Bose-Einstein condensation dynamics in three dimensions by the pseudospectral and finite-difference methods

We suggest a pseudospectral method for solving the three-dimensional time-dependent Gross-Pitaevskii (GP) equation, and use it to study the resonance dynamics of a trapped Bose-Einstein condensate induced by a periodic variation in the atomic scattering length. When the frequency of oscillation of the scattering length is an even multiple of one of the trapping frequencies along the x, y or z direction, the corresponding size of the condensate executes resonant oscillation. Using the concept of the differentiation matrix, the partial-differential GP equation is reduced to a set of coupled ordinary differential equations, which is solved by a fourth-order adaptive step-size control Runge-Kutta method. The pseudospectral method is contrasted with the finite-difference method for the same problem, where the time evolution is performed by the Crank-Nicholson algorithm. The latter method is illustrated to be more suitable for a three-dimensional standing-wave optical-lattice trapping potential.

Approximations for the generalized temperature integral: a method based on quadrature rules

The generalized temperature integral I(m, x) appears in non-isothermal kinetic analysis when the frequency factor depends on the temperature. A procedure based on Gaussian quadrature to obtain analytical approximations for the integral I(m, x) was proposed. The results showed good agreement between the obtained approximation values and those obtained by numerical integration. Unless other approximations found in literature, the methodology presented in this paper can be easily generalized in order to obtain approximations with the maximum of accurate.

Whitham method for the Benjamin-Ono-Burgers equation and dispersive shocks

The Whitham modulation equations for the parameters of a periodic solution are derived using the generalized Lagrangian approach for the case of the damped Benjamin-Ono equation. The structure of the dispersive shock is considered in this method.

Generalized simulated annealing: Application to silicon clusters

We have compared the recently introduced generalized simulated annealing (GSA) with conventional simulated annealing (CSA). GSA was tested as a tool to obtain the ground-state geometry of molecules. We have used selected silicon clusters (Sin, n=4-7,10) as test cases. Total energies were calculated through tight-binding molecular dynamics. We have found that the replacement of Boltzmann statistics (CSA) by Tsallis's statistics (GSA) has the potential to speed up optimizations with no loss of accuracy. Next, we applied the GSA method to study the ground-state geometry of a 20-atom silicon cluster. We found an original geometry, apparently lower in energy than those previously described in the literature.

Some comments on the bi(tri)-Hamiltonian structure of generalized AKNS and DNLS hierarchies

We give the correct prescriptions for the terms involving ∂ -1 xδ(x - y), in the Hamiltonian structures of the AKNS and DNLS systems, necessary for the Jacobi identities to hold. We establish that the sl(2) and sl(3) AKNS systems are tri-Hamiltonians and construct two compatible Hamiltonian structures for the sl(n) AKNS system. We give a method for the derivation of the recursion operator for the sl(n + 1) DNLS system, and apply it explicitly to the sl(2) case, showing that such a system is tri-Hamiltonian. © 1998 Elsevier Science B.V.

Generalized ladder operators for shape-invariant potentials

A general form for ladder operators is used to construct a method to solve bound-state Schrödinger equations. The characteristics of supersymmetry and shape invariance of the system are the start point of the approach. To show the elegance and the utility of the method we use it to obtain energy spectra and eigenfunctions for the one-dimensional harmonic oscillator and Morse potentials and for the radial harmonic oscillator and Coulomb potentials.

A decoding method of an n length binary BCH code through (n + 1)n length binary cyclic code

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

Batalin-Fradkin-Vilkovisky quantization of the generalized scalar electrodynamics

This work comprises a study upon the quantization and the renormalizability of the generalized electrodynamics of spinless charged particles (mesons), namely, the generalized scalar electrodynamics (GSQED4). The theory is quantized in the covariant framework of the Batalin-Fradkin-Vilkovisky method. Thereafter, the complete Green's functions are obtained through functional methods and a proper discussion on the theory's renormalizability is also given. Next, we present the computation and further discussion on the radiative correction at α order; and, as it turns out, an unexpected mP-dependent divergence on the mesonic sector of the theory is found. Furthermore, in order to show the effectiveness of the renormalization procedure on the present theory, we also give a diagrammatic discussion on the photon self-energy at α2 order, where we observe contributions from the meson self-energy function. Afterwards, we present the expressions of the counterterms and effective coupling of the theory, obtaining from the latter an energy range where the theory is defined by m2≤k2

Computer intensive methods for controlling bias in a generalized species diversity index

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Generalized interval vector spaces and interval optimization

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On the Newton method for solving fuzzy optimization problems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Nanodisplacement measurements of piezoelectric flextensional actuators using a new interferometry homodyne method

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)