Conformal structures and twistors in the paravector model of spacetime

Some properties of the Clifford algebras Cl-3,Cl-0, Cl-1,Cl-3, Cl-4,Cl-1 similar or equal to C circle times Cl-1,Cl-3 and Cl-2,Cl-4 are presented, and three isomorphisms between the Dirac-Clifford algebra C circle times Cl-1,Cl-3 and Cl-4,Cl-1 are exhibited, in order to construct conformal maps and twistors, using the paravector model of spacetime. The isomorphism between the twistor space inner product isometry group SU( 2,2) and the group $pin(+)(2,4) is also investigated, in the light of a suitable isomorphism between C circle times Cl-1,Cl-3 and Cl-4,Cl-1. After reviewing the conformal spacetime structure, conformal maps are described in Minkowski spacetime as the twisted adjoint representation of $ pin(+)(2,4), acting on paravectors. Twistors are then presented via the paravector model of Clifford algebras and related to conformal maps in the Clifford algebra over the Lorentzian R-4,(1) spacetime.We construct twistors in Minkowski spacetime as algebraic spinors associated with the Dirac-Clifford algebra C circle times Cl-1,Cl-3 using one lower spacetime dimension than standard Clifford algebra formulations, since for this purpose, the Clifford algebra over R-4,R-1 is also used to describe conformal maps, instead of R-2,(4). Our formalism sheds some new light on the use of the paravector model and generalizations.

Integrability vs supersymmetry: Poisson structures of the pohlmeyer reduction

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Comments on energy confinement in non-periodic structures

In this study, we investigate the possibility of mode localization occurrence in a non-periodic Pfluger's column model of a rocket with an intermediate concentrated mass at its middle point. We discuss the effects of varying the intermediate mass magnitude and its position and the resulting energy confinement for two cases. Free vibration analysis and the severity of mode localization are appraised, without decoupling the system, by considering as a solution basis the fundamental free response or dynamical solution. This allows for the reduction of the dimension of the algebraic modal equation that arises from satisfying the boundary and continuity conditions. By using the same methodology, we also consider the case of a cantilevered Pluger's column with rotational stiffness at the middle support instead of an intermediate concentrated mass. (c) 2008 Elsevier Ltd. All rights reserved.

Robust tori-like Lagrangian coherent structures

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Dynamical scaling in fractal structures in the aggregation of tetraethoxysilane-derived sonogels

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Universal zero-bias conductance for the single-electron transistor

The thermal dependence of the zero-bias conductance for the single electron transistor is the target of two independent renormalization-group approaches, both based on the spin-degenerate Anderson impurity model. The first approach, an analytical derivation, maps the Kondo-regime conductance onto the universal conductance function for the particle-hole symmetric model. Linear, the mapping is parametrized by the Kondo temperature and the charge in the Kondo cloud. The second approach, a numerical renormalization-group computation of the conductance as a function the temperature and applied gate voltages offers a comprehensive view of zero-bias charge transport through the device. The first approach is exact in the Kondo regime; the second, essentially exact throughout the parametric space of the model. For illustrative purposes, conductance curves resulting from the two approaches are compared.

Crystal Structures of Xanthomonas Small Heat Shock Protein Provide a Structural Basis for an Active Molecular Chaperone Oligomer

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Molecular structures and vibrational frequencies for [PdX2(tdmPz)] (X = Cl-, SCN-): A DFT study

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

When decisions on homologous structures cause ambiguous taxa relationships: the Neomorphinae (Aves, Cuculidae) example

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Synthesis, electrochemical behavior and X-ray crystal and molecular structures of [Fe(diene)(CO)(2)PPh3] (diene = chalcone, sorbic acid)

The compounds [Fe(ch)(CO)(2)PP3] (1) (ch = chalcone) and [Fe(sba)(CO)(2)PPh3] (2) (sba = sorbic acid) were prepared by irradiating the tetracarbonyltriphenylphosphineiron(0) complex in benzene in the presence of ch or sba. The compounds were characterized by infrared and P-31 NMR spectroscopies. Their electrochemical behavior was investigated by cyclic voltammetry and the results suggest that their oxidations occur by more than one electrochemical step, producing free ch and sba, free PPh3 and solvated Fe(III). It was observed that sba ligand contributes more effectively to the stabilization of metal center in these complexes, the X-ray crystal and molecular structures of 1 and 2 were determined; it was shown that the Fe atom adopts a distorted octahedral coordinated geometry in which three of the sites are occupied by the ch or sba ligand. The [Fe(ch)(CO)(2)PPh3] complex is a monomer and the unit cell of complex 2 contains exist two identical and crystallographically independent molecules of [Fe(sba)(CO)(2)PPh3] which are linked by short hydrogen bonds O-H . . .O (C) 2001 Published by Elsevier B.V. Ltd.

Molecular structures and vibrational frequencies for cis-[PdCl2(tmen)] and cis-[Pd(N-3)(2)(tmen)]: A DFT study

Theoretical molecular structures of the complexes cis-[PdCl2(tmen)] and cis-[Pd(N-3)(2)(tmen)] (tmen = N,N,N',N'-tetramethylethylenediamine) were investigated using B3LYP/DFT method. The calculated molecular parameters, bond distances and angles, revealed a square-planar geometry around the metallic center for both compounds with the azide being linear. The theoretical infrared spectra of C, symmetry (electronic state (1)A) of the compounds are in agreement with the experimental data. (C) 2007 Elsevier B.V. All rights reserved.

Fabrication and analysis of self-assembled photonic crystals structures

This paper presents the fabrication and analysis of a three-dimensional FCC photonic crystal (PhC) based on a self-assembly synthesis of monodispersive latex spheres. Experimental optical characterization, achieved by measurements of the specular reflectance under variable angles, indicated the clear presence of a Bragg diffraction pattern. Results are further explored by theoretical calculations based on the Finite Difference Time Domain (FDTD) method to determine the full PhC band structure.