Geometrical wave equation and the cauchy-like theorem for octonions

Riemann surfaces, cohomology and homology groups, Cartan's spinors and triality, octonionic projective geometry, are all well supported by Complex Structures [1], [2], [3], [4]. Furthermore, in Theoretical Physics, mainly in General Relativity, Supersymmetry and Particle Physics, Complex Theory Plays a Key Role [5], [6], [7], [8]. In this context it is expected that generalizations of concepts and main results from the Classical Complex Theory, like conformal and quasiconformal mappings [9], [10] in both quaternionic and octonionic algebra, may be useful for other fields of research, as for graphical computing enviromment [11]. In this Note, following recent works by the autors [12], [13], the Cauchy Theorem will be extended for Octonions in an analogous way that it has recentely been made for quaternions [14]. Finally, will be given an octonionic treatment of the wave equation, which means a wave produced by a hyper-string with initial conditions similar to the one-dimensional case.

The fractional-nonlinear robotic manipulator: Modeling and dynamic simulations

In this paper, we applied the Riemann-Liouville approach and the fractional Euler-Lagrange equations in order to obtain the fractional-order nonlinear dynamics equations of a two link robotic manipulator. The aformentioned equations have been simulated for several cases involving: integer and non-integer order analysis, with and without external forcing acting and some different initial conditions. The fractional nonlinear governing equations of motion are coupled and the time evolution of the angular positions and the phase diagrams have been plotted to visualize the effect of fractional order approach. The new contribution of this work arises from the fact that the dynamics equations of a two link robotic manipulator have been modeled with the fractional Euler-Lagrange dynamics approach. The results reveal that the fractional-nonlinear robotic manipulator can exhibit different and curious behavior from those obtained with the standard dynamical system and can be useful for a better understanding and control of such nonlinear systems. © 2012 American Institute of Physics.

Competitiveness and labour regulations

Includes bibliography

Industrial policy, comparative advantages and growth

Includes bibliography

Regional integration and macroeconomic coordination in Latin America

Includes bibliography

Scaling attractors in interacting teleparallel dark energy

It has been proposed recently the existence of a non-minimal coupling between a canonical scalar field (quintessence) and gravity in the framework of teleparallel gravity, motivated by similar constructions in the context of General Relativity. The dynamics of the model, known as teleparallel dark energy, has been further developed, but no scaling attractor has been found. Here we consider a model in which the non-minimal coupling is ruled by a dynamically changing coefficient α≡f,φ/(f)1/2, with f(φ) an arbitrary function of the scalar field φ. It is shown that in this case the existence of scaling attractors is possible, which means that the universe will eventually enter these scaling attractors, regardless of the initial conditions. As a consequence, the cosmological coincidence problem could be alleviated without fine-tunings. © 2013 IOP Publishing Ltd and Sissa Medialab srl.

A rescaling of the phase space for Hamiltonian map: Applications on the Kepler map and mappings with diverging angles in the limit of vanishing action

A rescale of the phase space for a family of two-dimensional, nonlinear Hamiltonian mappings was made by using the location of the first invariant Kolmogorov-Arnold-Moser (KAM) curve. Average properties of the phase space are shown to be scaling invariant and with different scaling times. Specific values of the control parameters are used to recover the Kepler map and the mapping that describes a particle in a wave packet for the relativistic motion. The phase space observed shows a large chaotic sea surrounding periodic islands and limited by a set of invariant KAM curves whose position of the first of them depends on the control parameters. The transition from local to global chaos is used to estimate the position of the first invariant KAM curve, leading us to confirm that the chaotic sea is scaling invariant. The different scaling times are shown to be dependent on the initial conditions. The universality classes for the Kepler map and mappings with diverging angles in the limit of vanishing action are defined. © 2013 Published by Elsevier Inc. All rights reserved.

Dynamics of rotation of super-Earths

We numerically investigate the dynamics of rotation of several close-in terrestrial exoplanet candidates. In our model, the rotation of the planet is disturbed by the torque of the central star due to the asymmetric equilibrium figure of the planet. We model the shape of the planet by a Jeans spheroid. We use surfaces of section and spectral analysis to explore numerically the rotation phase space of the systems adopting different sets of parameters and initial conditions close to the main spin-orbit resonant states. One of the parameters, the orbital eccentricity, is critically discussed here within the domain of validity of orbital circularization timescales given by tidal models. We show that, depending on some parameters of the system like the radius and mass of the planet, eccentricity etc., the rotation can be strongly perturbed and a chaotic layer around the synchronous state may occupy a significant region of the phase space. 55 Cnc e is an example. © 2013 Springer Science+Business Media Dordrecht.

Sudden change of quantum discord for a system of two qubits

It is known that quantum discord might experience a sudden transition in its dynamics when calculated for certain Bell-diagonal states (BDS) that are in interaction with their surroundings. We examine this phenomenon, known as the sudden change of quantum discord, considering the case of two qubits independently interacting with dephasing reservoirs. We first demonstrate that, for a class of initial states which can be chosen arbitrarily close to BDS, the transition is in fact not sudden, although it might numerically appear so if not studied carefully. Then, we provide an extension of this discussion covering the X-shaped density matrices. Our findings suggest that the transition of quantum discord might be sudden only for an highly idealized zero-measure subset of states within the set of all possible initial conditions of two qubits. © 2013 American Physical Society.

Projeto de reguladores fuzzy Takagi-Sugeno utilizando as condições iniciais da planta

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Istmo Centroamericano: estadísticas del subsector eléctrico (datos actualizados a 2001)

Incluye Bibliografía

Encontros próximos: captura gravitacional temporária e esfera de influência

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Captura, difusão e acreção num sistema coorbital imerso em um meio gasoso

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Dinâmica de uma partícula coorbital a um sistema de satélites

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

Satélites irregulares de Júpiter: análise da captura de asteróides binários

Pós-graduação em Física - FEG