Search results for "methods"
showing 10 items of 4526 documents
PNO-CI and CEPA studies of electron correlation effects
1974
Ab initio calculations of the potential curves of low laying electronic states of OH are performed on the basis of a variational configuration interaction wavefunction (PNO-CI) and the coupled electron pair approximation (CEPA). The latter approach yields a ground state potential curve which deviates from the RKR curve by less than 200 cm−1 in the region from 0.7 to 1.6 A. Calculated ground state constants are as follows (experimental values in parentheses): r e = 0.972 (0.971) A, B e = 18.85 (18.87) cm−1, α e = 0.727 (0.714) cm−1, ω e = 3742 (3739) cm−1, ω e χ e = 85.3 (86.4) cm−1, μ0 = 1.686 (1.66) D, D e = 4.35 (4.63) eV,IP = 12.78 (13.36?) eV, El.Aff. = 1.51 (1.83) eV, v 00(2Π↔2Σ+) = 32…
Linear Methods in Nilpotent Groups
1982
The subject of this chapter is commutator calculation. It will be recalled that the commutator [x, y] of two elements x, y of a group is defined by the relation $$ [x,y] = {{x}^{{ - 1}}}{{y}^{{ - 1}}}xy. $$ . We then have $$ [xy,z] = {{[x,z]}^{y}}[y,z],\quad [x,yz] = [x,z]{{[x,y]}^{z}}. $$ . These relations are rather similar to the conditions for bilinearity of forms, and there are a number of ways of formalizing this similarity. Once this is done, commutator calculations can be done by linear methods. Several examples of theorems proved by this method will be given in this chapter.
An inquiry-based approach to Maxwell distribution: a case study with engineering students
2013
The concept of distribution is a fundamental component of statistical thinking. This paper describes a teaching approach for it that uses a specific activity related to the field of statistical mechanics. The concept of the velocity distribution of a particle system is dealt with using an inquiry-based approach involving an experimental examination of Maxwell’s distribution. Some outcomes of a teaching experiment held at the Faculty of Engineering of the University of Palermo, Italy are described.
Coherence loss in phase-referenced VLBI observations
2010
Context. Phase-referencing is a standard calibration technique in radio interferometry, particularly suited for the detection of weak sources close to the sensitivity limits of the interferometers. However, effects from a changing atmosphere and inaccuracies in the correlator model may affect the phase-referenced images, and lead to wrong estimates of source flux densities and positions. A systematic observational study of signal decoherence in phase-referencing and its effects in the image plane has not been performed yet. Aims. We systematically studied how the signal coherence in Very-Long-Baseline-Interferometry (VLBI) observations is affected by a phase-reference calibration at differe…
A New Look at Spitzer Primary Transit Observations of the Exoplanet HD 189733b
2014
Blind source separation techniques are used to reanalyse two exoplanetary transit lightcurves of the exoplanet HD189733b recorded with the IR camera IRAC on board the Spitzer Space Telescope at 3.6$\mu$m during the "cold" era. These observations, together with observations at other IR wavelengths, are crucial to characterise the atmosphere of the planet HD189733b. Previous analyses of the same datasets reported discrepant results, hence the necessity of the reanalyses. The method we used here is based on the Independent Component Analysis (ICA) statistical technique, which ensures a high degree of objectivity. The use of ICA to detrend single photometric observations in a self-consistent wa…
Permanent electric dipoles andΛ-doubling constants in the lowestΠ1states of RbCs
2005
The article presents first experimental data on the Stark induced $e\text{\ensuremath{-}}f$ mixing in the $(4)\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}$ state of the $^{85}\mathrm{Rb}^{133}\mathrm{Cs}$ molecule, as well as the ab initio calculations of permanent electric dipole moments $(d)$ in the $(1,2,3,4)\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}$ states and $q$ factors in the $(2,4)\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}$ states. The appearance of the ``forbidden'' lines in the laser-induced $(4)\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}\ensuremath{\rightarrow}X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}^{+}$ fluorescence spectrum in the presence of an elect…
Ordered helium trapping and bonding in compressed arsenolite: Synthesis ofAs4O6·2He
2016
Compression of arsenolite has been studied from a joint experimental and theoretical point of view. Experiments on this molecular solid at high pressures with different pressure-transmitting media have been interpreted thanks to state-of-the-art ab initio calculations. Our results confirm arsenolite as one of the most compressible minerals and provide evidence for ordered helium trapping above 3 GPa between adamantane-type $\mathrm{A}{\mathrm{s}}_{4}{\mathrm{O}}_{6}$ cages. Our calculations indicate that, at relatively small pressures, helium establishes rather localized structural bonds with arsenic forming a compound with stoichiometry $\mathrm{A}{\mathrm{s}}_{4}{\mathrm{O}}_{6}\ifmmode\c…
Revised values for the nuclear quadrupole moments ofS33andS35
2014
High-level quantum-chemical calculations are reported for the sulfur electric-field gradients of the CS and SiS molecules. Highly accurate values are obtained in these calculations by using coupled-cluster methods for the treatment of electron correlation together with large atomic-orbital basis sets and by taking into account relativistic effects. The computational results for the sulfur electric-field gradient are used to determine revised values for the $^{33}\mathrm{S}$ and $^{35}\mathrm{S}$ quadrupole moments, thereby taking advantage of available accurate values for the sulfur quadrupole couplings of CS and SiS from the analysis of rotational spectra. The derived values of $\ensuremat…
On the estimation and detection of the Rees Sciama effect
2017
Maps of the Rees–Sciama (RS) effect are simulated using the parallel N-body code, hydra, and a run-time ray-tracing procedure. A method designed for the analysis of small, square cosmic microwave background (CMB) maps is applied to our RS maps. Each of these techniques has been tested and successfully applied in previous papers. Within a range of angular scales, our estimate of the RS angular power spectrum due to variations in the peculiar gravitational potential on scales smaller than 42/h megaparsecs is shown to be robust. An exhaustive study of the redshifts and spatial scales relevant for the production of RS anisotropy is developed for the first time. Results from this study demonstra…
On the Measurements of Numerical Viscosity and Resistivity in Eulerian MHD Codes
2016
We propose a simple ansatz for estimating the value of the numerical resistivity and the numerical viscosity of any Eulerian MHD code. We test this ansatz with the help of simulations of the propagation of (magneto)sonic waves, Alfven waves, and the tearing mode instability using the MHD code Aenus. By comparing the simu- lation results with analytical solutions of the resistive-viscous MHD equations and an empirical ansatz for the growth rate of tearing modes we measure the numerical viscosity and resistivity of Aenus. The comparison shows that the fast-magnetosonic speed and wavelength are the characteristic velocity and length, respectively, of the aforementioned (relatively simple) syst…