Search results for "Symmetry group"
showing 10 items of 41 documents
Structure of Kac-Moody groups
2008
For a phys ic i s t , a Kac-Moody algebra is the current algebra of a quantum f i e l d theory model in I + I space-time dimensions with an in terna l symmetry group G [ I ] . A More p rec ise ly , l e t ~ be the Lie algebra of G . The Kac-Moody algebra g is a one-dimensional central extension of the loop algebra Map(S I , g ) . I f f l ' f2 C Map(S I ,~ ) , then the commutator is defined point -wise,
The integral‐direct coupled cluster singles and doubles model
1996
An efficient and highly vectorized implementation of the coupled cluster singles and doubles (CCSD) model using a direct atomic integral technique is presented. The minimal number of n6processes has been implemented for the most time consuming terms and point group symmetry is used to further reduce operation counts and memory requirements. The significantly increased application range of the CCSD method is illustrated with sample calculations on several systems with more than 500 basis functions. Furthermore, we present the basic trends of an open ended algorithm and discuss the use of integral prescreening. © 1996 American Institute of Physics.
Symmetry and Stability of the Rutile-Based TiO2 Nanowires: Models and Comparative LCAO-Plane Wave DFT Calculations
2012
The rod symmetry groups for monoperiodic (1D) nanostructures have been applied for construction of models for bulk-like titania nanowires (NWs) cut from a rutile-based 3D crystal along the direction of a chosen crystallographic symmetry axis (in this study we consider only Ti atom-centered axes). The most stable [001]-oriented TiO2 NWs with rhombic cross sections are found to display the energetically preferable {110} facets only, while the nanowires with quasi-square sections across the [110] axis are formed by the alternating {110} and {001} facets. For simulations on rutile-based nanowires possessing four different diameters for each NW type, we have performed comparative large-scale ab …
Ab initiosimulations on rutile-based titania nanowires
2012
The rod symmetry groups for monoperiodic (1D) nanostructures have been applied for construction of models for bulk-like TiO2 nanowires (NWs) cut from a rutile-based 3D crystal along the chosen [001] and [110] directions of crystallographic axes. In this study, we have considered nanowires described by both the Ti-atom centered rotation axes as well as the hollow site centered axes passing through the interstitial positions between the Ti and O atoms closest to the axes. The most stable [001]-oriented TiO2 NWs with rhombic cross sections are found to display the energetically preferable {110} facets only while the nanowires with quasi-square sections across the [110] axis are formed by the a…
Stability of Borane−Adduct Complexes: A G-2 Molecular Orbital Study
1997
Complexation energies of H3BXHn and [H3BXHn-1]- complexes (X = N, O, F, P, S, and Cl) (n = 3, 2, 1) have been computed at the G-2 level of theory. The formation of H3BXH3 (X = N, P) is found to be more favored than the formations of H3BXH2 (X = O, S) and H3BXH (X = F, Cl). The qualitative features of the molecular orbital interaction (the correlation diagrams) of H3BNH3 (C3v symmetry group), H3BOH2 (Cs symmetry group), and H3BFH (Cs symmetry group) complexes are presented. These diagrams show that the σ character of the B−X bond decreases and the π character increases when the electronegativity of X increases and indicate that the B−X bond cannot be treated only in terms of the simplest mod…
Differential Regularization of a Non-relativistic Anyon Model
1994
Differential regularization is applied to a field theory of a non-relativistic charged boson field $\phi$ with $\lambda (\phi {}^{*} \phi)^2$ self-interaction and coupling to a statistics-changing $U(1)$ Chern-Simons gauge field. Renormalized configuration-space amplitudes for all diagrams contributing to the $\phi {}^{*} \phi {}^{*} \phi \phi$ 4-point function, which is the only primitively divergent Green's function, are obtained up to 3-loop order. The renormalization group equations are explicitly checked, and the scheme dependence of the $\beta$-function is investigated. If the renormalization scheme is fixed to agree with a previous 1-loop calculation, the 2- and 3-loop contributions …
Mirror quintics, discrete symmetries and Shioda maps
2008
In a recent paper, Doran, Greene and Judes considered one parameter families of quintic threefolds with finite symmetry groups. A surprising result was that each of these six families has the same Picard Fuchs equation associated to the holomorphic 3-form. In this paper we give an easy argument, involving the family of Mirror Quintics, which implies this result. Using a construction due to Shioda, we also relate certain quotients of these one parameter families to the family of Mirror Quintics. Our constructions generalize to degree n Calabi Yau varieties in (n-1)-dimensional projective space.
Textile and tile pattern design automatic cataloguing using detection of the plane symmetry group
2004
We present an integrated management system of pattern design for the textile and tile industries providing automatic cataloguing capabilities based on the application of the scientific theory of symmetry groups. To do this, a process of analysis is performed which starts from an initial image of the decorative element, which in turn is subjected to a number of segmentation and labelling operators that allow to detect the objects present in the image. These objects are vectorized, compared, and their isometries obtained; subsequently they are grouped and the isometries of the groups of objects detected. Finally, a composition analysis is carried out that, on the basis of the repetitions and …
Photoionization of adsorbates on sites with non-axial local symmetry. An example of the symmetry group
1996
We present an analysis of the influence of the local adsorption site symmetry on the angular distribution of photoelectrons ejected from adsorbed atoms or molecules. This analysis applies to photoelectron spectra obtained with photons of any energy in the VUV (photoelectron spectroscopy) or x-ray (XPS) regions, provided that the associated wave of the electron `sees' the neighbouring surface atoms. The adsorbate - substrate system is modelled by a cluster of symmetry group consisting of an adsorbate and several atoms of the substrate. The analysis applies also to clean surfaces of symmetry and to molecules of the symmetry group fixed in space. This local symmetry analysis is an alternative …
Titchener's T in context 2 - Symmetric patterns of two Ts.
2019
Abstract Patterns of two Ts, materializing different symmetry groups, were used to explore conditions that would lead to a modulation of the typically observed overestimation of the length of a T's undivided line relative to its divided line. Observers either had to compare the lengths of the lines of one or the other of the Ts in a pattern, or noncorresponding lines between the two Ts. For both tasks alike, the T-illusion was found to be markedly greater with twofold mirror-symmetric 2-T patterns than it usually is with individual Ts. A control experiment suggested that the effect was probably due to the collinearity of the two Ts' undivided lines in these patterns rather than the addition…