Three-dimensional, fully adaptive simulations of phase-field fluid models

We present an efficient numerical methodology for the 31) computation of incompressible multi-phase flows described by conservative phase-field models We focus here on the case of density matched fluids with different viscosity (Model H) The numerical method employs adaptive mesh refinements (AMR) in concert with an efficient semi-implicit time discretization strategy and a linear, multi-level multigrid to relax high order stability constraints and to capture the flow`s disparate scales at optimal cost. Only five linear solvers are needed per time-step. Moreover, all the adaptive methodology is constructed from scratch to allow a systematic investigation of the key aspects of AMR in a conservative, phase-field setting. We validate the method and demonstrate its capabilities and efficacy with important examples of drop deformation, Kelvin-Helmholtz instability, and flow-induced drop coalescence (C) 2010 Elsevier Inc. All rights reserved

Thermal entanglement in a two-spin-qutrit system under a nonuniform external magnetic field

The thermal entanglement in a two-spin-qutrit system with two spins coupled by exchange interaction under a magnetic field in an arbitrary direction is investigated. Negativity, the measurement of entanglement is calculated. We find that for any temperature the evolvement of negativity is symmetric with respect to magnetic field. The behavior of negativity is presented for four different cases. The results show that for different temperature; different magnetic field give maximum entanglement. Both the parallel and antiparallel magnetic field cases are investigated qualitatively (not quantitatively) in detail, we find that the entanglement may be enhanced under an antiparallel magnetic field.

Analysis of the evanescent field coupling between a fiber and a planar waveguide using the explicit finite difference method with a nonuniform mesh (Journal Paper)

We investigate an optical waveguide system consisting of an unclad fiber core suspended at a constant distance parallel to the surface of a planar waveguide. The coupling and propagation of light in the combined system is studied using the three-dimensional explicit finite difference beam propagation method with a nonuniform mesh configuration. The power loss in the fiber and the field distribution in the waveguide are studied as a function of various parameters, such as index changes, index profile, and propagation distance, for the combined system.

Prebreakdown Current and Sparking Potential in a Nonuniform Electric Field with a Crossed Magnetic Field

Prebreakdown currents in a coaxial cylindrical geometry in nitrogen have been measured with and without a crossed magnetic field. The range of parameters used in the investigation are 2.6 ÿ p ÿ 14.5 torr, 50 ÿ (E/p) ÿ 420 V cm-1 torr-1, and 43.0 ÿ H/p ÿ 1185 Oe torr-1 (p is the pressure, E is the electric field, and H is the magnetic field). The initial photoelectric current is obtained by allowing photons produced in an auxiliary glow discharge to strike the cathode. Ions and electrons produced in the auxiliary discharge are prevented from reaching the main gap by suitable shielding. By modifying the Rice equation for back diffusion, the measured ionization current multiplication without a crossed magnetic field is compared with the multiplication predicted by the Townsend growth equation for nonuniform electric fields. It is observed that over the range of 50 Ã�¿ (E/P)max Ã�¿ 250 [(E/P)max is the value of E/p at the central electrode of the coaxial system] measured and calculated multiplication of current agree with each other. With a crossed magnetic field the prebreakdown currents have been measured and compared with the theoretically calculated currents using the equivalent pressure concept. Agreement between the calculated and measured currents is not satisfactory, and this has been attributed more to the uncertainty in the collision frequency data available than nonuniformity of the electric field. Sparking potentials have been measured with and without a crossed magnetic field.

Rossby Vortex Simulation on a Paraboloidal Coordinate System Using the Lattice Boltzmann Method

In this paper, we apply our compressible lattice Boltzmann model to a rotating parabolic coordinate system to simulate Rossby vortices emerging in a layer of shallow water flowing zonally in a rotating paraboloidal vessel. By introducing a scaling factor, nonuniform curvilinear mesh can be mapped to a flat uniform mesh and then normal lattice Boltzmann method works. Since the mass per unit area on the two-dimensional (2D) surface varies with the thickness of the water layer, the 2D flow seems to be "compressible" and our compressible model is applied. Simulation solutions meet with the experimental observations qualitatively. Based on this research, quantitative solutions and many natural phenomena simulations in planetary atmospheres, oceans, and magnetized plasma, such as the famous Jovian Giant Red Spot, the Galactic Spiral-vortex, the Gulf Stream, and the Kuroshio Current, etc,, can be expected.

The interaction of two pairs of solitary waves in a two-fluid system

This paper deals with the interaction of solitary waves in a two-fluid system which consistsof two superimposed incompressible inviscid fluids with a free surface and a horizontal rigidbottom. Under the assumption of shallow water wave, we first derive the basic equationssuitable for the model considered, a generalized form of the Boussinesq equations, then usingthe PLK method and the reductive perturbation method, obtain the second-order approximatesolution for the head-on collision between two pairs of interface and surface solitary waves,and give their maximum amplitudes during the collision and the nonuniform phase shiftsafter the collision which lead to the distortion of the wave profiles.

Asymptotic stability for time-variant systems and observability: Uniform and nonuniform criteria

This paper presents some new criteria for uniform and nonuniform asymptotic stability of equilibria for time-variant differential equations and this within a Lyapunov approach. The stability criteria are formulated in terms of certain observability conditions with the output derived from the Lyapunov function. For some classes of systems, this system theoretic interpretation proves to be fruitful since - after establishing the invariance of observability under output injection - this enables us to check the stability criteria on a simpler system. This procedure is illustrated for some classical examples.

Electronic states of a two-dimensional electron system in a lateral superlattice and a perpendicular magnetic field

The electronic state of a two-dimensional electron system (2DES) in the presence of a perpendicular uniform magnetic field and a lateral superlattice (LS) is investigated theoretically. A comparative study is made between a LS induced by a spatial electrostatic potential modulation (referred to as a PMLS) and that induced by a spatial magnetic-field modulation (referred ro asa MMLS). By utilizing a finite-temperature self-consistent Hartree-Fock approximation scheme; the dependence of the electronic state on different system parameters (e.g., the modulation period, the modulation strength, the effective electron-electron interaction strength, the averaged electron density, and the system temperature) is studied in detail. The inclusion of exchange effect is found to bring qualitative changes to the electronic state of a PMLS, leading generally to a nonuniform spin splitting, and consequently the behavior of the electronic state becomes similar to that of a MMLS. The Landau-level coupling is taken into account, and is found to introduce some interesting features not observed before. It is also found that, even in the regime of intermediate modulation strength, the density dependence of the spin splitting of energy levels, either for a PMLS or a MMLS, can be qualitatively understood within the picture of a 2DES in a perpendicular magnetic field with the modulation viewed as a perturbation. [S0163-1829(97)02248-0].

Electronic states and magnetotransport in quantum waveguides with nonuniform magnetic fields

The electronic states and magnetotransport properties of quantum waveguides (QW's) in the presence of nonuniform magnetic fields perpendicular to the QW plane are investigated theoretically. It is found that the magnetoconductance of those structures as a function of Fermi energy exhibits stepwise variation or square-wave-like oscillations, depending on the specific distributions (both in magnitude and direction) of nonuniform magnetic fields in QW's. We have investigated the dual magnetic strip structures and three magnetic strip structures. The character of the magnetotransport is closely related to the effective magnetic potential and the energy-dispersion spectrum of electron in the structures. It is found that dispersion relations seem to be combined by different sets of dispersion curves that belong to different individual magnetic subwaveguides. The magnetic effective potential leads to the coupling of states and the substantial distortion of the original dispersion curves at the interfaces in which the abrupt change of magnetic fields appears. Magnetic scattering states are created. Only in some three magnetic strip structures, these scattering states produce the dispersion relations with oscillation structures superimposed on the bulk Landau levels. It is the oscillatory behavior in dispersions that leads to the occurrence of square-wave-like modulations in conductance.

VLSI architecture for an Underwater Robot Vision System

It is well known that image processing requires a huge amount of computation, mainly at low level processing where the algorithms are dealing with a great number of data-pixel. One of the solutions to estimate motions involves detection of the correspondences between two images. For normalised correlation criteria, previous experiments shown that the result is not altered in presence of nonuniform illumination. Usually, hardware for motion estimation has been limited to simple correlation criteria. The main goal of this paper is to propose a VLSI architecture for motion estimation using a matching criteria more complex than Sum of Absolute Differences (SAD) criteria. Today hardware devices provide many facilities for the integration of more and more complex designs as well as the possibility to easily communicate with general purpose processors