Assessment of a high-order finite difference upwind scheme for the simulation of convection-diffusion problems

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

Formation of bright solitons and soliton trains in a fermion-fermion mixture by modulational instability

We employ a time- dependent mean- field- hydrodynamic model to study the generation of bright solitons in a degenerate fermion - fermion mixture in a cigar- shaped geometry using variational and numerical methods. Due to a strong Pauli- blocking repulsion among identical spin- polarized fermions at short distances there cannot be bright solitons for repulsive interspecies interactions. Employing a linear stability analysis we demonstrate the formation of stable solitons due to modulational instability of a constant-amplitude solution of the model equations for a sufficiently attractive interspecies interaction. We perform a numerical stability analysis of these solitons and also demonstrate the formation of soliton trains by jumping the effective interspecies interaction from repulsive to attractive. These fermionic solitons can be formed and studied in laboratory with present technology.

Tightly bound gap solitons in a Fermi gas

Within the framework of the mean-field hydrodynamic model of a degenerate Fermi gas ( DFG), we study, by means of numerical methods and variational approximation ( VA), the formation of fundamental gap solitons ( FGSs) in a DFG ( or in a BCS superfluid generated by weak interaction between spin- up and spin- down fermions), which is trapped in a periodic optical- lattice ( OL) potential. An effectively one- dimensional ( 1D) con. guration is considered, assuming strong transverse confinement; in parallel, a proper 1D model of the DFG ( which amounts to the known quintic equation for the Tonks- Girardeau gas in the OL) is considered too. The FGSs found in the first two bandgaps of the OL- induced spectrum ( unless they are very close to edges of the gaps) feature a ( tightly bound) shape, being essentially confined to a single cell of the OL. In the second bandgap, we also find antisymmetric tightly bound subfundamental solitons ( SFSs), with zero at the midpoint. The SFSs are also confined to a single cell of the OL, but, unlike the FGSs, they are unstable. The predicted solitons, consisting of similar to 10(4) - 10(5) atoms, can be created by available experimental techniques in the DFG of Li-6 atoms.

Bright solitons and soliton trains in a fermion-fermion mixture

We use a time-dependent dynamical mean-field-hydrodynamic model to predict and study bright solitons in a degenerate fermion-fermion mixture in a quasi-one-dimensional cigar-shaped geometry using variational and numerical methods. Due to a strong Pauli-blocking repulsion among identical spin-polarized fermions at short distances there cannot be bright solitons for repulsive interspecies fermion-fermion interactions. However, stable bright solitons can be formed for a sufficiently attractive interspecies interaction. We perform a numerical stability analysis of these solitons and also demonstrate the formation of soliton trains. These fermionic solitons can be formed and studied in laboratory with present technology.

Cubic interactions and quantum criticality in dimerized antiferromagnets

In certain Mott-insulating dimerized antiferromagnets, triplet excitations of the paramagnetic phase display both three-particle and four-particle interactions. When such a magnet undergoes a quantum phase transition into a magnetically ordered state, the three-particle interaction becomes part of the critical theory provided that the lattice ordering wave vector is zero. One microscopic example is the staggered-dimer antiferromagnet on the square lattice, for which deviations from O(3) universality have been reported in numerical studies. Using both symmetry arguments and microscopic calculations, we show that a nontrivial cubic term arises in the relevant order-parameter quantum field theory, and we assess its consequences using a combination of analytical and numerical methods. We also present finite-temperature quantum Monte Carlo data for the staggered-dimer antiferromagnet which complement recently published results. The data can be consistently interpreted in terms of critical exponents identical to that of the standard O(3) universality class, but with anomalously large corrections to scaling. We argue that the cubic interaction of critical triplons, although irrelevant in two spatial dimensions, is responsible for the leading corrections to scaling due to its small scaling dimension.

High-order upwinding and the hydraulic jump

This work is concerned with the computation of incompressible axisymmetric and fall three-dimensional free-surface flows. In particular, the circular-hydraulic jump is simulated and compared with approximate analytic solutions. However, the principal thrust of this paper is to provide a real problem as a test bed for comparing the many existing convective approximations. Their performance is compared; SMART, HLPA and VONOS emerge as acceptable upwinding methods for this problem. Copyright (C) 2002 John Wiley Sons, Ltd.

Escape and transport for an open bouncer: Stretched exponential decays

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On non-linear dynamics and an optimal control synthesis of the action potential of membranes (ideal and non-ideal cases) of the Hodgkin-Huxley (HH) mathematical model

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

Solitons in Bose-Einstein condensates trapped in a double-well potential

We investigate, analytically and numerically, families of bright solitons in a system of two linearly coupled nonlinear Schrodinger/Gross-Pitaevskii equations, describing two Bose-Einstein condensates trapped in an asymmetric double-well potential, in particular, when the scattering lengths in the condensates have arbitrary magnitudes and opposite signs. The solitons are found to exist everywhere where they are permitted by the dispersion law. Using the Vakhitov-Kolokolov criterion and numerical methods, we show that, except for small regions in the parameter space, the solitons are stable to small perturbations. Some of them feature self-trapping of almost all the atoms in the condensate with no atomic interaction or weak repulsion is coupled to the self-attractive condensate. An unusual bifurcation is found, when the soliton bifurcates from the zero solution with vanishing amplitude and width simultaneously diverging but at a finite number of atoms in the soliton. By means of numerical simulations, it is found that, depending on values of the parameters and the initial perturbation, unstable solitons either give rise to breathers or completely break down into incoherent waves (radiation). A version of the model with the self-attraction in both components, which applies to the description of dual-core fibers in nonlinear optics, is considered too, and new results are obtained for this much studied system. (C) 2003 Elsevier B.V. All rights reserved.

Gap solitons in superfluid boson-fermion mixtures

Using coupled equations for the bosonic and fermionic order parameters, we construct families of gap solitons (GSs) in a nearly one-dimensional Bose-Fermi mixture trapped in a periodic optical-lattice (OL) potential, the boson and fermion components being in the states of the Bose-Einstein condensation and Bardeen-Cooper-Schrieffer superfluid, respectively. Fundamental GSs are compact states trapped, essentially, in a single cell of the lattice. Full families of such solutions are constructed in the first two band gaps of the OL-induced spectrum, by means of variational and numerical methods, which are found to be in good agreement. The families include both intragap and intergap solitons, with the chemical potentials of the boson and fermion components falling in the same or different band gaps, respectively. Nonfundamental states, extended over several lattice cells, are constructed too. The GSs are stable against strong perturbations.

Another prefiltering algorithm for adaptive IIR filtering

An algorithm for adaptive IIR filtering that uses prefiltering structure in direct form is presented. This structure has an estimation error that is a linear function of the coefficients. This property greatly simplifies the derivation of gradient-based algorithms. Computer simulations show that the proposed structure improves convergence speed.

Associated symmetric quadrature rules

We prove a relation between two different types of symmetric quadrature rules, where one of the types is the classical symmetric interpolatory quadrature rules. Some applications of a new quadrature rule which was obtained through this relation are also considered.

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.

Synchronous machines parameters identification using load rejection test data

This work shows a computational methodology for the determination of synchronous machines parameters using load rejection test data. The quadrature axis parameters are obtained with a rejection under an arbitrary reference, reducing the present difficulties.

Solid mass falling into the reservoirs shallow water equations validity from the engineering point of view

Water waves generated by a solid mass is a complex phenomenon discussed in this paper by numerical and experimental approaches. A model based on shallow water equations with shocks (Saint Venant) has developed. It can reproduce the amplitude and the energy of the wave quite well, but because it consistently generates a hydraulic jump, it is able to reproduce the profile, in the case of high relative thickness of slide, but in the case of small relative thickness it is unable to reproduce the amplitude of the wave. As the momentum conservation is not verified during the phase of wave creation, a second technique based on discharge transfer coefficient α, is introduced at the zone of impact. Numerical tests have been performed and validated this technique from the experimental results of the wave's height obtained in a flume.