Analytization of elastic scattering amplitude
Troshin, S M
2016-01-01
Dependence of the real part of the elastic scattering amplitude on the transferred momentum -t at the asymptotical energies has been restored from the corresponding imaginary part on the basis of derivative analyticity relations (analytization).
Analytic Representations of Yang-Mills Amplitudes
Bjerrum-Bohr, N E J; Damgaard, Poul H; Feng, Bo
2016-01-01
Scattering amplitudes in Yang-Mills theory can be represented in the formalism of Cachazo, He and Yuan (CHY) as integrals over an auxiliary projective space---fully localized on the support of the scattering equations. Because solving the scattering equations is difficult and summing over the solutions algebraically complex, a method of directly integrating the terms that appear in this representation has long been sought. We solve this important open problem by first rewriting the terms in a manifestly Mobius-invariant form and then using monodromy relations (inspired by analogy to string theory) to decompose terms into those for which combinatorial rules of integration are known. The result is a systematic procedure to obtain analytic, covariant forms of Yang-Mills tree-amplitudes for any number of external legs and in any number of dimensions. As examples, we provide compact analytic expressions for amplitudes involving up to six gluons of arbitrary helicities.
Analytic amplitude models for forward scattering
Kang, K.; Cudell, Jean-René; Ezhela, V. V.; Gauron, P.; Kuyanov, Yu. V.; Lugovsky, S. V.; Nicolescu, B.; Tkachenko, N. P.
2001-01-01
We report on fits of a large class of analytic amplitude models for forward scattering against the comprehensive data for all available reactions. To differentiate the goodness of the fits of many possible parametrizations to a large sample of data, we developed and used a set of quantitative indicators measuring statistical quality of the fits over and beyond the typical criterion of the $\\Chi^2 /dof$. These indicators favor models with a universal $ log^2 s$ Pomeron term, which enables one ...
Analytic amplitudes for hadronic forward scattering: COMPETE update
We consider several classes of analytic parametrizations of hadronic scattering amplitudes, and compare their predictions to all available forward data (pp, p-bar p, πp, Kp, γp, γγ, Σp). Although these parametrizations are very close for √s ≥ 9 GeV, it turns out that they differ markedly at low energy, where a universal Pomeron term ∼ ln2 s enables one to extend the fit down to √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 (ρ parameter) for present and future pp and p-bar p colliders, and on the total cross sections for γp → hadrons at cosmic-ray energies and for γγ → hadrons up to √s = 1 TeV
Full phase and amplitude control in computer-generated holography.
Fratz, Markus; Fischer, Peer; Giel, Dominik M
2009-12-01
We report what we believe to be the first realization of a computer-generated complex-valued hologram recorded in a single film of photoactive polymer. Complex-valued holograms give rise to a diffracted optical field with control over its amplitude and phase. The holograms are generated by a one-step direct laser writing process in which a spatial light modulator (SLM) is imaged onto a polymer film. Temporal modulation of the SLM during exposure controls both the strength of the induced birefringence and the orientation of the fast axis. We demonstrate that complex holograms can be used to impart arbitrary amplitude and phase profiles onto a beam and thereby open new possibilities in the control of optical beams. PMID:19953153
Analytic Computations of Massive One-Loop Amplitudes
Badger, Simon; Yundin, Valery
2010-01-01
We show some new applications of on-shell methods to calculate compact helicity amplitudes for t tbar production through gluon fusion. The rational and mass renormalisation contributions are extracted from two independent Feynman diagram based approaches.
Analytical approximations for stick-slip vibration amplitudes
Thomsen, Jon Juel; Fidlin, A.
2003-01-01
The classical "mass-on-moving-belt" model for describing friction-induced vibrations is considered, with a friction law describing friction forces that first decreases and then increases smoothly with relative interface speed. Approximate analytical expressions are derived for the conditions, the...
Maharana, Jnanadeva
2016-01-01
The properties of the high energy behavior of the scattering amplitude of massive, neutral and spinless particles in higher dimensional field theories are investigated. The axiomatic formulation of Lehmann, Symanzik and Zimmermann is adopted. The analyticity properties of the causal, the retarded and the advanced functions associated with the four point elastic amplitudes are studied. The analog of the Lehmann-Jost-Dyson representation is obtained in higher dimensional field theories. The generalized J-L-D representation is utilized to derive the t-plane analyticity property of the amplitude. The existence of an ellipse analogous to the Lehmann ellipse is demonstrated. Thus a fixed-t dispersion relation can be written down with finite number of subtractions due to the temperedness of the amplitudes. The domain of analyticity of scattering amplitude in $s$ and $t$ variables is extended by imposing unitarity constraints. A generalized version of Martin's theorem is derived to prove the existence of such a domai...
Analytical approximations for the amplitude and period of a relaxation oscillator
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.
Hardware architecture for full analytical Fraunhofer computer-generated holograms
Pang, Zhi-Yong; Xu, Zong-Xi; Xiong, Yi; Chen, Biao; Dai, Hui-Min; Jiang, Shao-Ji; Dong, Jian-Wen
2015-09-01
Hardware architecture of parallel computation is proposed for generating Fraunhofer computer-generated holograms (CGHs). A pipeline-based integrated circuit architecture is realized by employing the modified Fraunhofer analytical formulism, which is large scale and enables all components to be concurrently operated. The architecture of the CGH contains five modules to calculate initial parameters of amplitude, amplitude compensation, phases, and phase compensation, respectively. The precalculator of amplitude is fully adopted considering the "reusable design" concept. Each complex operation type (such as square arithmetic) is reused only once by means of a multichannel selector. The implemented hardware calculates an 800×600 pixels hologram in parallel using 39,319 logic elements, 21,074 registers, and 12,651 memory bits in an Altera field-programmable gate array environment with stable operation at 50 MHz. Experimental results demonstrate that the quality of the images reconstructed from the hardware-generated hologram can be comparable to that of a software implementation. Moreover, the calculation speed is approximately 100 times faster than that of a personal computer with an Intel i5-3230M 2.6 GHz CPU for a triangular object.
R. A. Jafari-Talookolaei
2011-01-01
Full Text Available The aim of this paper is to present analytical and exact expressions for the frequency and buckling of large amplitude vibration of the symmetrical laminated composite beam (LCB with simple and clamped end conditions. The equations of motion are derived by using Hamilton's principle. The influences of axial force, Poisson effect, shear deformation, and rotary inertia are taken into account in the formulation. First, the geometric nonlinearity based on the von Karman's assumptions is incorporated in the formulation while retaining the linear behavior for the material. Then, the displacement fields used for the analysis are coupled using the equilibrium equations of the composite beam. Substituting this coupled displacement fields in the potential and kinetic energies and using harmonic balance method, we obtain the ordinary differential equation in time domain. Finally, applying first order of homotopy analysis method (HAM, we get the closed form solutions for the natural frequency and deflection of the LCB. A detailed numerical study is carried out to highlight the influences of amplitude of vibration, shear deformation and rotary inertia, slenderness ratios, and layup in the case of laminates on the natural frequency and buckling load.
Full Complex Amplitude Digital Holograms:Design,Fabrication and Optical Characterization
Neto L G; Cardona P S P; Cirino G A; Mansanoc R D; Verdonck P
2004-01-01
Diffractive optical elements have a large number of industrial applications, such as beam shaping and optical filtering. Traditionally, these elements modulate the phase of the incoming light or its amplitude, but not both. To overcome this limitation, full complex-amplitude modulation diffractive optical elements were developed. Well-established integrated circuit fabrication steps were employed to fabricate the devices with high precision. Using this approach, the new element's optical performances are improved also for near field operations. With this device it is possible to obtain 100% efficient spatial filtering and low noise reconstructed images.
Elastic scattering processes at large angles are considered in the framework of the method of generalized reaction matrix. The power law for the decrease of the differential cross section appears as a consequence of the analytical properties of the scattering amplitude. Angular dependence for the cross section is calculated
Analytic properties of high energy production amplitudes in N=4 SUSY
Lipatov, L.N. [St. Petersburg Inst. of Nuclear Physics, Gatchina (Russian Federation); Hamburg Univ. (Germany). 1. Inst. fuer Theoretische Physik
2010-08-15
We investigate analytic properties of the six point planar amplitude in N=4 SUSY at the multi-Regge kinematics for final state particles. For inelastic processes the Steinmann relations play an important role because they give a possibility to fix the phase structure of the Regge pole and Mandelstam cut contributions. The analyticity and factorization constraints allow us to reproduce the two-loop correction to the 6- point BDS amplitude in N=4 SUSY obtained earlier in the leading logarithmic approximation with the use of the s-channel unitarity. The cut contribution has the Moebius invariant form in the transverse momentum subspace. The exponentiation hypothesis for the amplitude in the multi-Regge kinematics is also investigated in LLA. (orig.)
Analytic Properties of DPE Amplitudes or Collinear Factorisation for Central Exclusive Production
Teryaev, O V
2010-01-01
Analytic and crossing properties of amplitudes of the central exclusive production (CEP) are considered using the formalism of collinear Generalised Parton Distributions (GPDs). The analytic continuation from unphysical region is considered which leads to the finite expression. The natural interpretation of the emerging cuts corresponds to double spectral density in overlapping channel due to the instability of produced particle and inapplicability of Steinmann relations. The relations of CEP amplitudes to the exclusive decay rates are discussed. The direct calculation in physical region results in violation of factorisation similar to the discussed recently for pion transition and electromagnetic form-factors. The similarity between Feynman mechanism for form-factor and Durham model is pointed out.
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
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.
Full Analytic Progress Curves of Enzymic Reactions in Vitro
Vasile Ostafe
2006-11-01
Full Text Available Assuming the in vitro conditions for the enzyme-catalyzed reactions, the basic Michaelis-Menten description is modified in a logistic (mathematical manner such that the inherent limitations that appear in the previous method are removed. Beside its generality, the reliability of the present approach is proved through applications on the competitive multi- and bi- substrate enzyme catalyses.
You, Jiachun; Li, Guangcai; Liu, Xuewei; Han, Wengong; Zhang, Guangde
2016-03-01
Most depth extrapolation schemes are based on a one-way wave equation, which possesses limited ability to provide the true amplitude values of reflectors that are highly important for amplitude-versus-offset inversion. After analysing the weaknesses of current migration methods and explaining the reason why wavefields cannot be extrapolated using the full-wave equation in the depth direction, a full-wave-equation migration method based on a new seismic acquisition system is proposed to provide accurately dynamic information of reflection interfaces for migration. In this new seismic acquisition system, double sensor data are provided to solve the acoustic wave equation in the depth domain accurately. To test the performance of recovering the true amplitudes of the full-wave-equation migration, we used a single shot gather and several multiple shot gathers produced by a 2-D numerical modelling technique to demonstrate that our methodology provides better estimated true amplitudes than that of the conventional Kirchhoff and reverse time migration algorithms through comparison of the amplitudes of the target reflectors with its theoretical reflection coefficients. Because double sensors are applied to implement the full-wave-equation migration, it is necessary to study the perfect distance between the double sensors to diminish the migration error for future practical exploration. Based on the application of the full-wave-equation migration method to the first set of actual seismic data collected from our double sensor acquisition system, our proposed method yields higher imaging quality than that of conventional methods. Numerical experiments and actual seismic data show that our proposed method has built a new bridge between true amplitude common-shot migration and full-wave-equation depth extrapolation.
Badger, Simon; Hackl, Lucas; Plefka, Jan; Schuster, Theodor; Uwer, Peter
2012-01-01
Recent advances in our understanding of tree-level QCD amplitudes in the massless limit exploiting an effective (maximal) supersymmetry have led to the complete analytic construction of tree-amplitudes with up to four external quark-anti-quark pairs. In this work we compare the numerical efficiency of evaluating these closed analytic formulae to a numerically efficient implementation of the Berends-Giele recursion. We compare calculation times for tree-amplitudes with parton numbers ranging from 4 to 25 with no, one, two and three external quark lines. We find that the exact results are generally faster in the case of MHV and NMHV amplitudes. Starting with the NNMHV amplitudes the Berends-Giele recursion becomes more efficient. In addition to the runtime we also compared the numerical accuracy. The analytic formulae are on average more accurate than the off-shell recursion relations though both are well suited for complicated phenomenological applications. In both cases we observe a reduction in the average a...
Analytic Result for the Two-loop Six-point NMHV Amplitude in N = 4 Super Yang-Mills Theory
Dixon, Lance J.; /SLAC; Drummond, James M.; /CERN /Annecy, LAPTH; Henn, Johannes M.; /Humboldt U., Berlin /Princeton, Inst. Advanced Study
2012-02-15
We provide a simple analytic formula for the two-loop six-point ratio function of planar N = 4 super Yang-Mills theory. This result extends the analytic knowledge of multi-loop six-point amplitudes beyond those with maximal helicity violation. We make a natural ansatz for the symbols of the relevant functions appearing in the two-loop amplitude, and impose various consistency conditions, including symmetry, the absence of spurious poles, the correct collinear behavior, and agreement with the operator product expansion for light-like (super) Wilson loops. This information reduces the ansatz to a small number of relatively simple functions. In order to fix these parameters uniquely, we utilize an explicit representation of the amplitude in terms of loop integrals that can be evaluated analytically in various kinematic limits. The final compact analytic result is expressed in terms of classical polylogarithms, whose arguments are rational functions of the dual conformal cross-ratios, plus precisely two functions that are not of this type. One of the functions, the loop integral {Omega}{sup (2)}, also plays a key role in a new representation of the remainder function R{sub 6}{sup (2)} in the maximally helicity violating sector. Another interesting feature at two loops is the appearance of a new (parity odd) x (parity odd) sector of the amplitude, which is absent at one loop, and which is uniquely determined in a natural way in terms of the more familiar (parity even) x (parity even) part. The second non-polylogarithmic function, the loop integral {tilde {Omega}}{sup (2)}, characterizes this sector. Both {Omega}{sup (2)} and {tilde {Omega}}{sup (2)} can be expressed as one-dimensional integrals over classical polylogarithms with rational arguments.
Nuss, E
1997-01-01
We discuss the tests of general Three Gauge Boson Vertices (TGV) through bosonic pair production at present and future hadron colliders. All bosonic final states are reviewed via the tree level quark-antiquark annihilation sub-process. The full analytic expressions of the helicity amplitudes and cross-sections are given. These expressions should be useful in any attempt to disentangle the effects of the most general non standard $WWV (V=\\gamma,Z)$ vertices including 14 free parameters. We investigate the sensitivity of the invariant mass and transverse momentum distributions to the full set of anomalous couplings including final state polarization structures. We particularly consider these features at the projected CERN Large Hadron Collider (LHC) energy scale.
Thomas, Robert E; Overy, Catherine; Knowles, Peter J; Alavi, Ali; 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 suf...
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.
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
A Big Data Analytics Pipeline for the Analysis of TESS Full Frame Images
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.
Analytic model of near-field radio-frequency sheaths. II. Full plasma dielectric
An analytic model is derived for electromagnetic radio-frequency (rf) wave propagation in a plasma-filled waveguide with rf sheath boundary conditions. The model gives a simplified description of the rf fields and sheath potentials near an ion cyclotron range of frequencies antenna under certain conditions. The present work lifts the restriction to a low density plasma ('tenuous plasma model') described in a previous paper [D. A. D'Ippolito and J. R. Myra, Phys. Plasmas 16, 022506 (2009)] to include the full plasma dielectric tensor with the ordering εperpendicular∼εx∼1, ε||>>1 for the case where the magnetic field is well aligned with the antenna. It is shown that retaining εx∼1 provides an additional drive term for the rf sheath. This effect is shown to be negligible in most practical situations suggesting that the tenuous plasma model does not miss any essential finite-density effects. The condition to recover the tenuous plasma result is derived. Expressions for the sheath voltage and sheath power dissipation are given in the arbitrary density limit, and a comparison of several mechanisms for dissipating power in rf sheaths is discussed.
Twist-2 at seven loops in planar N=4 SYM theory: Full result and analytic properties
Marboe, Christian
2016-01-01
The anomalous dimension of twist-2 operators of arbitrary spin in planar N=4 SYM theory is found at seven loops by using the quantum spectral curve to compute values at fixed spin, and reconstructing the general result using the LLL-algorithm together with modular arithmetic. The result of the analytic continuation to negative spin is presented, and its relation with the recently computed correction to the BFKL and double-logarithmic equation is discussed.
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.
The evolution of the binary population in globular clusters: a full analytical computation
Sollima, A
2008-01-01
I present a simplified analytical model that simulates the evolution of the binary population in a dynamically evolving globular cluster. A number of simulations have been run spanning a wide range in initial cluster and environmental conditions by taking into account the main mechanisms of formation and destruction of binary systems. Following this approach, I investigate the evolution of the fraction, the radial distribution, the distribution of mass ratios and periods of the binary population. According to these simulations, the fraction of surviving binaries appears to be dominated by the processes of binary ionization and evaporation. In particular, the frequency of binary systems changes by a factor 1-5 depending on the initial conditions and on the assumed initial distribution of periods. The comparison with the existing estimates of binary fractions in Galactic globular clusters suggests that significant variations in the initial binary content could exist among the analysed globular cluster. This mod...
Two new types of IP-2 (Industrial Package Type 2) to transport low and intermediate level radioactive waste (LILW) steel drums from nuclear power plants to a disposal facility have been developed in accordance with the IAEA and Korean regulations for radioactive materials. According to the regulations, both packages must preserve their structural performance after they are subjected to 0.9 m free drop tests, which are prescribed as normal conditions. In this study, an advanced analytical simulation and an evaluation process using the finite element (FE) method have been developed for the design assessment of the newly developed IP-2s. Then, analytical simulations for the various drop orientations were performed to evaluate the structural performance of the packages and demonstrate their compliance with the regulatory requirements. Also, full-scale drop tests were carried out to verify the numerical tools and modeling methodology used in the analyses and to confirm the performance of the IP-2s. In addition, parametric studies are carried out to investigate the sensitivity of the analytical variables, such as the material model and modeling methodology. In addition, this paper intends to provide basic guidance on the analytical simulation and evaluation process specifically for Korean types of transport packages, because numerous transport packages must now be developed for the various kinds of LILW that have accumulated in temporary storage facilities in Korea.
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)
Discontinuity formulas for multiparticle amplitudes
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
Discontinuity formulas for multiparticle amplitudes
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.
In the framework of the chemical characterisation of low alloy steels, we carry out the analytical determination of C and S by total combustion, followed by a Non Dispersive Infra Red (NDIR) quantitative detection. Accurately weighed samples are fully oxidised under a controlled flow of pure oxygen passing through a tubular furnace heated up to 1350 deg. C. The combustion gases are filtered and dried by flowing through adequate chemical traps. Next, the gases pass along two detection chambers mounted in series where the IR absorbance of carbon dioxide (at λ = 4.26 μm) and sulphur dioxide (at λ = 7.3 μm) are measured and integrated with respect to time. The present report describes the detailed analytic procedures and the validation of the method. Several practical aspects related to the technique are being highlighted as well. (author)
Direct Calculation of the Scattering Amplitude Without Partial Wave Analysis
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.
Latyshev, A V
2016-01-01
In the present work the second Stokes problem about behaviour of the rarefied gas filling half-space is formulated. A plane limiting half-space makes harmonious fluctuations with variable amplitude in the plane. The amplitude changes on the exponential law. The kinetic equation with model integral of collisions in the form $\\tau$-model is used. The case of diffusion reflexions of gas molecules from a wall is considered. Eigen solutions (continuous modes) of the initial kinetic equation corresponding to the continuous spectrum are searched. Properties of dispersion function are studied. It is investigated the discrete spectrum of the problem consisting of zero of the dispersion functions in the complex plane. It is shown, that number of zero of dispersion function to equally doubled index of problem coefficient. The problem coefficient is understood as the relation of boundary values of dispersion function from above and from below on the real axis. Further are eigen solutions (discrete modes) of the initial k...
Hurlbatt, A.; O’Connell, D.; Gans, T.
2016-08-01
Analytical and numerical models allow investigation of complicated discharge phenomena and the interplay that makes plasmas such a complex environment. Global models are quick to implement and can have almost negligible computation cost, but provide only bulk or spatially averaged values. Full fluid models take longer to develop, and can take days to solve, but provide accurate spatio-temporal profiles of the whole plasma. The work presented here details a different type of model, analytically similar to fluid models, but computationally closer to a global model, and able to give spatially resolved solutions for the challenging environment of electronegative plasmas. Included are non-isothermal electrons, gas heating, and coupled neutral dynamics. Solutions are reached in seconds to minutes, and spatial profiles are given for densities, fluxes, and temperatures. This allows the semi-analytical model to fill the gap that exists between global and full fluid models, extending the tools available to researchers. The semi-analytical model can perform broad parameter sweeps that are not practical with more computationally expensive models, as well as exposing non-trivial trends that global models cannot capture. Examples are given for a low pressure oxygen CCP. Excellent agreement is shown with a full fluid model, and comparisons are drawn with the corresponding global model.
CHY formula and MHV amplitudes
Du, Yi-jian; Wu, Yong-shi
2016-01-01
In this paper, we study the relation between the Cachazo-He-Yuan (CHY) formula and the maximal-helicity-violating (MHV) amplitudes of Yang-Mills and gravity in four dimensions. We prove that only one special rational solution of the scattering equations found by Weinzierl support the MHV amplitudes. Namely, localized at this solution, the integrated CHY formula reproduces the Parke-Taylor formula for Yang-Mills amplitudes as well as the Hodges formula for gravitational amplitudes. This is achieved by developing techniques, in a manifestly M\\"obius covariant formalism, to explicitly compute relevant reduced Pfaffians/determinants. We observe and prove two interesting properties (or identities), which facilitate the computations. We also check that all the other $(n-3)!-1$ solutions to the scattering equations do not support the MHV amplitudes, and prove analytically that this is indeed true for the other special rational solution proposed by Weinzierl, that actually supports the anti-MHV amplitudes.
张志田; 陈政清
2011-01-01
涡激共振是大跨桥梁最易出现的一种风振现象,其研究手段以节段模型风洞试验为主。节段模型涡振振幅与实桥涡振振幅如何转换,目前我国《公路桥梁抗风设计规范》缺少相关说明。本文首先介绍了桥梁涡激共振时三种涡振力理论模型的特点,包括线性模型、非线性模型以及修正的非线性模型。根据输入能量相等则振幅相等的原理推导了主梁等效质量与涡振振型函数的关系。在此基础上,提出了不同涡振力理论模型下节段模型涡振振幅与实桥最大涡振振幅的换算关系。研究表明,影响该换算关系的主要因素有两方面,一是主梁发生涡振时的振型,二是所采用的涡振力理论%Vortex-induced resonance is caused by wind to which long-span bridges are most susceptible.One method of study is to use section model test in wind tunnel.How can the vortex-induced amplitude of sectional model be converted to that of the full bridge is an unresolved issue in the present Chinese wind-resistant design specifications of highway bridges.The present paper introduces three kinds of theoretical models for vortex-induced aerodynamic forces,including the linear model,the nonlinear model,and the modified nonlinear model.The relation between the equivalent mass density of girder and the modal function is deduced according to the principle that equal energy input should result in equal amplitude.Based on these,a group of conversions between amplitude of sectional model and that of full bridge,corresponding to different theoretical models,are presented.The study indicates that there are two major factors to influence the conversion relationship,with one being the structural modal shape,and the other the theoretical model adopted in the expression of vortex-induced loading.Based on the amplitude of sectional model,the amplitude of full bridge from using the linear model is obviously larger than that from the nonlinear one.
Differential equations, associators, and recurrences for amplitudes
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′.
杨旦旦; 岳宝增; 祝乐梅; 宋晓娟
2011-01-01
为得到航天器上燃料晃动频率,针对Cassini贮箱内液体小幅晃动,将贮箱的柱段近似为非常扁长的椭球,建立了原点位于与箱内静液面接触线处相切的圆锥顶点的球坐标系,用高斯超几何级数解析表达速度势和波高的模态函数,采用伽辽金方法将变分方程转变为一个标准的特征值问题形式的频率方程,求解了不同尺寸比例的旋转椭球形贮箱和Cassini贮箱在不同的充液比和不同的Bond数情况下液体小幅晃动的基频,并与已有的理论和实验结果进行对照.结果表明,本文方法用于求解旋转椭球形贮箱和Cassini贮箱内液体小幅晃动频率是可行的.%In order to get the small amplitude sloshing eigenfrequency of liquid in spacecraft, for Cassini tanks, the cylindrical part of the tank is considered to be a part of a very prolate ellipsoid approximately. Spherical coordinates is built, whose origin is at the top of the cone that is tangent to the tank at the contact line of the hydrostatic surface with the tank wall. The velocity potential and the liquid surface displacement were determined analytically in terms of the Gauss hypergeometric series. The variation function was transformed into a frequency equation in the form of a standard eigenvalue problem by Galerkin method. The achieved first eigenfrequencies of liquid in spheroidal tanks and Cassini tanks with different dimension, different liquid filling level and different Bond number were compared with those from other theoretical and experimental methods. Large calculations prove that this analytical method is practicable to find the solution of small amplitude sloshing eigenfrequencies of liquid in spheroidal tanks and Cassini tanks.
Scattering amplitudes in gauge theories
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 ...
CHY formula and MHV amplitudes
Du, Yi-Jian; Teng, Fei; Wu, Yong-Shi
2016-05-01
In this paper, we study the relation between the Cachazo-He-Yuan (CHY) formula and the maximal-helicity-violating (MHV) amplitudes of Yang-Mills and gravity in four dimensions. We prove that only one special rational solution of the scattering equations found by Weinzierl supports the MHV amplitudes. Namely, localized at this solution, the integrated CHY formula produces the Parke-Taylor formula for MHV Yang-Mills amplitudes as well as the Hodges formula for MHV gravitational amplitudes, with an arbitrary number of external gluons/gravitons. This is achieved by developing techniques, in a manifestly Möbius covariant formalism, to explicitly compute relevant reduced Pfaffians/determinants. We observe and prove two interesting properties (or identities), which facilitate the computations. We also check that all the other ( n - 3)! - 1 solutions to the scattering equations do not support the MHV amplitudes, and prove analytically that this is indeed true for the other special rational solution proposed by Weinzierl, that actually supports the anti-MHV amplitudes. Our results reveal a mysterious feature of the CHY formalism that in Yang-Mills and gravity theory, solutions of scattering equations, involving only external momenta, somehow know about the configuration of external polarizations of the scattering amplitudes.
New identities among gauge theory amplitudes
Bjerrum-Bohr, N. E. J.; Damgaard, Poul H.; Feng, Bo; Søndergaard, Thomas
2010-08-01
Color-ordered amplitudes in gauge theories satisfy non-linear identities involving amplitude products of different helicity configurations. We consider the origin of such identities and connect them to the Kawai-Lewellen-Tye (KLT) relations between gravity and gauge theory amplitudes. Extensions are made to one-loop order of the full N = 4 super Yang-Mills multiplet.
New identities among gauge theory amplitudes
Bjerrum-Bohr, N.E.J., E-mail: bjbohr@nbi.d [Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen (Denmark); Damgaard, Poul H. [Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen (Denmark); Feng Bo [Center of Mathematical Science, Zhejiang University, Hangzhou (China); Kavli Institute for Theoretical Physics China, CAS, Beijing 100190 (China); Sondergaard, Thomas [Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen (Denmark)
2010-08-09
Color-ordered amplitudes in gauge theories satisfy non-linear identities involving amplitude products of different helicity configurations. We consider the origin of such identities and connect them to the Kawai-Lewellen-Tye (KLT) relations between gravity and gauge theory amplitudes. Extensions are made to one-loop order of the full N=4 super Yang-Mills multiplet.
New Identities among Gauge Theory Amplitudes
Bjerrum-Bohr, N E J; Feng, Bo; Sondergaard, Thomas
2010-01-01
Color-ordered amplitudes in gauge theories satisfy non-linear identities involving amplitude products of different helicity configurations. We consider the origin of such identities and connect them to the Kawai-Lewellen-Tye (KLT) relations between gravity and gauge theory amplitudes. Extensions are made to one-loop order of the full N=4 super Yang-Mills multiplet.
New identities among gauge theory amplitudes
Color-ordered amplitudes in gauge theories satisfy non-linear identities involving amplitude products of different helicity configurations. We consider the origin of such identities and connect them to the Kawai-Lewellen-Tye (KLT) relations between gravity and gauge theory amplitudes. Extensions are made to one-loop order of the full N=4 super Yang-Mills multiplet.
In recent years design methods for impact-resistant concrete structures subjected to impact loads caused by an aircraft crash have become of considerable interest. Muto et al. performed impact tests on reinforced concrete slabs using an aircraft engine missile and evaluated certain critical design slab thicknesses such as perforation thickness and scabbing thickness. Taking actual construction conditions of roof slabs into consideration, they also qualitatively studied the beneficial influence of a deck-plate attached to the rear of the slab in preventing scatter of scabbed concrete. Other studies have also been carried out, such as those by the UKAEA and Walter where the effect of a liner attached to a rear surface is assessed in terms of an equivalent concrete slab thickness. However, there have been no quantitative studies of liner effect considered in the time domain. However, Kasai et al. made a quantitative appraisal of liner benefit for local damage from the impact of a rigid missile on a reinforced concrete (R/C) panel with a steel plate on the rear side from impact tests using a scale model. Furthermore, Morikawa et al. have drawn attention to the use of the discrete element method (DEM) for modeling local damage phenomena accompanying rear-face scabbing or penetration into the reinforced concrete panel. They demonstrated that impact phenomena could be assessed qualitatively. Koshika et al. also described a method for establishing parameters for a DEM analysis, making feasible a quantitative assessment of local damage to R/C panels. Based on this background, this paper takes the impact tests by a rigid projectile reported in Part I, and demonstrates that the difference in damage to an R/C panel with and without a steel liner plate may be simulated analytically. The impact test results of Muto et al. for the real engine impacting an R/C panel with a steel liner are then analyzed, and it is demonstrated that even for the full-size impact from a real engine
Scattering amplitudes in gauge theories
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.
Amplitude mediated chimera states
Sethia, Gautam C.; Sen, Abhijit; Johnston, George L.
2013-01-01
We investigate the possibility of obtaining chimera state solutions of the non-local Complex Ginzburg-Landau Equation (NLCGLE) in the strong coupling limit when it is important to retain amplitude variations. Our numerical studies reveal the existence of a variety of amplitude mediated chimera states (including stationary and non-stationary two cluster chimera states), that display intermittent emergence and decay of amplitude dips in their phase incoherent regions. The existence regions of t...
Periods and Feynman amplitudes
Brown, Francis
2016-01-01
Feynman amplitudes in perturbation theory form the basis for most predictions in particle collider experiments. The mathematical quantities which occur as amplitudes include values of the Riemann zeta function and relate to fundamental objects in number theory and algebraic geometry. This talk reviews some of the recent developments in this field, and explains how new ideas from algebraic geometry have led to much progress in our understanding of amplitudes. In particular, the idea that certain transcendental numbers, such as $\\pi$, can be viewed as a representation of a group, provides a powerful framework to study amplitudes which reveals many hidden structures.
Communication: A simple full range analytical potential for H2 b3∑u+, H–He 2∑+, and He2 1∑g+
The Tang-Toennies potential for the weakly interacting systems H2 b3Σu+, H–He 2Σ+, and He2 1Σg+ is extended down to the united atom limit of vanishing internuclear distance. A simple analytic expression connects the united atom limiting potential with the Tang-Toennies potential in the well region. The new potential model is compared with the most recent ab initio calculations for all three systems. The agreement is better than 20% (H2 and He2) or comparable with the differences in the available ab initio calculations (H–He) over six orders of magnitude corresponding to the entire range of internuclear distances
Luo, Yu; Zhang, Jingjing; Ran, Lixin; Kong, Jin Au
2007-01-01
We investigate a general class of electromagnetic devices created with any continuous transformation functions by rigorously calculating the analytical expressions of the electromagnetic field in the whole space. Some interesting phenomena associated with these transformation devices, including the invisibility cloaks, concentrators, and field rotators, are discussed. By carefully choosing the transformation function, we can realize cloaks which are insensitive to perturbations at both the inner and outer boundaries. Furthermore, we find that when the coating layer of the concentrator is realized with left-handed materials, energy will circulate between the coating and the core, and the energy transmits through the core of the concentrator can be much bigger than that transmits through the concentrator. Therefore, such concentrator is also a power flux amplifier. Finally, we propose a spherical field rotator, which functions as not only a wave vector rotator, but also a polarization rotator, depending on the ...
Softness and Amplitudes' Positivity for Spinning Particles
Bellazzini, Brando
2016-01-01
We derive positivity bounds for scattering amplitudes of particles with arbitrary spin using unitarity, analyticity and crossing symmetry. The bounds imply the positivity of certain low-energy coefficients of the effective action that controls the dynamics of the light degrees of freedom. We show that low-energy amplitudes strictly softer than $O(p^4)$ do not admit unitary ultraviolet completions unless the theory is free. This enforces a bound on the energy growth of scattering amplitudes in the region of validity of the effective theory. We discuss explicit examples including the Goldstino from spontaneous supersymmetry breaking, and the theory of a spin-1/2 fermion with a shift symmetry.
Nonsinglet pentagons and NMHV amplitudes
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.
Flohr, Michael [Physikalisches Institut, University of Bonn, Nussallee 12, D-53115 Bonn (Germany); Gaberdiel, Matthias R [Institut fuer Theoretische Physik, ETH Zuerich, ETH-Hoenggerberg, 8093 Zurich (Switzerland)
2006-02-24
For the example of the logarithmic triplet theory at c = -2, the chiral vacuum torus amplitudes are analysed. It is found that the space of these torus amplitudes is spanned by the characters of the irreducible representations, as well as a function that can be associated with the logarithmic extension of the vacuum representation. A few implications and generalizations of this result are discussed.
Amplitudes, acquisition and imaging
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.
Exact solution to the Coulomb wave using the linearized phase-amplitude method
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.
Generalised Unitarity for Dimensionally Regulated Amplitudes
Bobadilla, W J Torres; Mastrolia, P; Mirabella, E
2015-01-01
We present a novel set of Feynman rules and generalised unitarity cut-conditions for computing one-loop amplitudes via d-dimensional integrand reduction algorithm. Our algorithm is suited for analytic as well as numerical result, because all ingredients turn out to have a four-dimensional representation. We will apply this formalism to NLO QCD corrections.
Two-loop amplitudes with nested sums Fermionic contributions to e+ e- --> q qbar g
Moch, S; Weinzierl, S; Moch, Sven; Uwer, Peter; Weinzierl, Stefan
2002-01-01
We present the calculation of the nf-contributions to the two-loop amplitude for e+ e- --> q qbar g and give results for the full one-loop amplitude to order eps^2 in the dimensional regularization parameter. Our results agree with those recently obtained by Garland et al.. The calculation makes extensive use of an efficient method based on nested sums to calculate two-loop integrals with arbitrary powers of the propagators. The use of nested sums leads in a natural way to multiple polylogarithms with simple arguments, which allow a straightforward analytic continuation.
Accurate Period Approximation for Any Simple Pendulum Amplitude
XUE De-Sheng; ZHOU Zhao; GAO Mei-Zhen
2012-01-01
Accurate approximate analytical formulae of the pendulum period composed of a few elementary functions for any amplitude are constructed.Based on an approximation of the elliptic integral,two new logarithmic formulae for large amplitude close to 180° are obtained.Considering the trigonometric function modulation results from the dependence of relative error on the amplitude,we realize accurate approximation period expressions for any amplitude between 0 and 180°.A relative error less than 0.02％ is achieved for any amplitude.This kind of modulation is also effective for other large-amplitude logarithmic approximation expressions.%Accurate approximate analytical formulae of the pendulum period composed of a few elementary functions for any amplitude are constructed. Based on an approximation of the elliptic integral, two new logarithmic formulae for large amplitude close to 180° are obtained. Considering the trigonometric function modulation results from the dependence of relative error on the amplitude, we realize accurate approximation period expressions for any amplitude between 0 and 180°. A relative error less than 0.02% is achieved for any amplitude. This kind of modulation is also effective for other large-amplitude logarithmic approximation expressions.
Stability of full-amplitude solutions for RR Lyrae variables
Since the discovery of numerous double-mode RR Lyrae variables in the globular cluster M15 by Cox, Hodson, and Clancy (1981a and 1983, CHC), double-mode behavior in these Population II variables has made it possible to theoretically determine their masses, composition, and maybe even their evolution direction. The most unusual characteristic of these new double-mode pulsators is that they are found in a narrow range of first overtone periods (P1=0./sup d/38-0./sup d/43) and period ratios (P1/P0=0.746+-0.001), where P0 is the fundamental mode period. This compares with P1=0./sup d/41 and P1/P0=0.746 for AQ Leonis, the only known field double-mode RR Lyrae star. Recent linear studies by CHC (1981a and 1983) suggest that double-mode behavior in this class of stars results from mode switching between the fundamental (F) and first overtone (1H) radial pulsation modes at the transition line just to the red of the F-mode blue edge
Protostring Scattering Amplitudes
Thorn, Charles B
2016-01-01
We calculate some tree level scattering amplitudes for a generalization of the protostring, which is a novel string model implied by the simplest string bit models. These bit models produce a lightcone worldsheet which supports $s$ integer moded Grassmann fields. In the generalization we supplement this Grassmann worldsheet system with $d=24-s$ transverse coordinate worldsheet fields. The protostring corresponds to $s=24$ and the bosonic string to $s=0$. The interaction vertex is a simple overlap with no operator insertions at the break/join point. Assuming that $s$ is even we calculate the multi-string scattering amplitudes by bosonizing the Grassmann fields, each pair equivalent to one compactified bosonic field, and applying Mandelstam's interacting string formalism to a system of $s/2$ compactified and $d$ uncompactified bosonic worldsheet fields. We obtain all amplitudes for open strings with no oscillator excitations and for closed strings with no oscillator excitations and zero winding number. We then ...
Softness, Polynomial Boundedness and Amplitudes' Positivity
Bai, Dong
2016-01-01
In this note, we study the connection between infrared (IR) and ultraviolet (UV) behaviors of scattering amplitudes of massless channels by exploiting dispersion relations and positivity bounds. Given forward scattering amplitudes which scale as $\\mathcal{A}(s)\\sim s^M$ in the IR ($s\\to0$) and could be embedded into UV completions satisfying unitarity, analyticity, crossing symmetry and polynomial boundedness $|\\mathcal{A}(s)|< c\\, |s|^N$ ($|s|\\to\\infty$), with $M$ and $N$ integers, we show that the inequality $2\\ceil*{\\frac{N}{2}}\\ge M \\ge 0$ must hold, where $\\ceil*{x}$ is the smallest integer greater than or equal to $x$.
Properties of the scattering amplitude for electron-atom collisions
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 in four- and six-dimensional gauge theories
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.
Light Meson Distribution Amplitudes
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.
Periods and Superstring Amplitudes
Stieberger, S
2016-01-01
Scattering amplitudes which describe the interaction of physical states play an important role in determining physical observables. In string theory the physical states are given by vibrations of open and closed strings and their interactions are described (at the leading order in perturbation theory) by a world-sheet given by the topology of a disk or sphere, respectively. Formally, for scattering of N strings this leads to N-3-dimensional iterated real integrals along the compactified real axis or N-3-dimensional complex sphere integrals, respectively. As a consequence the physical observables are described by periods on M_{0,N} - the moduli space of Riemann spheres of N ordered marked points. The mathematical structure of these string amplitudes share many recent advances in arithmetic algebraic geometry and number theory like multiple zeta values, single-valued multiple zeta values, Drinfeld, Deligne associators, Hopf algebra and Lie algebra structures related to Grothendiecks Galois theory. We review the...
HIGH AMPLITUDE PROPAGATED CONTRACTIONS
Bharucha, Adil E.
2012-01-01
While most colonic motor activity is segmental and non-propulsive, colonic high amplitude propagated contractions (HAPC) can transfer colonic contents over long distances and often precede defecation. HAPC occur spontaneously, in response to pharmacological agents or colonic distention. In this issue of Neurogastroenterology and Motility, Rodriguez and colleagues report that anal relaxation during spontaneous and bisacodyl-induced HAPC exceeds anal relaxation during rectal distention in const...
Scaling of saturation amplitudes in baroclinic instability
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
Connecting physical resonant amplitudes and lattice QCD
Bolton, Daniel R.; Briceño, Raúl A.; Wilson, David J.
2016-06-01
We present a determination of the isovector, P-wave ππ scattering phase shift obtained by extrapolating recent lattice QCD results from the Hadron Spectrum Collaboration using mπ = 236 MeV. The finite volume spectra are described using extensions of Lüscher's method to determine the infinite volume Unitarized Chiral Perturbation Theory scattering amplitude. We exploit the pion mass dependence of this effective theory to obtain the scattering amplitude at mπ = 140 MeV. The scattering phase shift is found to agree with experiment up to center of mass energies of 1.2 GeV. The analytic continuation of the scattering amplitude to the complex plane yields a ρ-resonance pole at Eρ = [ 755 (2) (1) (20 02) -i/2 129 (3) (1) (7 1) ] MeV. The techniques presented illustrate a possible pathway towards connecting lattice QCD observables of few-body, strongly interacting systems to experimentally accessible quantities.
Amplitude and Frequency Control: Stability of Limit Cycles in Phase-Shift and Twin-T Oscillators
J. P. Dada
2008-01-01
Full Text Available We show a technique for external direct current (DC control of the amplitudes of limit cycles both in the Phase-shift and Twin-T oscillators. We have found that amplitudes of the oscillator output voltage depend on the DC control voltage. By varying the total impedance of each oscillator oscillatory network, frequencies of oscillations are controlled using potentiometers. The main advantage of the proposed circuits is that both the amplitude and frequency of the waveforms generated can be independently controlled. Analytical, numerical, and experimental methods are used to determine the boundaries of the states of the oscillators. Equilibrium points, stable limit cycles, and divergent states are found. Analytical results are compared with the numerical and experimental solutions, and a good agreement is obtained.
Effective gluon interactions from superstring disk amplitudes
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)
Effective gluon interactions from superstring disk amplitudes
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)
Amplitude analysis of two-body meson-baryon scattering
Information on high-energy scattering amplitudes is extracted from experimental data for πN and KN elastic and charge-exchange scattering using model independent methods based on isospin symmetry and analyticity. These analyses provide numerical knowledge of the scattering amplitudes and make it possible to answer the questions: which amplitudes are responsible for the different experimental features, which models are able to produce such amplitudes and to which extent are duality, SU(3) and quark model relations consistent with the experimental data
Closed string amplitudes as single-valued open string amplitudes
We show that the single trace heterotic N-point tree-level gauge amplitude ANHET can be obtained from the corresponding type I amplitude ANI by the single-valued (sv) projection: ANHET=sv(ANI). This projection maps multiple zeta values to single-valued multiple zeta values. The latter represent a subclass of multiple zeta values originating from single-valued multiple polylogarithms at unity. Similar relations between open and closed string amplitudes or amplitudes of different string vacua can be established. As a consequence the α′-expansion of a closed string amplitude is dictated by that of the corresponding open string amplitude. The combination of single-valued projections, Kawai–Lewellen–Tye relations and Mellin correspondence reveal a unity of all tree-level open and closed superstring amplitudes together with the maximally supersymmetric Yang–Mills and supergravity theories
Phonological awareness and sinusoidal amplitude modulation in phonological dislexia
Yolanda Peñaloza-López
2016-04-01
Full Text Available ABSTRACT Objective 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. Methods 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. Results 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. Conclusion Alterations in PA and SAM found can help to explain basis of deficient language processing exhibited by children with PD.
A Closed Form Solution for Nonlinear Oscillators Frequencies Using Amplitude-Frequency Formulation
A. Barari
2012-01-01
Full Text Available Many nonlinear systems in industry including oscillators can be simulated as a mass-spring system. In reality, all kinds of oscillators are nonlinear due to the nonlinear nature of springs. Due to this nonlinearity, most of the studies on oscillation systems are numerically carried out while an analytical approach with a closed form expression for system response would be very useful in different applications. Some analytical techniques have been presented in the literature for the solution of strong nonlinear oscillators as well as approximate and numerical solutions. In this paper, Amplitude-Frequency Formulation (AFF approach is applied to analyze some periodic problems arising in classical dynamics. Results are compared with another approximate analytical technique called Energy Balance Method developed by the authors (EBM and also numerical solutions. Close agreement of the obtained results reveal the accuracy of the employed method for several practical problems in engineering.
Quadrupole and monopole large amplitude vibrations
A set of nonlinear dynamical equations for quadrupole and monopole moments of nuclei is derived from the TDHF equation with the help of the so-called Wigner function moments. It allows the description of coupled large amplitude monopole and quadrupole vibrations. These equations are solved numerically for 208Pb and 40Ca in a model with separable forces. The giant quadrupole and monopole resonances are reproduced very well. However the essential feature of the large amplitude motion is the existence of multiphonon states. They are analyzed in detail. The classical and quantum aspects of the analytically solvable one-dimensional pure monopole model are studied to clarify the problem of the anharmonicity of the collective spectrum. 26 refs., 2 figs., 2 tabs
Differential equations, associators, and recurrences for amplitudes
Puhlfürst, Georg; Stieberger, Stephan
2016-01-01
We provide new methods to straightforwardly obtain compact and analytic expressions for ɛ-expansions of functions appearing in both field and string theory amplitudes. An algebraic method is presented to explicitly solve for recurrence relations connecting different ɛ-orders of a power series solution in ɛ 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 ɛ-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 ɛ-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‧.
Differential Equations, Associators, and Recurrences for Amplitudes
Puhlfuerst, Georg
2015-01-01
We provide new methods to straightforwardly obtain compact and analytic expressions for epsilon-expansions of functions appearing in both field and string theory amplitudes. An algebraic method is presented to explicitly solve for recurrence relations connecting different epsilon-orders of a power series solution in epsilon 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 epsilon-expansion of specific generalized hypergeometric functions with the underlying Drinfeld associator with proper Lie algebra and monodromy representations. We also setup up our tools for computing epsilon-expansions for solutions to generic first-order Fuchsian equations (Schlesinger system). Finally, we apply our methods to systematically get compact and explicit alpha'-expansions of tree-level superstring amplitudes to any order in alpha'.
All tree-level amplitudes in massless QCD
Dixon, Lance [Theory Group, Physics Department, CERN, Ch-1211 Geneva 23 (Switzerland); SLAC National Accelerator Laboratory, Stanford University, Stanford, CA 94309 (United States); Henn, Johannes; Plefka, Jan; Schuster, Theodor [Institut fuer Physik, Humboldt-Universitaet, Newtonstrasse 15, D-12489 Berlin (Germany)
2011-07-01
We derive compact analytical formulae for all tree-level color-ordered gauge theory amplitudes involving any number of external gluons and up to three massless quark-anti-quark pairs. A general formula for all gluon-gluino tree amplitudes is presented, based on the combinatorics of paths along a rooted tree and associated determinants. Our results are obtained by projecting the previously-found expressions for the super-amplitudes of the maximally supersymmetric super Yang-Mills theory (N=4 SYM) onto the relevant components. We show how these results carry over to the corresponding QCD amplitudes, including massless quarks of different flavors as well as a single electroweak vector boson. The public Mathematica package GGT is described, which encodes the results of this work and yields analytical formulae for all N = 4 SYM gluon-gluino trees. These in turn yield all QCD trees with up to four external arbitrary-flavored massless quark-anti-quark-pairs.
Stoyanov Svetlin
2015-03-01
Full Text Available An analytical solution for a specific case of the forced Duffing oscillator is proposed. The excitation force contains two harmonics with significant difference frequencies. This case corresponds to a presence of a defect in the machinery and is in the art of the machinery vibration diagnostics. The results obtained show an amplitude modulation. Therefore, the presence of an amplitude modulation in the vibration signal may be used as an indicator for a malfunction. Analytical solution derived clarifies how the amplitude modulation occurs. Also, a numerical solution is realized and compared with the analytical one. For this, the Duffing equation is solved numerically and then, the spectrograms of vibrations are obtained through a Discrete-time Fourier Transform.
On Superstring Disk Amplitudes in a Rolling Tachyon Background
Jokela, Niko; Keski-Vakkuri, Esko; Majumder, Jaydeep
2005-01-01
We study the tree level scattering or emission of n closed superstrings from a decaying non-BPS brane in Type II superstring theory. We attempt to calculate generic n-point superstring disk amplitudes in the rolling tachyon background. We show that these can be written as infinite power series of Toeplitz determinants, related to expectation values of a periodic function in Circular Unitary Ensembles. Further analytical progress is possible in the special case of bulk-boundary disk amplitudes...
Bootstrapping a Five-Loop Amplitude from Steinmann Relations
Caron-Huot, Simon; McLeod, Andrew; von Hippel, Matt
2016-01-01
The analytic structure of scattering amplitudes is restricted by Steinmann relations, which enforce the vanishing of certain discontinuities of discontinuities. We show that these relations dramatically simplify the function space for the hexagon function bootstrap in planar maximally supersymmetric Yang-Mills theory. Armed with this simplification, along with the constraints of dual conformal symmetry and Regge exponentiation, we obtain the complete five-loop six-particle amplitude.
Bulk and edge quasihole tunneling amplitudes in the Laughlin state
Hu, Zi-Xiang; Lee, Ki Hoon; Wan, Xin
2012-01-01
The tunneling between the Laughlin state and its quasihole excitations are studied by using the Jack polynomial. We find a universal analytical formula for the tunneling amplitude, which can describe both bulk and edge quasihole excitations. The asymptotic behavior of the tunneling amplitude reveals the difference and the crossover between bulk and edge states. The effects of the realistic coulomb interaction with a background-charge confinement potential and disorder are also discussed. The ...
Hidden Beauty in Multiloop Amplitudes
Cachazo, Freddy(Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada); 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 the 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 argue that t...
Amplitude oscillation of DCLC mode
A quasilinear model and a simulation code taking into account the electron bounce resonance damping have been developed to describe the amplitude oscillation of the drift cyclotron loss-cone mode, which has been observed in mirror experiments. It was found that this oscillatory behavior of the amplitude is caused by the temporal variation of the growth rate and the effect of electron bounce resonance damping on the amplitude of this mode. (author)
Motivic amplitudes and cluster coordinates
J.K. Golden; Goncharov, A. B.; M. Spradlin; C. Vergu; 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 MH...
Gluon scattering amplitudes at strong coupling
Alday, Luis F
2007-01-01
We describe how to compute planar gluon scattering amplitudes at strong coupling in N=4 super Yang Mills by using the gauge/string duality. The computation boils down to finding a certain classical string configuration whose boundary conditions are determined by the gluon momenta. The results are infrared divergent. We introduce the gravity version of dimensional regularization to define finite quantities. The leading and subleading IR divergencies are characterized by two functions of the coupling that we compute at strong coupling. We compute also the full finite form for the four point amplitude and we find agreement with a recent ansatz by Bern, Dixon and Smirnov.
Graviton amplitudes from collinear limits of gauge amplitudes
Stephan Stieberger; Taylor, Tomasz R.
2015-01-01
We express all tree-level graviton amplitudes in Einstein's gravity as the collinear limits of a linear combination of pure Yang–Mills amplitudes in which each graviton is represented by two gauge bosons, each of them carrying exactly one half of graviton's momentum and helicity.
MEASUREMENT OF ANGULAR VIBRATION AMPLITUDE BY ACTIVELY BLURRED IMAGES
GUAN Baiqing; WANG Shigang; LIU Chong; LI Qian
2007-01-01
A novel motion-blur-based method for measuring the angular amplitude of a high-frequency rotational vibration is schemed. The proposed approach combines the active vision concept and the mechanism of motion-from-blur, generates motion blur on the image plane actively by extending exposure time, and utilizes the motion blur information in polar images to estimate the angular amplitude of a high-frequency rotational vibration. This method obtains the analytical results of the angular vibration amplitude from the geometric moments of a motion blurred polar image and an unblurred image for reference. Experimental results are provided to validate the presented scheme.
Analytic continuation as a bridge between continuum and bound states
Blokhintsev Leonid
2015-01-01
Full Text Available The problem of obtaining characteristics of bound nuclear states from continuum states data is discussed. It is shown that the ambiguities due to the existence of phase-equivalent potentials can be resolved by using the analytic properties of scattering amplitudes. The methods of determination of asymptotic normalization coefficients and vertex constants are considered. The asymptotic normalization coefficients for 6Li in the α + d channel are found by analytic continuation of the two-channel effective range expansion. The account of inelastic channels within the effective range approach is discussed.
Large amplitude oscillatory elongation flow
Rasmussen, Henrik K.; Laillé, Philippe; Yu, Kaijia
2008-01-01
A filament stretching rheometer (FSR) was used for measuring the elongation flow with a large amplitude oscillative elongation imposed upon the flow. The large amplitude oscillation imposed upon the elongational flow as a function of the time t was defined as epsilon(t) =(epsilon) over dot(0)t...
Bender, Emily
2012-01-01
Half Full is a film about a woman who has a rare genetic disorder that causes her to want to continue eating. Since she is unable to control her drive towards food, she can never be left alone with food. Her parents share their journey through trying to navigate her care and keep her from being institutionalized.
Connecting physical resonant amplitudes and lattice QCD
Bolton, Daniel R. [Univ. of Colorado, Boulder, CO (United States); Baylor Univ., Waco, TX (United States); Briceño, Raúl A. [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Wilson, David J. [Old Dominion Univ., Norfolk, VA (United States)
2016-03-01
We present a determination of the isovector, $P$-wave $\\pi\\pi$ scattering phase shift obtained by extrapolating recent lattice QCD results from the Hadron Spectrum Collaboration using $m_\\pi =236$ MeV. The finite volume spectra are described using extensions of L\\"uscher's method to determine the infinite volume Unitarized Chiral Perturbation Theory scattering amplitude. We exploit the pion mass dependence of this effective theory to obtain the scattering amplitude at $m_\\pi= 140$ MeV. The scattering phase shift is found to be in good agreement with experiment up to center of mass energies of 1.2 GeV. The analytic continuation of the scattering amplitude to the complex plane yields a $\\rho$-resonance pole at $E_\\rho= \\left[755(2)(1)(^{20}_{02})-\\frac{i}{2}\\,129(3)(1)(^{7}_{1})\\right]~{\\rm MeV}$. The techniques presented illustrate a possible pathway towards connecting lattice QCD observables of few-body, strongly interacting systems to experimentally accessible quantities.
Logarithmic Singularities and Maximally Supersymmetric Amplitudes
Bern, Zvi; Litsey, Sean; Stankowicz, James; Trnka, Jaroslav
2014-01-01
The dual formulation of planar N = 4 super-Yang-Mills scattering amplitudes makes manifest that the integrand has only logarithmic singularities and no poles at infinity. Recently, Arkani-Hamed, Bourjaily, Cachazo and Trnka conjectured the same singularity properties hold to all loop orders in the nonplanar sector as well. Here we conjecture that to all loop orders these constraints give us the key analytic information contained in dual conformal symmetry. We also conjecture that to all loop orders, while N = 8 supergravity has poles at infinity, at least at four points it has only logarithmic singularities at finite locations. We provide nontrivial evidence for these conjectures. For the three-loop four-point N = 4 super-Yang-Mills amplitude, we explicitly construct a complete basis of diagram integrands that has only logarithmic singularities and no poles at infinity. We then express the complete amplitude in terms of the basis diagrams, with the coefficients determined by unitarity. We also give examples a...
Sadchenko A. V.
2016-02-01
Full Text Available Directivity pattern (DP or graphical representation of the dependence of gain factor (directivity gain of antennas on the direction of the antenna in the target plane is the main characteristic that describes its directional properties. Running DP measurements directly in the microwave range is very expensive. While generating and receiving devices for the acoustic frequency range are reasonably priced. In this paper, we propose a method for measuring the amplitude directivity pattern of parabolic mirrored antennas on the basis of sound equivalent, which is based on the identity of the numerical values of the directivity gain of microwave range, and at audio frequencies. The paper presents analytical expressions for the calculation of equivalent frequency and defines the requirements for the minimum size of the antenna. The paper contains a modified block diagram for an amplitude directivity pattern meter for parabolic mirrored antennas in the audio frequency range.
Teleporting Superpositions of Chiral Amplitudes
Maierle, C S; Harris, R A; Maierle, Christopher S.; Lidar, Daniel A.; Harris, Robert A.
1998-01-01
Chiral molecules may exist in superpositions of left- and right-handed states. We show how the amplitudes of such superpositions may be teleported to the polarization degrees of freedom of a photon. Two experimental schemes are proposed, one leading to perfect, the other to state-dependent teleportation. Both methods yield complete information about the amplitudes. This is the first explicit example of "inter-species" teleportation, where the amplitudes of the quantum superposition of one species are transferred at the end of the process to a different species. The latter is then easily accessible for measurement.
Positive Amplitudes In The Amplituhedron
Arkani-Hamed, Nima; Trnka, Jaroslav
2014-01-01
The all-loop integrand for scattering amplitudes in planar N = 4 SYM is determined by an "amplitude form" with logarithmic singularities on the boundary of the amplituhedron. In this note we provide strong evidence for a new striking property of the superamplitude, which we conjecture to be true to all loop orders: the amplitude form is positive when evaluated inside the amplituhedron. The statement is sensibly formulated thanks to the natural "bosonization" of the superamplitude associated with the amplituhedron geometry. However this positivity is not manifest in any of the current approaches to scattering amplitudes, and in particular not in the cellulations of the amplituhedron related to on-shell diagrams and the positive grassmannian. The surprising positivity of the form suggests the existence of a "dual amplituhedron" formulation where this feature would be made obvious. We also suggest that the positivity is associated with an extended picture of amplituhedron geometry, with the amplituhedron sitting...
Model selection for amplitude analysis
Model complexity in amplitude analyses is often a priori under-constrained since the underlying theory permits a large number of possible amplitudes to contribute to most physical processes. The use of an overly complex model results in reduced predictive power and worse resolution on unknown parameters of interest. Therefore, it is common to reduce the complexity by removing from consideration some subset of the allowed amplitudes. This paper studies a method for limiting model complexity from the data sample itself through regularization during regression in the context of a multivariate (Dalitz-plot) analysis. The regularization technique applied greatly improves the performance. An outline of how to obtain the significance of a resonance in a multivariate amplitude analysis is also provided
One loop multiphoton helicity amplitudes
Mahlon, G
1994-01-01
We use the solutions to the recursion relations for double-off-shell fermion currents to compute helicity amplitudes for $n$-photon scattering and electron-positron annihilation to photons in the massless limit of QED. The form of these solutions is simple enough to allow {\\it all}\\ of the integrations to be performed explicitly. For $n$-photon scattering, we find that unless $n=4$, the amplitudes for the helicity configurations (+++...+) and (-++...+) vanish to one-loop order.
Motivic amplitudes and cluster coordinates
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 Confn(ℙ3) underlies the structure of motivic amplitudes. Specifically, we compute explicitly the coproduct of the two-loop seven-particle MHV motivic amplitude A7,2M 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 Confn(ℙ3). 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 A7,2M 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
Some Heterodox Analytic Philosophy
Guillermo E. Rosado Haddock
2013-04-01
Full Text Available Analytic philosophy has been the most influential philosophical movement in 20th century philosophy. It has surely contributed like no other movement to the elucidation and demarcation of philosophical problems. Nonetheless, the empiricist and sometimes even nominalist convictions of orthodox analytic philosophers have served them to inadequately render even philosophers they consider their own and to propound very questionable conceptions.
Liang Yonggang; Liu Tiebing; Liu Hongxing; Si Junfeng; Huang Xiaolin; Wang Rui
2013-01-01
Classical Amplitude Spectrum analysis and Full Amplitude Spectrum analysis exhibit deficiencies in analyzing the two perpendicular directional vibration displacement signals of a rotating rotor. The shape of Classical Amplitude Spectrum is influenced by the installing position of its sensor. Neither Classical Amplitude Spectrum nor Full Amplitude Spectrum can indicate the actual radial rotor vibration amplitude on every frequency. Therefore, the previous two methods are not convenient to be u...
High Frequency Amplitude Detector for GMI Magnetic Sensors
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.
Analytic Multi-Regge Theory and the Pomeron in QCD
The formalism of Analytic Multi-Regge Theory is 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 hexographs. Further consequences are distinct Sommerfeld-Watson representations for each hexograph 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, the simultaneous modification of hadrons and the Pomeron can be studies. 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'' (Reggeised vector particle) coupling pair-wise to the Pomeron
Analytic Multi-Regge Theory and the Pomeron in QCD
White, A.R.
1990-05-10
The formalism of Analytic Multi-Regge Theory is 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 hexographs. Further consequences are distinct Sommerfeld-Watson representations for each hexograph 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, the simultaneous modification of hadrons and the Pomeron can be studies. 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'' (Reggeised vector particle) coupling pair-wise to the Pomeron.
Nonsinglet pentagons and NMHV amplitudes
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.
Factorization of Chiral String Amplitudes
Huang, Yu-tin; Yuan, Ellis Ye
2016-01-01
We re-examine a closed-string model defined by altering the boundary conditions for one handedness of two-dimensional propagators in otherwise-standard string theory. We evaluate the amplitudes using Kawai-Lewellen-Tye factorization into open-string amplitudes. The only modification to standard string theory is effectively that the spacetime Minkowski metric changes overall sign in one open-string factor. This cancels all but a finite number of states: As found in earlier approaches, with enough supersymmetry (e.g., type II) the tree amplitudes reproduce those of the massless truncation of ordinary string theory. However, we now find for the other cases that additional fields, formerly thought to be auxiliary, describe new spin-2 states at the two adjacent mass levels (tachyonic and tardyonic). The tachyon is always a ghost, but can be avoided in the heterotic case.
Integrable spin chains and scattering amplitudes
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.)
OPE for all Helicity Amplitudes
Basso, Benjamin; Cordova, Lucia; Sever, Amit; Vieira, Pedro
2014-01-01
We extend the Operator Product Expansion (OPE) for scattering amplitudes in planar N=4 SYM to account for all possible helicities of the external states. This is done by constructing a simple map between helicity configurations and so-called charged pentagon transitions. These OPE building blocks are generalizations of the bosonic pentagons entering MHV amplitudes and they can be bootstrapped at finite coupling from the integrable dynamics of the color flux tube. A byproduct of our map is a simple realization of parity in the super Wilson loop picture.
Bruce, William J; Maxwell, E A; Sneddon, I N
1963-01-01
Analytic Trigonometry details the fundamental concepts and underlying principle of analytic geometry. The title aims to address the shortcomings in the instruction of trigonometry by considering basic theories of learning and pedagogy. The text first covers the essential elements from elementary algebra, plane geometry, and analytic geometry. Next, the selection tackles the trigonometric functions of angles in general, basic identities, and solutions of equations. The text also deals with the trigonometric functions of real numbers. The fifth chapter details the inverse trigonometric functions
Double unresolved approximations to multiparton scattering amplitudes
We present approximations to tree-level multiparton scattering amplitudes which are appropriate when two partons are unresolved. These approximations are required for the analytic isolation of infrared singularities of n+2 parton scattering processes contributing to the next-to-next-to-leading order corrections to n jet cross sections. In each case the colour ordered matrix elements factorise and yield a function containing the singular factors multiplying the n-parton amplitudes. When the unresolved particles are colour unconnected, the approximations are simple products of the familiar eikonal and Altarelli-Parisi splitting functions used to describe single unresolved emission. However, when the unresolved particles are colour connected the factorisation is more complicated and we introduce new and general functions to describe the triple collinear and soft/collinear limits in addition to the known double soft gluon limits of Berends and Giele. As expected the triple collinear splitting functions obey an N=1 SUSY identity. To illustrate the use of these double unresolved approximations, we have examined the singular limits of the tree-level matrix elements for e+e- →5 partons when only three partons are resolved. When integrated over the unresolved regions of phase space, these expressions will be of use in evaluating the O(αs3) corrections to the three-jet rate in electron-positron annihilation. (orig.)
All tree-level amplitudes in massless QCD
Dixon, Lance J.; Henn, Johannes M.; Plefka, Jan; Schuster, Theodor
2011-01-01
We derive compact analytical formulae for all tree-level color-ordered gauge theory amplitudes involving any number of external gluons and up to four massless quarkanti-quark pairs. A general formula is presented based on the combinatorics of paths along a rooted tree and associated determinants. Explicit expressions are displayed for the next-to-maximally helicity violating (NMHV) and next-to-next-to-maximally helicity violating (NNMHV) gauge theory amplitudes. Our results are obtained by projecting the previously-found expressions for the super-amplitudes of the maximally supersymmetric super Yang-Mills theory ( mathcal{N} = 4 SYM) onto the relevant components yielding all gluon-gluino tree amplitudes in mathcal{N} = 4 SYM. We show how these results carry over to the corresponding QCD amplitudes, including massless quarks of different avors as well as a single electroweak vector boson. The public Mathematica package GGT is described, which encodes the results of this work and yields analytical formulae for all mathcal{N} = 4 SYM gluon-gluino trees. These in turn yield all QCD trees with up to four external arbitrary-flavored massless quark-anti-quark pairs.
All tree-level amplitudes in massless QCD
Dixon, Lance J; Plefka, Jan; Schuster, Theodor
2011-01-01
We derive compact analytical formulae for all tree-level color-ordered gauge theory amplitudes involving any number of external gluons and up to three massless quark-anti-quark pairs. A general formula is presented based on the combinatorics of paths along a rooted tree and associated determinants. Explicit expressions are displayed for the next-to-maximally helicity violating (NMHV) and next-to-next-to-maximally helicity violating (NNMHV) gauge theory amplitudes. Our results are obtained by projecting the previously-found expressions for the super-amplitudes of the maximally supersymmetric Yang-Mills theory (N=4 SYM) onto the relevant components yielding all gluon-gluino tree amplitudes in N=4 SYM. We show how these results carry over to the corresponding QCD amplitudes, including massless quarks of different flavors as well as a single electroweak vector boson. The public Mathematica package GGT is described, which encodes the results of this work and yields analytical formulae for all N=4 SYM gluon-gluino ...
All Tree-level Amplitudes in Massless QCD
Dixon, Lance J.; /CERN /SLAC; Henn, Johannes M.; Plefka, Jan; Schuster, Theodor; /Humboldt U., Berlin
2010-10-25
We derive compact analytical formulae for all tree-level color-ordered gauge theory amplitudes involving any number of external gluons and up to three massless quark-anti-quark pairs. A general formula is presented based on the combinatorics of paths along a rooted tree and associated determinants. Explicit expressions are displayed for the next-to-maximally helicity violating (NMHV) and next-to-next-to-maximally helicity violating (NNMHV) gauge theory amplitudes. Our results are obtained by projecting the previously-found expressions for the super-amplitudes of the maximally supersymmetric Yang-Mills theory (N = 4 SYM) onto the relevant components yielding all gluon-gluino tree amplitudes in N = 4 SYM. We show how these results carry over to the corresponding QCD amplitudes, including massless quarks of different flavors as well as a single electroweak vector boson. The public Mathematica package GGT is described, which encodes the results of this work and yields analytical formulae for all N = 4 SYM gluon-gluino trees. These in turn yield all QCD trees with up to four external arbitrary-flavored massless quark-anti-quark-pairs.
Employing helicity amplitudes for resummation
Moult, Ian; Stewart, Iain W.; Tackmann, Frank J.; Waalewijn, Wouter J.
2016-05-01
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 p p →H +0 , 1, 2 jets, p p →W /Z /γ +0 , 1, 2 jets, and p p →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.
Positivity of spin foam amplitudes
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 (eiS) 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
Moult, Ian; Tackmann, Frank J; Waalewijn, Wouter J
2015-01-01
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 m...
Employing helicity amplitudes for resummation
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.
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
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. (LEW)
Veneziano Amplitude for Winding Strings
Khuri, Ramzi R.
1993-01-01
String configurations with nonzero winding number describe soliton string states. We compute the Veneziano amplitude for the scattering of arbitrary winding states and show that in the large radius limit the strings always scatter trivially and with no change in the individual winding numbers of the strings. In this limit, then, these states scatter as true solitons.
Radiative corrections to chiral amplitudes in quasiperipheral kinematics
Bytev, V; Galynsky, M V; Kuraev, E A
2005-01-01
Chiral amplitudes for quasi-peripheral processes are calculated in Born and one loop corrections level. Amplitudes of subprocess describing interaction of virtual photon and real photon with creation of the charged fermion pair for various chiral states are considered in details. The similar results are presented for Compton subprocess with virtual photon. Contribution of emission of virtual, soft and hard real additional photons was taken into account explicitly. The relevant cross sections expressed in terms of impact factors are in agreement with structure functions approach in leading logarithmical approximation Contributions of next to leading terms are presented in analytical form. Accuracy estimation is discussed.
HOU Chunfeng; LI Yan; YUAN Baohong; SUN Xiudong
2000-01-01
The low-amplitude spatial solitons in biased photovoltaic photorefractive crystals are investigated theoretically. The analytical solutions for both the bright and the dark low-amplitude screening-photovoltaic spatial solitons in photorefractive crystals are obtained. The expressions for the width of these solitons are given. The explicit expressions for the spatial deflection and angular deviation of the bright low-amplitude screening-photovoltaic spatial soliton are also presented by taking into account the effect of diffusion.
Renormalization of massless Feynman amplitudes in configuration space
Nikolov, Nikolay M.; Stora, Raymond; Todorov, Ivan
2014-05-01
A systematic study of recursive renormalization of Feynman amplitudes is carried out both in Euclidean and in Minkowski configuration spaces. For a massless quantum field theory (QFT), we use the technique of extending associate homogeneous distributions to complete the renormalization recursion. A homogeneous (Poincaré covariant) amplitude is said to be convergent if it admits a (unique covariant) extension as a homogeneous distribution. For any amplitude without subdivergences — i.e. for a Feynman distribution that is homogeneous off the full (small) diagonal — we define a renormalization invariant residue. Its vanishing is a necessary and sufficient condition for the convergence of such an amplitude. It extends to arbitrary — not necessarily primitively divergent — Feynman amplitudes. This notion of convergence is finer than the usual power counting criterion and includes cancellation of divergences.
Renormalization of Massless Feynman Amplitudes in Configuration Space
Nikolov, Nikolay M; Todorov, Ivan
2014-01-01
A systematic study of recursive renormalization of Feynman amplitudes is carried out both in Euclidean and in Minkowski configuration space. For a massless quantum field theory (QFT) we use the technique of extending associate homogeneous distributions to complete the renormalization recursion. A homogeneous (Poincare covariant) amplitude is said to be convergent if it admits a (unique covariant) extension as a homogeneous distribution. For any amplitude without subdivergences - i.e. for a Feynman distribution that is homogeneous off the full (small) diagonal - we define a renormalization invariant residue. Its vanishing is a necessary and sufficient condition for the convergence of such an amplitude. It extends to arbitrary - not necessarily primitively divergent - Feynman amplitudes. This notion of convergence is finer than the usual power counting criterion and includes cancellation of divergences.
Equality of some integrals from real and imaginary parts of a scattering amplitude
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
Amplitude-modulated fiber-ring laser
Caputo, J. G.; Clausen, Carl A. Balslev; Sørensen, Mads Peter; Bischoff, Svend
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......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...... by comparison with the full numerical simulations. Finally, we discuss possible sources of instability that are due to resonances in the device....
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
Scattering amplitudes over finite fields and multivariate functional reconstruction
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 topol...
Organizational Models for Big Data and Analytics
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.
Business analytics a practitioner's guide
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
Gauge and Gravity Amplitude Relations
Carrasco, John Joseph M
2015-01-01
In these lectures I talk about simplifications and universalities found in scattering amplitudes for gauge and gravity theories. In contrast to Ward identities, which are understood to arise from familiar symmetries of the classical action, these structures are currently only understood in terms of graphical organizational principles, such as the gauge-theoretic color-kinematics duality and the gravitational double-copy structure, for local representations of multi-loop S-matrix elements. These graphical principles make manifest new relationships in and between gauge and gravity scattering amplitudes. My lectures will focus on arriving at such graphical organizations for generic theories with examples presented from maximal supersymmetry, and their use in unitarity-based multi-loop integrand construction.
Scruncher phase and amplitude control
The analog controller for phase and amplitude control of a 402.5 MHz super conducting cavity is described in this paper. The cavity is a single cell with niobium explosively bonded to a copper cavity. It is used as an energy compressor for pions at the Clinton P. Anderson Meson Physics Facility (LAMPF). The controller maintains cavity frequency to within 4 degrees in phase of the LAMPF beam frequency. Field amplitude is maintained to within 2 percent. This control is accomplished at critical coupling (Q load of 1 x 109) with the use of only a 30 watt rf amplifier for accelerating fields of 6 MV/m. The design includes the use of piezoelectric crystals for fast resonance control. Three types of control, self excited, VCO, and a reference frequency driven, were tried on this cavity and we present a comparison of their performance. (Author) 4 figs., ref
Pulse amplitude modulated chlorophyll fluorometer
Greenbaum, Elias; Wu, Jie
2015-12-29
Chlorophyll fluorometry may be used for detecting toxins in a sample because of changes in micro algae. A portable lab on a chip ("LOAC") based chlorophyll fluorometer may be used for toxin detection and environmental monitoring. In particular, the system may include a microfluidic pulse amplitude modulated ("PAM") chlorophyll fluorometer. The LOAC PAM chlorophyll fluorometer may analyze microalgae and cyanobacteria that grow naturally in source drinking water.
Federal Laboratory Consortium — NETL’s analytical laboratories in Pittsburgh, PA, and Albany, OR, give researchers access to the equipment they need to thoroughly study the properties of materials...
Flannelly, W. G.; Fabunmi, J. A.; Nagy, E. J.
1981-01-01
Analytical methods for combining flight acceleration and strain data with shake test mobility data to predict the effects of structural changes on flight vibrations and strains are presented. This integration of structural dynamic analysis with flight performance is referred to as analytical testing. The objective of this methodology is to analytically estimate the results of flight testing contemplated structural changes with minimum flying and change trials. The category of changes to the aircraft includes mass, stiffness, absorbers, isolators, and active suppressors. Examples of applying the analytical testing methodology using flight test and shake test data measured on an AH-1G helicopter are included. The techniques and procedures for vibration testing and modal analysis are also described.
Recovery of the fidelity amplitude for the Gaussian ensembles
Using supersymmetry techniques analytical expressions for the average of the fidelity amplitude fε(τ) (ψ(0)|exp(2πiHετ) exp(-2πiH0τ)|ψ(0)) are obtained, where Hε = H0+√ε/2π) V, and H0 and Hε are taken from the Gaussian unitary ensemble (GUE) or the Gaussian orthogonal ensemble (GOE), respectively. As long as the perturbation strength is small compared to the mean level spacing, a Gaussian decay of the fidelity amplitude is observed, whereas for stronger perturbations a change to a single-exponential decay takes place, in accordance with results from the literature. Close to the Heisenberg time τ = 1, however, a partial revival of the fidelity is found, which hitherto remained unnoticed. Random matrix simulations have been performed for the three Gaussian ensembles. For the case of the GOE and the GUE they are in perfect agreement with the analytical results
Universal finite-size scaling amplitudes in anisotropic scaling
Phenomenological scaling arguments suggest the existence of universal amplitudes in the finite-size scaling of certain correlation lengths in strongly anisotropic or dynamical phase transitions. For equilibrium systems, provided that translation invariance and hyperscaling are valid, the Privman-Fisher scaling form of isotropic equilibrium phase transitions is readily generalized. For non-equilibrium systems, universality is shown analytically for directed percolation and is tested numerically in the annihilation-coagulation model and in the pair contact process with diffusion. In these models, for both periodic and free boundary conditions, the universality of the finite-size scaling amplitude of the leading relaxation time is checked. Amplitude universality reveals strong transient effects along the active-inactive transition line in the pair contact process. (author)
BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes
Bartels, J. [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); Sabio Vera, A. [CERN, Geneva (Switzerland)
2008-02-15
After a brief review of the BFKL approach to Regge processes in QCD and in supersymmetric (SUSY) gauge theories we propose a strategy for calculating the next-to-next-to-leading order corrections to the BFKL kernel. They can be obtained in terms of various cross-sections for Reggeized gluon interactions. The corresponding amplitudes can be calculated in the framework of the effective action for high energy scattering. In the case of N=4 SUSY it is also possible to use the Bern-Dixon-Smirnov (BDS) ansatz. For this purpose the analytic properties of the BDS amplitudes at high energies are investigated, in order to verify their self-consistency. It is found that, for the number of external particles being larger than five, these amplitudes, beyond one loop, are not in agreement with the BFKL approach which predicts the existence of Regge cuts in some physical channels. (orig.)
Amplitude Modulation in the δ Sct star KIC 7106205
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.
Large-amplitude motion in the Suzuki model
The classical and quantum aspects for the analytically solvable one-dimensional pure monopole Suzuki model are studied to clarify the problem of quantization of classical collective motion. A set of nonlinear dynamic equations for a monopole moment of a nucleus are derived from the TDHF equation using the Wigner function moments model. It provides to describe large-amplitude monopole vibrations. The corresponding collective Hamiltonian is constructed and quantized. The anharmonicity of the collective spectra is analyzed in detal
Small Amplitude Solitons in Bose Einstein Condensates with External Perturbation
Wang, Feng-Jiao; Yan, Xiao-Hong; Wang, Deng-Long
2008-01-01
By developing a small amplitude soliton approximation method, we study analytically weak nonlinear excitations in cigar-shaped condensates with repulsive interatomic interaction under consideration of external perturbation potential. It is shown that matter wave solitons may exist and travel over a long distance without attenuation and change in shape by properly adjusting the strength of interatomic interaction to compensate for the effect of external perturbation potential.
Radiation Belt Electron Dynamics Driven by Large-Amplitude Whistlers
Khazanov, G. V.; Tel'nikhin, A. A.; Kronberg, T. K.
2013-01-01
Acceleration of radiation belt electrons driven by oblique large-amplitude whistler waves is studied. We show analytically and numerically that this is a stochastic process; the intensity of which depends on the wave power modified by Bessel functions. The type of this dependence is determined by the character of the nonlinear interaction due to coupling between action and phase. The results show that physically significant quantities have a relatively weak dependence on the wave power.
Broadband metasurface for independent control of reflected amplitude and phase
Sheng Li Jia; Xiang Wan; Pei Su; Yong Jiu Zhao; Tie Jun Cui
2016-01-01
We propose an ultra-thin metasurface to control the amplitudes and phases independently of the reflected waves by changing geometries and orientations of I-shaped metallic particles. We demonstrate that the particles can realize independent controls of reflection amplitudes and phases with a magnitude range of [0, 0.82] and a full phase range of 360° in broad frequency band. Based on such particles, two ultrathin metasurface gratings are further proposed to form anomalous reflection with pola...
Large-N QCD and the Veneziano amplitude
Adi Armoni
2016-05-01
Full Text Available We consider four scalar mesons scattering in large-Nc QCD. Using the worldline formalism we show that the scattering amplitude can be written as a formal sum over Wilson loops. The AdS/CFT correspondence maps this sum into a sum over string worldsheets in a confining background. We then argue that for well separated mesons the sum is dominated by flat space configurations. Under additional assumptions about the dual string path integral we obtain the Veneziano amplitude.
Amplitude recruitment of cochlear potential
LI Xingqi; SUN Wei; SUN Jianhe; YU Ning; JIANG Sichang
2001-01-01
Intracellular recordings were made from outer hair cells (OHC) and the cochlear microphonics (CM) were recorded from scala media (SM) in three turn of guinea pig cochlea,the compound action potential (CAP) were recorded at the round window (RW) before and after the animal were exposed to white noise. The results suggest that the nonlinear properties with “saduration” of Input/output (I/O) function of OHC AC recepter potential and CM were founded; the nonlinear properties with “Low”, “Platean” and “high” of CAP also were investigated. After explosion, the threshold shift of CAP has about 10 dB. The I/O of OHC responses and CM were changed in a linearizing (i.e., nonlinearity loss), the “platean” of I/O CAP disappeared and the growth rate of CAP amplitude were larger than before explosion. The response amplitude recruitment of OHC appears to result from reduction in gain (i.e., hearing loss); It was due to the nonlinear growth function of OHC receptor potentials was changed in linearzing that the basilar membrance motion was changed in linearizing. Since intensity coding in the inner ear depends on an interactions of nonlinear basilar membrance and nerve fibers. So that it must lead to a linearizing of CAP as input responses.
Seif El-Nasr, Magy; Drachen, Anders; Canossa, Alessandro
2013-01-01
Game Analytics has gained a tremendous amount of attention in game development and game research in recent years. The widespread adoption of data-driven business intelligence practices at operational, tactical and strategic levels in the game industry, combined with the integration of quantitative...... measures in user-oriented game research, has caused a paradigm shift. Historically, game development has not been data-driven, but this is changing as the benefits of adopting and adapting analytics to inform decision making across all levels of the industry are becoming generally known and accepted....
Spain, Barry; Ulam, S; Stark, M
1960-01-01
Analytical Quadrics focuses on the analytical geometry of three dimensions. The book first discusses the theory of the plane, sphere, cone, cylinder, straight line, and central quadrics in their standard forms. The idea of the plane at infinity is introduced through the homogenous Cartesian coordinates and applied to the nature of the intersection of three planes and to the circular sections of quadrics. The text also focuses on paraboloid, including polar properties, center of a section, axes of plane section, and generators of hyperbolic paraboloid. The book also touches on homogenous coordi
N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops
Boucher-Veronneau, C
2011-01-01
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.
N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops
Boucher-Veronneau, C.; Dixon, L.J.; /SLAC
2012-02-15
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.
General tree-level amplitudes by factorization limits
Zhou, Kang; Qiao, Chenkai [Zhejiang University, Zhejiang Institute of Modern Physics, Hangzhou (China)
2015-04-01
To find boundary contributions is a rather difficult problem when applying the BCFW recursion relation. In this paper, we propose an approach to bypass this problem by calculating general tree amplitudes that contain no polynomial using factorization limits. More explicitly, we construct an expression iteratively, which produces the correct factorization limits for all physical poles, and does not contain other poles, then it should be the correct amplitude. To some extent, this approach can be considered as an alternative way to find boundary contributions. To demonstrate our approach, we present several examples: φ{sup 4} theory, pure gauge theory, Einstein-Maxwell theory, and Yukawa theory. While the amplitude allows the existence of polynomials which satisfy the correct mass dimension and helicities, this approach is not applicable to determining the full amplitude. (orig.)
Pappas, Marjorie L.
1995-01-01
Discusses analytical searching, a process that enables searchers of electronic resources to develop a planned strategy by combining words or phrases with Boolean operators. Defines simple and complex searching, and describes search strategies developed with Boolean logic and truncation. Provides guidelines for teaching students analytical…
Search for analytic extensions of combinations of thermal two-point functions at one loop
Full text: In this paper, we study the analytic properties of two and three-point amplitudes at Finite Temperature in the Closed Time Path formalism at one loop. In [Phys. Rev. D 71, 036002 (2005)], Weldon has shown the impossibility of analytic continuation for the 2n different n-points functions that appear in the Real Time Formalism in Quantum Field Theory at Finite Temperature, due to the presence of branch cuts at various energy values. Even though none of these functions alone can be extended to complex regions he has found the particular combination of these n-point functions which admit analytic extension to complex energies. In his work, he has considered general properties of thermal average of field operators to analyse the results. On the other hand, at one loop in the perturbation theory more analytic structures appear inside the loop integrals and it is not clear how these results will appear. Here, we consider the λφ3 and the Schwinger Models and study how these analytic properties manifest specifically inside a loop integral. We explicitly extract the branch cuts of the various amplitudes for the self-energies and vertex corrections and show which combinations of them admit analytic continuation for complex energy values. We will extend this paper of n-point functions. (author)
A generalized fidelity amplitude for open systems.
Gorin, T; Moreno, H J; Seligman, T H
2016-06-13
We consider a central system which is coupled via dephasing to an open system, i.e. an intermediate system which in turn is coupled to another environment. Considering the intermediate and far environment as one composite system, the coherences in the central system are given in the form of fidelity amplitudes for a certain perturbed echo dynamics in the composite environment. On the basis of the Born-Markov approximation, we derive a master equation for the reduction of that dynamics to the intermediate system alone. In distinction to an earlier paper (Moreno et al 2015 Phys. Rev. A 92, 030104. (doi:10.1103/PhysRevA.92.030104)), where we discussed the stabilizing effect of the far environment on the decoherence in the central system, we focus here on the possibility of using the measurable coherences in the central system for probing the open quantum dynamics in the intermediate system. We illustrate our results for the case of chaotic dynamics in the near environment, where we compare random matrix simulations with our analytical result. PMID:27140969
The Construction of Spin Foam Vertex Amplitudes
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.
Grassmannian geometry of scattering amplitudes
Arkani-Hamed, Nima; Cachazo, Freddy; Goncharov, Alexander; Postnikov, Alexander; Trnka, Jaroslav
2016-01-01
Outlining a revolutionary reformulation of the foundations of perturbative quantum field theory, this book is a self-contained and authoritative analysis of the application of this new formulation to the case of planar, maximally supersymmetric Yang–Mills theory. The book begins by deriving connections between scattering amplitudes and Grassmannian geometry from first principles before introducing novel physical and mathematical ideas in a systematic manner accessible to both physicists and mathematicians. The principle players in this process are on-shell functions which are closely related to certain sub-strata of Grassmannian manifolds called positroids - in terms of which the classification of on-shell functions and their relations becomes combinatorially manifest. This is an essential introduction to the geometry and combinatorics of the positroid stratification of the Grassmannian and an ideal text for advanced students and researchers working in the areas of field theory, high energy physics, and the...
This book is comprised of nineteen chapters, which describes introduction of analytical chemistry, experimental error and statistics, chemistry equilibrium and solubility, gravimetric analysis with mechanism of precipitation, range and calculation of the result, volume analysis on general principle, sedimentation method on types and titration curve, acid base balance, acid base titration curve, complex and firing reaction, introduction of chemical electro analysis, acid-base titration curve, electrode and potentiometry, electrolysis and conductometry, voltammetry and polarographic spectrophotometry, atomic spectrometry, solvent extraction, chromatograph and experiments.
The division for Analytical Chemistry continued to try and develope an accurate method for the separation of trace amounts from mixtures which, contain various other elements. Ion exchange chromatography is of special importance in this regard. New separation techniques were tried on certain trace amounts in South African standard rock materials and special ceramics. Methods were also tested for the separation of carrier-free radioisotopes from irradiated cyclotron discs
On Benjamin-Feir instability and evolution of a nonlinear wave with finite-amplitude sidebands
L. Shemer
2010-11-01
Full Text Available In the past decade it became customary to relate the probability of appearance of extremely steep (the so-called freak, or rogue waves to the value of the Benjamin-Feir Index (BFI that represents the ratio of wave nonlinearity to the spectral width. This ratio appears naturally in the cubic Schrödinger equation that describes evolution of unidirectional narrow-banded wave field. The notion of this index stems from the Benjamin-Feir linear stability analysis of Stokes wave. The application of BFI to evaluate the evolution of wave fields, with non-vanishing amplitudes of sideband disturbances, is investigated using the Zakharov equation as the theoretical model. The present analysis considers a 3-wave system for which the exact analytical solution of the model equations is available.
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 k2 → 0 and k3 → 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
Analytical solutions of the simplified Mathieu’s equation
Nicolae MARCOV
2016-03-01
Full Text Available Consider a second order differential linear periodic equation. The periodic coefficient is an approximation of the Mathieu’s coefficient. This equation is recast as a first-order homogeneous system. For this system we obtain analytical solutions in an explicit form. The first solution is a periodic function. The second solution is a sum of two functions, the first is a continuous periodic function, but the second is an oscillating function with monotone linear increasing amplitude. We give a formula to directly compute the slope of this increase, without knowing the second numeric solution. The periodic term of the second solution may be computed directly. The coefficients of fundamental matrix of the system are analytical functions.
Quantum Amplitude Amplification and Estimation
Brassard, G; Mosca, M; Tapp, A; Brassard, Gilles; Hoyer, Peter; Mosca, Michele; Tapp, Alain
2000-01-01
Consider a Boolean function $\\chi: X \\to \\{0,1\\}$ that partitions set $X$ between its good and bad elements, where $x$ is good if $\\chi(x)=1$ and bad otherwise. Consider also a quantum algorithm $\\mathcal A$ such that $A \\ket{0} = \\sum_{x\\in X} \\alpha_x \\ket{x}$ is a quantum superposition of the elements of $X$, and let $a$ denote the probability that a good element is produced if $A \\ket{0}$ is measured. If we repeat the process of running $A$, measuring the output, and using $\\chi$ to check the validity of the result, we shall expect to repeat $1/a$ times on the average before a solution is found. *Amplitude amplification* is a process that allows to find a good $x$ after an expected number of applications of $A$ and its inverse which is proportional to $1/\\sqrt{a}$, assuming algorithm $A$ makes no measurements. This is a generalization of Grover's searching algorithm in which $A$ was restricted to producing an equal superposition of all members of $X$ and we had a promise that a single $x$ existed such tha...
Rorty, Pragmatism, and Analytic Philosophy
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.
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.
Generalised unitarity for dimensionally regulated amplitudes within FDF
Bobadilla, William J Torres
2016-01-01
We review the Four-Dimensional-Formulation variant of the Four-Dimensional-Helicity scheme, by showing two applications of this regularisation scheme. The first one is the computation of one-loop helicity amplitudes, for which we present preliminary results for the analytic expressions of the one-loop Higgs plus five- gluon amplitudes. In the second part, we study the Colour-Kinematics duality for off-shell diagrams in gauge theories coupled to matter, showing in a diagrammatic way that the Jacobi relations for the kinematic numerators of off-shell diagrams, built with Feynman rules in axial gauge, reduce to definite set of violating terms due to the contributions of sub-graphs only.
Large amplitude electromagnetic solitons in intense laser plasma interaction
Li Bai-Wen; Ishiguro S; Skoric M M
2006-01-01
This paper shows that the standing, backward- and forward-accelerated large amplitude relativistic electromagnetic solitons induced by intense laser pulse in long underdense collisionless homogeneous plasmas can be observed by particle simulations. In addition to the inhomogeneity of the plasma density, the acceleration of the solitons also depends upon not only the laser amplitude but also the plasma length. The electromagnetic frequency of the solitons is between about half and one of the unperturbed electron plasma frequency. The electrostatic field inside the soliton has a one-cycle structure in space, while the transverse electric and magnetic fields have half-cycle and one-cycle structure respectively.Analytical estimates for the existence of the solitons and their electromagnetic frequencies qualitatively coincide with our simulation results.
Radiative corrections to chiral amplitudes in quasi-peripheral kinematics
Chiral amplitudes for two jets processes in quasi-peripheral kinematics are calculated at the Born and one-loop correction levels. The amplitudes of subprocesses describing interaction of virtual and real photons with creation of a charged fermion pair for various chiral states are considered in detail. Similar results are presented for Compton subprocess with virtual photon. Contributions of emission of virtual, soft, and hard real additional photons are taken into account explicitly. The relevant cross sections expressed in terms of impact factors are in agreement with structure function approach in the leading logarithmic approximation. Contributions of the next-to-leading terms are presented in an analytical form. Accuracy estimation is discussed
Amplitude modulation control of escape from a potential well
Chacón, R. [Departamento de Física Aplicada, Escuela de Ingenierías Industriales, Universidad de Extremadura, Apartado Postal 382, E-06006 Badajoz (Spain); Martínez García-Hoz, A. [Departamento de Física Aplicada, Escuela Universitaria Politécnica, Universidad de Castilla-La Mancha, E-13400 Almadén (Ciudad Real) (Spain); Miralles, J.J. [Departamento de Física Aplicada, Escuela de Ingenieros Industriales, Universidad de Castilla-La Mancha, E-02071 Albacete (Spain); Martínez, P.J. [Departamento de Física Aplicada, E.I.N.A., Universidad de Zaragoza, E-50018 Zaragoza (Spain); Instituto de Ciencia de Materiales de Aragón, CSIC – Universidad de Zaragoza, E-50009 Zaragoza (Spain)
2014-03-01
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.
Scattering amplitudes in gauge theories with and without supersymmetry
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 ...
Radiative Corrections to Chiral Amplitudes in Quasi-Peripheral Kinematics
Bytev, V V; Galynsky, M V; Kuraev, E A
2006-01-01
Chiral amplitudes for two jets processes in quasi-peripheral kinematics are calculated at the Born and one-loop correction levels. The amplitudes of subprocesses describing interaction of virtual and real photons with creation of a charged fermion pair for various chiral states are considered in detail. Similar results are presented for Compton subprocess with virtual photon. Contributions of emission of virtual, soft, and hard real additional photons are taken into account explicitly. The relevant cross sections expressed in terms of impact factors are in agreement with structure function approach in the leading logarithmic approximation. Contributions of the next-to-leading terms are presented in an analytical form. Accuracy estimation is discussed.
Compact QED tree-level amplitudes from dressed BCFW recursion relations
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.)
The structure of instantaneous frequencies of periodic analytic signals
无
2010-01-01
In this paper, the structure of analytic signals is investigated by means of the relation between analytic signals and functions in the Hardy space. It is shown that an analytic signal is made up of two parts, one depending on the amplitude of the signal and another on the boundary value of an inner function. Based on this result, properties of the instantaneous frequencies of these two parts are studied, and it is found that negative instantaneous frequencies are caused by the amplitude of a signal. Finally, such conditions that an analytic signal is of positive instantaneous frequency are presented.
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
Gravity and Yang-Mills amplitude relations
Using only general features of the S matrix and quantum field theory, we prove by induction the Kawai-Lewellen-Tye relations that link products of gauge theory amplitudes to gravity amplitudes at tree level. As a bonus of our analysis, we provide a novel and more symmetric form of these relations. We also establish an infinite tower of new identities between amplitudes in gauge theories.
On the singularities of massive superstring amplitudes
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.
On the singularities of massive superstring amplitudes
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.)
On the singularities of massive superstring amplitudes
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 require an off-shell formalism.
The Trace Formula of the Spinoriel Amplitude
Mekhfi, M.
2009-01-01
We re express the fermion's probability amplitude as a trace over spinor indices, which formulation surprisingly does not exist in literature. This formulation puts the probabilty amplitude and the the probabilty(squared amplitude) of a given process on equal footing at the compuational level and this is our principal motivation to write the present paper. We test the power of the trace formula in three applications: Calculation of the charge-current of fermions by using symbolic programs, wh...
Covariant method for calculating helicity amplitudes
We present an alternative approach for calculating helicity amplitudes for processes involving both massless and massive fermions. With this method one can easily obtain covariant expressions for the helicity amplitudes. The final expressions involve only four-vector products and are independent of the basis for γ matrices or specific form of the spinors. We use the method to obtain the helicity amplitudes for several processes involving top quark production. copyright 1996 The American Physical Society
Oscillations of a simple pendulum with extremely large amplitudes
Large oscillations of a simple rigid pendulum with amplitudes close to 180° are treated on the basis of a physically justified approach in which the cycle of oscillation is divided into several stages. The major part of the almost closed circular path of the pendulum is approximated by the limiting motion, while the motion in the vicinity of the inverted position is described on the basis of the linearized equation. The accepted approach provides additional insight into the dynamics of nonlinear physical systems. The final simple analytical expression gives values for the period of large oscillations that coincide with high precision with the values given by the exact formula. (paper)
FEASIBILITY OF INVESTMENT IN BUSINESS ANALYTICS
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.
The paper concerns the physical principles behind the analytical techniques employing high energy ion microbeams, with special attention to features that affect their use with microbeams. Particle-induced x-ray emission (PIXIE) is discussed with respect to X-ray production, thick-target PIXIE, a microbeam PIXIE system, sensitivity, and microbeam PIXIE applications. An explanation of nuclear reaction analysis (NRA) is given for NRA with charged particle detection, NRA with neutron detection and NRA with gamma detection. The essentials of Rutherford back scattering (RBS) are given, along with the elastic recoil detection analysis, which has very close connections with RBS but was introduced much more recently. Finally a comparison of the microbeam's capability with those of its main competitors is presented. (UK)
Light-cone distribution amplitudes of the baryon octet
Bali, Gunnar S; Göckeler, Meinulf; Gruber, Michael; Hutzler, Fabian; Schäfer, Andreas; Simeth, Jakob; Söldner, Wolfgang; Sternbeck, Andre; Wein, Philipp
2015-01-01
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.
Enhancing amplitude changes by mode localization in trio cantilevers with mass perturbation
A simplified three-cantilever array was designed and micro-fabricated for demonstrating the response enhancement in amplitude changes when applying small mass perturbations. Three micro-cantilevers, defined as side (outermost) cantilever, center cantilever and another side cantilever, are identical in geometry and are connected micro-mechanically with each other by two coupling overhangs. In the case of analytical characterizations, by applying a picogram order mass perturbation (10 pg) on one side cantilever, significant enhancements in amplitude changes were obtained at the 2nd resonance mode from both of the unloaded cantilevers. The amplitude change from the center cantilever is about 7000 times higher than that with no mass perturbation, while the change in amplitude from another side cantilever is about 4000 times higher. In the aspect of experimental characterizations, the enhancement in amplitude change at the 2nd resonance mode was verified by applying two polystyrene micro-spheres (about 8.8 pg) as a picogram order mass perturbation onto one side cantilever. Due to the operational difficulties in quantitatively manipulating polystyrene micro-spheres, the effects of mass variations on the enhancement in amplitude changes from unloaded cantilevers were further analytically characterized under a range of 0.01–100 pg for three resonance modes respectively. This work is the first comparative study using three identical spring-mass beams on both analytical characterizations by applying small mass perturbations and sensing verification by manipulating a picogram polystyrene micro-sphere. (paper)
Croatian Analytical Terminology
Kastelan-Macan; M.
2008-04-01
Full Text Available Results of analytical research are necessary in all human activities. They are inevitable in making decisions in the environmental chemistry, agriculture, forestry, veterinary medicine, pharmaceutical industry, and biochemistry. Without analytical measurements the quality of materials and products cannot be assessed, so that analytical chemistry is an essential part of technical sciences and disciplines.The language of Croatian science, and analytical chemistry within it, was one of the goals of our predecessors. Due to the political situation, they did not succeed entirely, but for the scientists in independent Croatia this is a duty, because language is one of the most important features of the Croatian identity. The awareness of the need to introduce Croatian terminology was systematically developed in the second half of the 19th century, along with the founding of scientific societies and the wish of scientists to write their scientific works in Croatian, so that the results of their research may be applied in economy. Many authors of textbooks from the 19th and the first half of the 20th century contributed to Croatian analytical terminology (F. Rački, B. Šulek, P. Žulić, G. Pexidr, J. Domac, G. Janeček , F. Bubanović, V. Njegovan and others. M. DeŢelić published the first systematic chemical terminology in 1940, adjusted to the IUPAC recommendations. In the second half of 20th century textbooks in classic analytical chemistry were written by V. Marjanović-Krajovan, M. Gyiketta-Ogrizek, S. Žilić and others. I. Filipović wrote the General and Inorganic Chemistry textbook and the Laboratory Handbook (in collaboration with P. Sabioncello and contributed greatly to establishing the terminology in instrumental analytical methods.The source of Croatian nomenclature in modern analytical chemistry today are translated textbooks by Skoog, West and Holler, as well as by Günnzler i Gremlich, and original textbooks by S. Turina, Z.
Stationary Large Amplitude Dynamics of the Finite Chain of Harmonically Coupled Pendulums
Smirnov, Valeri V
2016-01-01
We present an analytical description of the large-amplitude stationary oscillations of the finite discrete system of harmonically-coupled pendulums without any restrictions to their amplitudes (excluding a vicinity of $\\pi$). Although this model has numerous applications in different fields of physics it was studied earlier in the infinite limit only. The developed approach allows to find the dispersion relations for arbitrary amplitudes of the nonlinear normal modes. We underline that the long-wavelength approximation, which is described by well- known sine-Gordon equation leads to inadequate zone structure for the amplitude order of $\\pi/2$ even if the chain is long enough. The extremely complex zone structure at the large amplitudes corresponds to lot of resonances between nonlinear normal modes even with strongly different wave numbers. Due to complexity of the dispersion relations the more short wavelength modes can possess the smaller frequencies. The numerical simulation of the dynamics of the finite-l...
Propagation of Aberrations through Phase Induced Amplitude Apodization coronagraph
Pueyo, Laurent; Shaklan, Stuart; 10.1364/JOSAA.28.000189
2011-01-01
The specification of polishing requirements for the optics in coronagraphs dedicated to exo-planet detection requires careful and accurate optical modelling. Numerical representations of the propagation of aberrations through the system as well as simulations of the broadband wavefront compensation system using multiple DMs are critical when one devises an error budget for such a class of instruments. In this communication we introduce an analytical tool that serves this purpose for Phase Induced Amplitude Apodisation (PIAA) coronagraphs. We first start by deriving the analytical form of the propagation of a harmonic ripple through a PIAA unit. Using this result we derive the chromaticity of the field at any plane in the optical train of a telescope equipped with such a coronagraph. Finally we study the chromatic response of a sequential DM wavefront actuator correcting such a corrugated field and thus quantify the requirements on the manufacturing of PIAA mirrors
Gauge dependence in QED amplitudes in expanding de Sitter space
Nicolaevici, Nistor
2016-04-01
We consider first-order transition amplitudes in external fields in QED in the expanding de Sitter space and point out that they are gauge dependent quantities. We examine the gauge variations of the amplitudes assuming a decoupling of the interaction at large times, which allows to conclude that the source of the problem lies in the fact that the frequencies of the modes in the infinite future become independent of the comoving momenta. We show that a possibility to assure the gauge invariance of the external field amplitudes is to restrict to potentials which vanish sufficiently fast at infinite times, and briefly discuss a number of options in the face of the possible gauge invariance violation in the full interacting theory.
Heptagon amplitude in the multi-Regge regime
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 AdS5. 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.
Amplitude of Accommodation and its Relation to Refractive Errors
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
Amplitudes and Correlators to Ten Loops Using Simple, Graphical Bootstraps
Bourjaily, Jacob L; Tran, Vuong-Viet
2016-01-01
We introduce two new graphical-level relations among possible contributions to the four-point correlation function and scattering amplitude in planar, maximally supersymmetric Yang-Mills theory. When combined with the rung rule, these prove powerful enough to fully determine both functions through ten loops. This then also yields the full five-point amplitude to eight loops and the parity-even part to nine loops. We derive these rules, illustrate their applications, compare their relative strengths for fixing coefficients, and survey some of the features of the previously unknown nine and ten loop expressions. Explicit formulae for amplitudes and correlators through ten loops are available at: http://goo.gl/JH0yEc.
Optimization of phase contrast in bimodal amplitude modulation AFM
Mehrnoosh Damircheli
2015-04-01
Full Text Available Bimodal force microscopy has expanded the capabilities of atomic force microscopy (AFM by providing high spatial resolution images, compositional contrast and quantitative mapping of material properties without compromising the data acquisition speed. In the first bimodal AFM configuration, an amplitude feedback loop keeps constant the amplitude of the first mode while the observables of the second mode have not feedback restrictions (bimodal AM. Here we study the conditions to enhance the compositional contrast in bimodal AM while imaging heterogeneous materials. The contrast has a maximum by decreasing the amplitude of the second mode. We demonstrate that the roles of the excited modes are asymmetric. The operational range of bimodal AM is maximized when the second mode is free to follow changes in the force. We also study the contrast in trimodal AFM by analyzing the kinetic energy ratios. The phase contrast improves by decreasing the energy of second mode relative to those of the first and third modes.
The amplitude of solar oscillations using stellar techniques
Kjeldsen, Hans; Arentoft, Torben; Butler, R Paul; Dall, Thomas H; Karoff, Christoffer; Kiss, Laszlo L; Tinney, C G; Chaplin, William J
2008-01-01
The amplitudes of solar-like oscillations depend on the excitation and damping, both of which are controlled by convection. Comparing observations with theory should therefore improve our understanding of the underlying physics. However, theoretical models invariably compute oscillation amplitudes relative to the Sun, and it is therefore vital to have a good calibration of the solar amplitude using stellar techniques. We have used daytime spectra of the Sun, obtained with HARPS and UCLES, to measure the solar oscillations and made a detailed comparison with observations using the BiSON helioseismology instrument. We find that the mean solar amplitude measured using stellar techniques, averaged over one full solar cycle, is 18.7 +/- 0.7 cm/s for the strongest radial modes (l=0) and 25.2 +/- 0.9 cm/s for l=1. In addition, we use simulations to establish an equation that estimates the uncertainty of amplitude measurements that are made of other stars, given that the mode lifetime is known. Finally, we also give ...
Analysis of Peak-to-Peak Current Ripple Amplitude in Seven-Phase PWM Voltage Source Inverters
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.
Interpretation of magnetic anomalies using the horizontal gradient analytic signal
H. A. Bake
2001-06-01
Full Text Available In recent years the analytic signal method has been of great utility in the interpretation of potential field data. The amplitude of the 3D analytic signal of magnetic data yields information on the location of the edges of the sources in both the horizontal and vertical dimensions, with the main advantage that the magnetic field and magnetic source parameters need not be known or assumed. Accurate detection of source body coordinates is becoming the main goal for interpreters and therefore enhanced techniques are acquiring an increasing revival in data interpretation. This paper presents a high-resolution approach for detecting source boundaries. These boundaries can be determined from the maxima of the analytic signal computed from the horizontal gradient of the field, defined here as a vector, the components of which are the analytic signals of x- and y-horizontal derivatives, respectively. Synthetic examples have shown the high resolving power of the proposed technique. This approach has also given very good results when applied to real data.
Causality and analyticity in quantum fields theory
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.)
Chen Guanghua; Ma Shiwei; Qin Tinghao; Wang Jian; Li Ming; Cao Jialin
2005-01-01
The instantaneous frequency (IF) estimation of the linear frequency modulated (LFM) signals with time-varying amplitude using the peak of the Wigner-Ville distribution (WVD) is studied. Theoretical analysis shows that the estimation on LFM signals with time-varying amplitude is unbiased, only if WVD of time-varying amplitude reaches its maximum at frequency zero no matter in which time. The statistical performance in the case of additive white Guassian noise is evaluated and an analytical expression for the variance is provided. The simulations using LFM signals with Gaussian envelope testify that IF can be estimated accurately using the peak of WVD for four models of amplitude variation. Furthermore the statistical result of estimation on the signals with amplitude descending before rising is better than that of the signals with constant amplitude when the amplitude variation rate is moderate.
On the nullification of threshold amplitudes
Gonera, Joanna
2002-01-01
The nullification of threshold amplitudes is considered within the conventional framework of quantum field theory. The relevant Ward identities for the reduced theory are derived both on path-integral and diagrammatic levels. They are then used to prove the vanishing of tree-graph threshold amplitudes.
On the singularities of massive superstring amplitudes
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 n
Production amplitude for a single scalar resonance
We derive a simple expression for the production amplitude of two pseudoscalar mesons involving a single scalar resonance. This amplitude is determined by a combination of Watson's phase δ(s) and another phase ω(s), related to an unambiguous two-meson propagator. With a lagrangian model, we study the σππ system
Finite amplitude dynamic motion of viscoelastic materials.
Yen, H.-C.; Mcintire, L. V.
1972-01-01
It is shown that an integral constitutive relation containing a memory function depending on strain tensor invariants can describe the rheological behavior of finite amplitude oscillatory motion of polymer solutions both qualitatively and quantitatively. Values of the material constants are obtained by a numerical technique of simultaneously curve fitting simple shearing viscosity, first normal stress difference, and small amplitude oscillatory motion data.
Scattering Amplitudes via Algebraic Geometry Methods
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...
Amplitude death in steadily forced chaotic systems
Feng Guo-Lin; He Wen-Ping
2007-01-01
Steady forcing can induce the amplitude death in chaotic systems, which generally exists in coupled dynamic systems. Using the Lorenz system as a typical example, this paper investigates the dynamic behaviours of the chaotic system with steady forcing numerically, and finds that amplitude death can occur as the strength of the steady forcing goes beyond a critical constant.
Consistent Off-Shell Tree String Amplitudes
Liccardo, A; Marotta, R
1999-01-01
We give a construction of off-shell tree bosonic string amplitudes, based on the operatorial formalism of the N-string Vertex, with three external massless states both for open and closed strings by requiring their being projective invariant. In particular our prescription leads, in the low-energy limit, to the three-gluon amplitude in the usual covariant gauge.
New relations for gauge-theory amplitudes
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.
The Lorentzian proper vertex amplitude: Asymptotics
Engle, Jonathan; Zipfel, Antonia
2015-01-01
In previous work, the Lorentzian proper vertex amplitude for a spin-foam model of quantum gravity was derived. In the present work, the asymptotics of this amplitude are studied in the semi-classical limit. The starting point of the analysis is an expression for the amplitude as an action integral with action differing from that in the EPRL case by an extra `projector' term which scales linearly with spins only in the asymptotic limit. New tools are introduced to generalize stationary phase methods to this case. For the case of boundary data which can be glued to a non-degenerate Lorentzian 4-simplex, the asymptotic limit of the amplitude is shown to equal the single Feynman term, showing that the extra term in the asymptotics of the EPRL amplitude has been eliminated.
New Relations for Gauge-Theory Amplitudes
Bern, Z; 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 multi-loop 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 KLT relations between gauge and gravity tree amplitudes. This can be used to obtain novel relations similar to the KLT ones. We expect this to be helpful in higher-loop studies of the ultraviolet properties of gravity theories.
DETERMINATION OF COORDINATES OF SEISMIC WAVE SOURCE BY AMPLITUDE METHOD OF PASSIVE LOCATION
Vasily D. Syten’ky
2015-10-01
Full Text Available The paper presents results of the mathematical synthesis of the method of passive location of a seismic wave source. The method employs measurements of regular attenuation of seismic oscillation amplitudes. If it is impossible to determine the location of a seismic event by means of direct measurements, indirect measurements are needed. A priori information for the mathematical synthesis was obtained from functional equations showing inverse proportions of measured amplitudes, arbitrary effective attenuation coefficients and corresponding coordinates. An original method was applied to process the data. The method providing for passive location of seismic waves sources has been developed; it is called the radial basic method. In the one-dimensional case, a distance is determined on the basis of seismic oscillation amplitudes measured by two seismographs that are located at a known base distance coinciding with the direction to the source of seismic waves. The distance is calculated from the receiver that is nearest to the source. If the base distance and the direct line between the seismograph and the seismic wave source do not coincide, a projection of the distance between the receivers to the given straight line is taken into account.Three seismographs were placed at mutually perpendicular base distances in a plane (i.e. the two-dimensional space. This allowed us to obtain an analytical equation for determining the direction to the seismic wave source using measured amplitudes. The value of the angle is taken into account when calculating the distance.For the seismic wave source located in the three-dimensional space, transition equations for combined coordinate systems (i.e. the Descartes (Cartesian, at the axes of which the seismographs were placed, and the spherical coordinate systems were applied, and analytical equations were obtained for determination of coordinates, such as distance/polar radius, elevation
Erik Duval
2012-06-01
Full Text Available This paper provides a brief introduction to the domain of ‘learning analytics’. We first explain the background and idea behind the concept. Then we give a brief overview of current research issues. We briefly list some more controversial issues before concluding.
Relations Between Closed String Amplitudes at Higher-order Tree Level and Open String Amplitudes
Chen, Yi-Xin; Ma, Qian
2009-01-01
KLT relations almost factorize closed string amplitudes on $S_2$ by two open string tree amplitudes which correspond to the left- and the right- moving sectors. In this paper, we investigate string amplitudes on $D_2$ and $RP_2$. We find that KLT factorization relations do not hold in these two cases. The relations between closed and open string amplitudes have new forms. On $D_2$ and $RP_2$, the left- and the right- moving sectors are connected into a single sector. Then an amplitude with closed strings on $D_2$ or $RP_2$ can be given by one open string tree amplitude except for a phase factor. The relations depends on the topologies of the world-sheets. In the low energy limits of these two cases, the factorization relations for graviton amplitudes do not hold. The amplitudes for gravitons must be given by the new relations instead.
Source-Space Cross-Frequency Amplitude-Amplitude Coupling in Tinnitus
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.
Gearbox Vibration Signal Amplitude and Frequency Modulation
Fakher Chaari
2012-01-01
Full Text Available Gearboxes usually run under fluctuating load conditions during service, however most of papers available in the literature describe models of gearboxes under stationary load conditions. Main task of published papers is fault modeling for their detection. Considering real situation from industry, the assumption of stationarity of load conditions cannot be longer kept. Vibration signals issued from monitoring in maintenance operations differ from mentioned models (due to load non-stationarity and may be difficult to analyze which lead to erroneous diagnosis of the system. The objective of this paper is to study the influence of time varying load conditions on a gearbox dynamic behavior. To investigate this, a simple spur gear system without defects is modeled. It is subjected to a time varying load. The speed-torque characteristic of the driving motor is considered. The load variation induces speed variation, which causes a variation in the gearmesh stiffness period. Computer simulation shows deep amplitude modulations with sidebands that don't differ from those obtained when there is a defective tooth. In order to put in evidence the time varying load effects, Short Time Fourier Transform and then Smoothed Wigner-Ville distribution are used. Results show that the last one is well suited for the studied case.
Effects of strength training on mechanomyographic amplitude
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)
Multigluon helicity amplitudes involving a quark loop
Mahlon, G
1994-01-01
We apply the solution to the recursion relation for the double-off-shell quark current to the problem of computing one loop amplitudes with an arbitrary number of gluons. We are able to compute amplitudes for photon-gluon scattering, electron-positron annihilation to gluons, and gluon-gluon scattering via a quark loop in the case of like-helicity gluons. In addition, we present the result for the one-loop gluon-gluon scattering amplitude when one of the gluons has opposite helicity from the others.
Form Factor and Boundary Contribution of Amplitude
Huang, Rijun; Feng, Bo
2016-01-01
The boundary contribution of an amplitude in the BCFW recursion relation can be considered as a form factor involving boundary operator and unshifted particles. At the tree-level, we show that by suitable construction of Lagrangian, one can relate the leading order term of boundary operators to some composite operators of N=4 super-Yang-Mills theory, then the computation of form factors is translated to the computation of amplitudes. We compute the form factors of these composite operators through the computation of corresponding double trace amplitudes.
A new analytical approximation to the Duffing-harmonic oscillator
Fesanghary, M. [Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA 70803 (United States); Pirbodaghi, T. [School of Mechanical Engineering, Sharif University of Technology, Azadi Ave., 11365-9567 Tehran (Iran, Islamic Republic of); Asghari, M. [School of Mechanical Engineering, Sharif University of Technology, Azadi Ave., 11365-9567 Tehran (Iran, Islamic Republic of)], E-mail: asghari@sharif.edu; Sojoudi, H. [Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA 70803 (United States)
2009-10-15
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.
One-loop helicity amplitudes for t anti t production at hadron colliders
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.)
Saffar, Saber; Abdullah, Amir
2014-01-01
The acoustic impedances of matching layers, their internal loss and vibration amplitude are the most important and influential parameters in the performance of high power airborne ultrasonic transducers. In this paper, the optimum acoustic impedances of the transducer matching layers were determined by using a genetic algorithm, the powerful tool for optimizating domain. The analytical results showed that the vibration amplitude increases significantly for low acoustic impedance matching layers. This enhancement is maximum and approximately 200 times higher for the last matching layer where it has the same interface with the air than the vibration amplitude of the source, lead zirconate titanate-pizo electric while transferring the 1 kW is desirable. This large amplitude increases both mechanical failure and temperature of the matching layers due to the internal loss of the matching layers. It has analytically shown that the temperature in last matching layer with having the maximum vibration amplitude is high enough to melt or burn the matching layers. To verify suggested approach, the effect of the amplitude of vibration on the induced temperature has been investigated experimentally. The experimental results displayed good agreement with the theoretical predictions. PMID:23664304
Broadband metasurface for independent control of reflected amplitude and phase
Sheng Li Jia
2016-04-01
Full Text Available We propose an ultra-thin metasurface to control the amplitudes and phases independently of the reflected waves by changing geometries and orientations of I-shaped metallic particles. We demonstrate that the particles can realize independent controls of reflection amplitudes and phases with a magnitude range of [0, 0.82] and a full phase range of 360° in broad frequency band. Based on such particles, two ultrathin metasurface gratings are further proposed to form anomalous reflection with polarization orthogonal to the incident waves. The simulated and measured results of the presented metasurfaces show very good agreements. The proposed method has potential applications in engineering high-efficiency holography and complex electromagnetic and optical patterns.
Motivic multiple zeta values and superstring amplitudes
The structure of tree-level open and closed superstring amplitudes is analyzed. For the open superstring amplitude we find a striking and elegant form, which allows one to disentangle its α′-expansion into several contributions accounting for different classes of multiple zeta values. This form is bolstered by the decomposition of motivic multiple zeta values, i.e. the latter encapsulate the α′-expansion of the superstring amplitude. Moreover, a morphism induced by the coproduct maps the α′-expansion onto a non-commutative Hopf algebra. This map represents a generalization of the symbol of a transcendental function. In terms of elements of this Hopf algebra the α′-expansion assumes a very simple and symmetric form, which carries all the relevant information. Equipped with these results we can also cast the closed superstring amplitude into a very elegant form. (paper)
Off-shell amplitudes in superstring theory
Sen, Ashoke [Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad, 211019 (India)
2015-04-01
Computing the renormalized masses and S-matrix elements in string theory, involving states whose masses are not protected from quantum corrections, requires defining off-shell amplitude with certain factorization properties. While in the bosonic string theory one can in principle construct such an amplitude from string field theory, there is no fully consistent field theory for type II and heterotic string theory. In this paper we give a practical construction of off-shell amplitudes satisfying the desired factorization property using the formalism of picture changing operators. We describe a systematic procedure for dealing with the spurious singularities of the integration measure that we encounter in superstring perturbation theory. This procedure is also useful for computing on-shell amplitudes, as we demonstrate by computing the effect of Fayet-Iliopoulos D-terms in four dimensional heterotic string theory compactifications using this formalism. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
The singular behavior of massive QCD amplitudes
We discuss the structure of infrared singularities in on-shell QCD amplitudes with massive partons and present a general factorization formula in the limit of small parton masses. The factorization formula gives rise to an all-order exponentiation of both, the soft poles in dimensional regularization and the large collinear logarithms of the parton masses. Moreover, it provides a universal relation between any on-shell amplitude with massive external partons and its corresponding massless amplitude. For the form factor of a heavy quark we present explicit results including the fixed-order expansion up to three loops in the small mass limit. For general scattering processes we show how our constructive method applies to the computation of all singularities as well as the constant (mass-independent) terms of a generic massive n-parton QCD amplitude up to the next-to-next-to-leading order corrections. (orig.)
Amplitudes for left-handed strings
Siegel, W
2015-01-01
We consider a class of string-like models introduced previously where all modes are left-handed, all states are massless, T-duality is manifest, and only a finite number of orders in the string tension can appear. These theories arise from standard string theories by a singular gauge limit and associated change in worldsheet boundary conditions. In this paper we show how to calculate amplitudes by using the gauge parameter as an infrared regulator. The amplitudes produce the Cachazo-He-Yuan delta-functions after some modular integration; the Mason-Skinner string-like action and amplitudes arise from the zero-tension (infinite-slope) limit. However, without the limit the amplitudes have the same problems as found in the Mason-Skinner formalism.
Open string amplitudes of closed topological vertex
Takasaki, Kanehisa
2016-01-01
The closed topological vertex is the simplest "off-strip" case of non-compact toric Calabi-Yau threefolds with acyclic web diagrams. By the diagrammatic method of topological vertex, open string amplitudes of topological string theory therein can be obtained by gluing a single topological vertex to an "on-strip" subdiagram of the tree-like web diagram. If non-trivial partitions are assigned to just two parallel external lines of the web diagram, the amplitudes can be calculated with the aid of techniques borrowed from the melting crystal models. These amplitudes are thereby expressed as matrix elements, modified by simple prefactors, of an operator product on the Fock space of 2D charged free fermions. This fermionic expression can be used to derive $q$-difference equations for generating functions of special subsets of the amplitudes. These $q$-difference equations may be interpreted as the defining equation of a quantum mirror curve.
Holomorphic Factorization of Superstring Scattering Amplitudes
Simon Davis
2011-01-01
The holomorphic factorization of the superstring partition function is verified at arbitrary genus.The evaluation of scattering amplitudes and the implications of genus-dependent estimates on the string coupling are given.
Lectures on Scattering Amplitudes in String Theory
Staessens, Wieland
2010-01-01
In these lecture notes, we take a closer look at the calculation of scattering amplitudes for the bosonic string. It is believed that string theories form the UV completions of (super)gravity theories. Support for this claim can be found in the (on-shell) scattering amplitudes of strings. On the other hand, studying these string scattering amplitudes opens a window on the UV behavior of the string theories themselves. In these short set of lectures, we discuss the two-dimensional Polyakov path integral for the string, and its gauge symmetries, the connection to Riemann surfaces and how to obtain some of the simplest string scattering amplitudes. We end with some comments on more advanced topics. For simplicity we limit ourselves to bosonic open string theory in 26 dimensions.
Open string amplitudes of closed topological vertex
The closed topological vertex is the simplest ‘off-strip’ case of non-compact toric Calabi–Yau threefolds with acyclic web diagrams. By the diagrammatic method of topological vertex, open string amplitudes of topological string theory therein can be obtained by gluing a single topological vertex to an ‘on-strip’ subdiagram of the tree-like web diagram. If non-trivial partitions are assigned to just two parallel external lines of the web diagram, the amplitudes can be calculated with the aid of techniques borrowed from the melting crystal models. These amplitudes are thereby expressed as matrix elements, modified by simple prefactors, of an operator product on the Fock space of 2D charged free fermions. This fermionic expression can be used to derive q-difference equations for generating functions of special subsets of the amplitudes. These q-difference equations may be interpreted as the defining equation of a quantum mirror curve. (paper)
Stora's fine notion of divergent amplitudes
Várilly, Joseph C
2016-01-01
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.
Numerical calculation of spin echo amplitude in pulsed NMR: effects of quadrupole interaction
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.)
Path integral evaluation of Dbrane amplitudes
Chaudhuri, Shyamoli
1999-01-01
We extend Polchinski's evaluation of the measure for the one-loop closed string path integral to open string tree amplitudes with boundaries and crosscaps embedded in Dbranes. We explain how the nonabelian limit of near-coincident Dbranes emerges in the path integral formalism. We give a careful path integral derivation of the cylinder amplitude including the modulus dependence of the volume of the conformal Killing group.
Employing Helicity Amplitudes for Resummation in SCET
Moult, Ian; Tackmann, Frank J; Waalewijn, Wouter J
2016-01-01
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.
Quartic amplitudes for Minkowski higher spin
Bengtsson, Anders K H
2016-01-01
The problem of finding general quartic interaction terms between fields of higher helicities on the light-front is discussed from the point of view of calculating the corresponding amplitudes directly from the cubic vertices using BCFW recursion. Amplitude based no-go results that has appeared in the literature are reviewed and discussed and it is pointed out how they may perhaps be circumvented.
Research on High Frequency Amplitude Attenuation of Electric Fast Transient Generator
Huafu Zhang
2013-01-01
Full Text Available In order to solve the amplitude attenuation of electric fast transient (EFT generator operating in high frequency, the charging and discharging process of energy storage capacitor in EFT generator are analyzed, the main circuit voltage variation mathematical model is established, the parameters of main loop circuit and the parameters of switch driving waveform which affect burst amplitude are discussed. Through the simulation, this paper puts forward effective methods to overcome burst amplitude attenuation in high frequency. The simulation results show that when the frequency is low, the duty ratio of drive signal have little effect on energy storage capacitor voltage amplitude attenuation. when the charging resistance is less than 500 Ω, the duty ratio of drive signal is less than 0.125, the repetition frequency of burst reaches 1.2 MHz, the amplitude attenuation of energy storage capacitor voltage is less than 9%, the amplitude of burst satisfies IEC61000-4-4 standards.
Mirror symmetry, toric branes and topological string amplitudes as polynomials
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
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.)
Relations between closed string amplitudes at higher-order tree level and open string amplitudes
KLT relations almost factorize closed string amplitudes on S2 by two open string tree amplitudes which correspond to the left- and the right-moving sectors. In this paper, we investigate string amplitudes on D2 and RP2. We find that KLT factorization relations do not hold in these two cases. The relations between closed and open string amplitudes have new forms. On D2 and RP2, the left- and the right-moving sectors are connected into a single sector. Then an amplitude with closed strings on D2 or RP2 can be given by one open string tree amplitude except for a phase factor. The relations depends on the topologies of the world-sheets. Under T-duality, the relations on D2 and RP2 give the amplitudes between closed strings scattering from D-brane and O-plane respectively by open string partial amplitudes. In the low energy limits of these two cases, the factorization relations for graviton amplitudes do not hold. The amplitudes for gravitons must be given by the new relations instead.
Relations between closed string amplitudes at higher-order tree level and open string amplitudes
Chen Yixin, E-mail: yxchen@zimp.zju.edu.c [Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027 (China); Du Yijian, E-mail: yjdu@zju.edu.c [Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027 (China); Ma Qian, E-mail: mathons@gmail.co [Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027 (China)
2010-01-01
KLT relations almost factorize closed string amplitudes on S{sub 2} by two open string tree amplitudes which correspond to the left- and the right-moving sectors. In this paper, we investigate string amplitudes on D{sub 2} and RP{sub 2}. We find that KLT factorization relations do not hold in these two cases. The relations between closed and open string amplitudes have new forms. On D{sub 2} and RP{sub 2}, the left- and the right-moving sectors are connected into a single sector. Then an amplitude with closed strings on D{sub 2} or RP{sub 2} can be given by one open string tree amplitude except for a phase factor. The relations depends on the topologies of the world-sheets. Under T-duality, the relations on D{sub 2} and RP{sub 2} give the amplitudes between closed strings scattering from D-brane and O-plane respectively by open string partial amplitudes. In the low energy limits of these two cases, the factorization relations for graviton amplitudes do not hold. The amplitudes for gravitons must be given by the new relations instead.
Relations between closed string amplitudes at higher-order tree level and open string amplitudes
Chen, Yi-Xin; Du, Yi-Jian; Ma, Qian
2010-01-01
KLT relations almost factorize closed string amplitudes on S by two open string tree amplitudes which correspond to the left- and the right-moving sectors. In this paper, we investigate string amplitudes on D and RP. We find that KLT factorization relations do not hold in these two cases. The relations between closed and open string amplitudes have new forms. On D and RP, the left- and the right-moving sectors are connected into a single sector. Then an amplitude with closed strings on D or RP can be given by one open string tree amplitude except for a phase factor. The relations depends on the topologies of the world-sheets. Under T-duality, the relations on D and RP give the amplitudes between closed strings scattering from D-brane and O-plane respectively by open string partial amplitudes. In the low energy limits of these two cases, the factorization relations for graviton amplitudes do not hold. The amplitudes for gravitons must be given by the new relations instead.
Multi-parton loop amplitudes and next-to-leading order jet cross-sections
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
Scattering amplitudes in open superstring theory
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
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
CARRIER-FREQUENCY HARMONIZATION STRUCTURE FOR ENHANCED AMPLITUDE MODULATION FUNCTION
B.V.Subba Rao
2013-06-01
Full Text Available Amplitude Modulation was the major method of influencing sound on a radio signal and is still extensively used in the present days. The characteristic amplitude modulation radio receivers’ automatic gain-control to circumvent bass distortion, generally reacts extreme moreover slowly to average out or overwhelm these intercarrier beat modulations as a result, these extremely aggravating modulation effects are mainly distributed on unbroken to the eavesdropper. A GPS-referenced frequency-synchronizer unit could be organized at transmitter sites capable of holding both current and big transmitters as a result basically eradicating carrier beat interference between co-channel amplitude modulation stations. The beat-related properties are a main aspect in the deprivation of dusk and night-time amplitude modulation fringe-area function excellence and the subsequent damage of hearers for effectively all stations. Commonly, an amplitude modulation radio listener for the duration of the sundown and nightfall hours and to a slighter amount in the first day break, obtains undesired sky wave indications from numerous distant locations as well as the desired local signal. The simple oscillator is naturally a predictable high-stability quartz-crystal kind, temperature compensated. To stand long-term drifts, advanced years effects, and loading-circuit variations, the simple oscillator is somewhat adjusted through electronic or mechanical resources to path a high-precision cause of standard frequency. The steady local reference frequency is then used as a timer for a typical numerically applied frequency synthesizer, which is planned to create the speciﬁc receiver carrier frequency expected.
Determination of Rebar Corrosion Rate Using Amplitude Attenuation Method
Kamaruddin Mohd Yusof
2009-09-01
Full Text Available This study is to determine whether the amplitude attenuation method can be used to measure the corrosionrate of rebars without having to hack the sructure nor it need not to be in saturated form. A pressure wave is generated by dropping a small steel ball onto the concrete surface. This wave will propagate through theconcrete and will be reflected by defects and the opposite surface of the concrete. The wave in the formof amplitude verses frequency is recorded. The frequency reflected by the rebar, fst, can be determinedbased on CP, the wave velocity in concrete, and the thickness of the concrete cover. Concrete prisms (300× 150 × 150 mm3 of Grade 15 and 20, embedded with 20 mm diameter of rebar were immersed in 120g/lNaCl concentration for 42 days (G15N and G20N. Other samples were left immersed for 20 days and thecorrosion process is accelerated by connecting the rebars to a direct current supply (G15E and G20E.Results show that the amplitud at fst for G15N reduces 21% from the 20th day of immersion to the 42ndday and 24% for G20N. For the samples that had undergone accelerated corrosion process (G15E, the fstamplitude reduction from day 14th of immersion to day 20th is 15% and 18% for G20E. The percentagereductions of electrical potential in the half-cell test are 52%, 50%, 28% and 16% during the same timeduration. It can be seen that the amplitude attenuation measurement can determine the corrosion activityof the steel rebars. The overall reductions of amplitude are 46% (G15N, 43% (G20N, 54% (G15E and 52%(G20E respectively.
The Correlation between Electroencephalography Amplitude and Interictal Abnormalities: Audit study
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.
Amplitude scaling of asymmetry-induced transport
Our initial experiments on asymmetry-induced transport in non-neutral plasmas found the radial particle flux at small radii to be proportional to φa2, where φa is the applied asymmetry amplitude. Other researchers, however, using the global expansion rate as a measure of the transport, have observed a φa1 scaling when the rigidity (the ratio of the axial bounce frequency to the azimuthal rotation frequency) is in the range one to ten. In an effort to resolve this discrepancy, we have extended our measurements to different radii and asymmetry frequencies. Although the results to date are generally in agreement with those previously reported (φa2 scaling at low asymmetry amplitudes falling off to a weaker scaling at higher amplitudes), we have observed some cases where the low amplitude scaling is closer to φa1. Both the φa2 and φa1 cases, however, have rigidities less than ten. Instead, we find that the φa1 cases are characterized by an induced flux that is comparable in magnitude but opposite in sign to the background flux. This suggests that the mixing of applied and background asymmetries plays an important role in determining the amplitude scaling of this transport
Single-energy amplitudes for pion photoproduction in the first resonance region
Workman, R. L.
2010-01-01
We consider multipole amplitudes for low-energy pion photoproduction, constructed with minimal model dependence, at single energies. Comparisons with fits to the full resonance region are made. Explanations are suggested for the discrepancies and further experiments are motivated.