Reversibility properties of semigroup actions on homogeneous spaces

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

HOPF BIFURCATION FROM LINES of EQUILIBRIA WITHOUT PARAMETERS IN MEMRISTOR OSCILLATORS

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Global dynamics of the Rikitake system

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Large amplitude oscillations for a class of symmetric polynomial differential systems in R³

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Elétrons fortemente correlacionados na vizinhança de uma transição de fase quântica

The aim of this work is to derive theWard Identity for the low energy effective theory of a fermionic system in the presence of a hyperbolic Fermi surface coupled with a U(1) gauge field in 2+1 dimensions. These identities are important because they establish requirements for the theory to be gauge invariant. We will see that the identity associated Ward Identity (WI) of the model is not preserved at 1-loop order. This feature signalizes the presence of a quantum anomaly. In other words, a classical symmetry is broken dynamically by quantum fluctuations. Furthermore, we are considering that the system is close to a Quantum Phase Transitions and in vicinity of a Quantum Critical Point the fermionic excitations near the Fermi surface, decay through a Landau damping mechanism. All this ingredients need to be take explicitly to account and this leads us to calculate the vertex corrections as well as self energies effects, which in this way lead to one particle propagators which have a non-trivial frequency dependence

Minimum size for the occurrence of vortex matter in a square mesoscopic superconductor

The study of superconducting samples in mesoscopic scale presented a remarkable improvement during the last years. Certainly, such interest is based on the fact that when the size of the samples is close to the order of the temperature dependent coherence length xi(T), and/or the size of the penetration depth lambda(T), there are some significant modifications on the physical properties of the superconducting state. This contribution tests the square cross-section size limit for the occurrence (or not) of vortices in mesoscopic samples of area L-2, where L varies discretely from 1 xi(0) to 8 xi(0).The time dependent Ginzburg-Landau (TDGL) equations approach is used upon taking the order parameter and the local magnetic field invariant along the z-direction. The vortex configurations at the equilibrium can be obtained from the TDGL equations for superconductivity as the system relaxes to the stationary state.The obtained results show that the limit of vortex penetration is for the square sample of size 3 xi(0) x 3 xi(0) in which only a single vortex are allowed into the sample. For smaller specimens, no vortex can be formed and the field entrance into the sample is continuous and the total flux penetration occurs at higher values of H/H-c2(0), where H-c2(T) is the upper critical field. Otherwise, for larger samples different vortices patterns can be observed depending on the sample size. (c) 2007 Elsevier B.V. All rights reserved.

On retarded differential equations with impulses

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

Métodos numéricos para resolução de equações diferenciais ordinárias lineares baseados em interpolação por spline

In this work we have elaborated a spline-based method of solution of inicial value problems involving ordinary differential equations, with emphasis on linear equations. The method can be seen as an alternative for the traditional solvers such as Runge-Kutta, and avoids root calculations in the linear time invariant case. The method is then applied on a central problem of control theory, namely, the step response problem for linear EDOs with possibly varying coefficients, where root calculations do not apply. We have implemented an efficient algorithm which uses exclusively matrix-vector operations. The working interval (till the settling time) was determined through a calculation of the least stable mode using a modified power method. Several variants of the method have been compared by simulation. For general linear problems with fine grid, the proposed method compares favorably with the Euler method. In the time invariant case, where the alternative is root calculation, we have indications that the proposed method is competitive for equations of sifficiently high order.

Multiflavor soldering

In two dimensions the simple addition of two chiral bosons of opposite chiralities does not lead to a full massless scalar field. Similarly, in three dimensions the addition of two Maxwell-Chern-Simons fields of opposite helicities +/- 1 will not produce a parity invariant Maxwell-Proca theory. An interference term between the opposite chiralities (helicities) states is required in order to obtain the expected result. The so-called soldering procedure provides the missing interference Lagrangian in both 2D and 3D cases. In two dimensions such interference term allows to fuse two chiral fermionic determinants into, a non-chiral one. In a recent work we have generalized this procedure by allowing the appearance of an extra parameter which takes two possible values and leads to two different soldered Lagrangians. Here we apply this generalized soldering in a bosonic theory which has appeared in a partial bosonization of the 3D gauged Thirring model with N flavors. The multiplicity of flavors allow new types of solderings and help us to understand the connection between different perturbative approaches to bosonization in 3D. In particular, we obtain an interference term which takes us from a multiflavor Niaxwell-Chern-Simons theory to a pair of self-dual and anti-self-dual theories when we combine together both fermionic determinants of +1/2 and -1/2 helicity fermions. An important role is played by a set of pure non-interacting Chern-Simons fields which amount to a normalization factor in the fermionic determinants and act like spectators in the original theory but play an active role in the soldering procedure. Our results suggest that the generalized soldering could be used to provide dual theories in both 2D and 3D cases. (c) 2007 Elsevier B.V. All rights reserved.

Generalized duality between local vector theories in D=2+1

The existence of an interpolating master action does not guarantee the same spectrum for the interpolated dual theories. In the specific case of a generalized self-dual (GSD) model defined as the addition of the Maxwell term to the self-dual model in D = 2 + 1, previous master actions have furnished a dual gauge theory which is either nonlocal or contains a ghost mode. Here we show that by reducing the Maxwell term to first order by means of an auxiliary field we are able to define a master action which interpolates between the GSD model and a couple of non-interacting Maxwell-Chern-Simons theories of opposite helicities. The presence of an auxiliary field explains the doubling of fields in the dual gauge theory. A generalized duality transformation is defined and both models can be interpreted as self-dual models. Furthermore, it is shown how to obtain the gauge invariant correlators of the non-interacting MCS theories from the correlators of the self-dual field in the GSD model and vice-versa. The derivation of the non-interacting MCS theories from the GSD model, as presented here, works in the opposite direction of the soldering approach.

Dual descriptions of spin-two massive particles in D=2+1 via master actions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Duality of parity doublets of helicity +/- 2 in D=2+1 dimensions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Mitigation of symmetry condition in positive realness for adaptive control

Feasibility of nonlinear and adaptive control methodologies in multivariable linear time-invariant systems with state-space realization (A, B, C) is apparently limited by the standard strictly positive realness conditions that imply that the product CB must be positive definite symmetric. This paper expands the applicability of the strictly positive realness conditions used for the proofs of stability of adaptive control or control with uncertainty by showing that the not necessarily symmetric CB is only required to have a diagonal Jordan form and positive eigenvalues. The paper also shows that under the new condition any minimum-phase systems can be made strictly positive real via constant output feedback. The paper illustrates the usefulness of these extended properties with an adaptive control example. (C) 2006 Elsevier Ltd. All rights reserved.

Stabilizability and Disturbance Rejection with State-Derivative Feedback

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Dynamic Tracking with Zero Variation and Disturbance Rejection Applied to Discrete-Time Systems

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