Search results for "Linear Algebra"
showing 10 items of 552 documents
Incoherent frequency-to-time mapping: application to incoherent pulse shaping
2007
After temporal amplitude modulation of a spectrally incoherent optical source the averaged intensity profile at the so-called temporal far-zone regime coalesces with a magnified replica of the spectral density function of the source. This has provided the basis for the generalization of the frequency-to-time mapping technique in the partially coherent case. Based on this fact, temporal intensity waveform generation is demonstrated by spectral filtering the incoherent source before the temporal modulation stage. We refer to this technique as full incoherent pulse shaping. Although only the average intensity of the output signal is properly shaped, intensity fluctuations between the different…
Reduction to finite dimensions of continuous systems having only a few amplified modes
2008
In the approach of Guckenheimer and Knobloch the amplitudes of trajectories on the unstable manifold 0 are the pivotal quantities. This places a certain restriction on the applicability of this approach, as only neighbourhoods of 0 of the unstable manifold of 0 are accessible, which have a one-to-one projection into their tangent at 0, the linear space spanned by the amplified modes. This restriction may be lifted, using the arc lengths of trajectories instead.
Classical form factor for nlm→n′l′m transitions in the hydrogen atom
2000
Abstract The form factor for nlm → n ′ l ′ m transitions in the hydrogen atom is deduced on the basis of kinematics of the classical mechanics. The consistency of this approach is verified by derivation of the known result for the transition probability averaged over m . The classical transition probability as a function of the final state energy and angular momentum is investigated comprehensively in the case of l = m =0.
On the importance of background subtraction in the analysis of coronal loops observed with TRACE
2010
In the framework of TRACE coronal observations, we compare the analysis and diagnostics of a loop after subtracting the background with two different and independent methods. The dataset includes sequences of images in the 171 A, 195 A filter bands of TRACE. One background subtraction method consists in taking as background values those obtained from interpolation between concentric strips around the analyzed loop. The other method is a pixel-to-pixel subtraction of the final image when the loop had completely faded out, already used by Reale & Ciaravella 2006. We compare the emission distributions along the loop obtained with the two methods and find that they are considerably differen…
Baryon Properties with Three-Quark Forces
1987
The Constituent Quark Model (CQM) is very useful for the description of many baryon properties, leading to a fair agreement with the experimental data, especially in the case of the baryon spectrum 1) and of the electromagnetic processes involving baryons2,3). The model is based on a non relativistic QCD-inspired dynamics, which includes a confinement potential and a spin-dependent short-range part, the so called hyperfine interaction4,1). The confinement potential contains as its major part a harmonic oscillator (h.o.) interaction, which has however a too degenerate spectrum with respect to the experimental one and leads to an unreasonable damping of the form factors even at moderate momen…
Next-to-leading order Balitsky-Kovchegov equation beyond large Nc
2020
We calculate finite-Nc corrections to the next-to-leading order (NLO) Balitsky-Kovchegov (BK) equation. We find analytical expressions for the necessary correlators of six Wilson lines in terms of the two-point function using the Gaussian approximation. In a suitable basis, the problem reduces from the diagonalization of a six-by-six matrix to the diagonalization of a three-by-three matrix, which can easily be done analytically. We study numerically the effects of these finite-Nc corrections on the NLO BK equation. In general, we find that the finite-Nc corrections are smaller than the expected 1/Nc2∼10%. The corrections may be large for individual correlators, but have less of an influence…
Spherical symmetric parabolic dust collapse: ${\cal C}^{1}$ matching metric with zero intrinsic energy
2016
The collapse of marginally bound, inhomogeneous, pressureless (dust) matter, in spherical symmetry, is considered. The starting point is not, in this case, the integration of the Einstein equations from some suitable initial conditions. Instead, starting from the corresponding general exact solution of these equations, depending on two arbitrary functions of the radial coordinate, the fulfillment of the Lichnerowicz matching conditions of the interior collapsing metric and the exterior Schwarzschild one is tentatively assumed (the continuity of the metric and its first derivatives on the time-like hypersurface describing the evolution of the spherical 2-surface boundary of the collapsing cl…
Convergence of Nuclear Magnetic Shieldings in the Kohn-Sham Limit for Several Small Molecules.
2015
Convergence patterns and limiting values of isotropic nuclear magnetic shieldings were studied for several small molecules (N2, CO, CO2, NH3, CH4, C2H2, C2H4, C2H6, and C6H6) in the Kohn-Sham limit. Individual results of calculations using dedicated families of Jensen's basis sets (pcS-n and pcJ-n) were fitted toward the complete basis set limit (CBS) using a simple two-parameter formula. Several density functionals were used; calculated vibrational corrections (ZPV) applied; and, for comparison purposes, similar calculations performed using RHF, MP2, SOPPA, SOPPA(CCSD), and CCSD(T) methods and additionally, the aug-cc-pVTZ-J basis set. Finally, the CBS estimated results were critically com…
Parallel Calculation of CCSD and CCSD(T) Analytic First and Second Derivatives.
2007
In this paper we present a parallel adaptation of a highly efficient coupled-cluster algorithm for calculating coupled-cluster singles and doubles (CCSD) and coupled-cluster singles and doubles augmented by a perturbative treatment of triple excitations (CCSD(T)) energies, gradients, and, for the first time, analytic second derivatives. A minimal-effort strategy is outlined that leads to an amplitude-replicated, communication-minimized implementation by parallelizing the time-determining steps for CCSD and CCSD(T). The resulting algorithm is aimed at affordable cluster architectures consisting of compute nodes with sufficient memory and local disk space and that are connected by standard co…
Models of Metal Clusters and Quantum Dots
2007
The electronic structure of simple metal clusters and quantum dots is studied on the basis of the density functional theory and simple models. It is demonstrated that single-particle models explain well the gross features of deformation and magnetism in small clusters, nuclei and quantum dots and that the local density approximation can give valuable information of the internal structure of the manybody state.