wisper and WisperX spectra, the recently developed NewWisper2 spectrum was used. Based on these variable amplitude fatigue results the prediction accuracy of 4 CLD formulations is investigated. In the study a piecewise linear CLD based on the S-N curves for 9 load ratios compares favourably in terms of prediction accuracy and conservativeness. For the specific laminate used in this study Boerstra's Multislope model provides a good alternative at reduced test effort

Fatigue life prediction of rotor blade composites: Validation of constant amplitude formulations with variable amplitude experiments

Science.gov (United States)

Westphal, T.; Nijssen, R. P. L.

2014-12-01

The effect of Constant Life Diagram (CLD) formulation on the fatigue life prediction under variable amplitude (VA) loading was investigated based on variable amplitude tests using three different load spectra representative for wind turbine loading. Next to the Wisper and WisperX spectra, the recently developed NewWisper2 spectrum was used. Based on these variable amplitude fatigue results the prediction accuracy of 4 CLD formulations is investigated. In the study a piecewise linear CLD based on the S-N curves for 9 load ratios compares favourably in terms of prediction accuracy and conservativeness. For the specific laminate used in this study Boerstra's Multislope model provides a good alternative at reduced test effort.

Two-nucleon S10 amplitude zero in chiral effective field theory

Science.gov (United States)

Sánchez, M. Sánchez; Yang, C.-J.; Long, Bingwei; van Kolck, U.

2018-02-01

We present a new rearrangement of short-range interactions in the S10 nucleon-nucleon channel within chiral effective field theory. This is intended to address the slow convergence of Weinberg's scheme, which we attribute to its failure to reproduce the amplitude zero (scattering momentum ≃340 MeV) at leading order. After the power counting scheme is modified to accommodate the zero at leading order, it includes subleading corrections perturbatively in a way that is consistent with renormalization-group invariance. Systematic improvement is shown at next-to-leading order, and we obtain results that fit empirical phase shifts remarkably well all the way up to the pion-production threshold. An approach in which pions have been integrated out is included, which allows us to derive analytic results that also fit phenomenology surprisingly well.

Some bounds on pion-scattering amplitudes and their applications

International Nuclear Information System (INIS)

Chung, B.K.; Vinh Mau, R.

1976-01-01

If one uses the method introduced by Meinam and further developed by Martin, together with unitarity crossing symmetry and analyticity, upper and lower bounds to the πdeg πged scattering amplitudes inside the Mandelstam triangle are obtained in terms of the scattering lengths. These bounds are used to set a lower bound to the renormalized pion coupling constant lambda. In terms of the D-wave scattering length a 2 , the results are a 0 greater than or equal to -23.18 square root a 2 + 129.07a 2 and -7.71 square root a 2 less than or equal to lambda less than or equal to 7.71 square root a 2 +2.5a 2 . For a 2 =7.10 -4 they yield a 2 greater than or equal to -0.52 and lambda less than or equal to 0.20 where the pion, mass is set equal to unity

Analytical and Numerical Modeling of Tsunami Wave Propagation for double layer state in Bore

Science.gov (United States)

Yuvaraj, V.; Rajasekaran, S.; Nagarajan, D.

2018-04-01

Tsunami wave enters into the river bore in the landslide. Tsunami wave propagation are described in two-layer states. The velocity and amplitude of the tsunami wave propagation are calculated using the double layer. The numerical and analytical solutions are given for the nonlinear equation of motion of the wave propagation in a bore.

Effective string theory and QCD scattering amplitudes

International Nuclear Information System (INIS)

Makeenko, Yuri

2011-01-01

QCD string is formed at distances larger than the confinement scale and can be described by the Polchinski-Strominger effective string theory with a nonpolynomial action, which has nevertheless a well-defined semiclassical expansion around a long-string ground state. We utilize modern ideas about the Wilson-loop/scattering-amplitude duality to calculate scattering amplitudes and show that the expansion parameter in the effective string theory is small in the Regge kinematical regime. For the amplitudes we obtain the Regge behavior with a linear trajectory of the intercept (d-2)/24 in d dimensions, which is computed semiclassically as a momentum-space Luescher term, and discuss an application to meson scattering amplitudes in QCD.

Constructing QCD one-loop amplitudes

International Nuclear Information System (INIS)

Forde, D

2008-01-01

In the context of constructing one-loop amplitudes using a unitarity bootstrap approach we discuss a general systematic procedure for obtaining the coefficients of the scalar bubble and triangle integral functions of one-loop amplitudes. Coefficients are extracted after examining the behavior of the cut integrand as the unconstrained parameters of a specifically chosen parameterization of the cut loop momentum approach infinity. Measurements of new physics at the forthcoming experimental program at CERN's Large Hadron Collider (LHC) will require a precise understanding of processes at next-to-leading order (NLO). This places increased demands for the computation of new one-loop amplitudes. This in turn has spurred recent developments towards improved calculational techniques. Direct calculations using Feynman diagrams are in general inefficient. Developments of more efficient techniques have usually centered around unitarity techniques [1], where tree amplitudes are effectively 'glued' together to form loops. The most straightforward application of this method, in which the cut loop momentum is in D = 4, allows for the computation of 'cut-constructible' terms only, i.e. (poly)logarithmic containing terms and any related constants. QCD amplitudes contain, in addition to such terms, rational pieces which cannot be derived using such cuts. These 'missing' rational parts can be extracted using cut loop momenta in D = 4-2 (var e psilon). The greater difficulty of such calculations has restricted the application of this approach, although recent developments [3, 4] have provided new promise for this technique. Recently the application of on-shell recursion relations [5] to obtaining the 'missing' rational parts of one-loop processes [6] has provided an alternative very promising solution to this problem. In combination with unitarity methods an 'on-shell bootstrap' approach provides an efficient technique for computing complete one-loop QCD amplitudes [7]. Additionally

Three-dimensional finite amplitude electroconvection in dielectric liquids

Science.gov (United States)

Luo, Kang; Wu, Jian; Yi, Hong-Liang; Tan, He-Ping

2018-02-01

Charge injection induced electroconvection in a dielectric liquid lying between two parallel plates is numerically simulated in three dimensions (3D) using a unified lattice Boltzmann method (LBM). Cellular flow patterns and their subcritical bifurcation phenomena of 3D electroconvection are numerically investigated for the first time. A unit conversion is also derived to connect the LBM system to the real physical system. The 3D LBM codes are validated by three carefully chosen cases and all results are found to be highly consistent with the analytical solutions or other numerical studies. For strong injection, the steady state roll, polygon, and square flow patterns are observed under different initial disturbances. Numerical results show that the hexagonal cell with the central region being empty of charge and centrally downward flow is preferred in symmetric systems under random initial disturbance. For weak injection, the numerical results show that the flow directly passes from the motionless state to turbulence once the system loses its linear stability. In addition, the numerically predicted linear and finite amplitude stability criteria of different flow patterns are discussed.

Learning Analytics: drivers, developments and challenges

Directory of Open Access Journals (Sweden)

Rebecca Ferguson

2014-12-01

Full Text Available Learning analytics is a significant area of Technology-Enhanced Learning (TEL that has emerged during the last decade. This review of the field begins with an examination of the technological, educational and political factors that have driven the development of analytics in educational settings. It goes on to chart the emergence of learning analytics, including their origins in the 20th century, the development of data-driven analytics, the rise of learning-focused perspectives and the influence of national economic concerns. It next focuses on the relationships between learning analytics, educational data mining and academic analytics. Finally, it examines developing areas of learning analytics research, and identifies a series of future challenges.

High energy hadron spin-flip amplitude

International Nuclear Information System (INIS)

Selyugin, O.V.

2016-01-01

The high-energy part of the hadron spin-flip amplitude is examined in the framework of the new high-energy general structure (HEGS) model of the elastic hadron scattering at high energies. The different forms of the hadron spin-flip amplitude are compared in the impact parameter representation. It is shown that the existing experimental data of the proton-proton and proton-antiproton elastic scattering at high energy in the region of the diffraction minimum and at large momentum transfer give support in the presence of the energy-independent part of the hadron spin-flip amplitude with the momentum dependence proposed in the works by Galynskii-Kuraev. [ru

Hidden simplicity of gauge theory amplitudes

Energy Technology Data Exchange (ETDEWEB)

Drummond, J M, E-mail: drummond@lapp.in2p3.f [LAPTH, Universite de Savoie, CNRS, B.P. 110, F-74941 Annecy-le-Vieux, Cedex (France)

2010-11-07

These notes were given as lectures at the CERN Winter School on Supergravity, Strings and Gauge Theory 2010. We describe the structure of scattering amplitudes in gauge theories, focussing on the maximally supersymmetric theory to highlight the hidden symmetries which appear. Using the Britto, Cachzo, Feng and Witten (BCFW) recursion relations we solve the tree-level S-matrix in N=4 super Yang-Mills theory and describe how it produces a sum of invariants of a large symmetry algebra. We review amplitudes in the planar theory beyond tree level, describing the connection between amplitudes and Wilson loops, and discuss the implications of the hidden symmetries.

On the singularities of massive superstring amplitudes

Energy Technology Data Exchange (ETDEWEB)

Foda, O.

1987-06-04

Superstring one-loop amplitudes with massive external states are shown to be in general ill-defined due to internal on-shell propagators. However, we argue that since any massive string state (in the uncompactified theory) has a finite lifetime to decay into massless particles, such amplitudes are not terms in the perturbative expansion of physical S-matrix elements: These can be defined only with massless external states. Consistent massive amplitudes repuire an off-shell formalism.

A New Approach to Eliminate High Amplitude Artifacts in EEG Signals

Directory of Open Access Journals (Sweden)

Ana Rita Teixeira

2016-09-01

Full Text Available High amplitude artifacts represent a problem during EEG recordings in neuroscience research. Taking this into account, this paper proposes a method to identify high amplitude artifacts with no requirement for visual inspection, electrooscillogram (EOG reference channel or user assigned parameters. A potential solution to the high amplitude artifacts (HAA elimination is presented based on blind source separation methods. The assumption underlying the selection of components is that HAA are independent of the EEG signal and different HAA can be generated during the EEG recordings. Therefore, the number of components related to HAA is variable and depends on the processed signal, which means that the method is adaptable to the input signal. The results show, when removing the HAA artifacts, the delta band is distorted but all the other frequency bands are preserved. A case study with EEG signals recorded while participants performed on the Halstead Category Test (HCT is presented. After HAA removal, data analysis revealed, as expected, an error-related frontal ERP wave: the feedback-related negativity (FRN in response to feedback stimuli.

Amplitude based feedback control for NTM stabilisation at ASDEX Upgrade

Energy Technology Data Exchange (ETDEWEB)

Rapson, Christopher, E-mail: chris.rapson@ipp.mpg.de; Giannone, Louis; Maraschek, Marc; Reich, Matthias; Stober, Joerg; Treutterer, Wolfgang

2014-05-15

Highlights: • Two algorithms have been developed which use the NTM amplitude to control ECCD deposition and stabilise NTMs. • Both algorithms were tested and tuned in a simulation of the full feedback loop including an MRE. • Both algorithms have been successfully deployed in ASDEX Upgrade experiments. • Use of the NTM amplitude adds considerable robustness, which is necessary when trying to target ECCD to within 1 cm of the island location. • This is part of ongoing work to reliably and quickly stabilise NTMs in any plasma scenario. - Abstract: Neoclassical Tearing Modes (NTMs) degrade the confinement in tokamak plasmas at high beta, placing a major limitation on the projected fusion performance. Furthermore, NTMs can lead to disruptions with even more severe consequences. Therefore methods to stabilise NTMs are being developed with high priority at several research institutes worldwide. The favoured method is to deposit Electron Cyclotron Current Drive (ECCD) precisely at the mode location by controlling a movable mirror in the ECCD launcher. This method requires both the mode location and the deposition location to be known with high accuracy in real time. The required accuracy is given by half of the marginal island width, or approximately 1 cm for a m/n = 3/2 NTM at ASDEX Upgrade. Despite considerable development on a range of diagnostics, it remains challenging to provide the necessary accuracy reliably and in real time. To relax the accuracy requirements and add robustness, the feedback controller can additionally consider the effect of ECCD on the NTM amplitude directly. Then the optimal deposition location is simply where the NTM amplitude is minimised. The simplest implementation sweeps the ECCD beam across the expected NTM location. After the sweep, the beam can be returned to the optimal location and held there to stabilise the NTM. Unfortunately, waiting for a full sweep takes too long. Therefore a second method assesses the NTM growth every

Nonlinear (super)symmetries and amplitudes

Energy Technology Data Exchange (ETDEWEB)

Kallosh, Renata [Physics Department, Stanford University,382 Via Pueblo Mall, Stanford, CA 94305-4060 (United States)

2017-03-07

There is an increasing interest in nonlinear supersymmetries in cosmological model building. Independently, elegant expressions for the all-tree amplitudes in models with nonlinear symmetries, like D3 brane Dirac-Born-Infeld-Volkov-Akulov theory, were recently discovered. Using the generalized background field method we show how, in general, nonlinear symmetries of the action, bosonic and fermionic, constrain amplitudes beyond soft limits. The same identities control, for example, bosonic E{sub 7(7)} scalar sector symmetries as well as the fermionic goldstino symmetries. We present a universal derivation of the vanishing amplitudes in the single (bosonic or fermionic) soft limit. We explain why, universally, the double-soft limit probes the coset space algebra. We also provide identities describing the multiple-soft limit. We discuss loop corrections to N≥5 supergravity, to the D3 brane, and the UV completion of constrained multiplets in string theory.

Cluster polylogarithms for scattering amplitudes

International Nuclear Information System (INIS)

Golden, John; Paulos, Miguel F; Spradlin, Marcus; Volovich, Anastasia

2014-01-01

Motivated by the cluster structure of two-loop scattering amplitudes in N=4 Yang-Mills theory we define cluster polylogarithm functions. We find that all such functions of weight four are made up of a single simple building block associated with the A 2 cluster algebra. Adding the requirement of locality on generalized Stasheff polytopes, we find that these A 2 building blocks arrange themselves to form a unique function associated with the A 3 cluster algebra. This A 3 function manifests all of the cluster algebraic structure of the two-loop n-particle MHV amplitudes for all n, and we use it to provide an explicit representation for the most complicated part of the n = 7 amplitude as an example. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Cluster algebras in mathematical physics’. (paper)

Eikonal representation of N-body Coulomb scattering amplitudes

International Nuclear Information System (INIS)

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

1983-01-01

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

Characterizing Alzheimer's disease severity via resting-awake EEG amplitude modulation analysis.

Directory of Open Access Journals (Sweden)

Francisco J Fraga

Full Text Available Changes in electroencephalography (EEG amplitude modulations have recently been linked with early-stage Alzheimer's disease (AD. Existing tools available to perform such analysis (e.g., detrended fluctuation analysis, however, provide limited gains in discriminability power over traditional spectral based EEG analysis. In this paper, we explore the use of an innovative EEG amplitude modulation analysis technique based on spectro-temporal signal processing. More specifically, full-band EEG signals are first decomposed into the five well-known frequency bands and the envelopes are then extracted via a Hilbert transform. Each of the five envelopes are further decomposed into four so-called modulation bands, which were chosen to coincide with the delta, theta, alpha and beta frequency bands. Experiments on a resting-awake EEG dataset collected from 76 participants (27 healthy controls, 27 diagnosed with mild-AD, and 22 with moderate-AD showed significant differences in amplitude modulations between the three groups. Most notably, i delta modulation of the beta frequency band disappeared with an increase in disease severity (from mild to moderate AD, ii delta modulation of the theta band appeared with an increase in severity, and iii delta modulation of the beta frequency band showed to be a reliable discriminant feature between healthy controls and mild-AD patients. Taken together, it is hoped that the developed tool can be used to assist clinicians not only with early detection of Alzheimer's disease, but also to monitor its progression.

The pion-deuteron forward elastic amplitude in the non-overlapping potentials model

International Nuclear Information System (INIS)

Butterworth, D.S.

1978-01-01

The pion-deuteron forward elastic amplitude has been calculated in the non-overlapping potentials model, which enables a description of off-shell propagation effects in terms of on-shell amplitudes. Calculations include spin, isospin and deuteron D-state probability effects. Two energy regions are considered. First the pion-nucleon P 33 resonance region, where, using a formalism developed by Agassi and Gal (Ann. Phys.; 75:56 (1973) and 94:184 (1975)), the full multiple-scattering series is summed in an approximation of P 33 wave dominance of the higher-order scatterings. Second, for the subsequent highest-energy region, the double-scattering term only is calculated. Fermi smearing effects are included in both cases. Predictions for the total cross section, its dependence on the deuteron alignment and the real part of the forward elastic amplitude are compared with those of Glauber theory, and data where available. Convergence of the multiple-scattering series is also discussed. (author)

Variability of Surface Reflection Amplitudes of GPR Horn Antenna Depending on Distance between Antenna and Surface

Directory of Open Access Journals (Sweden)

Komačka Jozef

2016-05-01

Full Text Available The study focused on variability of surface reflections amplitudes of GPR horn antenna in relation to distance between an antenna and a surface is presented in the paper. The air-coupled antenna with the central frequency of 1 GHz was used in the investigation. Four types of surfaces (dry pavement, wet pavement, metal plate and composite layer from gypsum and wood were tested. The distance of antenna above the surfaces was changed in the range from 37.5 cm to 53.5 cm. The amplitudes of negative and positive peaks and their variability were analysed in relation to the distance of antenna above the surfaces. Moreover, the influence of changes in the peaks of negative and positive amplitudes on the total amplitudes was assessed. It was found out the amplitudes of negative peaks for all investigated surfaces were relatively consistent in the range from 40.5 cm to 48.5 cm and the moderate decline was identified in the case of amplitudes of positive peaks in the range of distances from 37.5 cm to 51.5 cm. This decline influences the tendency of total amplitudes. Based on the results of analysis it can be stated the distance of air-coupled antenna above the surface can influence the value of total amplitude and the differences depend on the type of surface.

Effect of electron temperature on small-amplitude electron acoustic solitary waves in non-planar geometry

Science.gov (United States)

Bansal, Sona; Aggarwal, Munish; Gill, Tarsem Singh

2018-04-01

Effects of electron temperature on the propagation of electron acoustic solitary waves in plasma with stationary ions, cold and superthermal hot electrons is investigated in non-planar geometry employing reductive perturbation method. Modified Korteweg-de Vries equation is derived in the small amplitude approximation limit. The analytical and numerical calculations of the KdV equation reveal that the phase velocity of the electron acoustic waves increases as one goes from planar to non planar geometry. It is shown that the electron temperature ratio changes the width and amplitude of the solitary waves and when electron temperature is not taken into account,our results completely agree with the results of Javidan & Pakzad (2012). It is found that at small values of τ , solitary wave structures behave differently in cylindrical ( {m} = 1), spherical ( {m} = 2) and planar geometry ( {m} = 0) but looks similar at large values of τ . These results may be useful to understand the solitary wave characteristics in laboratory and space environments where the plasma have multiple temperature electrons.

New rigorous asymptotic theorems for inverse scattering amplitudes

International Nuclear Information System (INIS)

Lomsadze, Sh.Yu.; Lomsadze, Yu.M.

1984-01-01

The rigorous asymptotic theorems both of integral and local types obtained earlier and establishing logarithmic and in some cases even power correlations aetdeen the real and imaginary parts of scattering amplitudes Fsub(+-) are extended to the inverse amplitudes 1/Fsub(+-). One also succeeds in establishing power correlations of a new type between the real and imaginary parts, both for the amplitudes themselves and for the inverse ones. All the obtained assertions are convenient to be tested in high energy experiments when the amplitudes show asymptotic behaviour

On the singularities of massive superstring amplitudes

International Nuclear Information System (INIS)

Foda, O.

1987-01-01

Superstring one-loop amplitudes with massive external states are shown to be in general ill-defined due to internal on-shell propagators. However, we argue that since any massive string state (in the uncompactified theory) has a finite lifetime to decay into massless particles, such amplitudes are not terms in the perturbative expansion of physical S-matrix elements: These can be defined only with massless external states. Consistent massive amplitudes repuire an off-shell formalism. (orig.)

Integral relations in complex space and the global analytic and monodromic structure of Green's functions in quantum field theory

International Nuclear Information System (INIS)

Bros, J.

1980-01-01

In this lecture, we present some of the ideas of a global consistent approach to the analytic and monodromic structure of Green's functions and scattering amplitudes of elementary particles on the basis of general quantum field theory. (orig.)

Rorty, Pragmatism, and Analytic Philosophy

Directory of Open Access Journals (Sweden)

Cheryl Misak

2013-07-01

Full Text Available One of Richard Rorty's legacies is to have put a Jamesian version of pragmatism on the contemporary philosophical map. Part of his argument has been that pragmatism and analytic philosophy are set against each other, with pragmatism almost having been killed off by the reigning analytic philosophy. The argument of this paper is that there is a better and more interesting reading of both the history of pragmatism and the history of analytic philosophy.

Radiation Pattern Reconstruction from the Near-Field Amplitude Measurement on Two Planes Using PSO

Directory of Open Access Journals (Sweden)

Z. Novacek

2005-12-01

Full Text Available The paper presents a new approach to the radiation patternreconstruction from near-field amplitude only measurement over a twoplanar scanning surfaces. This new method for antenna patternreconstruction is based on the global optimization PSO (Particle SwarmOptimization. The paper presents appropriate phaseless measurementrequirements and phase retrieval algorithm together with a briefdescription of the particle swarm optimization method. In order toexamine the methodologies developed in this paper, phaselessmeasurement results for two different antennas are presented andcompared to results obtained by a complex measurement (amplitude andphase.

Scattering amplitudes in super-renormalizable gravity

International Nuclear Information System (INIS)

Donà, Pietro; Giaccari, Stefano; Modesto, Leonardo; Rachwał, Lesław; Zhu, Yiwei

2015-01-01

We explicitly compute the tree-level on-shell four-graviton amplitudes in four, five and six dimensions for local and weakly nonlocal gravitational theories that are quadratic in both, the Ricci and scalar curvature with form factors of the d’Alembertian operator inserted between. More specifically we are interested in renormalizable, super-renormalizable or finite theories. The scattering amplitudes for these theories turn out to be the same as the ones of Einstein gravity regardless of the explicit form of the form factors. As a special case the four-graviton scattering amplitudes in Weyl conformal gravity are identically zero. Using a field redefinition, we prove that the outcome is correct for any number of external gravitons (on-shell n−point functions) and in any dimension for a large class of theories. However, when an operator quadratic in the Riemann tensor is added in any dimension (with the exception of the Gauss-Bonnet term in four dimensions) the result is completely altered, and the scattering amplitudes depend on all the form factors introduced in the action.

Corrections to the large-angle scattering amplitude

International Nuclear Information System (INIS)

Goloskokov, S.V.; Kudinov, A.V.; Kuleshov, S.P.

1979-01-01

High-energy behaviour of scattering amplitudes is considered within the frames of Logunov-Tavchelidze quasipotential approach. The representation of scattering amplitude of two scalar particles, convenient for the study of its asymptotic properties is given. Obtained are corrections of the main value of scattering amplitude of the first and the second orders in 1/p, where p is the pulse of colliding particles in the system of the inertia centre. An example of the obtained formulas use for a concrete quasipotential is given

Aging increases compensatory saccade amplitude in the video head impulse test

Directory of Open Access Journals (Sweden)

Eric R Anson

2016-07-01

Full Text Available Objective: Rotational vestibular function declines with age resulting in saccades as a compensatory mechanism to improve impaired gaze stability. Small reductions in rotational vestibulo-ocular reflex (VOR gain that would be considered clinically normal have been associated with compensatory saccades. We evaluated whether compensatory saccade characteristics varied as a function of age, independent of semicircular canal function as quantified by VOR gain.Methods: Horizontal VOR gain was measured in 243 participants age 27-93 from the Baltimore Longitudinal Study of Aging using video head impulse testing (HIT. Latency and amplitude of the first saccade (either covert – occurring during head impulse, or overt – occurring following head impulse were measured for head impulses with compensatory saccades (n = 2230 head impulses. The relationship between age and saccade latency, as well as the relationship between age and saccade amplitude, were evaluated using regression analyses adjusting for VOR gain, gender, and race.Results: Older adults (mean age 75.9 made significantly larger compensatory saccades relative to younger adults (mean age 45.0. In analyses adjusted for VOR gain, there was a significant association between age and amplitude of the first compensatory covert saccade (β = 0.015, p = 0.008. In analyses adjusted for VOR gain, there was a significant association between age and amplitude of the first compensatory overt saccade (β = 0.02, p < 0.001. Compensatory saccade latencies did not vary significantly by age. Conclusions: We observed that aging increases the compensatory catch-up saccade amplitude in healthy adults after controlling for VOR gain. Size of compensatory saccades may be useful in addition to VOR gain for characterizing vestibular function in aging adults.

Helicity amplitudes for matter-coupled gravity

International Nuclear Information System (INIS)

Aldrovandi, R.; Novaes, S.F.; Spehler, D.

1992-07-01

The Weyl-van der Waerden spinor formalism is applied to the evaluation of helicity invariant amplitudes in the framework of linearized gravitation. The graviton couplings to spin-0, 1 - 2 , 1, and 3 - 2 particles are given, and, to exhibit the reach of this method, the helicity amplitudes for the process electron + positron → photon + graviton are obtained. (author)

Analytic Hypoellipticity and the Treves Conjecture

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Marco Mughetti

2016-12-01

Full Text Available We are concerned with the problem of the analytic hypoellipticity; precisely, we focus on the real analytic regularity of the solutions of sums of squares with real analytic coefficients. Treves conjecture states that an operator of this type is analytic hypoelliptic if and only if all the strata in the Poisson-Treves stratification are symplectic. We discuss a model operator, P, (firstly appeared and studied in [3] having a single symplectic stratum and prove that it is not analytic hypoelliptic. This yields a counterexample to the sufficient part of Treves conjecture; the necessary part is still an open problem.

Cosmophysical Factors in the Fluctuation Amplitude Spectrum of Brownian Motion

Directory of Open Access Journals (Sweden)

Kaminsky A. V.

2010-04-01

Full Text Available Phenomenon of the regular variability of the fine structure of the fluctuation in the amplitude distributions (shapes of related histograms for the case of Brownian motion was investigated. We took an advantage of the dynamic light scattering method (DLS to get a stochastically fluctuated signal determined by Brownian motion. Shape of the histograms is most likely to vary, synchronous, in two proximally located independent cells containing Brownian particles. The synchronism persists in the cells distant at 2m from each other, and positioned meridionally. With a parallel-wise positioning of the cells, high probability of the synchronous variation in the shape of the histograms by local time has been observed. This result meets the previous conclusion about the dependency of histogram shapes ("fluctuation amplitudes" of the spectra of stochastic processes upon rotation of the Earth.

GSC4813-0981 = V921 Mon, a new low-amplitude δ Scuti star with variable amplitude

Science.gov (United States)

Galeev, A.; Bikmaev, I.; Shimansky, V.; Deminova, N.

2014-11-01

GSC 4813-0981 = V921 Mon is a low-amplitude δ Scuti-type variable with an amplitude of 0.018^m-0.027^m in different bands and a period of 48.5 minutes. The fundamental parameters of the atmosphere and physical characteristics, determined from medium-resolution spectra, are: T_{eff}=8700 K, log g=3.95 dex, [M/H]=0, M=1.7 M_{⊙}, R=2.3 R_{⊙}. We performed a long-term analysis of the variations using a ten-year data set of CCD observations (2003-2013) acquired in BVR with the 1.5-m Russian-Turkish telescope (RTT150, TUBITAK National Observatory). A preliminary result is that the amplitude of the variability changes; it was decreasing during 2003-2008, but is now increasing.

Amplitude and timing properties of a Geiger discharge in a SiPM cell

Energy Technology Data Exchange (ETDEWEB)

Popova, E., E-mail: elenap73@mail.ru [National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), 115409, Kashirskoe Shosse 31 (Russian Federation); Buzhan, P.; Pleshko, A. [National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), 115409, Kashirskoe Shosse 31 (Russian Federation); Vinogradov, S. [University of Liverpool and Cockcroft Institute, Sci-Tech Daresbury, Keckwick Lane, Warrington WA4 4AD, Cheshire (United Kingdom); P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Leninskiy Prospect 53, Moscow 119991 (Russian Federation); Stifutkin, A.; Ilyin, A. [National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), 115409, Kashirskoe Shosse 31 (Russian Federation); Besson, D. [National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), 115409, Kashirskoe Shosse 31 (Russian Federation); Department of Physics and Astronomy, University of Kansas, Lawrence, KS 66045-2151 (United States); Mirzoyan, R. [Max-Planck-Institute for Physics, Föhringer Ring 6, 80805 München (Germany)

2015-07-01

The amplitude and timing properties of a Geiger discharge in a stand-alone SiPM cell have been investigated in detail. Use of a single stand-alone SiPM cell allows us to perform measurements with better accuracy than the multicell structure of conventional SiPMs. We have studied the dependence of the output charge and amplitude from an SiPM cell illuminated by focused light vs the number of primary photoelectrons. We propose a SPICE model which explains the amplitude over saturation (when the SiPM's amplitude is greater than the sum over all cells) characteristics of SiPM signals for more than one initial photoelectrons. The time resolutions of a SiPM cell have been measured for the case of single (SPTR) and multiphoton light pulses. The Full Width Half Max (FWHM) for SPTR has been found to be at the level of 30 ps for focused and 40 ps for unfocused light (100 μm cell size). - Highlights: • A stand-alone SiPM cell has been investigated in detail. • Amplitude and time properties have been measured with femtosecond 660 nm laser. • SPICE model for a Geiger discharge development has been proposed. • SPTR for a stand-alone 100 μm size SiPM cell has been found to be 40 ps FWHM.

Analytical modelling for ultrasonic surface mechanical attrition treatment

Directory of Open Access Journals (Sweden)

Guan-Rong Huang

2015-07-01

Full Text Available The grain refinement, gradient structure, fatigue limit, hardness, and tensile strength of metallic materials can be effectively enhanced by ultrasonic surface mechanical attrition treatment (SMAT, however, never before has SMAT been treated with rigorous analytical modelling such as the connection among the input energy and power and resultant temperature of metallic materials subjected to SMAT. Therefore, a systematic SMAT model is actually needed. In this article, we have calculated the averaged speed, duration time of a cycle, kinetic energy and kinetic energy loss of flying balls in SMAT for structural metallic materials. The connection among the quantities such as the frequency and amplitude of attrition ultrasonic vibration motor, the diameter, mass and density of balls, the sample mass, and the height of chamber have been considered and modelled in details. And we have introduced the one-dimensional heat equation with heat source within uniform-distributed depth in estimating the temperature distribution and heat energy of sample. In this approach, there exists a condition for the frequency of flying balls reaching a steady speed. With these known quantities, we can estimate the strain rate, hardness, and grain size of sample.

MHV Vertices And Tree Amplitudes In Gauge Theory

International Nuclear Information System (INIS)

Cachazo, Freddy; Svrcek, Peter; Witten, Edward

2004-01-01

As an alternative to the usual Feynman graphs, tree amplitudes in Yang-Mills theory can be constructed from tree graphs in which the vertices are tree level MHV scattering amplitudes, continued off shell in a particular fashion. The formalism leads to new and relatively simple formulas for many amplitudes, and can be heuristically derived from twistor space. (author)

Full Waveform Inversion for Reservoir Characterization - A Synthetic Study

KAUST Repository

Zabihi Naeini, E.; Kamath, N.; Tsvankin, I.; Alkhalifah, Tariq Ali

2017-01-01

Most current reservoir-characterization workflows are based on classic amplitude-variation-with-offset (AVO) inversion techniques. Although these methods have generally served us well over the years, here we examine full-waveform inversion (FWI

Correlation between vibration amplitude and tool wear in turning: Numerical and experimental analysis

Directory of Open Access Journals (Sweden)

Balla Srinivasa Prasad

2017-02-01

Full Text Available In this paper, a correlation between vibration amplitude and tool wear when in dry turning of AISI 4140 steel using uncoated carbide insert DNMA 432 is analyzed via experiments and finite element simulations. 3D Finite element simulations results are utilized to predict the evolution of cutting forces, vibration displacement amplitudes and tool wear in vibration induced turning. In the present paper, the primary concern is to find the relative vibration and tool wear with the variation of process parameters. These changes lead to accelerated tool wear and even breakage. The cutting forces in the feed direction are also predicted and compared with the experimental trends. A laser Doppler vibrometer is used to detect vibration amplitudes and the usage of Kistler 9272 dynamometer for recording the cutting forces during the cutting process is well demonstrated. A sincere effort is put to investigate the influence of spindle speed, feed rate, depth of cut on vibration amplitude and tool flank wear at different levels of workpiece hardness. Empirical models have been developed using second order polynomial equations for correlating the interaction and higher order influences of various process parameters. Analysis of variance (ANOVA is carried out to identify the significant factors that are affecting the vibration amplitude and tool flank wear. Response surface methodology (RSM is implemented to investigate the progression of flank wear and displacement amplitude based on experimental data. While measuring the displacement amplitude, R-square values for experimental and numerical methods are 98.6 and 97.8. Based on the R-square values of ANOVA it is found that the numerical values show good agreement with the experimental values and are helpful in estimating displacement amplitude. In the case of predicting the tool wear, R-square values were found to be 97.69 and 96.08, respectively for numerical and experimental measures while determining the tool

Efetividade do Programa de Fisioterapia Aquática na amplitude de movimento em idosas

Directory of Open Access Journals (Sweden)

Eduardo Aguilar Arca

2014-03-01

Full Text Available O objetivo deste estudo foi verificar os efeitos de um programa de fisioterapia aquática na amplitude de movimento em mulheres idosas. Estudo quase-experimental, sem grupo-controle, com 16 idosas, avaliadas em três momentos da intervenção. Verificou-se que o programa de fisioterapia aquática produziu efeitos expressivos no ganho da amplitude de movimento em todas as articulações e eixos de movimentos estudados, além do engajamento de pessoas idosas em atividades físicas importante para essa fase da vida.

Conformal higher spin scattering amplitudes from twistor space

Energy Technology Data Exchange (ETDEWEB)

Adamo, Tim [Blackett Laboratory, Imperial College, London, SW7 2AZ (United Kingdom); Hähnel, Philipp; McLoughlin, Tristan [School of Mathematics, Trinity College Dublin, College Green, Dublin 2 (Ireland)

2017-04-04

We use the formulation of conformal higher spin (CHS) theories in twistor space to study their tree-level scattering amplitudes, finding expressions for all three-point (MHV)-bar amplitudes and all MHV amplitudes involving positive helicity conformal gravity particles and two negative helicity higher spins. This provides the on-shell analogue for the covariant coupling of CHS fields to a conformal gravity background. We discuss the restriction of the theory to a ghost-free unitary subsector, analogous to restricting conformal gravity to general relativity with a cosmological constant. We study the flat-space limit and show that the restricted amplitudes vanish, supporting the conjecture that in the unitary sector the S-matrix of CHS theories is trivial. However, by appropriately rescaling the amplitudes we find non-vanishing results which we compare with chiral flat-space higher spin theories.

Conformal higher spin scattering amplitudes from twistor space

International Nuclear Information System (INIS)

Adamo, Tim; Hähnel, Philipp; McLoughlin, Tristan

2017-01-01

We use the formulation of conformal higher spin (CHS) theories in twistor space to study their tree-level scattering amplitudes, finding expressions for all three-point (MHV)-bar amplitudes and all MHV amplitudes involving positive helicity conformal gravity particles and two negative helicity higher spins. This provides the on-shell analogue for the covariant coupling of CHS fields to a conformal gravity background. We discuss the restriction of the theory to a ghost-free unitary subsector, analogous to restricting conformal gravity to general relativity with a cosmological constant. We study the flat-space limit and show that the restricted amplitudes vanish, supporting the conjecture that in the unitary sector the S-matrix of CHS theories is trivial. However, by appropriately rescaling the amplitudes we find non-vanishing results which we compare with chiral flat-space higher spin theories.

Modular amplitudes and flux-superpotentials on elliptic Calabi-Yau fourfolds

Science.gov (United States)

Cota, Cesar Fierro; Klemm, Albrecht; Schimannek, Thorsten

2018-01-01

We discuss the period geometry and the topological string amplitudes on elliptically fibered Calabi-Yau fourfolds in toric ambient spaces. In particular, we describe a general procedure to fix integral periods. Using some elementary facts from homological mirror symmetry we then obtain Bridgelands involution and its monodromy action on the integral basis for non-singular elliptically fibered fourfolds. The full monodromy group contains a subgroup that acts as PSL(2,Z) on the Kähler modulus of the fiber and we analyze the consequences of this modularity for the genus zero and genus one amplitudes as well as the associated geometric invariants. We find holomorphic anomaly equations for the amplitudes, reflecting precisely the failure of exact PSL(2,Z) invariance that relates them to quasi-modular forms. Finally we use the integral basis of periods to study the horizontal flux superpotential and the leading order Kähler potential for the moduli fields in F-theory compactifications globally on the complex structure moduli space. For a particular example we verify attractor behaviour at the generic conifold given an aligned choice of flux which we expect to be universal. Furthermore we analyze the superpotential at the orbifold points but find no stable vacua.

Amplitude-to-frequency converter of radioisotope instruments

International Nuclear Information System (INIS)

Demchenkov, V.P.; Korobkov, I.N.

1988-01-01

An amplitude-to-frequency converter designed for signal processing of radioisotope relay devices is descibed. The basic elements of the converter are a scaling amplifier, an analog-to-digital converter, a code-to-frequency converter, a null-organ, a delay unit and a clock-pulse generator. The designed amplitude-to-frequency converter takes into account a prior information about the signal shape of the energy spectrum. The converter processes input pulses of 0.10 V amplitude and duration more than 2μs. The energy channel number is 64

Amplitude-modulated fiber-ring laser

DEFF Research Database (Denmark)

Caputo, J. G.; Clausen, Carl A. Balslev; Sørensen, Mads Peter

2000-01-01

Soliton pulses generated by a fiber-ring laser are investigated by numerical simulation and perturbation methods. The mathematical modeling is based on the nonlinear Schrödinger equation with perturbative terms. We show that active mode locking with an amplitude modulator leads to a self......-starting of stable solitonic pulses from small random noise, provided the modulation depth is small. The perturbative analysis leads to a nonlinear coupled return map for the amplitude, phase, and position of the soliton pulses circulating in the fiber-ring laser. We established the validity of this approach...

The five-gluon amplitude and one-loop integrals

International Nuclear Information System (INIS)

Bern, Z.; Dixon, L.; Kosower, D.A.

1992-12-01

We review the conventional field theory description of the string motivated technique. This technique is applied to the one-loop five-gluon amplitude. To evaluate the amplitude a general method for computing dimensionally regulated one-loop integrals is outlined including results for one-loop integrals required for the pentagon diagram and beyond. Finally, two five-gluon helicity amplitudes are given

Higher order analytical approximate solutions to the nonlinear pendulum by He's homotopy method

International Nuclear Information System (INIS)

Belendez, A; Pascual, C; Alvarez, M L; Mendez, D I; Yebra, M S; Hernandez, A

2009-01-01

A modified He's homotopy perturbation method is used to calculate the periodic solutions of a nonlinear pendulum. The method has been modified by truncating the infinite series corresponding to the first-order approximate solution and substituting a finite number of terms in the second-order linear differential equation. As can be seen, the modified homotopy perturbation method works very well for high values of the initial amplitude. Excellent agreement of the analytical approximate period with the exact period has been demonstrated not only for small but also for large amplitudes A (the relative error is less than 1% for A < 152 deg.). Comparison of the result obtained using this method with the exact ones reveals that this modified method is very effective and convenient.

On the wave amplitude blow-up in the Berk-Breizman model for nonlinear evolution of a plasma wave driven resonantly by fast ions

International Nuclear Information System (INIS)

Zaleśny, Jarosław; Galant, Grzegorz; Berczyński, Paweł; Berczyński, Stefan; Lisak, Mietek

2011-01-01

In this paper the Berk-Breizman (BB) model of plasma wave instability arising on the stability threshold is considered. An interesting although physically unacceptable feature of the model is the explosive behaviour occurring in the regime of small values of the collision frequency parameter. We present an analytical description of the explosive solution, based on a fitting to the numerical solution of the BB equation with the collision parameter equal to zero. We find that the chaotic behaviour taking place for small but non-zero values of the collision parameter is absent in this case; therefore, chaotic behaviour seems to be an independent phenomenon not directly related to the blow-up regime. The time and the velocity dependence of the distribution function are found numerically and plotted to better understand what actually happens in the model. It allows us to obtain a good qualitative understanding of the time evolution of the mode amplitude including the linear growth of the amplitude, reaching its maximum and then decreasing towards the zero value. Nevertheless, we have no satisfactory physical explanation of the amplitude evolution when the amplitude vanishes at some time and then revives but with an opposite phase.

Responses of Medullary Lateral Line Units of the Goldfish, Carassius auratus, to Amplitude-Modulated Sinusoidal Wave Stimuli

Directory of Open Access Journals (Sweden)

Ramadan Ali

2010-01-01

Full Text Available This paper describes the responses of brainstem lateral line units in goldfish, Carassius auratus, to constant-amplitude and to amplitude-modulated sinusoidal water motions. If stimulated with constant-amplitude sinusoidal water motions, units responded with phasic (50% or with sustained (50% increases in dicharge rate. Based on isodisplacement curves, units preferred low (33 Hz, 12.5%, mid (50 Hz, 10% and 100 Hz, 30% or high (200 Hz, 47.5% frequencies. In most units, responses were weakly phase locked to the carrier frequency. However, at a carrier frequency of 50 Hz or 100 Hz, a substantial proportion of the units exhibited strong phase locking. If stimulated with amplitude-modulated water motions, units responded with a burst of discharge to each modulation cycle, that is, units phase locked to the amplitude modulation frequency. Response properties of brainstem units were in many respects comparable to those of midbrain units, suggesting that they emerge first in the lateral line brainstem.

An analytic thomism?

Directory of Open Access Journals (Sweden)

Daniel Alejandro Pérez Chamorro.

2012-12-01

Full Text Available For 50 years the philosophers of the Anglo-Saxon analytic tradition (E. Anscombre, P. Geach, A. Kenny, P. Foot have tried to follow the Thomas Aquinas School which they use as a source to surpass the Cartesian Epistemology and to develop the virtue ethics. Recently, J. Haldane has inaugurated a program of “analytical thomism” which main result until the present has been his “theory of identity mind/world”. Nevertheless, none of Thomás’ admirers has still found the means of assimilating his metaphysics of being.

The role of pulse shape in motor cortex transcranial magnetic stimulation using full-sine stimuli

DEFF Research Database (Denmark)

Delvendahl, Igor; Gattinger, Norbert; Berger, Thomas

2014-01-01

A full-sine (biphasic) pulse waveform is most commonly used for repetitive transcranial magnetic stimulation (TMS), but little is known about how variations in duration or amplitude of distinct pulse segments influence the effectiveness of a single TMS pulse to elicit a corticomotor response. Using......) compared monophasic, half-sine, and full-sine pulses, (ii) applied two-segment pulses consisting of two identical half-sines, and (iii) manipulated amplitude, duration, and current direction of the first or second full-sine pulse half-segments. RMT was significantly higher using half-sine or monophasic...... in considerably higher RMT, whereas varying the amplitude of the half-segment inducing anterior-posterior current had a smaller effect. These findings provide direct experimental evidence that the pulse segment inducing a posterior-anterior directed current in M1 contributes most to corticospinal pathway...

Correlation-Based Amplitude Estimation of Coincident Partials in Monaural Musical Signals

Directory of Open Access Journals (Sweden)

Jayme Garcia Arnal Barbedo

2010-01-01

Full Text Available This paper presents a method for estimating the amplitude of coincident partials generated by harmonic musical sources (instruments and vocals. It was developed as an alternative to the commonly used interpolation approach, which has several limitations in terms of performance and applicability. The strategy is based on the following observations: (a the parameters of partials vary with time; (b such a variation tends to be correlated when the partials belong to the same source; (c the presence of an interfering coincident partial reduces the correlation; and (d such a reduction is proportional to the relative amplitude of the interfering partial. Besides the improved accuracy, the proposed technique has other advantages over its predecessors: it works properly even if the sources have the same fundamental frequency, it is able to estimate the first partial (fundamental, which is not possible using the conventional interpolation method, it can estimate the amplitude of a given partial even if its neighbors suffer intense interference from other sources, it works properly under noisy conditions, and it is immune to intraframe permutation errors. Experimental results show that the strategy clearly outperforms the interpolation approach.

Large amplitude dynamics of micro-/nanomechanical resonators actuated with electrostatic pulses

International Nuclear Information System (INIS)

Juillard, J.; Bonnoit, A.; Avignon, E.; Hentz, S.; Colinet, E.

2010-01-01

In the field of resonant nano-electro-mechanical system (NEMS) design, it is a common misconception that large-amplitude motion, and thus large signal-to-noise ratio, can only be achieved at the risk of oscillator instability. In the present paper, we show that very simple closed-loop control schemes can be used to achieve stable large-amplitude motion of a resonant structure even when jump resonance (caused by electrostatic softening or Duffing hardening) is present in its frequency response. We focus on the case of a resonant accelerometer sensing cell, consisting of a nonlinear clamped-clamped beam with electrostatic actuation and detection, maintained in an oscillation state with pulses of electrostatic force that are delivered whenever the detected signal (the position of the beam) crosses zero. We show that the proposed feedback scheme ensures the stability of the motion of the beam much beyond the critical Duffing amplitude and that, if the parameters of the beam are correctly chosen, one can achieve almost full-gap travel range without incurring electrostatic pull-in. These results are illustrated and validated with transient simulations of the nonlinear closed-loop system.

Broadband metasurface holograms: toward complete phase and amplitude engineering.

Science.gov (United States)

Wang, Qiu; Zhang, Xueqian; Xu, Yuehong; Gu, Jianqiang; Li, Yanfeng; Tian, Zhen; Singh, Ranjan; Zhang, Shuang; Han, Jiaguang; Zhang, Weili

2016-09-12

As a revolutionary three-dimensional imaging technique, holography has attracted wide attention for its ability to photographically record a light field. However, traditional phase-only or amplitude-only modulation holograms have limited image quality and resolution to reappear both amplitude and phase information required of the objects. Recent advances in metasurfaces have shown tremendous opportunities for using a planar design of artificial meta-atoms to shape the wave front of light by optimal control of both its phase and amplitude. Inspired by the concept of designer metasurfaces, we demonstrate a novel amplitude-phase modulation hologram with simultaneous five-level amplitude modulation and eight-level phase modulation. Such a design approach seeks to turn the perceived disadvantages of the traditional phase or amplitude holograms, and thus enable enhanced performance in resolution, homogeneity of amplitude distribution, precision, and signal-to-noise ratio. In particular, the unique holographic approach exhibits broadband characteristics. The method introduced here delivers more degrees of freedom, and allows for encoding highly complex information into designer metasurfaces, thus having the potential to drive next-generation technological breakthroughs in holography.

Phase-space spinor amplitudes for spin-1/2 systems

International Nuclear Information System (INIS)

Watson, P.; Bracken, A. J.

2011-01-01

The concept of phase-space amplitudes for systems with continuous degrees of freedom is generalized to finite-dimensional spin systems. Complex amplitudes are obtained on both a sphere and a finite lattice, in each case enabling a more fundamental description of pure spin states than that previously given by Wigner functions. In each case the Wigner function can be expressed as the star product of the amplitude and its conjugate, so providing a generalized Born interpretation of amplitudes that emphasizes their more fundamental status. The ordinary product of the amplitude and its conjugate produces a (generalized) spin Husimi function. The case of spin-(1/2) is treated in detail, and it is shown that phase-space amplitudes on the sphere transform correctly as spinors under rotations, despite their expression in terms of spherical harmonics. Spin amplitudes on a lattice are also found to transform as spinors. Applications are given to the phase space description of state superposition, and to the evolution in phase space of the state of a spin-(1/2) magnetic dipole in a time-dependent magnetic field.

A new analytical framework for assessing the effect of sea-level rise and dredging on tidal damping in estuaries

NARCIS (Netherlands)

Cai, H.; Savenije, H.H.G.; Toffolon, M.

2012-01-01

This paper explores different analytical solutions of the tidal hydraulic equations in convergent estuaries. Linear and quasi-nonlinear models are compared for given geometry, friction, and tidal amplitude at the seaward boundary, proposing a common theoretical framework and showing that the main

Automation of loop amplitudes in numerical approach

International Nuclear Information System (INIS)

Fujimoto, J.; Ishikawa, T.; Shimizu, Y.; Kato, K.; Nakazawa, N.; Kaneko, T.

1997-01-01

An automatic calculating system GRACE-L1 of one-loop Feynman amplitude is reviewed. This system can be applied to 2 to 2-body one-loop processes. A sample calculation of 2 to 3-body one-loop amplitudes is also presented. (orig.)

BFKL approach and six-particle MHV amplitude in N=4 super Yang-Mills

International Nuclear Information System (INIS)

Lipatov, L.N.; Prygarin, A.

2010-12-01

We consider the planar MHV amplitude in N=4 supersymmetric Yang-Mills theory for 2→4 particle scattering at two and three loops in the Regge kinematics. We perform an analytic continuation of two-loop result for the remainder function found by Goncharov, Spradlin, Vergu and Volovich to the physical region, where the remainder function does not vanish in the Regge limit. After the continuation both the leading and the subleading in the logarithm of the energy terms are extracted and analyzed. Using this result we calculate the next-to-leading corrections to the impact factors required in the BFKL approach. The BFKL technique was used to find the leading imaginary and real parts of the remainder function at three loops. (orig.)

BFKL approach and six-particle MHV amplitude in N=4 super Yang-Mills

Energy Technology Data Exchange (ETDEWEB)

Lipatov, L.N. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; St. Petersburg Inst. of Nuclear Physics, Gatchina (Russian Federation); Prygarin, A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

2010-12-15

We consider the planar MHV amplitude in N=4 supersymmetric Yang-Mills theory for 2{yields}4 particle scattering at two and three loops in the Regge kinematics. We perform an analytic continuation of two-loop result for the remainder function found by Goncharov, Spradlin, Vergu and Volovich to the physical region, where the remainder function does not vanish in the Regge limit. After the continuation both the leading and the subleading in the logarithm of the energy terms are extracted and analyzed. Using this result we calculate the next-to-leading corrections to the impact factors required in the BFKL approach. The BFKL technique was used to find the leading imaginary and real parts of the remainder function at three loops. (orig.)

Quantum delta-kicked rotor: the effect of amplitude noise on the quantum resonances

CERN Document Server

Brouard, S

2003-01-01

We study analytically the effect of amplitude noise on the quantum resonances of an atom optics realization of the delta-kicked rotor. Noise is shown to add a time growth to the 'deterministic' energy and to induce a time increasing spreading in the momentum distribution; exact results are given for both effects. The ballistic peaks characteristic of the noiseless distribution for particular initial conditions broaden and eventually vanish, whereas the associated quadratic growth of energy persists; at large times, the survival probability decays as t sup - sup 1. Moreover, the nonexponential 'localization' linked to different initial conditions is gradually destroyed. Features specific to Gaussian noise, white and coloured, are analysed. The feasibility of experimental tests of these effects is discussed.

Small and large amplitude movement of the unstable interface between two immiscible fluids

Energy Technology Data Exchange (ETDEWEB)

Aribert, J M; Thirriot, C

1970-01-01

The flow of immiscible fluids in a confined flow channel is accompanied by a deformation of the surface of separation when the stability conditions are not fulfilled. A simplified schematic for the problem is given, and the characteristic surface perturbation is calculated analytically and numerically. The perturbation is characterized by a wavelength, an amplitude, and the shape of the perturbation at a sufficient distance from the front. Two asymptotic cases are fully discussed: the creation of a wave in the surface, and the shape of a fully developed perturbation. Experimental results from 2 Hele-Shaw models are in satisfactory agreement with the theoretical predictions. Further studies will be concerned with variable rate flow, geometrically divergent flow, layered flow with variable viscosity between layers, and non-Newtonian flow.

Analytical method for estimating the thermal expansion coefficient of metals at high temperature

International Nuclear Information System (INIS)

Takamoto, S; Izumi, S; Nakata, T; Sakai, S; Oinuma, S; Nakatani, Y

2015-01-01

In this paper, we propose an analytical method for estimating the thermal expansion coefficient (TEC) of metals at high-temperature ranges. Although the conventional method based on quasiharmonic approximation (QHA) shows good results at low temperatures, anharmonic effects caused by large-amplitude thermal vibrations reduces its accuracy at high temperatures. Molecular dynamics (MD) naturally includes the anharmonic effect. However, since the computational cost of MD is relatively high, in order to make an interatomic potential capable of reproducing TEC, an analytical method is essential. In our method, analytical formulation of the radial distribution function (RDF) at finite temperature realizes the estimation of the TEC. Each peak of the RDF is approximated by the Gaussian distribution. The average and variance of the Gaussian distribution are formulated by decomposing the fluctuation of interatomic distance into independent elastic waves. We incorporated two significant anharmonic effects into the method. One is the increase in the averaged interatomic distance caused by large amplitude vibration. The second is the variation in the frequency of elastic waves. As a result, the TECs of fcc and bcc crystals estimated by our method show good agreement with those of MD. Our method enables us to make an interatomic potential that reproduces the TEC at high temperature. We developed the GEAM potential for nickel. The TEC of the fitted potential showed good agreement with experimental data from room temperature to 1000 K. As compared with the original potential, it was found that the third derivative of the wide-range curve was modified, while the zeroth, first and second derivatives were unchanged. This result supports the conventional theory of solid state physics. We believe our analytical method and developed interatomic potential will contribute to future high-temperature material development. (paper)

Singularities in four-body final-state amplitudes

International Nuclear Information System (INIS)

Adhikari, S.K.

1978-01-01

Like three-body amplitudes, four-body amplitudes have subenergy threshold singularities over and above total-energy singularities. In the four-body problem we encounter a new type of subenergy singularity besides the usual two- and three-body subenergy threshold singularities. This singularity will be referred to as ''independent-pair threshold singularity'' and involves pair-subenergy threshold singularities in each of the two independent pair subenergies in four-body final states. We also study the particularly interesting case of resonant two- and three-body interactions in the four-body isobar model and the rapid (singular) dependence of the isobar amplitudes they generate in the four-body phase space. All these singularities are analyzed in the multiple-scattering formalism and it is shown that they arise from the ''next-to-last'' rescattering and hence may be represented correctly by an approximate amplitude which has that rescattering

Amplitude correlations for inelastic proton scattering from 48Ti

International Nuclear Information System (INIS)

Chou, B.H.; Mitchell, G.E.; Bilpuch, E.G.; Westerfeldt, C.R.

1981-01-01

The magnitudes and relative signs of inelastic proton channel amplitudes were determined for three decay channels for 45 5/2 + resonances in 49 V. The reduced widths in each channel follow a Porter-Thomas distribution, but extremely large amplitude correlations are observed - for one pair of channel amplitudes the relative sign is positive for 43 of 45 resonances. These results provide the first direct test of the Krieger-Porter reduced width amplitude distribution. (orig.)

Parametric instability of a large-amplitude nonmonochromatic Alfvacute en wave

International Nuclear Information System (INIS)

Malara, F.; Velli, M.

1996-01-01

The parametric instability of a finite-amplitude Alfvacute en wave is studied in a one-dimensional geometry. The pump wave is an exact solution of the nonlinear magnetohydrodynamic (MHD) equations, i.e., the magnetic field perturbation has a uniform intensity and rotates in the plane perpendicular to the propagation direction, but its Fourier spectrum contains several wavelengths. The weakly nonmonochromatic regime is first studied by an analytical approach. It is shown that the growth rate of the instability decreases quadratically with a parameter that measures the departure from the monochromatic case. The fully nonmonochromatic case is studied by numerically solving the instability equations, when the phase function of the pump wave has a power-law spectrum. Though the growth rate is maximum in the monochromatic case, it remains of the same order of magnitude also for wide spectrum pump waves. For quasimonochromatic waves the correction to the growth rate depends only on the spectral index of the phase function. copyright 1996 American Institute of Physics

Large amplitude ion-acoustic solitons in dusty plasmas

International Nuclear Information System (INIS)

Tiwari, R. S.; Jain, S. L.; Mishra, M. K.

2011-01-01

Characteristics of ion-acoustic soliton in dusty plasma, including the dynamics of heavily charged massive dust grains, are investigated following the Sagdeev Potential formalism. Retaining fourth order nonlinearities of electric potential in the expansion of the Sagdeev Potential in the energy equation for a pseudo particle and integrating the resulting energy equation, large amplitude soliton solution is determined. Variation of amplitude (A), half width (W) at half maxima and the product P = AW 2 of the Korteweg-deVries (KdV), dressed and large amplitude soliton as a function of wide range of dust concentration are numerically studied for recently observed parameters of dusty plasmas. We have also presented the region of existence of large amplitude ion-acoustic soliton in the dusty plasma by analyzing the structure of the pseudo potential. It is found that in the presence of positively charged dust grains, system supports only compressive solitons, on the other hand, in the presence of negatively charged dust grains, the system supports compressive solitons up to certain critical concentration of dust grains and above this critical concentration, the system can support rarefactive solitons also. The effects of dust concentration, charge, and mass of the dust grains, on the characteristics of KdV, dressed and large amplitude the soliton, i.e., amplitude (A), half width at half maxima (W), and product of amplitude (A) and half width at half maxima (P = AW 2 ), are discussed in detail

Investigating the amplitude of interactive footstep sounds and soundscape reproduction

DEFF Research Database (Denmark)

Turchet, Luca; Serafin, Stefania

2013-01-01

In this paper, we study the perception of amplitude of soundscapes and interactively generated footstep sounds provided both through headphones and a surround sound system. In particular, we investigate whether there exists a value for the amplitude of soundscapes and footstep sounds which...... of soundscapes does not significantly affect the selected amplitude of footstep sounds. Similarly, the perception of the soundscapes amplitude is not significantly affected by the selected amplitude of footstep sounds....

The focusing effect of P-wave in the Moon's and Earth's low-velocity core. Analytical solution

Science.gov (United States)

Fatyanov, A. G.; Burmin, V. Yu

2018-04-01

The important aspect in the study of the structure of the interiors of planets is the question of the presence and state of core inside them. While for the Earth this task was solved long ago, the question of whether the core of the Moon is in a liquid or solid state up to the present is debatable up to present. If the core of the Moon is liquid, then the velocity of longitudinal waves in it should be lower than in the surrounding mantle. If the core is solid, then most likely, the velocity of longitudinal waves in it is higher than in the mantle. Numerical calculations of the wave field allow us to identify the criteria for drawing conclusions about the state of the lunar core. In this paper we consider the problem of constructing an analytical solution for wave fields in a layered sphere of arbitrary radius. A stable analytic solution is obtained for the wave fields of longitudinal waves in a three-layer sphere. Calculations of the total wave fields and rays for simplified models of the Earth and the Moon with real parameters are presented. The analytical solution and the ray pattern showed that the low-velocity cores of the Earth and the Moon possess the properties of a collecting lens. This leads to the emergence of a wave field focusing area. As a result, focused waves of considerable amplitude appear on the surface of the Earth and the Moon. In the Earth case, they appear before the first PKP-wave arrival. These are so-called "precursors", which continue in the subsequent arrivals of waves. At the same time, for the simplified model of the Earth, the maximum amplitude growth is observed in the 147-degree region. For the Moon model, the maximum amplitude growth is around 180°.

Reconstruction of far-field tsunami amplitude distributions from earthquake sources

Science.gov (United States)

Geist, Eric L.; Parsons, Thomas E.

2016-01-01

The probability distribution of far-field tsunami amplitudes is explained in relation to the distribution of seismic moment at subduction zones. Tsunami amplitude distributions at tide gauge stations follow a similar functional form, well described by a tapered Pareto distribution that is parameterized by a power-law exponent and a corner amplitude. Distribution parameters are first established for eight tide gauge stations in the Pacific, using maximum likelihood estimation. A procedure is then developed to reconstruct the tsunami amplitude distribution that consists of four steps: (1) define the distribution of seismic moment at subduction zones; (2) establish a source-station scaling relation from regression analysis; (3) transform the seismic moment distribution to a tsunami amplitude distribution for each subduction zone; and (4) mix the transformed distribution for all subduction zones to an aggregate tsunami amplitude distribution specific to the tide gauge station. The tsunami amplitude distribution is adequately reconstructed for four tide gauge stations using globally constant seismic moment distribution parameters established in previous studies. In comparisons to empirical tsunami amplitude distributions from maximum likelihood estimation, the reconstructed distributions consistently exhibit higher corner amplitude values, implying that in most cases, the empirical catalogs are too short to include the largest amplitudes. Because the reconstructed distribution is based on a catalog of earthquakes that is much larger than the tsunami catalog, it is less susceptible to the effects of record-breaking events and more indicative of the actual distribution of tsunami amplitudes.

Examining the time dependence of DAMA's modulation amplitude

Science.gov (United States)

Kelso, Chris; Savage, Christopher; Sandick, Pearl; Freese, Katherine; Gondolo, Paolo

2018-03-01

If dark matter is composed of weakly interacting particles, Earth's orbital motion may induce a small annual variation in the rate at which these particles interact in a terrestrial detector. The DAMA collaboration has identified at a 9.3σ confidence level such an annual modulation in their event rate over two detector iterations, DAMA/NaI and DAMA/LIBRA, each with ˜ 7 years of observations. This data is well fit by a constant modulation amplitude for the two iterations of the experiment. We statistically examine the time dependence of the modulation amplitudes, which "by eye" appear to be decreasing with time in certain energy ranges. We perform a chi-squared goodness of fit test of the average modulation amplitudes measured by the two detector iterations which rejects the hypothesis of a consistent modulation amplitude at greater than 80, 96, and 99.6% for the 2-4, 2-5 and 2-6 keVee energy ranges, respectively. We also find that among the 14 annual cycles there are three ≳ 3σ departures from the average in our estimated data in the 5-6 keVee energy range. In addition, we examined several phenomenological models for the time dependence of the modulation amplitude. Using a maximum likelihood test, we find that descriptions of the modulation amplitude as decreasing with time are preferred over a constant modulation amplitude at anywhere between 1σ and 3σ , depending on the phenomenological model for the time dependence and the signal energy range considered. A time dependent modulation amplitude is not expected for a dark matter signal, at least for dark matter halo morphologies consistent with the DAMA signal. New data from DAMA/LIBRA-phase2 will certainly aid in determining whether any apparent time dependence is a real effect or a statistical fluctuation.

Transversity Amplitudes in Hypercharge Exchange Processes; Amplitudes de transversidad en procesos de intercambio de hipercarga

Energy Technology Data Exchange (ETDEWEB)

Aguilar Benitez de Lugo, M.

1979-07-01

In this work we present several techniques developed for the extraction of the. Transversity amplitudes governing quasi two-body meson baryon reactions with hypercharge exchange. We review the methods used In processes having a pure spin configuration, as well as the more relevant results obtained with data from K{sup p} and Tp interactions at intermediate energies. The predictions of the additive quark model and the ones following from exchange degeneracy and etoxicity are discussed. We present a formalism for amplitude analysis developed for reactions with mixed spin configurations and discuss the methods of parametric estimation of the moduli and phases of.the amplitudes, as well as the various tests employed to check the goodness of the fits. The calculation of the generalized joint density matrices is given and we propose a method based on the generalization of the idea of multipole moments, which allows to investigate the structure of the decay angular correlations and establishes the quality of the fits and the validity of the simplifying assumptions currently used in this type of studies. (Author) 43 refs.

On the singularities of massive superstring amplitudes

NARCIS (Netherlands)

Foda, O.

1987-01-01

Superstring one-loop amplitudes with massive external states are shown to be in general ill-defined due to internal on-shell propagators. However, we argue that since any massive string state (in the uncompactified theory) has a finite lifetime to decay into massless particles, such amplitudes are

Connected formulas for amplitudes in standard model

Energy Technology Data Exchange (ETDEWEB)

He, Song [CAS Key Laboratory of Theoretical Physics,Institute of Theoretical Physics, Chinese Academy of Sciences,Beijing 100190 (China); School of Physical Sciences, University of Chinese Academy of Sciences,No. 19A Yuquan Road, Beijing 100049 (China); Zhang, Yong [Department of Physics, Beijing Normal University,Beijing 100875 (China); CAS Key Laboratory of Theoretical Physics,Institute of Theoretical Physics, Chinese Academy of Sciences,Beijing 100190 (China)

2017-03-17

Witten’s twistor string theory has led to new representations of S-matrix in massless QFT as a single object, including Cachazo-He-Yuan formulas in general and connected formulas in four dimensions. As a first step towards more realistic processes of the standard model, we extend the construction to QCD tree amplitudes with massless quarks and those with a Higgs boson. For both cases, we find connected formulas in four dimensions for all multiplicities which are very similar to the one for Yang-Mills amplitudes. The formula for quark-gluon color-ordered amplitudes differs from the pure-gluon case only by a Jacobian factor that depends on flavors and orderings of the quarks. In the formula for Higgs plus multi-parton amplitudes, the massive Higgs boson is effectively described by two additional massless legs which do not appear in the Parke-Taylor factor. The latter also represents the first twistor-string/connected formula for form factors.

Analytic Solutions and Resonant Solutions of Hyperbolic Partial Differential Equations

Science.gov (United States)

Wagenmaker, Timothy Roger

This dissertation contains two main subject areas. The first deals with solutions to the wave equation Du/Dt + a Du/Dx = 0, where D/Dt and D/Dx represent partial derivatives and a(t,x) is real valued. The question I studied, which arises in control theory, is whether solutions which are real analytic with respect to the time variable are dense in the space of all solutions. If a is real analytic in t and x, the Cauchy-Kovalevsky Theorem implies that the solutions real analytic in t and x are dense, since it suffices to approximate the initial data by polynomials. The same positive result is valid when a is continuously differentiable and independent of t. This is proved by regularization in time. The hypothesis that a is independent of t cannot be replaced by the weaker assumption that a is real analytic in t, even when it is infinitely smooth. I construct a(t,x) for which the solutions which are analytic in time are automatically periodic in time. In particular these solutions are not dense in the space of all solutions. The second area concerns the resonant interaction of oscillatory waves propagating in a compressible inviscid fluid. An asymptotic description given by Andrew Majda, Rodolfo Rosales, and Maria Schonbek (MRS) involves the genuinely nonlinear quasilinear hyperbolic system Du/Dt + D(uu/2)/Dt + v = 0, Dv/Dt - D(vv/2)/Dt - u = 0. They performed many numerical simulations which indicated that small amplitude solutions of this system tend to evade shock formation, and conjectured that "smooth initial data with a sufficiently small amplitude never develop shocks throughout a long time interval of integration.". I proved that for smooth periodic U(x), V(x) and initial data u(0,x) = epsilonU(x), v(0,x) = epsilonV(x), the solution is smooth for time at least constant times | ln epsilon| /epsilon. This is longer than the lifetime order 1/ epsilon of the solution to the decoupled Burgers equations. The decoupled equation describes nonresonant interaction of

Analysis of correlation between full-waveform metrics, scan geometry and land-cover: an application over forests

Directory of Open Access Journals (Sweden)

F. Pirotti

2013-10-01

Full Text Available For a correct use of metrics derived from processing of the full-waveform return signal from airborne laser scanner sensors any correlation which is not related to properties of the reflecting target must be known and, if possible, removed. In the following article we report on an analysis of correlation between several metrics extracted from the full-waveform return signal and scan characteristics (mainly range and type of land-cover (urban, grasslands, forests. The metrics taken in consideration are the amplitude, normalized amplitude, width (full width at half maximum, asymmetry indicators, left and right energy content, and the cross-section calculated from width and normalized amplitude considering the range effect. The results show that scan geometry in this case does not have a significant impact scans over forest cover, except for range affecting amplitude and width distribution. Over complex targets such as vegetation canopy, other factors such as incidence angle have little meaning, therefore corrections of range effect are the most meaningful. A strong correlation with the type of land-cover is also shown by the distribution of the values of the metrics in the different areas taken in consideration.

The role of pulse shape in motor cortex transcranial magnetic stimulation using full-sine stimuli.

Directory of Open Access Journals (Sweden)

Igor Delvendahl

Full Text Available A full-sine (biphasic pulse waveform is most commonly used for repetitive transcranial magnetic stimulation (TMS, but little is known about how variations in duration or amplitude of distinct pulse segments influence the effectiveness of a single TMS pulse to elicit a corticomotor response. Using a novel TMS device, we systematically varied the configuration of full-sine pulses to assess the impact of configuration changes on resting motor threshold (RMT as measure of stimulation effectiveness with single-pulse TMS of the non-dominant motor hand area (M1. In young healthy volunteers, we (i compared monophasic, half-sine, and full-sine pulses, (ii applied two-segment pulses consisting of two identical half-sines, and (iii manipulated amplitude, duration, and current direction of the first or second full-sine pulse half-segments. RMT was significantly higher using half-sine or monophasic pulses compared with full-sine. Pulses combining two half-sines of identical polarity and duration were also characterized by higher RMT than full-sine stimuli resulting. For full-sine stimuli, decreasing the amplitude of the half-segment inducing posterior-anterior oriented current in M1 resulted in considerably higher RMT, whereas varying the amplitude of the half-segment inducing anterior-posterior current had a smaller effect. These findings provide direct experimental evidence that the pulse segment inducing a posterior-anterior directed current in M1 contributes most to corticospinal pathway excitation. Preferential excitation of neuronal target cells in the posterior-anterior segment or targeting of different neuronal structures by the two half-segments can explain this result. Thus, our findings help understanding the mechanisms of neural stimulation by full-sine TMS.

Numerical evaluation of one-loop QCD amplitudes

DEFF Research Database (Denmark)

Badger, Simon David; Biedermann, Benedikt; Uwer, Peter

2012-01-01

We present the publicly available program NGluon allowing the numerical evaluation of primitive amplitudes at one-loop order in massless QCD. The program allows the computation of one-loop amplitudes for an arbitrary number of gluons. The focus of the present article is the extension to one-loop ...

An Empirical Study of Atmospheric Correction Procedures for Regional Infrasound Amplitudes with Ground Truth.

Science.gov (United States)

Howard, J. E.

2014-12-01

This study focusses on improving methods of accounting for atmospheric effects on infrasound amplitudes observed on arrays at regional distances in the southwestern United States. Recordings at ranges of 150 to nearly 300 km from a repeating ground truth source of small HE explosions are used. The explosions range in actual weight from approximately 2000-4000 lbs. and are detonated year-round which provides signals for a wide range of atmospheric conditions. Three methods of correcting the observed amplitudes for atmospheric effects are investigated with the data set. The first corrects amplitudes for upper stratospheric wind as developed by Mutschlecner and Whitaker (1999) and uses the average wind speed between 45-55 km altitudes in the direction of propagation to derive an empirical correction formula. This approach was developed using large chemical and nuclear explosions and is tested with the smaller explosions for which shorter wavelengths cause the energy to be scattered by the smaller scale structure of the atmosphere. The second approach isa semi-empirical method using ray tracing to determine wind speed at ray turning heights where the wind estimates replace the wind values in the existing formula. Finally, parabolic equation (PE) modeling is used to predict the amplitudes at the arrays at 1 Hz. The PE amplitudes are compared to the observed amplitudes with a narrow band filter centered at 1 Hz. An analysis is performed of the conditions under which the empirical and semi-empirical methods fail and full wave methods must be used.

Backward wave oscillators with rippled wall resonators: Analytic theory and numerical simulation

International Nuclear Information System (INIS)

Swegle, J.A.; Poukey, J.W.

1985-01-01

The 3-D analytic theory is based on the approximation that the device is infinitely long. In the absence of an electron beam, the theory is exact and allows us to compute the dispersion characteristics of the cold structure. With the inclusion of a thin electron beam, we can compute the growth rates resulting from the interaction between a waveguide mode of the structure and the slower space charge wave on the beam. In the limit of low beam currents, the full dispersion relation based on an electromagnetic analysis can be placed in correspondence with the circuit theory of Pierce. Numerical simulations permit us to explore the saturated, large amplitude operating regime for TM axisymmetric modes. The scaling of operating frequency, peak power, and operating efficiency with beam and resonator parameters is examined. The analytic theory indicates that growth rates are largest for the TM 01 modes and decrease with both the radial and azimuthal mode numbers. Another interesting trend is that for a fixed cathode voltage and slow wave structure, growth rates peak for a beam current below the space charge limiting value and decrease for both larger and smaller currents. The simulations show waves that grow from noise without any input signal, so that the system functions as an oscillator. The TM 01 mode predominates in all simulations. While a minimum device length is required for the start of oscillations, it appears that if the slow wave structure is too long, output power is decreased by a transfer of wave energy back to the electrons. Comparisons have been made between the analytical and numerical results, as well as with experimental data obtained at Sandia National Laboratories

Phase and amplitude control system for Stanford Linear Accelerator

International Nuclear Information System (INIS)

Yoo, S.J.

1983-01-01

The computer controlled phase and amplitude detection system measures the instantaneous phase and amplitude of a 1 micro-second 2856 MHz rf pulse at a 180 Hz rate. This will be used for phase feedback control, and also for phase and amplitude jitter measurement. The program, which was originally written by John Fox and Keith Jobe, has been modified to improve the function of the system. The software algorithms used in the measurement are described, as is the performance of the prototype phase and amplitude detector system

Relativistic amplitudes in terms of wave functions

International Nuclear Information System (INIS)

Karmanov, V.A.

1978-01-01

In the framework of the invariant diagram technique which arises at the formulation of the fueld theory on the light front the question about conditions at which the relativistic amplitudes may be expressed through the wave functions is investigated. The amplitudes obtained depend on four-vector ω, determining the light front surface. The way is shown to find such values of the four-vector ω, at which the contribution of diagrams not expressed through wave functions is minimal. The investigation carried out is equivalent to the study of the dependence of amplitudes of the old-fashioned perturbation theory in the in the infinite momentum frame on direction of the infinite momentum

Multifrequency excitation of a clamped–clamped microbeam: Analytical and experimental investigation

KAUST Repository

Jaber, Nizar

2016-03-14

Using partial electrodes and a multifrequency electrical source, we present a large-bandwidth, large-amplitude clamped–clamped microbeam resonator excited near the higher order modes of vibration. We analytically and experimentally investigate the nonlinear dynamics of the microbeam under a two-source harmonic excitation. The first-frequency source is swept around the first three modes of vibration, whereas the second source frequency remains fixed. New additive and subtractive resonances are demonstrated. We illustrated that by properly tuning the frequency and amplitude of the excitation force, the frequency bandwidth of the resonator is controlled. The microbeam is fabricated using polyimide as a structural layer coated with nickel from the top and chromium and gold layers from the bottom. Using the Galerkin method, a reduced order model is derived to simulate the static and dynamic response of the device. A good agreement between the theoretical and experimental data are reported.

Multifrequency excitation of a clamped–clamped microbeam: Analytical and experimental investigation

KAUST Repository

Jaber, Nizar; Ramini, Abdallah; Younis, Mohammad I.

2016-01-01

Using partial electrodes and a multifrequency electrical source, we present a large-bandwidth, large-amplitude clamped–clamped microbeam resonator excited near the higher order modes of vibration. We analytically and experimentally investigate the nonlinear dynamics of the microbeam under a two-source harmonic excitation. The first-frequency source is swept around the first three modes of vibration, whereas the second source frequency remains fixed. New additive and subtractive resonances are demonstrated. We illustrated that by properly tuning the frequency and amplitude of the excitation force, the frequency bandwidth of the resonator is controlled. The microbeam is fabricated using polyimide as a structural layer coated with nickel from the top and chromium and gold layers from the bottom. Using the Galerkin method, a reduced order model is derived to simulate the static and dynamic response of the device. A good agreement between the theoretical and experimental data are reported.

Finite Amplitude Ocean Waves

Indian Academy of Sciences (India)

IAS Admin

wavelength, they are called shallow water waves. In the ... Deep and intermediate water waves are dispersive as the velocity of these depends on wavelength. This is not the ..... generation processes, the finite amplitude wave theories are very ...

Experimental Study on Variable-Amplitude Fatigue of Welded Cross Plate-Hollow Sphere Joints in Grid Structures

Directory of Open Access Journals (Sweden)

Jin-Feng Jiao

2018-01-01

Full Text Available The fatigue stress amplitude of the welded cross plate-hollow sphere joint (WCPHSJ in a grid structure varies due to the random loading produced by suspending cranes. A total of 14 specimens considering three different types of WCPHSJs were prepared and tested using a specially designed test rig. Four typical loading conditions, “low-high,” “high-low,” “low-high-low,” and “high-low-high,” were first considered in the tests to investigate the fatigue behavior under variable load amplitudes, followed by metallographic analyses. The experimental and metallographic analysis results provide a fundamental understanding on the fatigue fracture form and fatigue mechanism of WCPHSJs. Based on the available data from constant-amplitude fatigue tests, the variable-amplitude fatigue life of the three types of WCPHSJs was estimated using the Miner rule and Corten-Dolan theory. Since both accumulative damage theories yield virtually same damaging results, the Miner rule is hence suggested to estimate the fatigue life of WCPHSJs.

Operator product expansion on the lattice: analytic Wilson coefficients

Science.gov (United States)

Perlt, Holger

2006-12-01

We present first results for Wilson coefficients of operators up to first order in the covariant deriva- tives for the case of Wilson fermions. They are derived from the off-shell Compton scattering amplitude Wµν (a, p, q) of massless quarks with momentum p. The Wilson coefficients are clas- sified according to the transformation of the corresponding operators under the hypercubic group H(4). We give selected examples for a special choice of the momentum transfer q. All Wil- son coefficients are given in closed analytic form and in an expansion in powers of a up to first corrections.

ON MEASURING AMPLITUDES AND PERIODS OF PHYSICAL PENDULUM MICRO-SWINGS WITH ROLLING-CONTACT BEARING

Directory of Open Access Journals (Sweden)

N. N. Riznookaya

2011-01-01

Full Text Available The paper considers a method and an instrument for measuring amplitudes and  periods of physical pendulum oscillations with rolling-contact bearing in the regime of micro-swings when the oscillation amplitude is significantly less of an elastic contact angle. It has been established that the main factors limiting a measuring accuracy are noises of the measuring circuit, base vibration and analog-digital conversion. A new measuring methodology based on original algorithms of data processing and application of the well-known methods for statistic processing of a measuring signal is  proposed in the paper. The paper contains error estimations for measuring oscillation amplitudes justified by discreteness of a signal conversion in a photoelectric receptor and also by the influence of measuring circuit noise. The paper reveals that the applied methodologies make it possible to ensure measuring of amplitudes with an error of 0.2 second of arc and measuring of a period with an error of 10–4 s. The original measuring instrument including mechanical and optical devices and also an electric circuit of optical-to-electrical measuring signal conversion is described in the paper. 

Light Meson Distribution Amplitudes

CERN Document Server

Arthur, R.; Brommel, D.; Donnellan, M.A.; Flynn, J.M.; Juttner, A.; de Lima, H.Pedroso; Rae, T.D.; Sachrajda, C.T.; Samways, B.

2010-01-01

We calculated the first two moments of the light-cone distribution amplitudes for the pseudoscalar mesons ($\\pi$ and $K$) and the longitudinally polarised vector mesons ($\\rho$, $K^*$ and $\\phi$) as part of the UKQCD and RBC collaborations' $N_f=2+1$ domain-wall fermion phenomenology programme. These quantities were obtained with a good precision and, in particular, the expected effects of $SU(3)$-flavour symmetry breaking were observed. Operators were renormalised non-perturbatively and extrapolations to the physical point were made, guided by leading order chiral perturbation theory. The main results presented are for two volumes, $16^3\\times 32$ and $24^3\\times 64$, with a common lattice spacing. Preliminary results for a lattice with a finer lattice spacing, $32^3\\times64$, are discussed and a first look is taken at the use of twisted boundary conditions to extract distribution amplitudes.

Automated force controller for amplitude modulation atomic force microscopy

Energy Technology Data Exchange (ETDEWEB)

Miyagi, Atsushi, E-mail: atsushi.miyagi@inserm.fr, E-mail: simon.scheuring@inserm.fr; Scheuring, Simon, E-mail: atsushi.miyagi@inserm.fr, E-mail: simon.scheuring@inserm.fr [U1006 INSERM, Université Aix-Marseille, Parc Scientifique et Technologique de Luminy, 163 Avenue de Luminy, 13009 Marseille (France)

2016-05-15

Atomic Force Microscopy (AFM) is widely used in physics, chemistry, and biology to analyze the topography of a sample at nanometer resolution. Controlling precisely the force applied by the AFM tip to the sample is a prerequisite for faithful and reproducible imaging. In amplitude modulation (oscillating) mode AFM, the applied force depends on the free and the setpoint amplitudes of the cantilever oscillation. Therefore, for keeping the applied force constant, not only the setpoint amplitude but also the free amplitude must be kept constant. While the AFM user defines the setpoint amplitude, the free amplitude is typically subject to uncontrollable drift, and hence, unfortunately, the real applied force is permanently drifting during an experiment. This is particularly harmful in biological sciences where increased force destroys the soft biological matter. Here, we have developed a strategy and an electronic circuit that analyzes permanently the free amplitude of oscillation and readjusts the excitation to maintain the free amplitude constant. As a consequence, the real applied force is permanently and automatically controlled with picoNewton precision. With this circuit associated to a high-speed AFM, we illustrate the power of the development through imaging over long-duration and at various forces. The development is applicable for all AFMs and will widen the applicability of AFM to a larger range of samples and to a larger range of (non-specialist) users. Furthermore, from controlled force imaging experiments, the interaction strength between biomolecules can be analyzed.

Calculation and modular properties of multiloop superstring amplitudes

International Nuclear Information System (INIS)

Danilov, G. S.

2013-01-01

Multiloop superstring amplitudes are calculated within an extensively used gauge where the two-dimensional gravitino field carries Grassmann moduli. In general, the amplitudes possess, instead of modular symmetry, symmetry with respect to modular transformation supplemented with appropriate transformations of two-dimensional local supersymmetry. If the number of loops is larger than three, the integrationmeasures are notmodular forms, while the expression for the amplitude contains integrals along the boundary of the fundamental region of the modular group.

On the computation of the demagnetization tensor for uniformly magnetized particles of arbitrary shape. Part I: Analytical approach

International Nuclear Information System (INIS)

Tandon, S.; Beleggia, M.; Zhu, Y.; De Graef, M.

2004-01-01

A Fourier space formalism based on the shape amplitude of a particle is used to compute the demagnetization tensor field for uniformly magnetized particles of arbitrary shape. We provide a list of explicit shape amplitudes for important particle shapes, among others: the sphere, the cylindrical tube, an arbitrary polyhedral shape, a truncated paraboloid, and a cone truncated by a spherical cap. In Part I of this two-part paper, an analytical representation of the demagnetization tensor field for particles with cylindrical symmetry is provided, as well as expressions for the magnetostatic energy and the volumetric demagnetization factors

Effects of amplitude modulation on perception of wind turbine noise

Energy Technology Data Exchange (ETDEWEB)

Yoon, Ki Seop; Lee, Soo Gab; Gwak, Doo Young [Dept. of Mechanical and Aerospace Engineering, Seoul National University, Seoul (Korea, Republic of); Seong, Yeol Wan [Ammunition Engineering Team, Defense Agency for Technology and Quality, Daejeon (Korea, Republic of); Lee, Seung Hoon [Aerodynamics Research Team, Korea Aerospace Research Institute, Daejeon (Korea, Republic of); Hong, Ji Young [Transportation Environmental Research Team, Green Transport and Logistics Institute, Korea Railroad Research Institute, Uiwang (Korea, Republic of)

2016-10-15

Wind turbine noise is considered to be easily detectable and highly annoying at relatively lower sound levels than other noise sources. Many previous studies attributed this characteristic to amplitude modulation. However, it is unclear whether amplitude modulation is the main cause of these properties of wind turbine noise. Therefore, the aim of the current study is to identify the relationship between amplitude modulation and these two properties of wind turbine noise. For this investigation, two experiments were conducted. In the first experiment, 12 participants determined the detection thresholds of six target sounds in the presence of background noise. In the second experiment, 12 participants matched the loudness of modified sounds without amplitude modulation to that of target sounds with amplitude modulation. The results showed that the detection threshold was lowered as the modulation depth increased; additionally, sounds with amplitude modulation had higher subjective loudness than those without amplitude modulation.

Effects of amplitude modulation on perception of wind turbine noise

International Nuclear Information System (INIS)

Yoon, Ki Seop; Lee, Soo Gab; Gwak, Doo Young; Seong, Yeol Wan; Lee, Seung Hoon; Hong, Ji Young

2016-01-01

Wind turbine noise is considered to be easily detectable and highly annoying at relatively lower sound levels than other noise sources. Many previous studies attributed this characteristic to amplitude modulation. However, it is unclear whether amplitude modulation is the main cause of these properties of wind turbine noise. Therefore, the aim of the current study is to identify the relationship between amplitude modulation and these two properties of wind turbine noise. For this investigation, two experiments were conducted. In the first experiment, 12 participants determined the detection thresholds of six target sounds in the presence of background noise. In the second experiment, 12 participants matched the loudness of modified sounds without amplitude modulation to that of target sounds with amplitude modulation. The results showed that the detection threshold was lowered as the modulation depth increased; additionally, sounds with amplitude modulation had higher subjective loudness than those without amplitude modulation

Collinear and Regge behavior of 2{yields}4 MHV amplitude in N=4 super Yang-Mills theory

Energy Technology Data Exchange (ETDEWEB)

Bartels, J.; Prygarin, A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Lipatov, L.N. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; St. Petersburg Nuclear Physics Institute (Russian Federation)

2011-04-15

We investigate the collinear and Regge behavior of the 2{yields}4 MHV amplitude in N=4 super Yang-Mills theory in the BFKL approach. The expression for the remainder function in the collinear kinematics proposed by Alday, Gaiotto, Maldacena, Sever and Vieira is analytically continued to the Mandelstam region. The result of the continuation in the Regge kinematics shows an agreement with the BFKL approach up to to five-loop level. We present the Regge theory interpretation of the obtained results and discuss some issues related to a possible nonmultiplicative renormalization of the remainder function in the collinear limit. (orig.)

Conformal amplitude hierarchy and the Poincaré disk

Science.gov (United States)

Shimada, Hirohiko

2018-02-01

The amplitude for the singlet channels in the 4-point function of the fundamental field in the conformal field theory of the 2d O(n) model is studied as a function of n. For a generic value of n, the 4-point function has infinitely many amplitudes, whose landscape can be very spiky as the higher amplitude changes its sign many times at the simple poles, which generalize the unique pole of the energy operator amplitude at n = 0. In the stadard parameterization of n by angle in unit of π, we find that the zeros and poles happen at the rational angles, forming a hierarchical tree structure inherent in the Poincaré disk. Some relation between the amplitude and the Farey path, a piecewise geodesic that visits these zeros and poles, is suggested. In this hierarchy, the symmetry of the congruence subgroup Γ(2) of SL(2, ℤ) naturally arises from the two clearly distinct even/odd classes of the rational angles, in which one respectively gets the truncated operator algebras and the logarithmic 4-point functions.

Measurement of the amplitude and phase transfer functions of an optical modulator using a heterodyne technique

DEFF Research Database (Denmark)

Romstad, Francis Pascal; Birkedal, Dan; Mørk, Jesper

2001-01-01

We present a new technique that measures the full amplitude and phase transfer curves of the modulator as a function of the applied bias, from which the small signal α-parameter can be calculated. The technique measures the amplitude and phase transfer functions simultaneously and directly......, compared to techniques where a time-consuming data analysis is necessary to calculate the a-parameter and an additional measurement is necessary to estimate the phase. Additionally, the chirp profile for all operation points can be calculated....

Topological amplitudes in string theory

International Nuclear Information System (INIS)

Antoniadis, I.; Taylor, T.R.

1993-07-01

We show that certain type II string amplitudes at genus g are given by the topological partition F g discussed recently by Bershadsky, Cecotti, Ooguri and Vafa. These amplitudes give rise to a term in the four-dimensional effective action of the form Σ g F g W 2g , where W is the chiral superfield of N = 2 supergravitational multiplet. The holomorphic anomaly of F g is related to non-localities of the effective action due to the propagation of massless states. This result generalizes the holomorphic anomaly of the one loop case which is known to lead to non-harmonic gravitational couplings. (author). 22 refs, 2 figs

Mapping Pn amplitude spreading and attenuation in Asia

Energy Technology Data Exchange (ETDEWEB)

Yang, Xiaoning [Los Alamos National Laboratory; Phillips, William S [Los Alamos National Laboratory; Stead, Richard J [Los Alamos National Laboratory

2010-12-06

Pn travels most of its path in the mantle lid. Mapping the lateral variation of Pn amplitude attenuation sheds light on material properties and dynamics of the uppermost region of the mantle. Pn amplitude variation depends on the wavefront geometric spreading as well as material attenuation. We investigated Pn geometric spreading, which is much more complex than a traditionally assumed power-law spreading model, using both synthetic and observed amplitude data collected in Asia. We derived a new Pn spreading model based on the formulation that was proposed previously to account for the spherical shape of the Earth (Yang et. al., BSSA, 2007). New parameters derived for the spreading model provide much better correction for Pn amplitudes in terms of residual behavior. Because we used observed Pn amplitudes to construct the model, the model incorporates not only the effect of the Earth's spherical shape, but also the effect of potential upper-mantle velocity gradients in the region. Using the new spreading model, we corrected Pn amplitudes measured at 1, 2, 4 and 6 Hz and conducted attenuation tomography. The resulting Pn attenuation model correlates well with the regional geology. We see high attenuation in regions such as northern Tibetan Plateau and the western Pacific subduction zone, and low attenuation for stable blocks such as Sichuan and Tarim basins.

Effects of magnesium sulphate on amplitude-integrated continuous EEG in asphyxiated term neonates

NARCIS (Netherlands)

Groenendaal, F; Rademaker, CMA; Toet, MC; de Vries, LS

2002-01-01

In this study it is hypothesized that magnesium sulphate in asphyxiated full-term neonates could lead to a gradual improvement in background pattern of the amplitude integrated EEG (aEEG), an early marker of hypoxic-ischaemic brain injury. In a double-blind, randomized, controlled pilot study of 22

Simplicity in the structure of QED and gravity amplitudes

Energy Technology Data Exchange (ETDEWEB)

Badger, Simon [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Bjerrum-Bohr, N.E.J. [Institute for Advanced Study, Princeton, NJ (United States). School of Natural Sciences; Vanhove, Pierre [Institut des Hautes Etudes Scientifiques IHES, Bures sur Yvette (France); CEA, IPhT, CNRS, URA, Gif-sur-Yvette, (France). Inst. de Physique Theorique

2008-11-15

We investigate generic properties of one-loop amplitudes in unordered gauge theories in four dimensions. For such theories the organisation of amplitudes in manifestly crossing symmetric expressions poses restrictions on their structure and results in remarkable cancellations. We show that one-loop multi-photon amplitudes in QED with at least eight external photons are given only by scalar box integral functions. This QED 'no-triangle' property is true for all helicity configurations and has similarities to the 'notriangle' property found in the case of maximal N=8 supergravity. Results are derived both via a world-line formalism as well as using on-shell unitarity methods. We show that the simple structure of the loop amplitude originates from the extremely good BCFW scaling behaviour of the QED tree-amplitude. (orig.)

Simplicity in the structure of QED and gravity amplitudes

International Nuclear Information System (INIS)

Badger, Simon; Bjerrum-Bohr, N.E.J.; Vanhove, Pierre; CEA, IPhT, CNRS, URA, Gif-sur-Yvette,

2008-11-01

We investigate generic properties of one-loop amplitudes in unordered gauge theories in four dimensions. For such theories the organisation of amplitudes in manifestly crossing symmetric expressions poses restrictions on their structure and results in remarkable cancellations. We show that one-loop multi-photon amplitudes in QED with at least eight external photons are given only by scalar box integral functions. This QED 'no-triangle' property is true for all helicity configurations and has similarities to the 'notriangle' property found in the case of maximal N=8 supergravity. Results are derived both via a world-line formalism as well as using on-shell unitarity methods. We show that the simple structure of the loop amplitude originates from the extremely good BCFW scaling behaviour of the QED tree-amplitude. (orig.)

H-reflex amplitude depression as a marker of presynaptic inhibition in Painful Diabetic Neuropathy (PDN.

Directory of Open Access Journals (Sweden)

Ahmad Asmedi

2016-02-01

Full Text Available ABSTRACT Painful Diabetic Neuropathy (PDN is a common complication of diabetes mellitus (DM. Disruption in presynaptic inhibition in dorsal horn of the spinal cord has been proposed as one of the pathomechanism of PDN. Previous research showed that presynaptic inhibition can be detected by H-reflex examination. The aim of this study was to know whether the reduction of presynaptic inhibition in spinal dorsal horn of PDN patients really exist, and detectable by H-reflex examination. It was cohort prospective involving 141 (58 men, 83 women patients with DM and impaired glucose tolerance (IGT between the ages of 40 and 61 years from several health facilities in Yogyakarta. All patients underwent clinical, laboratory and electrodiagnostic examination. Demographic, clinical and electrodiagnostic data were collected and analyzed. By survival analysis there were 25 new cases of PDN (12.12% cumulative incidence. Using survival Kaplan Meier analysis, the significant hazard ratio for PDN were 12.81 for median motor nerve amplitude, 5.74 for median nerve distal latency, 3.71 for median sensory nerve amplitude, 6.33 for median sensory latency, 3.4 for tibial nerve amplitude, 3.48 for tibial nerve distal latency, 2.29 for sural nerve amplitude, 4.47 for sural nerve latency, 3.99 for H-reflex latency, 5.88 for H-reflex amplitude, and 17.83 for Diabetic Neuropathy (DN status. Using hazard proportional cox analysis, only H amplitude and DN status (DNS score were significantly correlated with PDN (p= 0.026; hazard ratio = 15.450; CI 95%= 1.39 – 171.62 for H amplitude and p= 0.030; hazard ratio = 10.766; CI 95%=1.26 – 92.09 for DN status. This study showed that depression of H-reflex amplitude was correlated with the occurrence of PDN. This result proves that there was presynaptic inhibition process in PDN that manifests as low H-reflex amplitude.

Multi-loop string amplitudes and Riemann surfaces

International Nuclear Information System (INIS)

Taylor, J.G.

1986-01-01

The paper was presented at the workshop on 'Supersymmetry and its applications', Cambridge, United Kingdom, 1985. Super-string theory is discussed under the following topic headings: the functional approach to the string amplitude, Rieman surfaces, the determinants Δsub(epsilon)(1) and Δsub(epsilon)(2), Green's functions, total amplitude, and divergence analysis. (U.K.)

Regional Seismic Amplitude Modeling and Tomography for Earthquake-Explosion Discrimination

Science.gov (United States)

Walter, W. R.; Pasyanos, M. E.; Matzel, E.; Gok, R.; Sweeney, J.; Ford, S. R.; Rodgers, A. J.

2008-12-01

Empirically explosions have been discriminated from natural earthquakes using regional amplitude ratio techniques such as P/S in a variety of frequency bands. We demonstrate that such ratios discriminate nuclear tests from earthquakes using closely located pairs of earthquakes and explosions recorded on common, publicly available stations at test sites around the world (e.g. Nevada, Novaya Zemlya, Semipalatinsk, Lop Nor, India, Pakistan, and North Korea). We are examining if there is any relationship between the observed P/S and the point source variability revealed by longer period full waveform modeling. For example, regional waveform modeling shows strong tectonic release from the May 1998 India test, in contrast with very little tectonic release in the October 2006 North Korea test, but the P/S discrimination behavior appears similar in both events using the limited regional data available. While regional amplitude ratios such as P/S can separate events in close proximity, it is also empirically well known that path effects can greatly distort observed amplitudes and make earthquakes appear very explosion-like. Previously we have shown that the MDAC (Magnitude Distance Amplitude Correction, Walter and Taylor, 2001) technique can account for simple 1-D attenuation and geometrical spreading corrections, as well as magnitude and site effects. However in some regions 1-D path corrections are a poor approximation and we need to develop 2-D path corrections. Here we demonstrate a new 2-D attenuation tomography technique using the MDAC earthquake source model applied to a set of events and stations in both the Middle East and the Yellow Sea Korean Peninsula regions. We believe this new 2-D MDAC tomography has the potential to greatly improve earthquake-explosion discrimination, particularly in tectonically complex regions such as the Middle East.

Particle Distribution Modification by Low Amplitude Modes

International Nuclear Information System (INIS)

White, R.B.; Gorelenkov, N.; Heidbrink, W.W.; Van Zeeland, M.A.

2009-01-01

Modification of a high energy particle distribution by a spectrum of low amplitude modes is investigated using a guiding center code. Only through resonance are modes effective in modifying the distribution. Diagnostics are used to illustrate the mode-particle interaction and to find which effects are relevant in producing significant resonance, including kinetic Poincare plots and plots showing those orbits with time averaged mode-particle energy transfer. Effects of pitch angle scattering and drag are studied, as well as plasma rotation and time dependence of the equilibrium and mode frequencies. A specific example of changes observed in a DIII-D deuterium beam distribution in the presence of low amplitude experimentally validated Toroidal Alfven (TAE) eigenmodes and Reversed Shear Alfven (RSAE) eigenmodes is examined in detail. Comparison with experimental data shows that multiple low amplitude modes can account for significant modification of high energy beam particle distributions. It is found that there is a stochastic threshold for beam profile modification, and that the experimental amplitudes are only slightly above this threshold.

Amplitude chimeras and chimera death in dynamical networks

International Nuclear Information System (INIS)

Zakharova, Anna; Kapeller, Marie; Schöll, Eckehard

2016-01-01

We find chimera states with respect to amplitude dynamics in a network of Stuart- Landau oscillators. These partially coherent and partially incoherent spatio-temporal patterns appear due to the interplay of nonlocal network topology and symmetry-breaking coupling. As the coupling range is increased, the oscillations are quenched, amplitude chimeras disappear and the network enters a symmetry-breaking stationary state. This particular regime is a novel pattern which we call chimera death. It is characterized by the coexistence of spatially coherent and incoherent inhomogeneous steady states and therefore combines the features of chimera state and oscillation death. Additionally, we show two different transition scenarios from amplitude chimera to chimera death. Moreover, for amplitude chimeras we uncover the mechanism of transition towards in-phase synchronized regime and discuss the role of initial conditions. (paper)

Euclidean to Minkowski Bethe-Salpeter amplitude and observables

International Nuclear Information System (INIS)

Carbonell, J.; Frederico, T.; Karmanov, V.A.

2017-01-01

We propose a method to reconstruct the Bethe-Salpeter amplitude in Minkowski space given the Euclidean Bethe-Salpeter amplitude - or alternatively the light-front wave function - as input. The method is based on the numerical inversion of the Nakanishi integral representation and computing the corresponding weight function. This inversion procedure is, in general, rather unstable, and we propose several ways to considerably reduce the instabilities. In terms of the Nakanishi weight function, one can easily compute the BS amplitude, the LF wave function and the electromagnetic form factor. The latter ones are very stable in spite of residual instabilities in the weight function. This procedure allows both, to continue the Euclidean BS solution in the Minkowski space and to obtain a BS amplitude from a LF wave function. (orig.)

Euclidean to Minkowski Bethe-Salpeter amplitude and observables

Energy Technology Data Exchange (ETDEWEB)

Carbonell, J. [Universite Paris-Sud, IN2P3-CNRS, Institut de Physique Nucleaire, Orsay Cedex (France); Frederico, T. [Instituto Tecnologico de Aeronautica, DCTA, Sao Jose dos Campos (Brazil); Karmanov, V.A. [Lebedev Physical Institute, Moscow (Russian Federation)

2017-01-15

We propose a method to reconstruct the Bethe-Salpeter amplitude in Minkowski space given the Euclidean Bethe-Salpeter amplitude - or alternatively the light-front wave function - as input. The method is based on the numerical inversion of the Nakanishi integral representation and computing the corresponding weight function. This inversion procedure is, in general, rather unstable, and we propose several ways to considerably reduce the instabilities. In terms of the Nakanishi weight function, one can easily compute the BS amplitude, the LF wave function and the electromagnetic form factor. The latter ones are very stable in spite of residual instabilities in the weight function. This procedure allows both, to continue the Euclidean BS solution in the Minkowski space and to obtain a BS amplitude from a LF wave function. (orig.)

Impact of non-white noises in pulse amplitude measurements: a time-domain approach

International Nuclear Information System (INIS)

Pullia, A.

1998-01-01

The contribution of the 1/f-noise to the spectral line broadening in pulse amplitude measurements is derived with a time-domain analysis. The known time-domain relationships which provide the contributions of the series and parallel white noises are generalised for the case of 1/f and other typical non-white noises, by using the fractional derivative of either the system impulse response (time-invariant linear filters) or its weight function folded (time-variant linear filters). It is shown that a time-domain approach is also effective to determine the contribution of Lorentzian noises. A simple rule suitable to derive numerically the fractional derivative is given, which permits to calculate the effect of non-white noises even when the filter impulse response is not known analytically but only in sampled form. (orig.)

Bäcklund transformation, analytic soliton solutions and numerical simulation for a (2+1)-dimensional complex Ginzburg-Landau equation in a nonlinear fiber

Science.gov (United States)

Yu, Ming-Xiao; Tian, Bo; Chai, Jun; Yin, Hui-Min; Du, Zhong

2017-10-01

In this paper, we investigate a nonlinear fiber described by a (2+1)-dimensional complex Ginzburg-Landau equation with the chromatic dispersion, optical filtering, nonlinear and linear gain. Bäcklund transformation in the bilinear form is constructed. With the modified bilinear method, analytic soliton solutions are obtained. For the soliton, the amplitude can decrease or increase when the absolute value of the nonlinear or linear gain is enlarged, and the width can be compressed or amplified when the absolute value of the chromatic dispersion or optical filtering is enhanced. We study the stability of the numerical solutions numerically by applying the increasing amplitude, embedding the white noise and adding the Gaussian pulse to the initial values based on the analytic solutions, which shows that the numerical solutions are stable, not influenced by the finite initial perturbations.

Amplitude and Ascoli analysis

International Nuclear Information System (INIS)

Hansen, J.D.

1976-01-01

This article discusses the partial wave analysis of two, three and four meson systems. The difference between the two approaches, referred to as amplitude and Ascoli analysis is discussed. Some of the results obtained with these methods are shown. (B.R.H.)

Algebraic evaluation of rational polynomials in one-loop amplitudes

International Nuclear Information System (INIS)

Binoth, Thomas; Guillet, Jean-Philippe; Heinrich, Gudrun

2007-01-01

One-loop amplitudes are to a large extent determined by their unitarity cuts in four dimensions. We show that the remaining rational terms can be obtained from the ultraviolet behaviour of the amplitude, and determine universal form factors for these rational parts by applying reduction techniques to the Feynman diagrammatic representation of the amplitude. The method is valid for massless and massive internal particles. We illustrate this method by evaluating the rational terms of the one-loop amplitudes for gg→H, γγ→γγ, gg→gg,γγ→ggg and γγ→γγγγ

Proof of the fundamental BCJ relations for QCD amplitudes

International Nuclear Information System (INIS)

Cruz, Leonardo de la; Kniss, Alexander; Weinzierl, Stefan

2015-01-01

The fundamental BCJ-relation is a linear relation between primitive tree amplitudes with different cyclic orderings. The cyclic orderings differ by the insertion place of one gluon. The coefficients of the fundamental BCJ-relation are linear in the Lorentz invariants 2p_ip_j. The BCJ-relations are well established for pure gluonic amplitudes as well as for amplitudes in N=4 super-Yang-Mills theory. Recently, it has been conjectured that the BCJ-relations hold also for QCD amplitudes. In this paper we give a proof of this conjecture. The proof is valid for massless and massive quarks.

Amplitude dependent damping in single crystalline high purity molybdenum

International Nuclear Information System (INIS)

Zelada-Lambri, G.I; Lambri, O.A; Garcia, J.A; Lomer, J.N

2004-01-01

Amplitude dependent damping measurements were performed on high purity single crystalline molybdenum at several different constant temperatures between room temperature and 1273K. The employed samples were single crystals with the orientation, having a residual resistivity ratio of about 8000. Previously to the amplitude dependent damping tests, the samples were subjected to different thermomechanical histories. Amplitude dependent damping effects appear only during the first heating run in temperature where the samples have the thermomechanical state of the deformation process at room temperature. In the subsequent run-ups in temperature, i.e, after subsequent annealings, amplitude dependent damping effects were not detected (au)

Tsunami waves generated by submarine landslides of variable volume: analytical solutions for a basin of variable depth

Directory of Open Access Journals (Sweden)

I. Didenkulova

2010-11-01

Full Text Available Tsunami wave generation by submarine landslides of a variable volume in a basin of variable depth is studied within the shallow-water theory. The problem of landslide induced tsunami wave generation and propagation is studied analytically for two specific convex bottom profiles (h ~ x^4/3 and h ~ x⁴. In these cases the basic equations can be reduced to the constant-coefficient wave equation with the forcing determined by the landslide motion. For certain conditions on the landslide characteristics (speed and volume per unit cross-section the wave field can be described explicitly. It is represented by one forced wave propagating with the speed of the landslide and following its offshore direction, and two free waves propagating in opposite directions with the wave celerity. For the case of a near-resonant motion of the landslide along the power bottom profile h ~ x^γ the dynamics of the waves propagating offshore is studied using the asymptotic approach. If the landslide is moving in the fully resonant regime the explicit formula for the amplitude of the wave can be derived. It is demonstrated that generally tsunami wave amplitude varies non-monotonically with distance.

Nonlinear Vibration of Oscillation Systems using Frequency-Amplitude Formulation

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A. Fereidoon

2012-01-01

Full Text Available In this paper we study the periodic solutions of free vibration of mechanical systems with third and fifth-order nonlinearity for two examples using He's Frequency-Amplitude Formulation (HFAF.The effectiveness and convenience of the method is illustrated in these examples. It will be shown that the solutions obtained with current method have a fabulous conformity with those achieved from time marching solution. HFAF is easy with powerful concepts and the high accuracy, so it can be found widely applicable in vibrations, especially strong nonlinearity oscillatory problems.

Scattering amplitudes from multivariate polynomial division

Energy Technology Data Exchange (ETDEWEB)

Mastrolia, Pierpaolo, E-mail: pierpaolo.mastrolia@cern.ch [Max-Planck-Institut fuer Physik, Foehringer Ring 6, 80805 Muenchen (Germany); Dipartimento di Fisica e Astronomia, Universita di Padova, Padova (Italy); INFN Sezione di Padova, via Marzolo 8, 35131 Padova (Italy); Mirabella, Edoardo, E-mail: mirabell@mppmu.mpg.de [Max-Planck-Institut fuer Physik, Foehringer Ring 6, 80805 Muenchen (Germany); Ossola, Giovanni, E-mail: GOssola@citytech.cuny.edu [New York City College of Technology, City University of New York, 300 Jay Street, Brooklyn, NY 11201 (United States); Graduate School and University Center, City University of New York, 365 Fifth Avenue, New York, NY 10016 (United States); Peraro, Tiziano, E-mail: peraro@mppmu.mpg.de [Max-Planck-Institut fuer Physik, Foehringer Ring 6, 80805 Muenchen (Germany)

2012-11-15

We show that the evaluation of scattering amplitudes can be formulated as a problem of multivariate polynomial division, with the components of the integration-momenta as indeterminates. We present a recurrence relation which, independently of the number of loops, leads to the multi-particle pole decomposition of the integrands of the scattering amplitudes. The recursive algorithm is based on the weak Nullstellensatz theorem and on the division modulo the Groebner basis associated to all possible multi-particle cuts. We apply it to dimensionally regulated one-loop amplitudes, recovering the well-known integrand-decomposition formula. Finally, we focus on the maximum-cut, defined as a system of on-shell conditions constraining the components of all the integration-momenta. By means of the Finiteness Theorem and of the Shape Lemma, we prove that the residue at the maximum-cut is parametrized by a number of coefficients equal to the number of solutions of the cut itself.

δ-Generalized Labeled Multi-Bernoulli Filter Using Amplitude Information of Neighboring Cells

Directory of Open Access Journals (Sweden)

Chao Liu

2018-04-01

Full Text Available The amplitude information (AI of echoed signals plays an important role in radar target detection and tracking. A lot of research shows that the introduction of AI enables the tracking algorithm to distinguish targets from clutter better and then improves the performance of data association. The current AI-aided tracking algorithms only consider the signal amplitude in the range-azimuth cell where measurement exists. However, since radar echoes always contain backscattered signals from multiple cells, the useful information of neighboring cells would be lost if directly applying those existing methods. In order to solve this issue, a new δ-generalized labeled multi-Bernoulli (δ-GLMB filter is proposed. It exploits the AI of radar echoes from neighboring cells to construct a united amplitude likelihood ratio, and then plugs it into the update process and the measurement-track assignment cost matrix of the δ-GLMB filter. Simulation results show that the proposed approach has better performance in target’s state and number estimation than that of the δ-GLMB only using single-cell AI in low signal-to-clutter-ratio (SCR environment.

Interference by amplitude division with extended sources by paraxial boundary conditions

International Nuclear Information System (INIS)

Liñares, J; Nistal, M C

2014-01-01

We present a wave-optics paraxial approach to the interference by amplitude division produced by plane-parallel films (or plates) and non-plane-parallel films, or by equivalent optical devices such as a Michelson interferometer, when they are illuminated with extended (spatially incoherent) quasi-monochromatic sources. To the best of our knowledge, the most common approaches to the study of interference are based, for simplicity, on the combined use of geometrical optics concepts, such as the optical path length along a ray, together with some wave-optics concepts such as optical phases. However, interference phenomena have been the means by which the wave nature of light has been established and therefore geometrical and wave concepts are so far-off that their simultaneous use can give rise to misleading concepts. Therefore, the primary aim of this work is to provide an analytical homogeneous description of interference by amplitude division using only paraxial spherical waves and boundary conditions at smooth interfaces or discontinuities in such a way that the calculation of the total optical field, interference irradiance, fringe visibility, coherence degree, localization of the interference and so on, can be made in a unified way by taking a fully wave-optics approach. The paraxial regime is enough in most cases and, moreover, interference is generally collected by an optical instrument such as a lens or the eye itself, in which a paraxial approximation is required. This work is particularly aimed at university physics teachers and undergraduate and first year postgraduate students. (papers)

Leningrad NPP full scope and analytical simulators as tools for MMI improvement and operator support systems development and testing

International Nuclear Information System (INIS)

Rakitin, I.D.; Malkin, S.D.; Shalia, V.V.; Fedorov, E.M.; Lebedev, N.N.; Khoudiakov, M.M.

1999-01-01

Training Support Center (TSC) created at the Leningrad NPP (LNPP), Sosnovy Bor, Russia, incorporates full-scope and analytical simulators working in parallel with the prototypes of the expert and interactive systems to provide a new scope of R and D MMI improvement work as for the developer as well as for the user. Possibilities of development, adjusting and testing of any new or up-graded Operators' Support System before its installation at the reference unit's Control Room are described in the paper. These Simulators ensure the modeling of a wide range of accidents and transients and provide with special software and ETHERNET data process communications with the Operators' Support systems' prototypes. The development and adjustment of two state-of-the-art Operators' Support Systems of interest with using of Simulators are described in the paper as an example. These systems have been developed jointly by RRC KI and LNPP team. (author)

The zerology of kaon-nucleon forward scattering amplitudes

International Nuclear Information System (INIS)

Dumbrajs, O.

1981-01-01

It has been realized for a long time that zeros of the forward kaon-nucleon scattering amplitudes are useful in correlating different low and high-energy scattering parameters and in providing a consistency test of available data. The simplest possibility of exploring zeros is to evaluate the ordinary dispersion relations in the complex energy plane. The more natural way of bringing zeros of amplitudes into play is to consider either one of the more sophisticated forms of dispersion relations: i) phase dispersion relations, ii) inverse-amplitude dispersion relations, iii) logarithmic dispersion relations, or to apply the maximum modulus theorem and a factorization theorem. The author concentrates on the use of logarithmic dispersion relations because this approach seems to be the most convenient one for future extensions to nonforward scattering data analyses based on the zeros of the amplitude. (Auth.)

MHV amplitudes for 3→3 gluon scattering in Regge limit

International Nuclear Information System (INIS)

Bartels, J.; Prygarin, A.

2010-12-01

We calculate corrections to the BDS formula for the six-particle planar MHV amplitude for the gluon transition 3 → 3 in the multi-Regge kinematics for the physical region, in which the Regge pole ansatz is not valid. The remainder function at two loops is obtained by an analytic continuation of the expression derived by Goncharov, Spradlin, Vergu and Volovich to the kinematic region described by the Mandelstam singularity exchange in the crossing channel. It contains both the imaginary and real contributions being in agreement with the BFKL predictions. The real part of the three loop expression is found from a dispersion-like all-loop formula for the remainder function in the multi-Regge kinematics derived by one of the authors. We also make a prediction for the all-loop real part of the remainder function multiplied by the BDS phase, which can be accessible through calculations in the regime of the strong coupling constant. (orig.)

MHV amplitudes for 3{yields}3 gluon scattering in Regge limit

Energy Technology Data Exchange (ETDEWEB)

Bartels, J.; Prygarin, A. [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik; Lipatov, L.N. [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik; St. Petersburg Nuclear Physics Institute (Russian Federation)

2010-12-15

We calculate corrections to the BDS formula for the six-particle planar MHV amplitude for the gluon transition 3 {yields} 3 in the multi-Regge kinematics for the physical region, in which the Regge pole ansatz is not valid. The remainder function at two loops is obtained by an analytic continuation of the expression derived by Goncharov, Spradlin, Vergu and Volovich to the kinematic region described by the Mandelstam singularity exchange in the crossing channel. It contains both the imaginary and real contributions being in agreement with the BFKL predictions. The real part of the three loop expression is found from a dispersion-like all-loop formula for the remainder function in the multi-Regge kinematics derived by one of the authors. We also make a prediction for the all-loop real part of the remainder function multiplied by the BDS phase, which can be accessible through calculations in the regime of the strong coupling constant. (orig.)

Jump phenomena. [large amplitude responses of nonlinear systems

Science.gov (United States)

Reiss, E. L.

1980-01-01

The paper considers jump phenomena composed of large amplitude responses of nonlinear systems caused by small amplitude disturbances. Physical problems where large jumps in the solution amplitude are important features of the response are described, including snap buckling of elastic shells, chemical reactions leading to combustion and explosion, and long-term climatic changes of the earth's atmosphere. A new method of rational functions was then developed which consists of representing the solutions of the jump problems as rational functions of the small disturbance parameter; this method can solve jump problems explicitly.

Collaborative Visual Analytics: A Health Analytics Approach to Injury Prevention

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Samar Al-Hajj

2017-09-01

Full Text Available Background: Accurate understanding of complex health data is critical in order to deal with wicked health problems and make timely decisions. Wicked problems refer to ill-structured and dynamic problems that combine multidimensional elements, which often preclude the conventional problem solving approach. This pilot study introduces visual analytics (VA methods to multi-stakeholder decision-making sessions about child injury prevention; Methods: Inspired by the Delphi method, we introduced a novel methodology—group analytics (GA. GA was pilot-tested to evaluate the impact of collaborative visual analytics on facilitating problem solving and supporting decision-making. We conducted two GA sessions. Collected data included stakeholders’ observations, audio and video recordings, questionnaires, and follow up interviews. The GA sessions were analyzed using the Joint Activity Theory protocol analysis methods; Results: The GA methodology triggered the emergence of ‘common ground’ among stakeholders. This common ground evolved throughout the sessions to enhance stakeholders’ verbal and non-verbal communication, as well as coordination of joint activities and ultimately collaboration on problem solving and decision-making; Conclusions: Understanding complex health data is necessary for informed decisions. Equally important, in this case, is the use of the group analytics methodology to achieve ‘common ground’ among diverse stakeholders about health data and their implications.

Phase and amplitude detection system for the Stanford Linear Accelerator

International Nuclear Information System (INIS)

Fox, J.D.; Schwarz, H.D.

1983-01-01

A computer controlled phase and amplitude detection system to measure and stabilize the rf power sources in the Stanford Linear Accelerator is described. This system measures the instantaneous phase and amplitude of a 1 microsecond 2856 MHz rf pulse and will be used for phase feedback control and for amplitude and phase jitter detection. This paper discusses the measurement system performance requirements for the operation of the Stanford Linear Collider, and the design and implementation of the phase and amplitude detection system. The fundamental software algorithms used in the measurement are described, as is the performance of the prototype phase and amplitude detector system

An Analysis of Fundamental Mode Surface Wave Amplitude Measurements

Science.gov (United States)

Schardong, L.; Ferreira, A. M.; van Heijst, H. J.; Ritsema, J.

2014-12-01

Seismic tomography is a powerful tool to decipher the Earth's interior structure at various scales. Traveltimes of seismic waves are widely used to build velocity models, whereas amplitudes are still only seldomly accounted for. This mainly results from our limited ability to separate the various physical effects responsible for observed amplitude variations, such as focussing/defocussing, scattering and source effects. We present new measurements from 50 global earthquakes of fundamental-mode Rayleigh and Love wave amplitude anomalies measured in the period range 35-275 seconds using two different schemes: (i) a standard time-domain amplitude power ratio technique; and (ii) a mode-branch stripping scheme. For minor-arc data, we observe amplitude anomalies with respect to PREM in the range of 0-4, for which the two measurement techniques show a very good overall agreement. We present here a statistical analysis and comparison of these datasets, as well as comparisons with theoretical calculations for a variety of 3-D Earth models. We assess the geographical coherency of the measurements, and investigate the impact of source, path and receiver effects on surface wave amplitudes, as well as their variations with frequency in a wider range than previously studied.

Light Diffraction by Large Amplitude Ultrasonic Waves in Liquids

Science.gov (United States)

Adler, Laszlo; Cantrell, John H.; Yost, William T.

2016-01-01

Light diffraction from ultrasound, which can be used to investigate nonlinear acoustic phenomena in liquids, is reported for wave amplitudes larger than that typically reported in the literature. Large amplitude waves result in waveform distortion due to the nonlinearity of the medium that generates harmonics and produces asymmetries in the light diffraction pattern. For standing waves with amplitudes above a threshold value, subharmonics are generated in addition to the harmonics and produce additional diffraction orders of the incident light. With increasing drive amplitude above the threshold a cascade of period-doubling subharmonics are generated, terminating in a region characterized by a random, incoherent (chaotic) diffraction pattern. To explain the experimental results a toy model is introduced, which is derived from traveling wave solutions of the nonlinear wave equation corresponding to the fundamental and second harmonic standing waves. The toy model reduces the nonlinear partial differential equation to a mathematically more tractable nonlinear ordinary differential equation. The model predicts the experimentally observed cascade of period-doubling subharmonics terminating in chaos that occurs with increasing drive amplitudes above the threshold value. The calculated threshold amplitude is consistent with the value estimated from the experimental data.

A proposed physical analog for a quantum probability amplitude

Science.gov (United States)

Boyd, Jeffrey

What is the physical analog of a probability amplitude? All quantum mathematics, including quantum information, is built on amplitudes. Every other science uses probabilities; QM alone uses their square root. Why? This question has been asked for a century, but no one previously has proposed an answer. We will present cylindrical helices moving toward a particle source, which particles follow backwards. Consider Feynman's book QED. He speaks of amplitudes moving through space like the hand of a spinning clock. His hand is a complex vector. It traces a cylindrical helix in Cartesian space. The Theory of Elementary Waves changes direction so Feynman's clock faces move toward the particle source. Particles follow amplitudes (quantum waves) backwards. This contradicts wave particle duality. We will present empirical evidence that wave particle duality is wrong about the direction of particles versus waves. This involves a paradigm shift; which are always controversial. We believe that our model is the ONLY proposal ever made for the physical foundations of probability amplitudes. We will show that our ``probability amplitudes'' in physical nature form a Hilbert vector space with adjoints, an inner product and support both linear algebra and Dirac notation.

Cyclic deformation and fatigue data for Ti–6Al–4V ELI under variable amplitude loading

Directory of Open Access Journals (Sweden)

Patricio E. Carrion

2017-08-01

Full Text Available This article presents the strain-based experimental data for Ti–6Al–4V ELI under non-constant amplitude cyclic loading. Uniaxial strain-controlled fatigue experiments were conducted under three different loading conditions, including two-level block loading (i.e. high-low and low-high, periodic overload, and variable amplitude loading. Tests were performed under fully-reversed, and mean strain/stress conditions. For each test conducted, two sets of data were collected; the cyclic stress–strain response (i.e. hysteresis loops in log10 increments, and the peak and valley values of stress and strain for each cycle. Residual fatigue lives are reported for tests with two-level block loading, while for periodic overload and variable amplitude experiments, fatigue lives are reported in terms of number of blocks to failure.

Superresolving Black Hole Images with Full-Closure Sparse Modeling

Science.gov (United States)

Crowley, Chelsea; Akiyama, Kazunori; Fish, Vincent

2018-01-01

It is believed that almost all galaxies have black holes at their centers. Imaging a black hole is a primary objective to answer scientific questions relating to relativistic accretion and jet formation. The Event Horizon Telescope (EHT) is set to capture images of two nearby black holes, Sagittarius A* at the center of the Milky Way galaxy roughly 26,000 light years away and the other M87 which is in Virgo A, a large elliptical galaxy that is 50 million light years away. Sparse imaging techniques have shown great promise for reconstructing high-fidelity superresolved images of black holes from simulated data. Previous work has included the effects of atmospheric phase errors and thermal noise, but not systematic amplitude errors that arise due to miscalibration. We explore a full-closure imaging technique with sparse modeling that uses closure amplitudes and closure phases to improve the imaging process. This new technique can successfully handle data with systematic amplitude errors. Applying our technique to synthetic EHT data of M87, we find that full-closure sparse modeling can reconstruct images better than traditional methods and recover key structural information on the source, such as the shape and size of the predicted photon ring. These results suggest that our new approach will provide superior imaging performance for data from the EHT and other interferometric arrays.

Measurement of amplitude fluctuations in a rapid response photomultiplier; Mesure des fluctuations d'amplitude d'un photo multiplicateur a reponse rapide

Energy Technology Data Exchange (ETDEWEB)

Raimbault, P [Commissariat a l' Energie Atomique, Saclay (France).Centre d' Etudes Nucleaires

1961-07-01

In order to measure amplitude fluctuations in a rapid response photomultiplier, two independent random variables are introduced which determine the shape of the anode pulse. The energy of each pulse, which depends directly on the gain and the variance, is the first variable; amplitude fluctuations, functions of the first variable, depend as well on the pulse width which in turn constitutes the second variable. The results obtained on the variations of the maximum impulse, using a steep-edged pulse broadening circuit, and those obtained on the statistical variations of the gain, are compared to show that the variance relative to the maximum amplitude of the signal is greater than that of the gain. Within the limits of these fluctuations are shown the contribution of the secondary emission coefficient of the first dynode, and that of the mean secondary emission coefficient of the multiplier. (author) [French] Pour etudier les fluctuations d'amplitude d'un photomultiplicateur a reponse rapide, on introduit deux variables aleatoires independantes qui determinent la forme de l'impulsion anodique. L'energie de chaque impulsion, directement fonction du gain et de sa variance, est la premiere variable; les fluctuations d'amplitude, fonctions de la premiere variable, dependent egalement de la largeur de l'impulsion qui, elle, constitue la deuxieme variable. Les resultats obtenus sur les variations de l'amplitude maximale, a l'aide d'un circuit elargisseur d'impulsions a front raide, et les resultats des variations statistiques du gain sont compares pour mettre en evidence le fait que la variance relative a l'amplitude maximale du signal est plus grande que celle du gain. Dans la mesure de ces fluctuations, sont mises en evidence la contribution du coefficient d'emission secondaire de la premiere dynode et celle du coefficient d'emission secondaire moyen du multiplicateur. (auteur)

Renormalization and applications of baryon distribution amplitudes QCD

International Nuclear Information System (INIS)

Rohrwild, Juergen Holger

2009-01-01

Higher-twist effects are relevant for precision calculations of hard exclusive reactions. Furthermore, they reveal fine details of the hadron structure. In this work we construct an operator basis for arbitrary twist respecting the conformal symmetry of QCD (which is realized on 1-loop level). Using this basis the 1-loop renormalization kernels of twist 4 are constructed for baryon operators. The full spectrum of anomalous dimensions and the multiplicatively renormalizable operators is obtained. As an application of these results the radiative N * (1535) decay is discussed. Employing light-cone sum rule, the transition form factors can be directly related to the N * distribution amplitudes. (orig.)

Renormalization and applications of baryon distribution amplitudes QCD

Energy Technology Data Exchange (ETDEWEB)

Rohrwild, Juergen Holger

2009-07-17

Higher-twist effects are relevant for precision calculations of hard exclusive reactions. Furthermore, they reveal fine details of the hadron structure. In this work we construct an operator basis for arbitrary twist respecting the conformal symmetry of QCD (which is realized on 1-loop level). Using this basis the 1-loop renormalization kernels of twist 4 are constructed for baryon operators. The full spectrum of anomalous dimensions and the multiplicatively renormalizable operators is obtained. As an application of these results the radiative N{sup *}(1535) decay is discussed. Employing light-cone sum rule, the transition form factors can be directly related to the N{sup *} distribution amplitudes. (orig.)

Reinforcing Saccadic Amplitude Variability

Science.gov (United States)

Paeye, Celine; Madelain, Laurent

2011-01-01

Saccadic endpoint variability is often viewed as the outcome of neural noise occurring during sensorimotor processing. However, part of this variability might result from operant learning. We tested this hypothesis by reinforcing dispersions of saccadic amplitude distributions, while maintaining constant their medians. In a first experiment we…

Pre-analytical and analytical factors influencing Alzheimer's disease cerebrospinal fluid biomarker variability.

Science.gov (United States)

Fourier, Anthony; Portelius, Erik; Zetterberg, Henrik; Blennow, Kaj; Quadrio, Isabelle; Perret-Liaudet, Armand

2015-09-20

A panel of cerebrospinal fluid (CSF) biomarkers including total Tau (t-Tau), phosphorylated Tau protein at residue 181 (p-Tau) and β-amyloid peptides (Aβ42 and Aβ40), is frequently used as an aid in Alzheimer's disease (AD) diagnosis for young patients with cognitive impairment, for predicting prodromal AD in mild cognitive impairment (MCI) subjects, for AD discrimination in atypical clinical phenotypes and for inclusion/exclusion and stratification of patients in clinical trials. Due to variability in absolute levels between laboratories, there is no consensus on medical cut-off value for the CSF AD signature. Thus, for full implementation of this core AD biomarker panel in clinical routine, this issue has to be solved. Variability can be explained both by pre-analytical and analytical factors. For example, the plastic tubes used for CSF collection and storage, the lack of reference material and the variability of the analytical protocols were identified as important sources of variability. The aim of this review is to highlight these pre-analytical and analytical factors and describe efforts done to counteract them in order to establish cut-off values for core CSF AD biomarkers. This review will give the current state of recommendations. Copyright © 2015. Published by Elsevier B.V.

Miracles in Scattering Amplitudes: from QCD to Gravity

Energy Technology Data Exchange (ETDEWEB)

Volovich, Anastasia [Brown Univ., Providence, RI (United States)

2016-10-09

The goal of my research project "Miracles in Scattering Amplitudes: from QCD to Gravity" involves deepening our understanding of gauge and gravity theories by exploring hidden structures in scattering amplitudes and using these rich structures as much as possible to aid practical calculations.

Multifactorial determinants of target and novelty-evoked P300 amplitudes in children of addicted parents.

Directory of Open Access Journals (Sweden)

Anja S Euser

Full Text Available BACKGROUND: Although P300 amplitude reductions constitute a persistent finding in children of addicted parents, relatively little is known about the specificity of this finding. The major aim of this study was to investigate the association between parental rearing, adverse life events, stress-reactivity, substance use and psychopathology on the one hand, and P300 amplitude in response to both target and novel distracter stimuli on the other hand. Moreover, we assessed whether risk group status (i.e., having a parental history of Substance Use Disorders [SUD] uniquely contributed to P300 amplitude variation above and beyond these other variables. METHODS: Event-related potentials were recorded in high-risk adolescents with a parental history of SUD (HR;n=80 and normal-risk controls (NR;n=100 while performing a visual Novelty Oddball paradigm. Stress-evoked cortisol levels were assessed and parenting, life adversities, substance use and psychopathology were examined by using self-reports. RESULTS: HR adolescents displayed smaller P300 amplitudes in response to novel- and to target stimuli than NR controls, while the latter only approached significance. Interestingly, the effect of having a parental history of SUD on target-P300 disappeared when all other variables were taken into account. Externalizing problem behavior was a powerful predictor of target-P300. In contrast, risk group status uniquely predicted novelty-P300 amplitude reductions above and beyond all other factors. CONCLUSION: Overall, the present findings suggest that the P300 amplitude reduction to novel stimuli might be a more specific endophenotype for SUD than the target-P300 amplitude. This pattern of results underscores the importance of conducting multifactorial assessments when examining important cognitive processes in at-risk adolescents.

High energy multi-gluon exchange amplitudes

International Nuclear Information System (INIS)

Jaroszewicz, T.

1980-11-01

We examine perturbative high energy n-gluon exchange amplitudes calculated in the Coulomb gauge. If n exceeds the minimum required by the t-channel quantum numbers, such amplitudes are non-leading in lns. We derive a closed system of coupled integral equations for the corresponding two-particle n-gluon vertices, obtained by summing the leading powers of ln(N μ psup(μ)), where psup(μ) is the incident momentum and Nsup(μ) the gauge-defining vector. Our equations are infra-red finite, provided the external particles are colour singlets. (author)

Precise generator of stability amplitude pulses

International Nuclear Information System (INIS)

Zhuk, N.A.; Zdesenko, Yu.G.; Kuts, V.N.

1989-01-01

A generator of stability amplitude pulses, designed for stabilization of a low-noise semiconducting spectrometer, used in investigations of 76 Ge2β-decay, is described. The generator contains a permanent-voltage source, a storage element and a switch based on a Hg relay. A thermostatic source provides a relative voltage instability less than ±5x10 -6 per 80h (standard deviation). The Hg relay is placed into a separate thermostat. The relative instability of output generator pulse amplitude does not exceed ±1.5x10 -5 per 24h

Amplitude Dependent Internal Friction in a Mg-Al-Zn Alloy Studied after Thermal and Mechanical Treatment

Directory of Open Access Journals (Sweden)

Zuzanka Trojanová

2017-10-01

Full Text Available The amplitude-dependent internal friction of continuously-cast and rolled AZ31 magnesium alloy was measured in this study. Samples were annealed and quenched step by step; immediately after the treatment, the amplitude dependence of the logarithmic decrement was measured. Changes in the microstructure due to thermomechanical treatment were reflected in changes in the damping. Internal friction is influenced by the dislocation substructure and its modification due to solute atoms migration, microplastic deformation, and twins’ formation. Internal friction in the rolled sheets is affected by the rolling texture.

REGIONAL SEISMIC AMPLITUDE MODELING AND TOMOGRAPHY FOR EARTHQUAKE-EXPLOSION DISCRIMINATION

Energy Technology Data Exchange (ETDEWEB)

Walter, W R; Pasyanos, M E; Matzel, E; Gok, R; Sweeney, J; Ford, S R; Rodgers, A J

2008-07-08

We continue exploring methodologies to improve earthquake-explosion discrimination using regional amplitude ratios such as P/S in a variety of frequency bands. Empirically we demonstrate that such ratios separate explosions from earthquakes using closely located pairs of earthquakes and explosions recorded on common, publicly available stations at test sites around the world (e.g. Nevada, Novaya Zemlya, Semipalatinsk, Lop Nor, India, Pakistan, and North Korea). We are also examining if there is any relationship between the observed P/S and the point source variability revealed by longer period full waveform modeling (e. g. Ford et al 2008). For example, regional waveform modeling shows strong tectonic release from the May 1998 India test, in contrast with very little tectonic release in the October 2006 North Korea test, but the P/S discrimination behavior appears similar in both events using the limited regional data available. While regional amplitude ratios such as P/S can separate events in close proximity, it is also empirically well known that path effects can greatly distort observed amplitudes and make earthquakes appear very explosion-like. Previously we have shown that the MDAC (Magnitude Distance Amplitude Correction, Walter and Taylor, 2001) technique can account for simple 1-D attenuation and geometrical spreading corrections, as well as magnitude and site effects. However in some regions 1-D path corrections are a poor approximation and we need to develop 2-D path corrections. Here we demonstrate a new 2-D attenuation tomography technique using the MDAC earthquake source model applied to a set of events and stations in both the Middle East and the Yellow Sea Korean Peninsula regions. We believe this new 2-D MDAC tomography has the potential to greatly improve earthquake-explosion discrimination, particularly in tectonically complex regions such as the Middle East. Monitoring the world for potential nuclear explosions requires characterizing seismic

Employing helicity amplitudes for resummation in SCET

International Nuclear Information System (INIS)

Moult, Ian; Stewart, Iain W.; Tackmann, Frank J.; Waalewijn, Wouter J.; Nikhef, Amsterdam

2016-05-01

Helicity amplitudes are the fundamental ingredients of many QCD calculations for multi-leg processes. We describe how these can seamlessly be combined with resummation in Soft-Collinear Effective Theory (SCET), by constructing a helicity operator basis for which the Wilson coefficients are directly given in terms of color-ordered helicity amplitudes. This basis is crossing symmetric and has simple transformation properties under discrete symmetries.

The Cepheid bump progression and amplitude equations

International Nuclear Information System (INIS)

Kovacs, G.; Buchler, J.R.

1989-01-01

It is shown that the characteristic and systematic behavior of the low-order Fourier amplitudes and phases of hydrodynamically generated radial velocity and light curves of Cepheid model sequences is very well captured not only qualitatively but also quantitatively by the amplitude equation formalism. The 2:1 resonance between the fundamental and the second overtone plays an essential role in the behavior of the models 8 refs

Beyond Panglossian Optimism: Larger N2 Amplitudes Probably Signal a Bilingual Disadvantage in Conflict Monitoring

Directory of Open Access Journals (Sweden)

Kenneth R. Paap

2015-01-01

Full Text Available In this special issue on the brain mechanisms that lead to cognitive benefits of bilingualism we discussed six reasons why it will be very difficult to discover those mechanisms. Many of these problems apply to the article by Fernandez, Acosta, Douglass, Doshi, and Tartar that also appears in the special issue. These concerns include the following: 1 an overly optimistic assessment of the replicability of bilingual advantages in behavioral studies, 2 reliance on risky small samples sizes, 3 failures to match the samples on demographic characteristics such as immigrant status, and 4 language group differences that occur in neural measures (i.e., N2 amplitude, but not in the behavioral data. Furthermore the N2 amplitude measure in general suffers from valence ambiguity: larger N2 amplitudes reported for bilinguals are more likely to reflect poorer conflict resolution rather than enhanced inhibitory control.

Study of inelastic decay of amplitudes in 49V

International Nuclear Information System (INIS)

Chou, B.H.

1980-01-01

Inelastic decay amplitudes from d-wave resonances in 49 V were obtained for 80 resonances in the proton energy range 2.2 to 3.1 MeV. With the 3 MV Van de Graaff accelerator and high resolution system at the Triangle Universities Nuclear Laboratory, an overall resolution of 350 eV was obtained. The experiment consisted of measurements of the angular distributions of the inelastically scattered protons and the subsequent deexcitation gamma rays. Forty five resonances were assigned J/sup π/ = 5/2 + , while thirty five resonances were assigned 3/2 + . The magnitudes of three inelastic decay amplitudes and the relative signs between these three amplitudes were determined. Large amplitude correlations were observed; the data are in the striking disagreement with the extreme statistical model. The present results provide the first explicit test of the multivariate reduced width amplitude distribution of Krieger and Porter; the agreement is excellent. The physical origin of these channel correlations has not yet been explained

Two-Loop Gluon to Gluon-Gluon Splitting Amplitudes in QCD

International Nuclear Information System (INIS)

Bern, Z.

2004-01-01

Splitting amplitudes are universal functions governing the collinear behavior of scattering amplitudes for massless particles. We compute the two-loop g → gg splitting amplitudes in QCD, N = 1, and N = 4 super-Yang-Mills theories, which describe the limits of two-loop n-point amplitudes where two gluon momenta become parallel. They also represent an ingredient in a direct x-space computation of DGLAP evolution kernels at next-to-next-to-leading order. To obtain the splitting amplitudes, we use the unitarity sewing method. In contrast to the usual light-cone gauge treatment, our calculation does not rely on the principal-value or Mandelstam-Leibbrandt prescriptions, even though the loop integrals contain some of the denominators typically encountered in light-cone gauge. We reduce the integrals to a set of 13 master integrals using integration-by-parts and Lorentz invariance identities. The master integrals are computed with the aid of differential equations in the splitting momentum fraction z. The ε-poles of the splitting amplitudes are consistent with a formula due to Catani for the infrared singularities of two-loop scattering amplitudes. This consistency essentially provides an inductive proof of Catani's formula, as well as an ansatz for previously-unknown 1/ε pole terms having non-trivial color structure. Finite terms in the splitting amplitudes determine the collinear behavior of finite remainders in this formula

Recent analytical applications of magnetic nanoparticles

Directory of Open Access Journals (Sweden)

Mohammad Faraji

2016-07-01

Full Text Available Analytical chemistry has experienced, as well as other areas of science, a big change due to the needs and opportunities provided by analytical nanoscience and nanotechnology. Now, nanotechnology is increasingly proving to be a powerful ally of analytical chemistry to achieve its objectives, and to simplify analytical processes. Moreover, the information needs arising from the growing nanotechnological activity are opening an exciting new field of action for analytical chemists. Magnetic nanoparticles have been used in various fields owing to their unique properties including large specific surface area and simple separation with magnetic fields. For Analytical applications, they have been used mainly for sample preparation techniques (magnetic solid phase extraction with different advanced functional groups (layered double hydroxide, β-cyclodextrin, carbon nanotube, graphen, polymer, octadecylsilane and automation of it, microextraction techniques enantioseparation and chemosensors. This review summarizes the basic principles and achievements of magnetic nanoparticles in sample preparation techniques, enantioseparation and chemosensors. Also, some selected articles recently published (2010-2016 have been reviewed and discussed.

Tensor exchange amplitudes in K +- N charge exchange reactions

International Nuclear Information System (INIS)

Svec, M.

1979-01-01

Tensor (A 2 ) exchange amplitudes in K +- N charge exchange (CEX) are constructed from the K +- N CEX data supplemented by information on the vector (rho) exchange amplitudes from πN sca tering. We observed new features in the t-structure of A 2 exchange amplitudes which contradict the t-de pendence anticipated by most of the Regge models. The results also provide evidence for violation of weak exchange degeneracy

Nonlinear Effects in Three-minute Oscillations of the Solar Chromosphere. I. An Analytical Nonlinear Solution and Detection of the Second Harmonic

International Nuclear Information System (INIS)

Chae, Jongchul; Litvinenko, Yuri E.

2017-01-01

The vertical propagation of nonlinear acoustic waves in an isothermal atmosphere is considered. A new analytical solution that describes a finite-amplitude wave of an arbitrary wavelength is obtained. Although the short- and long-wavelength limits were previously considered separately, the new solution describes both limiting cases within a common framework and provides a straightforward way of interpolating between the two limits. Physical features of the nonlinear waves in the chromosphere are described, including the dispersive nature of low-frequency waves, the steepening of the wave profile, and the influence of the gravitational field on wavefront breaking and shock formation. The analytical results suggest that observations of three-minute oscillations in the solar chromosphere may reveal the basic nonlinear effect of oscillations with combination frequencies, superposed on the normal oscillations of the system. Explicit expressions for a second-harmonic signal and the ratio of its amplitude to the fundamental harmonic amplitude are derived. Observational evidence of the second harmonic, obtained with the Fast Imaging Solar Spectrograph, installed at the 1.6 m New Solar Telescope of the Big Bear Observatory, is presented. The presented data are based on the time variations of velocity determined from the Na i D 2 and H α lines.

Nonlinear Effects in Three-minute Oscillations of the Solar Chromosphere. I. An Analytical Nonlinear Solution and Detection of the Second Harmonic

Energy Technology Data Exchange (ETDEWEB)

Chae, Jongchul [Astronomy Program, Department of Physics and Astronomy, Seoul National University, Seoul 08826 (Korea, Republic of); Litvinenko, Yuri E. [Department of Mathematics, University of Waikato, P. B. 3105, Hamilton 3240 (New Zealand)

2017-08-01

The vertical propagation of nonlinear acoustic waves in an isothermal atmosphere is considered. A new analytical solution that describes a finite-amplitude wave of an arbitrary wavelength is obtained. Although the short- and long-wavelength limits were previously considered separately, the new solution describes both limiting cases within a common framework and provides a straightforward way of interpolating between the two limits. Physical features of the nonlinear waves in the chromosphere are described, including the dispersive nature of low-frequency waves, the steepening of the wave profile, and the influence of the gravitational field on wavefront breaking and shock formation. The analytical results suggest that observations of three-minute oscillations in the solar chromosphere may reveal the basic nonlinear effect of oscillations with combination frequencies, superposed on the normal oscillations of the system. Explicit expressions for a second-harmonic signal and the ratio of its amplitude to the fundamental harmonic amplitude are derived. Observational evidence of the second harmonic, obtained with the Fast Imaging Solar Spectrograph, installed at the 1.6 m New Solar Telescope of the Big Bear Observatory, is presented. The presented data are based on the time variations of velocity determined from the Na i D{sub 2} and H α lines.

N=4 Scattering Amplitudes and the Deformed Graßmannian

CERN Document Server

Ferro, Livia; Staudacher, Matthias

2014-01-01

Some time ago the general tree-level scattering amplitudes of N=4 Super Yang-Mills theory were expressed as certain Grassmannian contour integrals. These remarkable formulas allow to clearly expose the super-conformal, dual super-conformal, and Yangian symmetries of the amplitudes. Using ideas from integrability it was recently shown that the building blocks of the amplitudes permit a natural multi-parameter deformation. However, this approach had been criticized by the observation that it seemed impossible to reassemble the building blocks into Yangian-invariant deformed non-MHV amplitudes. In this note we demonstrate that the deformations may be succinctly summarized by a simple modification of the measure of the Grassmannian integrals, leading to a Yangian-invariant deformation of the general tree-level amplitudes. Interestingly, the deformed building-blocks appear as residues of poles in the spectral parameter planes. Given that the contour integrals also contain information on the amplitudes at loop-leve...

Transversity Amplitudes in Hypercharge Exchange Processes

International Nuclear Information System (INIS)

Aguilar Benitez de Lugo, M.

1979-01-01

' In this work we present several techniques developed for the extraction of the. Transversity amplitudes governing quasi two-body meson baryon reactions with hypercharge exchange. We review the methods used in processes having a pure spin configuration, as well as the more relevant results obtained with data from K p and Tp interactions at intermediate energies. The predictions of the additive quark model and the ones following from exchange degeneracy and etoxicity are discussed. We present a formalism for amplitude analysis developed for reactions with mixed spin configurations and discuss the methods of parametric estimation of the moduli and phases of the amplitudes, as well as the various tests employed to check the goodness of the fits. The calculation of the generalized joint density matrices is given and we propose a method based on the generalization of the idea of multipole moments, which allows to investigate the structure of the decay angular correlations and establishes the quality of the fits and the validity of the simplifying assumptions currently used in this type of studies. (Author) 43 refs

Tree-level disk amplitude of three closed strings

Science.gov (United States)

Mousavi, Sepideh; Velni, Komeil Babaei

2018-05-01

It has been shown that the disk-level S-matrix elements of one Ramond-Ramond (RR) and two Neveu-Schwarz-Neveu-Schwarz (NSNS) states could be found by applying the Ward identity associated with the string duality and the gauge symmetry on a given component of the S matrix. These amplitudes have appeared as the components of six different T-dual multiplets. It is predicted in the literature that there are some nonzero disk-level scattering amplitudes, such as one RR (p -1 ) form with zero transverse index and two N S N S states, could not be captured by the T-dual Ward identity. We explicitly find this amplitude in terms of a minimal context of the integral functions by the insertion of one closed string RR vertex operator and two NSNS vertex operators. From the amplitude invariance under the Ward identity associated with the NSNS gauge transformations and T-duality, we also find some integral identities.

N-loop string amplitude

International Nuclear Information System (INIS)

Mandelstam, S.

1986-06-01

Work on the derivation of an explicit perturbation series for string and superstring amplitudes is reviewed. The light-cone approach is emphasized, but some work on the Polyakov approach is also mentioned, and the two methods are compared. The calculation of the measure factor is outlined in the interacting-string picture

Differential Amplitude Pulse-Position Modulation for Indoor Wireless Optical Communications

Directory of Open Access Journals (Sweden)

Sethakaset Ubolthip

2005-01-01

Full Text Available We propose a novel differential amplitude pulse-position modulation (DAPPM for indoor optical wireless communications. DAPPM yields advantages over PPM, DPPM, and DH-PIM in terms of bandwidth requirements, capacity, and peak-to-average power ratio (PAPR. The performance of a DAPPM system with an unequalized receiver is examined over nondispersive and dispersive channels. DAPPM can provide better bandwidth and/or power efficiency than PAM, PPM, DPPM, and DH-PIM depending on the number of amplitude levels and the maximum length of a symbol. We also show that, given the same maximum length, DAPPM has better bandwidth efficiency but requires about and more power than PPM and DPPM, respectively, at high bit rates over a dispersive channel. Conversely, DAPPM requires less power than DH-PIM . When the number of bits per symbol is the same, PAM requires more power, and DH-PIM less power, than DAPPM. Finally, it is shown that the performance of DAPPM can be improved with MLSD, chip-rate DFE, and multichip-rate DFE.

Loop Amplitudes in Pure Yang-Mills from Generalised Unitarity

OpenAIRE

Brandhuber, Andreas; McNamara, Simon; Spence, Bill; Travaglini, Gabriele

2005-01-01

We show how generalised unitarity cuts in D = 4 - 2 epsilon dimensions can be used to calculate efficiently complete one-loop scattering amplitudes in non-supersymmetric Yang-Mills theory. This approach naturally generates the rational terms in the amplitudes, as well as the cut-constructible parts. We test the validity of our method by re-deriving the one-loop ++++, -+++, --++, -+-+ and +++++ gluon scattering amplitudes using generalised quadruple cuts and triple cuts in D dimensions.

Loop amplitudes in pure Yang-Mills from generalised unitarity

International Nuclear Information System (INIS)

Brandhuber, Andreas; McNamara, Simon; Spence, Bill; Travaglini, Gabriele

2005-01-01

We show how generalised unitarity cuts in D = 4-2ε dimensions can be used to calculate efficiently complete one-loop scattering amplitudes in non-supersymmetric Yang-Mills theory. This approach naturally generates the rational terms in the amplitudes, as well as the cut-constructible parts. We test the validity of our method by re-deriving the one-loop ++++, -+++, --++, -+-+ and +++++ gluon scattering amplitudes using generalised quadruple cuts and triple cuts in D dimensions

Loop amplitudes in pure Yang-Mills from generalised unitarity

Energy Technology Data Exchange (ETDEWEB)

Brandhuber, Andreas [Department of Physics, Queen Mary, University of London, Mile End Road, London, E1 4NS (United Kingdom); McNamara, Simon [Department of Physics, Queen Mary, University of London, Mile End Road, London, E1 4NS (United Kingdom); Spence, Bill [Department of Physics, Queen Mary, University of London, Mile End Road, London, E1 4NS (United Kingdom); Travaglini, Gabriele [Department of Physics, Queen Mary, University of London, Mile End Road, London, E1 4NS (United Kingdom)

2005-10-15

We show how generalised unitarity cuts in D = 4-2{epsilon} dimensions can be used to calculate efficiently complete one-loop scattering amplitudes in non-supersymmetric Yang-Mills theory. This approach naturally generates the rational terms in the amplitudes, as well as the cut-constructible parts. We test the validity of our method by re-deriving the one-loop ++++, -+++, --++, -+-+ and +++++ gluon scattering amplitudes using generalised quadruple cuts and triple cuts in D dimensions.

R.G. Collingwood, Analytical Philosophy And Logical Positivism

Directory of Open Access Journals (Sweden)

James Connelly

2009-10-01

Full Text Available R.G. Collingwood is not normally associated with analytic philosophy, neither negatively nor positively. He neither regarded himself, nor was regarded by his contemporaries and their successors, as an analytical philosopher. However, the story is more interestingly complex than this, both because Collingwood is one of the few pre-analytics in the UK who continues to be of interest to current analytical philosophers, especially in relation to the philosophy of art and history and his conception of metaphysics, and because he mounted a critique of analytical philosophy in the years of its emergence.

Paper-Based Analytical Device for Zinc Ion Quantification in Water Samples with Power-Free Analyte Concentration

Directory of Open Access Journals (Sweden)

Hiroko Kudo

2017-04-01

Full Text Available Insufficient sensitivity is a general issue of colorimetric paper-based analytical devices (PADs for trace analyte detection, such as metal ions, in environmental water. This paper demonstrates the colorimetric detection of zinc ions (Zn2+ on a paper-based analytical device with an integrated analyte concentration system. Concentration of Zn2+ ions from an enlarged sample volume (1 mL has been achieved with the aid of a colorimetric Zn2+ indicator (Zincon electrostatically immobilized onto a filter paper substrate in combination with highly water-absorbent materials. Analyte concentration as well as sample pretreatment, including pH adjustment and interferent masking, has been elaborated. The resulting device enables colorimetric quantification of Zn2+ in environmental water samples (tap water, river water from a single sample application. The achieved detection limit of 0.53 μM is a significant improvement over that of a commercial colorimetric Zn2+ test paper (9.7 μM, demonstrating the efficiency of the developed analyte concentration system not requiring any equipment.

Analytical Study on Propagation Dynamics of Optical Beam in Parity-Time Symmetric Optical Couplers

International Nuclear Information System (INIS)

Zhou Zheng; Zhang Li-Juan; Zhu Bo

2015-01-01

We present exact analytical solutions to parity-time (PT) symmetric optical system describing light transport in PT-symmetric optical couplers. We show that light intensity oscillates periodically between two waveguides for unbroken PT-symmetric phase, whereas light always leaves the system from the waveguide experiencing gain when light is initially input at either waveguide experiencing gain or waveguide experiencing loss for broken PT-symmetric phase. These analytical results agree with the recent experimental observation reported by Rüter et al. [Nat. Phys. 6 (2010) 192]. Besides, we present a scheme for manipulating PT symmetry by applying a periodic modulation. Our results provide an efficient way to control light propagation in periodically modulated PT-symmetric system by tuning the modulation amplitude and frequency. (paper)

Generating tree amplitudes in N = 4 SYM and N = 8 SG

International Nuclear Information System (INIS)

Bianchi, Massimo; Elvang, Henriette; Freedman, Daniel Z.

2008-01-01

We study n-point tree amplitudes of N = 4 super Yang-Mills theory and N = 8 supergravity for general configurations of external particles of the two theories. We construct generating functions for n-point MHV and NMHV amplitudes with general external states. Amplitudes derived from them obey SUSY Ward identities, and the generating functions characterize and count amplitudes in the MHV and NMHV sectors. The MHV generating function provides an efficient way to perform the intermediate state helicity sums required to obtain loop amplitudes from trees. The NMHV generating functions rely on the MHV-vertex expansion obtained from recursion relations associated with a 3-line shift of external momenta involving a reference spinor |X]. When the shifted amplitude vanishes for large z for all |X], the sum of MHV-vertex diagrams is independent of |X] and gives the correct amplitude. If the shifted amplitude does not vanish for large z, Cauchy's theorem includes a term at infinity. Examples show that special choices of |X] eliminate this term and the MHV vertex expansion becomes valid at these values. We show that the MHV-vertex expansion of the n-graviton NMHV amplitude for n = 5,6,...,11 is independent of |X] and exhibits the asymptotic behavior z n-12 . Generating functions show how the symmetries of supergravity can be implemented in the quadratic map between supergravity and gauge theory embodied in the KLT and other similar relations between amplitudes in the two theories.

Study of a vibrating plate: comparison between experimental (ESPI) and analytical results

Science.gov (United States)

Romero, G.; Alvarez, L.; Alanís, E.; Nallim, L.; Grossi, R.

2003-07-01

Real-time electronic speckle pattern interferometry (ESPI) was used for tuning and visualization of natural frequencies of a trapezoidal plate. The plate was excited to resonant vibration by a sinusoidal acoustical source, which provided a continuous range of audio frequencies. Fringe patterns produced during the time-average recording of the vibrating plate—corresponding to several resonant frequencies—were registered. From these interferograms, calculations of vibrational amplitudes by means of zero-order Bessel functions were performed in some particular cases. The system was also studied analytically. The analytical approach developed is based on the Rayleigh-Ritz method and on the use of non-orthogonal right triangular co-ordinates. The deflection of the plate is approximated by a set of beam characteristic orthogonal polynomials generated by using the Gram-Schmidt procedure. A high degree of correlation between computational analysis and experimental results was observed.

Analytical Chemistry Laboratory: Progress report for FY 1988

International Nuclear Information System (INIS)

Green, D.W.; Heinrich, R.R.; Graczyk, D.G.; Lindahl, P.C.; Erickson, M.D.

1988-12-01

The purpose of this report is to summarize the activities of the Analytical Chemistry Laboratory (ACL) at Argonne National Laboratory (ANL) for fiscal year 1988 (October 1987 through September 1988). The Analytical Chemistry Laboratory is a full-cost recovery service center, with the primary mission of providing a broad range of analytical chemistry support services to the scientific and engineering programs at ANL. In addition, the ACL conducts a research program in analytical chemistry, works on instrumental and methods development, and provides analytical services for governmental, educational, and industrial organizations. The ACL handles a wide range of analytical problems, from routine standard analyses to unique problems that require significant development of methods and techniques

Analytical Chemistry Laboratory progress report for FY 1989

International Nuclear Information System (INIS)

Green, D.W.; Heinrich, R.R.; Graczyk, D.G.; Lindahl, P.C.; Erickson, M.D.

1989-12-01

The purpose of this report is to summarize the activities of the Analytical Chemistry Laboratory (ACL) at Argonne National Laboratory (ANL) for Fiscal Year 1989 (October 1988 through September 1989). The Analytical Chemistry Laboratory is a full-cost-recovery service center, with the primary mission of providing a broad range of analytical chemistry support services to the scientific and engineering programs at ANL. In addition, the ACL conducts a research program in analytical chemistry, works on instrumental and methods development, and provides analytical services for governmental, educational, and industrial organizations. The ACL handles a wide range of analytical problems, from routine standard analyses to unique problems that require significant development of methods and techniques

Analytical Chemistry Laboratory: Progress report for FY 1988

Energy Technology Data Exchange (ETDEWEB)

Green, D.W.; Heinrich, R.R.; Graczyk, D.G.; Lindahl, P.C.; Erickson, M.D.

1988-12-01

The purpose of this report is to summarize the activities of the Analytical Chemistry Laboratory (ACL) at Argonne National Laboratory (ANL) for fiscal year 1988 (October 1987 through September 1988). The Analytical Chemistry Laboratory is a full-cost recovery service center, with the primary mission of providing a broad range of analytical chemistry support services to the scientific and engineering programs at ANL. In addition, the ACL conducts a research program in analytical chemistry, works on instrumental and methods development, and provides analytical services for governmental, educational, and industrial organizations. The ACL handles a wide range of analytical problems, from routine standard analyses to unique problems that require significant development of methods and techniques.

Some tree-level string amplitudes in the NSR formalism

International Nuclear Information System (INIS)

Becker, Katrin; Becker, Melanie; Melnikov, Ilarion V.; Robbins, Daniel; Royston, Andrew B.

2015-01-01

We calculate tree level scattering amplitudes for open strings using the NSR formalism. We present a streamlined symmetry-based and pedagogical approach to the computations, which we first develop by checking two-, three-, and four-point functions involving bosons and fermions. We calculate the five-point amplitude for massless gluons and find agreement with an earlier result by Brandt, Machado and Medina. We then compute the five-point amplitudes involving two and four fermions respectively, the general form of which has not been previously obtained in the NSR formalism. The results nicely confirm expectations from the supersymmetric F 4 effective action. Finally we use the prescription of Kawai, Lewellen and Tye (KLT) to compute the amplitudes for the closed string sector.

On-shell recurrence relations for one-loop QCD amplitudes

International Nuclear Information System (INIS)

Bern, Zvi; Dixon, Lance J.; Kosower, David A.

2005-01-01

We present examples of on-shell recurrence relations for determining rational functions appearing in one-loop QCD amplitudes. In particular, we give relations for one-loop QCD amplitudes with all legs of positive helicity, or with one leg of negative helicity and the rest of positive helicity. Our recurrence relations are similar to the tree-level ones described by Britto, Cachazo, Feng, and Witten. A number of new features arise for loop amplitudes in nonsupersymmetric theories like QCD, including boundary terms and double poles. We show how to eliminate the boundary terms, which would interfere with obtaining useful relations. Using the relations we give compact explicit expressions for the n-gluon amplitudes with one negative-helicity gluon, up through n=7

Scattering Amplitudes and Worldsheet Models of QFTs

CERN Multimedia

CERN. Geneva

2016-01-01

I will describe recent progress on the study of scattering amplitudes via ambitwistor strings and the scattering equations. Ambitwistor strings are worldsheet models of quantum field theories, inspired by string theory. They naturally lead to a representation of amplitudes based on the scattering equations. While worldsheet models and related ideas have had a wide-ranging impact on the modern study of amplitudes, their direct application at loop level is a very recent success. I will show how a major difficulty in the loop-level story, the technicalities of higher-genus Riemann surfaces, can be avoided by turning the higher-genus surface into a nodal Riemann sphere, with the nodes representing the loop momenta. I will present new formulas for the one-loop integrands of gauge theory and gravity, with or without supersymmetry, and also some two-loop results.

Multiphoton amplitude in a constant background field

Science.gov (United States)

Ahmad, Aftab; Ahmadiniaz, Naser; Corradini, Olindo; Kim, Sang Pyo; Schubert, Christian

2018-01-01

In this contribution, we present our recent compact master formulas for the multiphoton amplitudes of a scalar propagator in a constant background field using the worldline fomulation of quantum field theory. The constant field has been included nonperturbatively, which is crucial for strong external fields. A possible application is the scattering of photons by electrons in a strong magnetic field, a process that has been a subject of great interest since the discovery of astrophysical objects like radio pulsars, which provide evidence that magnetic fields of the order of 1012G are present in nature. The presence of a strong external field leads to a strong deviation from the classical scattering amplitudes. We explicitly work out the Compton scattering amplitude in a magnetic field, which is a process of potential relevance for astrophysics. Our final result is compact and suitable for numerical integration.

Gluon cascades and amplitudes in light-front perturbation theory

International Nuclear Information System (INIS)

Cruz-Santiago, C.A.; Staśto, A.M.

2013-01-01

We construct the gluon wave functions, fragmentation functions and scattering amplitudes within the light-front perturbation theory. Recursion relations on the light-front are constructed for the wave functions and fragmentation functions, which in the latter case are the light-front analogs of the Berends–Giele recursion relations. Using general relations between wave functions and scattering amplitudes it is demonstrated how to obtain the maximally-helicity violating amplitudes, and explicit verification of the results is based on simple examples.

Top quark amplitudes with an anomalous magnetic moment

International Nuclear Information System (INIS)

Larkoski, Andrew J.; Peskin, Michael E.

2011-01-01

The anomalous magnetic moment of the top quark may be measured during the first run of the LHC at 7 TeV. For these measurements, it will be useful to have available tree amplitudes with tt and arbitrarily many photons and gluons, including both QED and color anomalous magnetic moments. In this paper, we present a method for computing these amplitudes using the Britto-Cachazo-Feng-Witten recursion formula. Because we deal with an effective theory with higher-dimension couplings, there are roadblocks to a direct computation with the Britto-Cachazo-Feng-Witten method. We evade these by using an auxiliary scalar theory to compute a subset of the amplitudes.

Generating Tree Amplitudes in $N$=4 SYM and $N$ = 8 SG

CERN Document Server

Bianchi, Massimo; Freedman, Daniel Z

2008-01-01

We study n-point tree amplitudes of N=4 super Yang-Mills theory and N=8 supergravity for general configurations of external particles of the two theories. We construct generating functions for n-point MHV and NMHV amplitudes with general external states. Amplitudes derived from them obey SUSY Ward identities, and the generating functions characterize and count amplitudes in the MHV and NMHV sectors. The MHV generating function provides an efficient way to perform the intermediate state helicity sums required to obtain loop amplitudes from trees. The NMHV generating functions rely on the MHV-vertex expansion obtained from recursion relations associated with a 3-line shift of external momenta involving a reference spinor |X]. The recursion relations remain valid for a subset of N=8 supergravity amplitudes although they do not vanish asymptotically for all |X]. The MHV-vertex expansion of the n-graviton NMHV amplitude for n=5,6,...,11 is independent of |X] and exhibits the asymptotic behavior z^{n-12}. This pres...

Disappearance of Anisotropic Intermittency in Large-amplitude MHD Turbulence and Its Comparison with Small-amplitude MHD Turbulence

Science.gov (United States)

Yang, Liping; Zhang, Lei; He, Jiansen; Tu, Chuanyi; Li, Shengtai; Wang, Xin; Wang, Linghua

2018-03-01

Multi-order structure functions in the solar wind are reported to display a monofractal scaling when sampled parallel to the local magnetic field and a multifractal scaling when measured perpendicularly. Whether and to what extent will the scaling anisotropy be weakened by the enhancement of turbulence amplitude relative to the background magnetic strength? In this study, based on two runs of the magnetohydrodynamic (MHD) turbulence simulation with different relative levels of turbulence amplitude, we investigate and compare the scaling of multi-order magnetic structure functions and magnetic probability distribution functions (PDFs) as well as their dependence on the direction of the local field. The numerical results show that for the case of large-amplitude MHD turbulence, the multi-order structure functions display a multifractal scaling at all angles to the local magnetic field, with PDFs deviating significantly from the Gaussian distribution and a flatness larger than 3 at all angles. In contrast, for the case of small-amplitude MHD turbulence, the multi-order structure functions and PDFs have different features in the quasi-parallel and quasi-perpendicular directions: a monofractal scaling and Gaussian-like distribution in the former, and a conversion of a monofractal scaling and Gaussian-like distribution into a multifractal scaling and non-Gaussian tail distribution in the latter. These results hint that when intermittencies are abundant and intense, the multifractal scaling in the structure functions can appear even if it is in the quasi-parallel direction; otherwise, the monofractal scaling in the structure functions remains even if it is in the quasi-perpendicular direction.

No Refund or Full Refund: When Should a Fashion Brand Offer Full Refund Consumer Return Service for Mass Customization Products?

Directory of Open Access Journals (Sweden)

Tsan-Ming Choi

2013-01-01

Full Text Available We analytically explore in this paper the consumer return policy under fashion mass customization (MC program. To be specific, we model the stochastic fashion MC program with the consideration of consumer demand uncertainty. If a consumer return policy is implemented, we further consider return uncertainty. By modeling the optimization objective of the risk averse MC fashion brand via a mean-variance approach, we derive the closed-form optimal solution under each case. We then conduct both analytical and numerical sensitivity analyses. For the scenario with full refund and return, we reveal the analytical conditions under which the optimal retail price and the optimal number of options available for customization (called the “optimal modularity level” vary monotonically with respect to the salvage value and the return service charge. For the scenario when there is no refund and return, we show that the optimal retail price and the optimal modularity level are decreasing in the MC fashion brand's degree of risk aversion, the demand uncertainty, and the price-demand sensitivity coefficient. In addition, our numerical analysis indicates that whether the risk averse MC fashion brand would prefer offering consumer return with full refund to no return depends heavily on the demand-return correlation (DRC parameter.

A Contrast on Conductor Galloping Amplitude Calculated by Three Mathematical Models with Different DOFs

Directory of Open Access Journals (Sweden)

Bin Liu

2014-01-01

Full Text Available It is pivotal to find an effective mathematical model revealing the galloping mechanism. And it is important to compare the difference between the existing mathematical models on the conductor galloping. In this paper, the continuum cable model for transmission lines was proposed using the Hamilton principle. Discrete models of one DOF, two DOFs, and three DOFs were derived from the continuum model by using the Garlekin method. And the three models were compared by analyzing the galloping vertical amplitude and torsional angle with different influence factors. The influence factors include wind velocity, flow density, span length, damping ratio, and initial tension. The three-DOF model is more accurate at calculating the galloping characteristics than the other two models, but the one-DOF and two-DOF models can also present the trend of galloping amplitude change from the point view of qualitative analysis. And the change of the galloping amplitude relative to the main factors was also obtained, which is very essential to the antigalloping design applied in the actual engineering.

Smart city analytics

DEFF Research Database (Denmark)

Hansen, Casper; Hansen, Christian; Alstrup, Stephen

2017-01-01

We present an ensemble learning method that predicts large increases in the hours of home care received by citizens. The method is supervised, and uses different ensembles of either linear (logistic regression) or non-linear (random forests) classifiers. Experiments with data available from 2013 ...... is very useful when full records are not accessible or available. Smart city analytics does not necessarily require full city records. To our knowledge this preliminary study is the first to predict large increases in home care for smart city analytics.......We present an ensemble learning method that predicts large increases in the hours of home care received by citizens. The method is supervised, and uses different ensembles of either linear (logistic regression) or non-linear (random forests) classifiers. Experiments with data available from 2013...... to 2017 for every citizen in Copenhagen receiving home care (27,775 citizens) show that prediction can achieve state of the art performance as reported in similar health related domains (AUC=0.715). We further find that competitive results can be obtained by using limited information for training, which...

Renormalization in the complete Mellin representation of Feynman amplitudes

International Nuclear Information System (INIS)

Calan, C. de; David, F.; Rivasseau, V.

1981-01-01

The Feynmann amplitudes are renormalized in the formalism of the CM representation. This Mellin-Barnes type integral representation, previously introduced for the study of asymptotic behaviours, is shown to have the following interesting property: in contrast with the usual subtraction procedures, the renormalization leaves the CM intergrand unchanged, and only results into translations of the integration path. The explicit CM representation of the renormalized amplitudes is given. In addition, the dimensional regularization and the extension to spinor amplitudes are sketched. (orig.)

Improving the signal visibility of optical-disk-drive sensors by analyte patterning and frequency-domain analysis

International Nuclear Information System (INIS)

Schaefer, S; Chau, K J

2011-01-01

One limitation of using compact disks (CDs) and optical disk drives for sensing and imaging of analytes placed on a CD is the fluctuations in the voltage signal from the disk drive generated while reading the data on the CD. In this study, we develop a simple, low-cost strategy for sensing and identification using CDs and optical disk drives that spectrally separates contributions to the voltage signal caused by an analyte intentionally placed onto the CD and that caused by the underlying data on the CD. Analytes are printed onto a CD surface with fixed spatial periodicity. As the laser beam in an optical disk drive scans over the section of the CD containing the analyte pattern, the intensity of the laser beam incident onto the photodiode integrated into the disk drive is modulated at a frequency dependent on the spatial periodicity of the analyte pattern and the speed of the optical-disk-drive motor. Fourier transformation of the voltage signal from the optical disk drive yields peaks in the frequency spectrum with amplitudes and locations that enable analyte sensing and identification, respectively. We study the influence of analyte area coverage, pattern periodicity, and CD rotational frequency on the peaks in the frequency spectrum associated with the patterned analyte. We apply this technique to discriminate differently-colored analytes, perform trigger-free detection of multiple analytes distributed on a single CD, and detect at least two different, overlapped analyte patterns on a single CD. The extension of this technique for sensing and identification of colorimetric chemical reagents is discussed

Corrections to the box diagram amplitude due to kaon mass

International Nuclear Information System (INIS)

Datta, A.; Kumbhakar, D.

1985-08-01

The K 0 -anti-K 0 mixing amplitude is calculated without using the standard zero external momentum approximation. The resulting corrections are numerically significant for the real part of the amplitude. In the imaginary part of the amplitude the effects of similar corrections are less important. Implications for Δmsub(k) and epsilon are discussed. (author)

Cryptography based on neural networks - analytical results

International Nuclear Information System (INIS)

Rosen-Zvi, Michal; Kanter, Ido; Kinzel, Wolfgang

2002-01-01

The mutual learning process between two parity feed-forward networks with discrete and continuous weights is studied analytically, and we find that the number of steps required to achieve full synchronization between the two networks in the case of discrete weights is finite. The synchronization process is shown to be non-self-averaging and the analytical solution is based on random auxiliary variables. The learning time of an attacker that is trying to imitate one of the networks is examined analytically and is found to be much longer than the synchronization time. Analytical results are found to be in agreement with simulations. (letter to the editor)

Nonlinear Saturation Amplitude in Classical Planar Richtmyer–Meshkov Instability

International Nuclear Information System (INIS)

Liu Wan-Hai; Jiang Hong-Bin; Ma Wen-Fang; Wang Xiang

2016-01-01

The classical planar Richtmyer–Meshkov instability (RMI) at a fluid interface supported by a constant pressure is investigated by a formal perturbation expansion up to the third order, and then according to definition of nonlinear saturation amplitude (NSA) in Rayleigh–Taylor instability (RTI), the NSA in planar RMI is obtained explicitly. It is found that the NSA in planar RMI is affected by the initial perturbation wavelength and the initial amplitude of the interface, while the effect of the initial amplitude of the interface on the NSA is less than that of the initial perturbation wavelength. Without marginal influence of the initial amplitude, the NSA increases linearly with wavelength. The NSA normalized by the wavelength in planar RMI is about 0.11, larger than that corresponding to RTI. (paper)

Gluon amplitudes as 2 d conformal correlators

Science.gov (United States)

Pasterski, Sabrina; Shao, Shu-Heng; Strominger, Andrew

2017-10-01

Recently, spin-one wave functions in four dimensions that are conformal primaries of the Lorentz group S L (2 ,C ) were constructed. We compute low-point, tree-level gluon scattering amplitudes in the space of these conformal primary wave functions. The answers have the same conformal covariance as correlators of spin-one primaries in a 2 d CFT. The Britto-Cachazo-Feng-Witten (BCFW) recursion relation between three- and four-point gluon amplitudes is recast into this conformal basis.

Multiphoton states and amplitude k-th power squeezing

International Nuclear Information System (INIS)

Buzek, V.; Jex, I.

1991-01-01

On the basis of the work of d'Ariano and coworkers a new type of multiphoton states is introduced. Amplitude k-th power squeezing of the multiphoton states are analysed. In particular, it is shown that even if the multiphoton states do not exhibit ordinary squeezing they can be amplitude k-th power squeezed

Higher-order spin effects in the amplitude and phase of gravitational waveforms emitted by inspiraling compact binaries: Ready-to-use gravitational waveforms

International Nuclear Information System (INIS)

Arun, K. G.; Buonanno, Alessandra; Ochsner, Evan; Faye, Guillaume

2009-01-01

We provide ready-to-use time-domain gravitational waveforms for spinning compact binaries with precession effects through 1.5 post-Newtonian (PN) order in amplitude, and compute their mode decomposition using spin-weighted -2 spherical harmonics. In the presence of precession, the gravitational-wave modes (l,m) contain harmonics originating from combinations of the orbital frequency and precession frequencies. We find that the gravitational radiation from binary systems with large mass asymmetry and large inclination angle can be distributed among several modes. For example, during the last stages of inspiral, for some maximally spinning configurations, the amplitude of the (2, 0) and (2, 1) modes can be comparable to the amplitude of the (2, 2) mode. If the mass ratio is not too extreme, the l=3 and l=4 modes are generally 1 or 2 orders of magnitude smaller than the l=2 modes. Restricting ourselves to spinning, nonprecessing compact binaries, we apply the stationary-phase approximation and derive the frequency-domain gravitational waveforms including spin-orbit and spin(1)-spin(2) effects through 1.5PN and 2PN order, respectively, in amplitude, and 2.5PN order in phase. Since spin effects in the amplitude through 2PN order affect only the first and second harmonics of the orbital phase, they do not extend the mass reach of gravitational-wave detectors. However, they can interfere with other harmonics and lower or raise the signal-to-noise ratio depending on the spin orientation. These ready-to-use waveforms could be employed in the data analysis of the spinning, inspiraling binaries as well as in comparison studies at the interface between analytical and numerical relativity.

Quantum Wronskian approach to six-point gluon scattering amplitudes at strong coupling