Search results for "Functions"
showing 10 items of 1066 documents
Beta decay studies with total absorption spectroscopy and the Lucrecia spectrometer at ISOLDE
2017
26 pags., 21 figs., tab. -- Open Access funded by Creative Commons Atribution Licence 3.0
nPDF constraints from the large hadron electron collider
2016
An updated analysis regarding the expected nuclear PDF constraints from the future Large Hadron Electron Collider (LHeC) experiment is presented. The new study is based on a more flexible small-$x$ parametrization which provides less biased uncertainty estimates in the region where there are currently no data constraints. The effect of the LHeC is quantified by directly including a sample of pseudodata according to the expected precision of this planned experiment. As a result, a significant reduction of the small-$x$ uncertainties in sea quarks and gluons is observed.
Method specific Cholesky decomposition : Coulomb and exchange energies
2008
We present a novel approach to the calculation of the Coulomb and exchange contributions to the total electronic energy in self consistent field and density functional theory. The numerical procedure is based on the Cholesky decomposition and involves decomposition of specific Hadamard product matrices that enter the energy expression. In this way, we determine an auxiliary basis and obtain a dramatic reduction in size as compared to the resolution of identity (RI) method. Although the auxiliary basis is determined from the energy expression, we have complete control of the errors in the gradient or Fock matrix. Another important advantage of this method specific Cholesky decomposition is t…
Extracting the impact parameter dependence of the nPDFs from the EKS98 and EPS09 global fits
2013
As all the globally fitted nuclear PDFs (nPDFs) have been so far impact parameter independent, it has not been possible to calculate the hard process cross sections in different centrality classes consistently with the global analyses. In \cite{Helenius:2012wd} we have offered a solution to this problem by determining two spatially dependent nPDF sets, \texttt{EPS09s} and \texttt{EKS98s}, using the $A$-systematics of the earlier global fits EPS09 and EKS98 and an assumption that the spatial dependence can be written as a power series of the nuclear thickness function. For a data comparison, we have calculated the nuclear modification factor of inclusive neutral pion production in d+Au colli…
Ultrarelativistic (Cauchy) spectral problem in the infinite well
2016
We analyze spectral properties of the ultrarelativistic (Cauchy) operator $|\Delta |^{1/2}$, provided its action is constrained exclusively to the interior of the interval $[-1,1] \subset R$. To this end both analytic and numerical methods are employed. New high-accuracy spectral data are obtained. A direct analytic proof is given that trigonometric functions $\cos(n\pi x/2)$ and $\sin(n\pi x)$, for integer $n$ are {\it not} the eigenfunctions of $|\Delta |_D^{1/2}$, $D=(-1,1)$. This clearly demonstrates that the traditional Fourier multiplier representation of $|\Delta |^{1/2}$ becomes defective, while passing from $R$ to a bounded spatial domain $D\subset R$.
Double parton correlations in constituent quark models
2013
Double parton correlations, having effects on the double parton scattering processes occurring in high-energy hadron-hadron collisions, for example at the LHC, are studied in the valence quark region by means of constituent quark models. In this framework, two particle correlations are present without any additional prescription, at variance with what happens, for example, in independent particle models, such as the MIT bag model in its simplest version. From the present analysis, conclusions similar to the ones obtained recently in a modified version of the bag model can be drawn: correlations in the longitudinal momenta of the active quarks are found to be sizable, while those in transver…
Effective bias and potentials in steady-state quantum transport: A NEGF reverse-engineering study
2016
Using non-equilibrium Green’s functions combined with many-body perturbation theory, we have calculated steady-state densities and currents through short interacting chains subject to a finite electric bias. By using a steady-state reverse-engineering procedure, the effective potential and bias which reproduce such densities and currents in a non-interacting system have been determined. The role of the effective bias is characterised with the aid of the so-called exchange-correlation bias, recently introduced in a steady-state density-functionaltheory formulation for partitioned systems. We find that the effective bias (or, equivalently, the exchange-correlation bias) depends strongly on th…
Scaling laws in the distribution of galaxies
2004
Research done during the previous century established our Standard Cosmological Model. There are many details still to be filled in, but few would seriously doubt the basic premise. Past surveys have revealed that the large-scale distribution of galaxies in the Universe is far from random: it is highly structured over a vast range of scales. To describe cosmic structures, we need to build mathematically quantifiable descriptions of structure. Identifying where scaling laws apply and the nature of those scaling laws is an important part of understanding which physical mechanisms have been responsible for the organization of clusters, superclusters of galaxies and the voids between them. Find…
Geometric efficiency for a parallel-surface source and detector system with at least one axisymmetric surface
2007
Abstract An exact and numerically friendly method is given to calculate the geometric efficiency G of a planar radiation source and cosine detector system. Either the source or the detector, but not necessarily both, must have axial symmetry. For two non-coaxial disks the results are in exact agreement with a recent generalization of Ruby's formula for G. Detailed formulas and sample numerical results are given for a disk combined with rectangles and triangles. A disk and a general polygon can be solved by dividing the polygon into triangles. The method can also be applied to electrical inductance calculations and a solution recently given for the inductance of circular and elliptic loops c…
Impact of a temporal sinusoidal phase modulation on the optical spectrum
2018
International audience; We discuss the effects of imparting a temporal sinusoidal phase modulation to a continuous wave on the frequency spectrum. While a practical analytical solution to this problem already exists, we present here a physical interpretation based on interference processes. This simple model will help the students better understand the origin of the oscillatory structure that can be observed in the resulting spectrum and that is characteristic of Bessel functions of the first kind. We illustrate our approach with an example from the field of optics.