A study of a numerical solution of the steady two dimensions Navier-Stokes equations in a constricted channel problem by a compact fourth order method

We present a numerical solution for the steady 2D Navier-Stokes equations using a fourth order compact-type method. The geometry of the problem is a constricted symmetric channel, where the boundary can be varied, via a parameter, from a smooth constriction to one possessing a very sharp but smooth corner allowing us to analyse the behaviour of the errors when the solution is smooth or near singular. The set of non-linear equations is solved by the Newton method. Results have been obtained for Reynolds number up to 500. Estimates of the errors incurred have shown that the results are accurate and better than those of the corresponding second order method. (C) 2002 Elsevier B.V. All rights reserved.

A General Solution of the Fokker-Planck Equation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Numerical solution of the two-dimensional Gross-Pitaevskii equation for trapped interacting atoms

We present a numerical scheme for solving the time-independent nonlinear Gross-Pitaevskii equation in two dimensions describing the Bose-Einstein condensate of trapped interacting neutral atoms at zero temperature. The trap potential is taken to be of the harmonic-oscillator type and the interaction both attractive and repulsive. The Gross-Pitaevskii equation is numerically integrated consistent with the correct boundary conditions at the origin and in the asymptotic region. Rapid convergence is obtained in all cases studied. In the attractive case there is a limit Co the maximum number of atoms in the condensate. (C) 2000 Published by Elsevier B.V. B.V. All rights reserved.

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.

SELF-CONSISTENT SOLUTION OF THE SCHWINGER-DYSON EQUATIONS FOR THE NUCLEON AND MESON PROPAGATORS

The Schwinger-Dyson equations for the nucleon and meson propagators are solved self-consistently in an approximation that goes beyond the Hartree-Fock approximation. The traditional approach consists in solving the nucleon Schwinger-Dyson equation with bare meson propagators and bare meson-nucleon vertices; the corrections to the meson propagators are calculated using the bare nucleon propagator and bare nucleon-meson vertices. It is known that such an approximation scheme produces the appearance of ghost poles in the propagators. In this paper the coupled system of Schwinger-Dyson equations for the nucleon and the meson propagators are solved self-consistently including vertex corrections. The interplay of self-consistency and vertex corrections on the ghosts problem is investigated. It is found that the self-consistency does not affect significantly the spectral properties of the propagators. In particular, it does not affect the appearance of the ghost poles in the propagators.

Reformulation of variational inequalities on a simplex and compactification of complementarity problems

Many variational inequality problems (VIPs) can be reduced, by a compactification procedure, to a VIP on the canonical simplex. Reformulations of this problem are studied, including smooth reformulations with simple constraints and unconstrained reformulations based on the penalized Fischer-Burmeister function. It is proved that bounded level set results hold for these reformulations under quite general assumptions on the operator. Therefore, it can be guaranteed that minimization algorithms generate bounded sequences and, under monotonicity conditions, these algorithms necessarily nd solutions of the original problem. Some numerical experiments are presented.

A new approach to the solution of the optimal power flow problem based on the modified Newton's method associated to an augmented Lagrangian function

This paper presents a new algorithm for optimal power flow problem. The algorithm is based on Newton's method which it works with an Augmented Lagrangian function associated with the original problem. The function aggregates all the equality and inequality constraints and is solved using the modified-Newton method. The test results have shown the effectiveness of the approach using the IEEE 30 and 638 bus systems.

Crystallization, preliminary X-ray analysis and molecular-replacement solution of the carboxy form of haemoglobin I from the fish Brycon cephalus

Haemoglobin, the 'honorary enzyme' [Brunori (1999), Trends Biochem. Sci. 24, 158-161], constitutes a prime prototype for allosteric models. Here, the crystallization and preliminary X-ray analysis of haemoglobin I from the South American fish Brycon cephalus are reported. X-ray diffraction data have been collected to 2.5 Angstrom resolution using synchrotron radiation (LNLS). Crystals were determined to belong to the space group P6(1)22 and preliminary structural analysis revealed the presence of one dimer (alpha beta) in the asymmetric unit. The structure was determined using standard molecular-replacement techniques.

Bound state solution of the grassmannian nonlinear sigma model with fermions

We construct the S-matrix for bound state (gauge-invariant) scattering for nonlinear sigma models defined on the manifold SU(n) S(U(p)⊗U(n-p)) with fermions. It is not possible to compute gauge non-singlet matrix elements. In the present language, constraints from higher conservation laws determine the bound state solution. An alternative derivation is also presented. © 1988.

Phase analysis of seeded and doped PbMg1/3Nb2/3O3 prepared by organic solution of citrates

PbMg1/3Nb2/3O3 (PMN) prepared by organic solution of citrates was analyzed by the Rietveld method to determine the influence of seeds and dopants on the perovskite and pyrochlore phase formation. It was observed that pyrochlore phase formation increases with an increase in calcination time when no additives are included during the preparation. It was also observed that a greater amount of perovskite phase appeared in doped or seeded samples. The fraction of perovskite phase increased from 88 mol % in pure sample to ∼95 mol % in doped and seeded samples calcined at 800°C for 1 h. It is clear that the addition of dopants or seeds during PMN preparation can enhance the formation of perovskite phase.

Substitution-newton-Raphson method for the solution of electric network equations

The power flow problem, in transmission networks, has been well solved, for most cases, using Newton-Raphson method (NR) and its decoupled versions. Generally speaking, the solution of a non-linear system of equations refers to two methods: NR and Successive Substitution. The proposal of this paper is to evaluate the potential of the Substitution-Newton-Raphson Method (SNR), which combines both methods, on the solution of the power flow problem. Simulations were performed using a two-bus test network in order to observe the characteristics of these methods. It was verified that the NR is faster than SNR, in terms of convergence, considering non-stressed scenarios. For those cases where the power flow in the network is closed to the limits (stressed system), the SNR converges faster. This paper presents the power flow formulation of the SNR and describes its potential for its application in special cases such as stressed scenarios. © 2006 IEEE.