Matter-wave localization in a weakly perturbed optical lattice

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

A generalized alternating-direction implicit scheme for incompressible magnetohydrodynamic viscous flows at low magnetic Reynolds number

This paper presents numerical simulations of incompressible fluid flows in the presence of a magnetic field at low magnetic Reynolds number. The equations governing the flow are the Navier-Stokes equations of fluid motion coupled with Maxwell's equations of electromagnetics. The study of fluid flows under the influence of a magnetic field and with no free electric charges or electric fields is known as magnetohydrodynamics. The magnetohydrodynamics approximation is considered for the formulation of the non-dimensional problem and for the characterization of similarity parameters. A finite-difference technique is used to discretize the equations. In particular, an extension of the generalized Peaceman and Rachford alternating-direction implicit (ADI) scheme for simulating two-dimensional fluid flows is presented. The discretized conservation equations are solved in stream function-vorticity formulation. We compare the ADI and generalized ADI schemes, and show that the latter is more efficient in simulating low Reynolds number and magnetic Reynolds number problems. Numerical results demonstrating the applicability of this technique are also presented. The simulation of incompressible magneto hydrodynamic fluid flows is illustrated by numerical solution for two-dimensional cases. (c) 2007 Elsevier B.V. All rights reserved.

A theoretical study of the A(2)Sigma(+)-X-2 Pi system of the SiP molecule

The A (2)Sigma(+) and X(2)Pi electronic states of the SiP species have been investigated theoretically at a very high level of correlation treatment (CASSCF/MRSDCI). Very accurate potential energy curves are presented for both states, as well as the associated spectroscopic constants as derived from the vib-rotational energy levels determined by means of the numerical solution of the radial Schrodinger equation. Electronic transition moment function, oscillator strengths, Einstein coefficients for spontaneous emission, and Franck-Condon factors for the A(2)Sigma(+)-X(2)Pi system have been calculated. Dipole moment functions and radiative lifetimes for both states have also been determined. Spin-orbit coupling constants are also reported. The radiative lifetimes for the A(2)Sigma(+) state, taking into account the spin-orbit diagonal correction to the X(2)Pi state, decrease from a value of 138 ms at v' = 0 to 0.48 ms at v' = 8, and, for the X(2)Pi state, from 2.32 s at v = 1 to 0.59 s at v = 5. Vibrational and rotational transitions are expected to be relatively strong.

Pump excited state absorption in holmium-doped fluoride glass

The primary excited state absorption processes relating to the (5)I(6) -> (5)I(7) 3 mu m laser transition in singly Ho(3+)-doped fluoride glass have been investigated in detail using time-resolved fluorescence spectroscopy. Selective laser excitation of the (5)I(6) and (5)I(7) energy levels established the occurrence of two excited state absorption transitions from these energy levels that compete with previously described energy transfer upconversion processes. The (5)I(7) -> (5)I(4) excited state absorption transition has peak cross sections at 1216 nm (sigma(esa)=2.8x10(-21) cm(2)), 1174 nm (sigma(esa)=1x10(-21) cm(2)), and 1134 nm (sigma(esa)=7.4x10(-22) cm(2)) which have a strong overlap with the (5)I(8) -> (5)I(6) ground state absorption. on the other hand, it was established that the excited state absorption transition (5)I(6) -> (5)S(2) had a weak overlap with ground state absorption. Using numerical solution of the rate equations, we show that Ho(3+)-doped fluoride fiber lasers employing pumping at 1100 nm rely on excited state absorption from the lowest excited state of Ho(3+) to maintain a population inversion and that energy transfer upconversion processes compete detrimentally with the excited state absorption processes in concentrated Ho(3+)-doped fluoride glass. (c) 2008 American Institute of Physics.

COMPLEX KOHN VARIATIONAL PRINCIPLE FOR 2-NUCLEON BOUND-STATE AND SCATTERING WITH THE TENSOR POTENTIAL

Complex Kohn variational principle is applied to the numerical solution of the fully off-shell Lippmann-Schwinger equation for nucleon-nucleon scattering for various partial waves including the coupled S-3(1), D-3(1), channel. Analytic expressions are obtained for all the integrals in the method for a suitable choice of expansion functions. Calculations with the partial waves S-1(0), P-1(1), D-1(2), and S-3(1)-D-3(1) of the Reid soft core potential show that the method converges faster than other solution schemes not only for the phase shift but also for the off-shell t matrix elements. We also show that it is trivial to modify this variational principle in order to make it suitable for bound-state calculation. The bound-state approach is illustrated for the S-3(1)-D-3(1) channel of the Reid soft-core potential for calculating the deuteron binding, wave function, and the D state asymptotic parameters. (c) 1995 Academic Press, Inc.

Lattice discretization in quantum scattering

The utility of lattice discretization technique is demonstrated for solving nonrelativistic quantum scattering problems and specially for the treatment of ultraviolet divergences in these problems with some potentials singular at the origin in two- and three-space dimensions. This shows that the lattice discretization technique could be a useful tool for the numerical solution of scattering problems in general. The approach is illustrated in the case of the Dirac delta function potential.

A finite element free convection model for the side wall heated cavity

This paper presents a finite element numerical solution of free convection in a cavity with side walls maintained at constant but different temperatures. The predictions from the model and the method of solution were validated by comparison with the 'bench mark' solution and Vahl Davis' results and good agreement was found. The present model was used to obtain additional results over a wide range of Rayleigh number (10(3)-10(6)) and L/H ratios varying from 0.1 to 1.0. The predicted stream function patterns, temperature and velocity profiles as well as the mean Nusselt number were presented and discussed. (C) 2000 Elsevier B.V. Ltd. All rights reserved.

Analytical attitude propagation with non-singular variables and gravity gradient torque for spin stabilized satellite

An analytical approach for the spin stabilized satellite attitude propagation is presented using the non-singular canonical variables to describe the rotational motion. Two sets of variables were introduced for Fukushima in 1994 by a canonical transformation and they are useful when the angle between z-satellite axis of a coordinate system fixed in artificial satellite and the rotational angular momentum vector is zero or when the angle between Z-equatorial axis and rotation angular momentum vector is zero. Analytical solutions for rotational motion equations and torque-free motion are discussed in terms of the elliptic functions and by the application of some simplification to get an approximated solution. These solutions are compared with a numerical solution and the results show a good agreement for many rotation periods. When the mean Hamiltonian associated with the gravity gradient torque is included, an analytical solution is obtained by the application of the successive approximations' method for the satellite in an elliptical orbit. These solutions show that the magnitude of the rotation angular moment is not affected by the gravity gradient torque but this torque causes linear and periodic variations in the angular variables, long and short periodic variations in Z-equatorial component of the rotation angular moment and short periodic variations in x-satellite component of the rotation angular moment. The goal of this analysis is to emphasize the geometrical and physical meaning of the non-singular variables and to validate the approximated analytical solution for the rotational motion without elliptic functions for a non-symmetrical satellite. The analysis can be applied for spin stabilized satellite and in this case the general solution and the approximated solution are coincidence. Then the results can be used in analysis of the space mission of the Brazilian Satellites. (C) 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

Models of liquid storage tanks

We present the results of a comparative study on thermally stratified tanks for hot storage. A two-dimensional model is employed. A numerical solution was obtained using the control-volume technique due to Patankar. The two-dimensional model was simplified for the pure conduction case. Results from the two models were compared with each other and with available numerical and experimental results. (C) 1997 Elsevier B.V. Ltd.

A steady-state model for heat pipes of circular or rectangular cross-sections

The objective of this paper is to present a generalized analytical-numerical model of the internal flow in heat pipes. The model formulation is based on two-dimensional formulation of the energy and momentum equations in the vapour and liquid regions and also in the metallic tube. The numerical solution of the model is obtained by using the descretization scheme LOAD and the SIMPLE numerical code. The flow fields, as well as the pressure fields, for different geometries were obtained and discussed. Copyright © 1996 Elsevier Science Ltd.

Optimization procedures in the design of continuous induction hardening and tempering installations for magnetic steel bars

An inverse problem concerning the industrial process of steel bars hardening and tempering is considered. The associated optimization problem is formulated in terms of membership functions and, for the sake of comparison, also in terms of quadratic residuals; both geometric and electromagnetic design variables have been considered. The numerical solution is achieved by coupling a finite difference procedure for the calculation of the electromagnetic and thermal fields to a deterministic strategy of minimization based on modified Flctcher and Reeves method. © 1998 IEEE.

A theoretical study of the A2 ∑+-X2∏ system of the SiP molecule

The A2∑+ and Z2∏ electronic states of the SiP species have been investigated theoretically at a very high level of correlation treatment (CASSCF/MRSDCI). Very accurate potential energy curves are presented for both states, as well as the associated spectroscopic constants as derived from the vib-rotational energy levels determined by means of the numerical solution of the radial Schrödinger equation. Electronic transition moment function, oscillator strengths, Einstein coefficients for spontaneous emission, and Franck-Condon factors for the A2∑+-X2∏ system have been calculated. Dipole moment functions and radiative lifetimes for both states have also been determined. Spin-orbit coupling constants are also reported. The radiative lifetimes for the A2∑+ state, taking into account the spin-orbit diagonal correction to the X2∏ state, decrease from a value of 138 ms at v′ = 0 to 0.48 ms at v′ = 8, and, for the X2∏ state, from 2.32 s at v″ = 1 to 0.59 s at v″ = 5. Vibrational and rotational transitions are expected to be relatively strong.

Study on transient ice formation of laminar flow inside externally supercooled rectangular duct

The transient process of solidification of laminar liquid flow (water) submitted to super-cooling was investigated both theoretically and experimentally. In this study an alternative analytical formulation and numerical approach were adopted resulting in the unsteady model with temperature dependent thermophysical properties in the solid region. The proposed model is based upon the fundamental equations of energy balance in the solid and liquid regions as well as across the solidification front. The basic equations and the associated boundary and initial conditions were made dimensionless by using the Landau transformation to immobilize the moving front and render the problem to a fixed plane type problem. A laminar velocity profile is admitted in the liquid domain and the resulting equations were discretized using the finite difference approach. The numerical predictions obtained were compared with the available results based on other models and concepts such as Neumann analytical model, the apparent thermal capacity model due to Bonacina and the conventional fixed grid energy model due to Goodrich. To obtain further comparisons and more validation of the model and the numerical solution, an experimental rig was constructed and instrumented permitting very well controlled experimental measurements. The numerical predictions were compared with the experimental results and the agreement was found satisfactory.

Mean-field model of interaction between bright vortex solitons in Bose-Einstein condensates

Using the explicit numerical solution of the axially symmetric Gross-Pitaevskii equation we study the dynamics of interaction among vortex solitons in a rotating matter-wave bright soliton train in a radially trapped and axially free Bose-Einstein condensate to understand certain features of the experiment by Strecker et al (2002 Nature 417 150). In a soliton train, solitons of opposite phase (phase δ = π) repel and stay apart without changing shape; solitons with δ = 0 attract, interact and coalesce, but eventually come out; solitons with a general δ usually repel but interact inelastically by exchanging matter. We study this and suggest future experiments with vortex solitons.

Chaotic thermalization in classical gauge theories

We explore the idea that chaos concepts might be useful for understanding the thermalization in gauge theories. The SU(2) Higgs model is discussed as a prototype of system with gauge fields coupled to matter fields. Through the numerical solution of the equations of motion, we are able to characterize chaotic behavior via the corresponding Lyapunov exponent. Then it is demonstrated that the system's approach to equilibrium can be understood through direct application of the principles of Statistical Mechanics. © 2013 AIP Publishing LLC.