Search results for " symmetry"
showing 10 items of 701 documents
The S-kernel: A measure of symmetry of objects
2007
In this paper we introduce a new symmetry feature named ''symmetry kernel'' (SK) to support a measure of symmetry. Given any symmetry transform S, SK of a pattern P is the maximal included symmetric sub-set of P for all directions and shifts. We provide a first algorithm to exhibit this kernel where the centre of symmetry is assumed to be the centre of mass. Then we prove that, in any direction, the optimal axis corresponds to the maximal correlation of a pattern with its symmetric version. That leads to a second algorithm. The associated symmetry measure is a modified difference between the respective surfaces of a pattern and its kernel. A series of experiments supports the actual algorit…
Visual Discrimination of the 17 Plane Symmetry Groups
2011
Within most of the 17 plane symmetry groups, individual symmetry operations act in multiple, nonequivalent ways. This, and the fact that many groups can be realized on the basis of different unit cells and generating regions, poses difficulties for visual discrimination and identification. Because of inherent confounds, only few of the groups can be studied by traditional experimental methodology. The use of an oddity paradigm and specific tiling patterns that camouflage groups in complex textures are recommended as partial remedy to this impasse. In order to prepare readers for an appreciation of the aforementioned issues and to provide a rationale for their investigation, the reporting of…
Passive time-multiplexing super-resolved technique for axially moving targets
2013
In this paper we present a super-resolving approach for detecting an axially moving target that is based upon a time-multiplexing concept and that overcomes the diffraction limit set by the optics of an imaging camera by a priori knowledge of the high-resolution background in front of which the target is moving. As the movement trajectory is axial, the approach can be applied to targets that are approaching or moving away from the camera. By recording a set of low-resolution images at different target axial positions, the super-resolving algorithm weights each image by demultiplexing them using the high-resolution background image and provides a super-resolved image of the target. Theoretic…
Study of Tetragonal Phase in 0.4Na1/2Bi1/2TiO3-(0.6-x)SrTiO3-xPbTiO3Solid Solutions by Second-Harmonic Generation
2015
Description of the local symmetry of relaxor ferroelectrics, especially in connection with nature of polar nanoregions, is one of the key questions in research of relaxor ferroelectrics. Unlike such well-known relaxor ferroelectrics as PbMg1/3Nb2/3O3 and (Pb,La)(Zr0.65Ti0.35)O3, ternary solid solutions 0.4Na1/2Bi1/2TiO3-(0.6-x)SrTiO3-xPbTiO3 show clear coexistence of phases of tetragonal and cubic symmetry, which is established by x-ray diffractometry. Since the second-harmonic generation spectroscopy is a sensitive tool in determination of deviation from symmetry, containing a centre of inversion, it is used as an additional method in characterization of structure in 0.4Na1/2Bi1/2TiO3-(0.6…
Electronic properties of graphene: A learning path for undergraduate students
2016
The purpose of this work is to present a learning path aimed at deepening student understanding of the fundamental concepts underlying the electronic properties of new materials, graphene in particular. To achieve this task, we propose a five-week long workshop where students may be introduced to fundamental concepts of advanced physics, rarely used in learning paths, such as the symmetry properties of the crystal lattice, the group theory , the features of the free electron wave functions and energy levels, the relativistic Dirac equation. Particular emphasis is given to the manner of introducing these concepts, since an essential knowledge of solid state physics, quantum physics and relat…
The su(2|1) Model of Electroweak Interactions and Its Connection to NC Geometry
2002
I review the su(2|1) model of electroweak interactions which is essentially based on the super Lie algebra su(2|1), thus incorporating both usual gauge fields and Higgs fields in one generalized Yang-Mills field. Special emphasis is put on the natural appearance of spontaneous symmetry breaking and other appealing features of the model like generation mixing. Also the connection of the model to noncommutative geometry is briefly discussed.
Copper-, cobalt-, and manganese-containing 17-tungsto-2-germanates.
2009
The sandwich-type tungstogermanates [Cu(3)(H(2)O)(B-beta-GeW(9)O(33)(OH))(B-beta-GeW(8)O(30)(OH))](12-) (1), [Co(H(2)O)(2){Co(3)(B-beta-GeW(9)O(33)(OH))(B-beta-GeW(8)O(30)(OH))}(2)](22-) (2), and [Mn(H(2)O)(2){Mn(3)(H(2)O)(B-beta-GeW(9)O(33)(OH))(B-beta-GeW(8)O(30)(OH))}(2)](22-) (3) were synthesized and characterized by single-crystal X-ray diffraction, elemental analysis, thermogravimetric analysis, and infrared spectroscopy. Polyanion 1 is composed of two nonequivalent Keggin units, (B-beta-GeW(8)O(31)) and (B-beta-GeW(9)O(34)), linked to each other via three copper(II) ions in such a way that there is a plane of symmetry passing through both Ge atoms and the unique Cu atom, resulting in…
S-4 as a natural flavor symmetry for lepton mixing
2008
Group theoretical arguments seem to indicate the discrete symmetry S4 as the minimal flavour symmetry compatible with tribimaximal neutrino mixing. We prove in a model independent way that indeed S4 can realize exact tribimaximal mixing through different symmetry breaking patterns. We present two models in which lepton tribimaximal mixing is realized in different ways and for each one we discuss the superpotential that leads to the correct breaking of the flavor symmetry.
Key Role of the Cation in the Crystallization of Chiral Tris(Anilato)Metalate Magnetic Anions
2015
A complete study of the role played by the usually considered “innocent” cation in the synthesis of chiral tris(anilato)metalate magnetic complexes is presented. This study is based on the rational synthesis of the family of compounds formulated as A3[MIII(C6O4X2)3] with A+ = [PPh3Et]+, [PPh3Pr]+, [PBu4]+, [NHep4]+, and [PPh4]+; MIII = CrIII, FeIII, and GaIII; and [C6O4X2]2– (X = Cl, Br, and NO2; [C6O4X2]2– = dianion of the 3,6-disubstituted derivatives of 2,5-dihydroxy-1,4-benzoquinone, H4C6O4). We show and explain the unexpected key role played by the cations in isolating chiral or achiral crystals of these [MIII(C6O4X2)3]3– anions with D3 point group symmetry. Thus, among the 18 new comp…
Resolution Dependence of the Tropopause Inversion Layer in an Idealized Model for Upper-Tropospheric Anticyclones
2009
Abstract This note investigates the dependence of the extratropical tropopause inversion layer (TIL) on numerical resolution in an idealized modeling framework. Axisymmetric upper-tropospheric anticyclones are constructed by specifying potential vorticity (PV) and solving the nonlinear PV-inversion problem. The PV distribution has a smooth but near-discontinuous change of PV across the tropopause in a transition zone with vertical depth δ. For fixed δ the strength of the TIL changes with changing resolution until the transition zone is resolved by a fairly large number of grid points. The quality-controlled numerical solutions are used to study the behavior for δ → 0. This limit can lead to…