Catastrophic regime shift in water reservoirs and São Paulo water supply crisis

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

Lachmann e a teoria do processo de mercado: entre o pensamento austríaco e o pós-keynesiano

Pós-graduação em Economia - FCLAR

Confluências entre mito, literatura e direito em Édipo Rei, de Sófocles

Pós-graduação em Letras - IBILCE

Effective theory for trapped few-fermion systems

We apply the general principles of effective field theories to the construction of effective interactions suitable for few- and many-body calculations in a no-core shell model framework. We calculate the spectrum of systems with three and four two-component fermions in a harmonic trap. In the unitary limit, we find that three-particle results are within 10% of known semianalytical values even in small model spaces. The method is very general, and can be readily extended to other regimes, more particles, different species (e.g., protons and neutrons in nuclear physics), or more-component fermions (as well as bosons). As an illustration, we present calculations of the lowest-energy three-fermion states away from the unitary limit and find a possible inversion of parity in the ground state in the limit of trap size large compared to the scattering length. Furthermore, we investigate the lowest positive-parity states for four fermions, although we are limited by the dimensions we can currently handle in this case.

Neural network based on adaptive resonance theory with continuous training for multi-configuration transient stability analysis of electric power systems

This work presents a methodology to analyze electric power systems transient stability for first swing using a neural network based on adaptive resonance theory (ART) architecture, called Euclidean ARTMAP neural network. The ART architectures present plasticity and stability characteristics, which are very important for the training and to execute the analysis in a fast way. The Euclidean ARTMAP version provides more accurate and faster solutions, when compared to the fuzzy ARTMAP configuration. Three steps are necessary for the network working, training, analysis and continuous training. The training step requires much effort (processing) while the analysis is effectuated almost without computational effort. The proposed network allows approaching several topologies of the electric system at the same time; therefore it is an alternative for real time transient stability of electric power systems. To illustrate the proposed neural network an application is presented for a multi-machine electric power systems composed of 10 synchronous machines, 45 buses and 73 transmission lines. (C) 2010 Elsevier B.V. All rights reserved.

Robust fault diagnosis in power distribution systems based on fuzzy ARTMAP neural network-aided evidence theory

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

Colombeau's theory and shock wave solutions for systems of PDEs

In this article we study the existence of shock wave solutions for systems of partial differential equations of hydrodynamics with viscosity in one space dimension in the context of Colombeau's theory of generalized functions. This study uses the equality in the strict sense and the association of generalized functions (that is the weak equality). The shock wave solutions are given in terms of generalized functions that have the classical Heaviside step function as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function that have to satisfy part of the equations in the strict sense and part of the equations in the sense of association.

Many-body theory for systems of composite hadrons

Many-body systems of composite hadrons are characterized by processes that involve the simultaneous presence of hadrons and their constituents. We briefly review several methods that have been devised to study such systems and present a novel method that is based on the ideas of mapping between physical and ideal Fock spaces. The method, known as the Fock-Tani representation, was invented years ago in the context of atomic physics problems and was recently extended to hadronic physics. Starting with the Fock-space representation of single-hadron states, a change of representation is implemented by a unitary transformation such that composites are redescribed by elementary Bose and Fermi field operators in an extended Fock space. When the unitary transformation is applied to the microscopic quark Hamiltonian, effective, Hermitian Hamiltonians with a clear physical interpretation are obtained. The use of the method in connection with the linked-cluster formalism to describe short-range correlations and quark deconfinement effects in nuclear matter is discussed. As an application of the method, an effective nucleon-nucleon interaction is derived from a constituent quark model and used to obtain the equation of state of nuclear matter in the Hartree-Fock approximation.

An algebraic q-deformed form for shape-invariant systems

A quantum deformed theory applicable to all shape-invariant bound-state systems is introduced by defining q-deformed ladder operators. We show that these new ladder operators satisfy new q-deformed commutation relations. In this context we construct an alternative q-deformed model that preserves the shape-invariance property presented by the primary system. q-deformed generalizations of Morse, Scarf and Coulomb potentials are given as examples.

GENERAL POTENTIALS DESCRIBED BY SO(2,1) DYNAMIC ALGEBRA IN PARABOLIC-COORDINATE SYSTEMS

We propose general three-dimensional potentials in rotational and cylindrical parabolic coordinates which are generated by direct products of the SO(2, 1) dynamical group. Then we construct their Green functions algebraically and find their spectra. Particular cases of these potentials which appear in the literature are also briefly discussed.

On the dissimilarity between the algorithms for computing the symmetric energy-momentum tensor in ordinary field theory and general relativity

The recipe used to compute the symmetric energy-momentum tensor in the framework of ordinary field theory bears little resemblance to that used in the context of general relativity, if any. We show that if one stal ts fi om the field equations instead of the Lagrangian density, one obtains a unified algorithm for computing the symmetric energy-momentum tensor in the sense that it can be used for both usual field theory and general relativity.

Slow-fast systems on algebraic varieties bordering piecewise-smooth dynamical systems

This article extends results contained in Buzzi et al. (2006) [4], Llibre et al. (2007, 2008) [12,13] concerning the dynamics of non-smooth systems. In those papers a piecewise C-k discontinuous vector field Z on R-n is considered when the discontinuities are concentrated on a codimension one submanifold. In this paper our aim is to study the dynamics of a discontinuous system when its discontinuity set belongs to a general class of algebraic sets. In order to do this we first consider F :U -> R a polynomial function defined on the open subset U subset of R-n. The set F-1 (0) divides U into subdomains U-1, U-2,...,U-k, with border F-1(0). These subdomains provide a Whitney stratification on U. We consider Z(i) :U-i -> R-n smooth vector fields and we get Z = (Z(1),...., Z(k)) a discontinuous vector field with discontinuities in F-1(0). Our approach combines several techniques such as epsilon-regularization process, blowing-up method and singular perturbation theory. Recall that an approximation of a discontinuous vector field Z by a one parameter family of continuous vector fields is called an epsilon-regularization of Z (see Sotomayor and Teixeira, 1996 [18]; Llibre and Teixeira, 1997 [15]). Systems as discussed in this paper turn out to be relevant for problems in control theory (Minorsky, 1969 [16]), in systems with hysteresis (Seidman, 2006 [17]) and in mechanical systems with impacts (di Bernardo et al., 2008 [5]). (C) 2011 Elsevier Masson SAS. All rights reserved.

Density functional theory study on the structural and electronic properties of low index rutile surfaces for TiO2/SnO2/TiO2 and SnO2/TiO2/SnO2 composite systems

The present study is concerned with the structural and electronic properties of the TiO2/SnO2/TiO2 and SnO2/TiO2/SnO2 composite systems. Periodic quantum mechanical method with density functional theory at the B3LYP level has been carried out. Relaxed surface energies, structural characteristics and electronic properties of the (I 10), (0 10), (10 1) and (00) low-index rutile surfaces for TiO2/SnO2/TiO2 and SnO2/TiO2/SnO2 models are studied. For, comparison purposes, the bare rutile TiO2 and SnO2 structures are also analyzed and compared with previous theoretical and experimental data. The calculated surface energy for both rutile TiO2 and SnO2 surfaces follows the sequence (110) < (010) < (101) < (001) and the energy increases as (010) < (101) < (110) < (001) and (010) approximate to (110) < (101) < (001) for SnO2/TiO2/SnO2 and TiO2/SnO2/TiO2 composite systems, respectively. SnO2/TiO2/SnO2 presents larger values of surface energy than the individual SnO2 and TiO2 metal oxides and the TiO2/SnO2/TiO2 system renders surface energy values of the same order that the TiO2 and lower than the SnO2. An analysis of the electronic structure of the TiO2/SnO2/TiO2 and SnO2/TiO2/SnO2 systems shows that the main characteristics of the upper part of the valence bands for all the studied surfaces are dominated by the external layers, i.e., by the TiO2 and the SnO2, respectively, and the topology of the lower part of the conduction bands looks like the core layers. There is an energy stabilization of both valence band top and conduction band bottom for (110) and (010) surfaces of the SnO2/TiO2/SnO2 composite system in relation to their core TiO2, whereas an opposite trend is found for the same surfaces of the TiO2/SnO2/TiO2 composite system in relation to the bare SnO2. The present theoretical results may explain the growth of TiO2@SnO2 bimorph composite nanotape.

Affine Toda systems coupled to matter fields

We investigate higher grading integrable generalizations of the affine Toda systems, where the flat connections defining the models take values in eigensubspaces of an integral gradation of an affine Kac-Moody algebra, with grades varying from l to -l (l > 1). The corresponding target space possesses nontrivial vacua and soliton configurations, which can be interpreted as particles of the theory, on the same footing as those associated to fundamental fields. The models can also be formulated by a hamiltonian reduction procedure from the so-called two-loop WZNW models. We construct the general solution and show the classes corresponding to the solitons. Some of the particles and solitons become massive when the conformal symmetry is spontaneously broken by a mechanism with an intriguing topological character and leading to a very simple mass formula. The massive fields associated to nonzero grade generators obey field equations of the Dirac type and may be regarded as matter fields. A special class of models is remarkable. These theories possess a U(1 ) Noether current, which, after a special gauge fixing of the conformal symmetry, is proportional to a topological current. This leads to the confinement of the matter field inside the solitons, which can be regarded as a one-dimensional bag model for QCD. These models are also relevant to the study of electron self-localization in (quasi-)one-dimensional electron-phonon systems.

3-Dimensional hopf bifurcation via averaging theory

We consider the Lorenz system ẋ = σ(y - x), ẏ = rx - y - xz and ż = -bz + xy; and the Rössler system ẋ = -(y + z), ẏ = x + ay and ż = b - cz + xz. Here, we study the Hopf bifurcation which takes place at q± = (±√br - b,±√br - b, r - 1), in the Lorenz case, and at s± = (c+√c2-4ab/2, -c+√c2-4ab/2a, c±√c2-4ab/2a) in the Rössler case. As usual this Hopf bifurcation is in the sense that an one-parameter family in ε of limit cycles bifurcates from the singular point when ε = 0. Moreover, we can determine the kind of stability of these limit cycles. In fact, for both systems we can prove that all the bifurcated limit cycles in a neighborhood of the singular point are either a local attractor, or a local repeller, or they have two invariant manifolds, one stable and the other unstable, which locally are formed by two 2-dimensional cylinders. These results are proved using averaging theory. The method of studying the Hopf bifurcation using the averaging theory is relatively general and can be applied to other 3- or n-dimensional differential systems.