Search results for "Fourier serie"
showing 10 items of 38 documents
Tracing the origin of azimuthal gluon correlations in the color glass condensate
2016
We examine the origins of azimuthal correlations observed in high energy proton-nucleus collisions by considering the simple example of the scattering of uncorrelated partons off color fields in a large nucleus. We demonstrate how the physics of fluctuating color fields in the color glass condensate (CGC) effective theory generates these azimuthal multiparticle correlations and compute the corresponding Fourier coefficients v_n within different CGC approximation schemes. We discuss in detail the qualitative and quantitative differences between the different schemes. We will show how a recently introduced color field domain model that captures key features of the observed azimuthal correlati…
Geometric Measurement Analysis Versus Fourier Series Analysis for Shape Characterization Using the Gastropod Shell (Trivia) as an Example
2003
Varied and efficient methods have been developed to describe and quantify natural objects. The most common ones use superimposition techniques (e.g. Procrustes methods; Bookstein, 1991), decomposition into harmonics (Fourier series and functions, wavelets; Anstey and Delmet, 1973; Christopher and Waters, 1974; Gevirtz, 1976; Lestrel, 1997; Toubin and others, 1999; Verrecchia, Van Grootel, and Guillemet, 1996; Younger and Ehrlich, 1977), analysis of spiral functions (e.g. Raup parameters; Raup, 1961, 1966; Tursch, 1998), and combinations of parameters from elementary geometry (e.g. circularity index, lengthening; Coster and Chermant, 1989; Schmidt-Kittler, 1986; Viriot, Chaline, and Schaaf, …
Mixed Circular Convolutions and Zak Transforms
2014
In this chapter the notion of mixed circular convolution is introduced. The polynomial and discrete periodic splines defined on uniform grids are special cases of such convolutions. The so-called Zak transforms provide tools to handle mixed circular convolutions
Harmonic solution of semiconductor transport equations for microwave and millimetre-wave device modelling
2004
The transport equations for charges in a semiconductor have been solved for a periodic voltage excitation by means of a harmonic approach, for modelling of microwave and millimetre-wave active devices. The solution is based on the expansion of the unknown physical quantities in Fourier series in the time domain, and on the discretisation in the space domain. A Waveform-Balance technique in the time domain is used to solve the resulting non-linear equations system. In this way the time step is determined only by Nyquist's sampling requirements at the operating frequency, irrespective of the relaxation times of the semiconductor. This approach allows for a longer time step, and therefore a sh…
Absolute parameters for binary systems
1997
New high-quality light curves of the late-type binary system BH Vir have been obtained during a 6 year photometric uvby and monitoring program of low mass eclipsing binaries (Clement et al. 1997), hereafter Papers I and II. This paper presents detailed analysis of this binary based on the four light curves obtained within our program. The activity wave superimposed on the eclipse-modulated light curves has been adjusted and removed by using a new iterative application of the standard EBOP code together with truncated Fourier Series fittings. Combining the recent radial velocity curves (Popper 1995) with the geometrical elements deduced from the "clean" photometric light curves, the absolute…
General relativistic neutrino transport using spectral methods
2014
We present a new code, Lorene's Ghost (for Lorene's gravitational handling of spectral transport) developed to treat the problem of neutrino transport in supernovae with the use of spectral methods. First, we derive the expression for the nonrelativistic Liouville operator in doubly spherical coordinates (r, theta, phi, epsilon, Theta, Phi)$, and further its general relativistic counterpart. We use the 3 + 1 formalism with the conformally flat approximation for the spatial metric, to express the Liouville operator in the Eulerian frame. Our formulation does not use any approximations when dealing with the angular arguments (theta, phi, Theta, Phi), and is fully energy-dependent. This approa…
Higher Harmonic Anisotropic Flow Measurements of Charged Particles in Pb-Pb Collisions atsNN=2.76 TeV
2011
We report on the first measurement of the triangular nu(3), quadrangular nu(4), and pentagonal nu(5) charged particle flow in Pb-Pb collisions at root s(NN) = 2.76 TeV measured with the ALICE detector at the CERN Large Hadron Collider. We show that the triangular flow can be described in terms of the initial spatial anisotropy and its fluctuations, which provides strong constraints on its origin. In the most central events, where the elliptic flow nu(2) and nu(3) have similar magnitude, a double peaked structure in the two-particle azimuthal correlations is observed, which is often interpreted as a Mach cone response to fast partons. We show that this structure can be naturally explained fr…
Wavelet-like orthonormal bases for the lowest Landau level
1994
As a first step in the description of a two-dimensional electron gas in a magnetic field, such as encountered in the fractional quantum Hall effect, we discuss a general procedure for constructing an orthonormal basis for the lowest Landau level, starting from an arbitrary orthonormal basis in L2(R). We discuss in detail two relevant examples coming from wavelet analysis, the Haar and the Littlewood-Paley bases.
Two-dimensional quantum scattering by non-isotropic interactions localized on a circle, applications to open billiards
2018
Two-dimensional quantum scattering by isotropic and non-isotropic interactions localized on a circle is considered. The expansion of the interaction on the circle in a Fourier series allows us to express basic objects of scattering theory (resolvent, T operator, differential cross length, cross length, and cross length averaged over all orientations of the incident particle), in terms of operations on matrices. For numerical applications, these matrices are truncated to a given order. If the interaction is isotropic, this general formulation reduces to the usual one, and the resonances in the isotropic cases are studied because they allow us to interpret resonances in some non-isotropic cas…
Introduction: Signals and Transforms
2015
In this chapter we outline some well known facts about periodic signals and transforms, which are needed throughout the book. For details we refer to the classical textbook Oppenheim and Schafer [2].