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.

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.

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.

On control and synchronization in chaotic and hyperchaotic systems via linear feedback control

This paper presents the control and synchronization of chaos by designing linear feedback controllers. The linear feedback control problem for nonlinear systems has been formulated under optimal control theory viewpoint. Asymptotic stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution of the Hamilton-Jacobi-Bellman equation thus guaranteeing both stability and optimality. The formulated theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations were provided in order to show the effectiveness of this method for the control of the chaotic Rossler system and synchronization of the hyperchaotic Rossler system. (C) 2007 Elsevier B.V. All rights reserved.

Intercalation processes and diffusion paths of lithium ions in spinel-type structured Li(1+x)Ti(2)O(4): Density functional theory study

Intercalation processes and corresponding diffusion paths of Li ions into spinel-type structured Li(1+x)Ti(2)O(4) (0 <= x <= 0.375) are systematically studied by means of periodic density functional theory calculations for different compositions and arrangements. An analysis of the site preference for intercalation processes is carried out, while energy barriers for the diffusion paths have been computed in detail. Our results indicate that the Li insertion is thermodynamically favorable at octahedral sites 16c in the studied composition range, and Li migration from tetrahedral sites 8a to octahedral sites 16c stabilizes the structure and becomes favorable for compositions x >= 0.25. Diffusion paths from less stable arrangements involving Li migrations between tetrahedral and octahedral sites exhibit the lowest energy barrier since the corresponding trajectories and energy profiles take place across a triangle made by three neighboring oxygen anions without structural modification. Theoretical and experimental diffusion coefficients are in reasonable agreement.

Thermoeconomic functional analysis applied in cogeneration systems associated to cellulose plants

Thermoeconomic Functional Analysis is a method developed for the analysis and optimal design of improvement of thermal systems (Frangopoulos, 1984). The purpose of this work is to discuss the cogeneration system optimization using a condensing steam turbine with two extractions. This cogeneration system is a rational alternative in pulp and paper plants in regard to the Brazilian conditions. The objective of this optimization consists of minimizing the global cost of the system acquisition and operation, based on the parametrization of actual data from a cellulose plant with a daily production of 1000 tons. Among the several possible decision variables, the pressure and temperature of live steam were selected. These variables significantly affect the energy performance of the cogeneration system. The conditions which determine a lower cost for the system are presented in conclusion.

Density functional theory calculation of the electronic structure of Ba0.5Sr0.5TiO3: Photoluminescent properties and structural disorder

First-principles quantum-mechanical techniques, based on density functional theory (B3LYP level) were employed to study the electronic structure of ordered and deformed asymmetric models for Ba0.5Sr 0.5TiO3. Electronic properties are analyzed and the relevance of the present theoretical and experimental results on the photoluminescence behavior is discussed. The presence of localized electronic levels in the band gap, due to the symmetry break, would be responsible for the visible photoluminescence of the amorphous state at room temperature. Thin films were synthesized following a soft chemical processing. Their structure was confirmed by x-ray data and the corresponding photoluminescence properties measured.

Optimal linear and nonlinear control design for chaotic systems

In this work, the linear and nonlinear feedback control techniques for chaotic systems were been considered. The optimal nonlinear control design problem has been resolved by using Dynamic Programming that reduced this problem to a solution of the Hamilton-Jacobi-Bellman equation. In present work the linear feedback control problem has been reformulated under optimal control theory viewpoint. The formulated Theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations for the Rössler system and the Duffing oscillator are provided to show the effectiveness of this method. Copyright © 2005 by ASME.

Reduction of infinite dimensional systems to finite dimensions: Compact convergence approach

We consider parameter dependent semilinear evolution problems for which, at the limit value of the parameter, the problem is finite dimensional. We introduce an abstract functional analytic framework that applies to many problems in the existing literature for which the study of asymptotic dynamics can be reduced to finite dimensions via the invariant manifolds technique. Some practical models are considered to show wide applicability of the theory. © 2013 Society for Industrial and Applied Mathematics.

RIEMANN ZETA ZEROS AND PRIME NUMBER SPECTRA IN QUANTUM FIELD THEORY

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A multiple intelligences theory-based 3D virtual lab environment for digital systems teaching.

This paper describes a 3D virtual lab environment that was developed using OpenSim software integrated into Moodle. Virtuald software tool was used to provide pedagogical support to the lab by enabling to create online texts and delivering them to the students. The courses taught in this virtual lab are methodologically in conformity to theory of multiple intelligences. Some results are presented.

Release of Cyanopyridine from a Ruthenium Complex Adsorbed on Gold: Surface-Enhanced Raman Scattering, Electrochemistry, and Density Functional Theory Analyses

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

TinO2n-1 Magneli phases studied using density functional theory

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

Geometric singular perturbartion theory for non-smooth dynamical systems

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

Capacitance spectroscopy and density functional theory

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