Interference of robust tori on the resonance overlap

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

The use of classification methods for modeling the antioxidant activity of flavonoid compounds

A study using two classification methods (SDA and SIMCA) was carried out in this work with the aim of investigating the relationship between the structure of flavonoid compounds and their free-radical-scavenging ability. In this work, we report the use of chemometric methods (SDA and SIMCA) able to select the most relevant variables (steric, electronic, and topological) responsible for this ability. The results obtained with the SDA and SIMCA methods agree perfectly with our previous model, in which we used other chemometric methods (PCA, HCA and KNN) and are also corroborated with experimental results from the literature. This is a strong indication of how reliable the selection of variables is.

Quantum equivalence between the self-dual and the Maxwell-Chern-Simons models nonlinearly coupled to U(1) scalar fields

The use of master actions to prove duality at quantum level becomes cumbersome if one of the dual fields interacts nonlinearly with other fields. This is the case of the theory considered here consisting of U(1) scalar fields coupled to a self-dual field through a linear and a quadratic term in the self-dual field. Integrating perturbatively over the scalar fields and deriving effective actions for the self-dual and the gauge field we are able to consistently neglect awkward extra terms generated via master action and establish quantum duality up to cubic terms in the coupling constant. The duality holds for the partition function and some correlation functions. The absence of ghosts imposes restrictions on the coupling with the scalar fields.

ALPHA-CONTRACTIONS AND ATTRACTORS FOR DISSIPATIVE SEMILINEAR HYPERBOLIC-EQUATIONS AND SYSTEMS

In this paper we discuss the existence of compact attractor for the abstract semilinear evolution equation u = Au + f (t, u); the results are applied to damped partial differential equations of hyperbolic type. Our approach is a combination of Liapunov method with the theory of alpha-contractions.

Charge-orbital ordering and phase separation in the two-orbital model for manganites: Roles of Jahn-Teller phononic and Coulombic interactions

The main properties of realistic models for manganites are studied using analytic mean-field approximations and computational numerical methods, focusing on the two-orbital model with electrons interacting through Jahn-Teller (JT) phonons and/or Coulombic repulsions. Analyzing the model including both interactions by the combination of the mean-field approximation and the exact diagonalization method, it is argued that the spin-charge-orbital structure in the insulating phase of the purely JT-phononic model with a large Hund couphng J(H) is not qualitatively changed by the inclusion of the Coulomb interactions. As an important application of the present mean-held approximation, the CE-type antiferromagnetic state, the charge-stacked structure along the z axis, and (3x(2) - r(2))/(3y(2) - r(2))-type orbital ordering are successfully reproduced based on the JT-phononic model with large JH for the half-doped manganite, in agreement with recent Monte Carlo simulation results. Topological arguments and the relevance of the Heisenberg exchange among localized t(2g) spins explains why the inclusion of the nearest-neighbor Coulomb interaction does not destroy the charge stacking structure. It is also verified that the phase-separation tendency is observed both in purely JT-phononic (large JH) and purely Coulombic models in the vicinity of the hole undoped region, as long as realistic hopping matrices are used. This highlights the qualitative similarities of both approaches and the relevance of mixed-phase tendencies in the context of manganites. In addition, the rich and complex phase diagram of the two-orbital Coulombic model in one dimension is presented. Our results provide robust evidence that Coulombic and JT-phononic approaches to manganites are not qualitatively different ways to carry out theoretical calculations, but they share a variety of common features.

A homological version of the implicit function theorem

Our objective in this paper is to prove an Implicit Function Theorem for general topological spaces. As a consequence, we show that, under certain conditions, the set of the invertible elements of a topological monoid X is an open topological group in X and we use the classical topological group theory to conclude that this set is a Lie group.

Faddeev-jackiw formalism for A topological-like oscillator in planar dimensions

The problem of a harmonic oscillator coupling to an electromagnetic potential plus a topological-like (Chern-Simons) massive term, in two-dimensional space, is studied in the light of the symplectic formalism proposed by Faddeev and Jackiw for constrained systems.

The magnetic field of a current carrying cosmic string

The magnetostatic field of an infinite rectilinear current placed in the stationary gravitational field of a rotating cosmic string is found. An interesting aspect of this problem is that although the metric is mathematically very simple, its physical meaning is not trivial. It depends only on topological parameters. So, the cosmic string vacuum space-time is locally equivalent to the Minkowski space-time, but not globally. The calculations are so simple that they can easily be shown in the classroom. © 1997 American Association of Physics Teachers.

Pre-weighted homogeneous map germs finite determinacy and topological triviality

In this paper we introduce the notion of G-pre-weighted homogeneous map germ, (G is one of Mather's groups A or K.) and show that any G-pre-weighted homogeneous map germ is G-finitely determined. We also give an explicit order, based on the Newton polyhedron of a pre-weighted homogeneous germ of function, such that the topological structure is preserved after perturbations by terms of higher order.

Teleparallel equivalent of the Kaluza-Klein theory

Relying upon the equivalence between a gauge theory for the translation group and general relativity, a teleparallel version of the original Kaluza-Klein theory is developed. In this model, only the internal space (fiber) turns out to be five dimensional, spacetime being kept always four dimensional. A five-dimensional translational gauge theory is obtained which unifies, in the sense of Kaluza-Klein theories, gravitational and electromagnetic interactions. ©2000 The American Physical Society.

Confinement and soliton solutions in the SL(3) Toda model coupled to matter fields

We consider an integrable conformally invariant two-dimensional model associated to the affine Kac-Moody algebra sl3(ℂ). It possesses four scalar fields and six Dirac spinors. The theory does not possesses a local Lagrangian since the spinor equations of motion present interaction terms which are bilinear in the spinors. There exists a submodel presenting an equivalence between a U(1) vector current and a topological current, which leads to a confinement of the spinors inside the solitons. We calculate the one-soliton and two-soliton solutions using a procedure which is a hybrid of the dressing and Hirota methods. The soliton masses and time delays due to the soliton interactions are also calculated. We give a computer program to calculate the soliton solutions. © 2002 Published by Elsevier Science B.V.

Construction of exact Riemannian instanton solutions

We present the exact construction of Riemannian (or stringy) instantons, which are classical solutions of 2D Yang-Mills theories that interpolate between initial and final string configurations. They satisfy the Hitchin equations with special boundary conditions. For the case of U(2) gauge group those equations can be written as the sinh-Gordon equation with a delta-function source. Using the techniques of integrable theories based on the zero curvature conditions, we show that the solution is a condensate of an infinite number of one-solitons with the same topological charge and with all possible rapidities.

Classical versus quantum equivalence between sine-Gordon, Liouville and other solitons

In this work we present a mapping between the classical solutions of the sine-Gordon, Liouville, λφ4 and other kinks in 1+1 dimensions. This is done by using an invariant quantity which relates the models. It is easily shown that this procedure is equivalent to that used to get the so called deformed solitons, as proposed recently by Bazeia et al. [Phys. Rev. D. 66 (2002) 101701(R)]. The classical equivalence is explored in order to relate the solutions of the corresponding models and, as a consequence, try to get new information about them. We discuss also the difficulties and consequences which appear when one tries to extend the deformation in order to take into account the quantum version of the models.

Pure spinor formalism as an N ≤ 2 topological string

Following suggestions of Nekrasov and Siegel, a non-minimal set of fields are added to the pure spinor formalism for the superstring. Twisted ĉ ≤ 3 N ≤ 2 generators are then constructed where the pure spinor BRST operator is the fermionic spin-one generator, and the formalism is interpreted as a critical topological string. Three applications of this topological string theory include the super-Poincaré covariant computation of multiloop superstring amplitudes without picture-changing operators, the construction of a cubic open superstring field theory without contact-term problems, and a new four-dimensional version of the pure spinor formalism which computes F-terms in the spacetime action. © SISSA 2005.

Experimental aspects of partially premixed pulsating combustion

The pulsating combustion process has won interest in current research due to indications that its application in energy generation can offer several advantages, such as: fuel economy, reduced pollutants formation, increased rate of convective heat transfer and reduced investment, when compared with conventional techniques. An experimental study has been conducted with the objective of investigating the effects of combustion driven acoustic oscillations in the emission rates of combustion gases, especially carbon monoxide and nitrogen oxides. The experiments were conducted in a water-jacketed 1-m long by 25-cm internal diameter stainless steel vertical tube. The combustor operated with liquefied petroleum gas (LPG) in both oscillatory and non oscillatory conditions, under the same input conditions. Part of the reactant mixture was excited acoustically, before the burner exit, by a speaker positioned strategically. The burner was aligned with the chamber longitudinal axis and positioned at its bottom. The experiments were conducted for 0.16 g/s of LPG burning in stoichiometric equivalence ratio. The main conclusions were: a) the pulsating combustion process produces more uniform fuel/air profile than the non pulsating process, b) close to stoichiometric equivalence ratio the pulsating combustion process generates higher rates of NO x; c) the frequency has a strong influence in NO x emission, but the pressure amplitude has a weak influence; d) the presence of the acoustic field may change drastically the combustion gas emissions in diffusion flames, but in pre-mixed flames the influence is not as strong.