STUDY ON THE FORMATIONAL MECHANISM OF THE NORTHERN YELLOW (HUANGHAI) SEA COLD WATER MASS .2. DISCUSSION ON THE SOLUTION OF THE MODEL

The theoretical solution of the model of the Northern Yellow (Huanghai) Sea Cold Water Mass (NYSCWM) reveals that the NYSCWM is mainly formed through the continuous temperature increase of the overwintered water body above the Northern Yellow Sea Depression (NYSD) after spring when heat is continuously conducted from the sea surface to the deeper layer. In the NYSCWM's growing period, (June-July), nonlinear vertical convection and advection effects continuously increase, and are gradually balanced by the heat diffusion effect as the temperature increases from the surface to the bottom, which leads to the formation of an intensive thermocline and lateral front. Meanwhile, the three-dimensional circulation correspondingly occurs. In the NYSCWM's entire growing period, the horizontal circulation is always in the cyclonic motion, while the vertical circulation passes through a transition from a period with the cold centre as downwelling to a period with the cold centre as upwelling.

A Solution of the Figure-ground Problem for Biological Vision

A neural network model of 3-D visual perception and figure-ground separation by visual cortex is introduced. The theory provides a unified explanation of how a 2-D image may generate a 3-D percept; how figures pop-out from cluttered backgrounds; how spatially sparse disparity cues can generate continuous surface representations at different perceived depths; how representations of occluded regions can be completed and recognized without usually being seen; how occluded regions can sometimes be seen during percepts of transparency; how high spatial frequency parts of an image may appear closer than low spatial frequency parts; how sharp targets are detected better against a figure and blurred targets are detector better against a background; how low spatial frequency parts of an image may be fused while high spatial frequency parts are rivalrous; how sparse blue cones can generate vivid blue surface percepts; how 3-D neon color spreading, visual phantoms, and tissue contrast percepts are generated; how conjunctions of color-and-depth may rapidly pop-out during visual search. These explanations arise derived from an ecological analysis of how monocularly viewed parts of an image inherit the appropriate depth from contiguous binocularly viewed parts, as during DaVinci stereopsis. The model predicts the functional role and ordering of multiple interactions within and between the two parvocellular processing streams that join LGN to prestriate area V4. Interactions from cells representing larger scales and disparities to cells representing smaller scales and disparities are of particular importance.

Discretization and solution of the inhomogeneous Bogoliubov-de Gennes equations

In the presence of inhomogeneities, defects and currents, the equations describing a Bose-condensed ensemble of alkali atoms have to be solved numerically. By combining both linear and nonlinear equations within a Discrete Variable Representation framework, we describe a computational scheme for the solution of the coupled Bogoliubov-de Gennes (BdG) and nonlinear Schrodinger (NLS) equations for fields in a 3D spheroidal potential. We use the method to calculate the collective excitation spectrum and quasiparticle mode densities for excitations of a Bose condensed gas in a spheroidal trap. The method is compared against finite-difference and spectral methods, and we find the DVR computational scheme to be superior in accuracy and efficiency for the cases we consider. (C) 2004 Elsevier B.V. All rights reserved.

A correction to the analytical solution of the mixed-mode bending (MMB) problem

This paper addresses the analytical solution of the mixed-mode bending (MMB) problem. The first published solutions used a load separation in pure mode I and mode II and were applied for a crack length less than the beam half-span, a <= L. In later publications, the same mode separation was used in deriving the analytical solution for crack lengths bigger than the beam half-span, a > L. In this paper it is shown that this mode separation is not valid when a > L and in some cases may lead to very erroneous results. The correct mode separation and the corresponding analytical solutions, when a > L, are presented. Results, of force vs. displacement and force vs. crack length graphs, obtained using the existing formulation and the corrected formulation are compared. A finite element solution, which does not use mode separation, is also presented

‘The “English Disease” is to Look for a “Solution of the Irish Problem”’: British Constitutional Policy in Northern Ireland after Sunningdale 1974–1976

This article reconstructs British constitutional policy in Northern Ireland after power-sharing collapsed in May 1974. Over the following two years, the British government publicly emphasised that Northern Ireland would decide its own future, but ministers secretly considered a range of options including withdrawal, integration and Dominion status. These discussions have been fundamentally misunderstood by previous authors, and this article shows that Harold Wilson did not seriously advocate withdrawal nor was policy as inconsistent as argued elsewhere. An historical approach, drawing from recently released archival material, shows that consociationalists such as Brendan O'Leary and Michael Kerr have neglected the proper context of government policy because of their commitment to a particular form of government, failing to recognise the constraints under which ministers operated. The British government remained committed to an internal devolved settlement including both communities but was unable to impose one.

On the numerical solution of the 2d wave equation with compact fdtd schemes

This paper discusses compact-stencil finite difference time domain (FDTD) schemes for approximating the 2D wave equation in the context of digital audio. Stability, accuracy, and efficiency are investigated and new ways of viewing and interpreting the results are discussed. It is shown that if a tight accuracy constraint is applied, implicit schemes outperform explicit schemes. The paper also discusses the relevance to digital waveguide mesh modelling, and highlights the optimally efficient explicit scheme.

Solution of the Hartree-Fock equations for atoms and diatomic molecules with the finite element method

The finite element method (FEM) is now developed to solve two-dimensional Hartree-Fock (HF) equations for atoms and diatomic molecules. The method and its implementation is described and results are presented for the atoms Be, Ne and Ar as well as the diatomic molecules LiH, BH, N_2 and CO as examples. Total energies and eigenvalues calculated with the FEM on the HF-level are compared with results obtained with the numerical standard methods used for the solution of the one dimensional HF equations for atoms and for diatomic molecules with the traditional LCAO quantum chemical methods and the newly developed finite difference method on the HF-level. In general the accuracy increases from the LCAO - to the finite difference - to the finite element method.

Solution of the Hartree-Fock-Slater equations for diatomic molecules by the finite-element method

We present the finite-element method in its application to solving quantum-mechanical problems for diatomic molecules. Results for Hartree-Fock calculations of H_2 and Hartree-Fock-Slater calculations for molecules like N_2 and CO are presented. The accuracy achieved with fewer than 5000 grid points for the total energies of these systems is 10^-8 a.u., which is about two orders of magnitude better than the accuracy of any other available method.

Solution of the time dependent Dirac-Fock-Slater equation for many-electron collisions systems using a time window method

We present a new scheme to solve the time dependent Dirac-Fock-Slater equation (TDDFS) for heavy many electron ion-atom collision systems. Up to now time independent self consistent molecular orbitals have been used to expand the time dependent wavefunction and rather complicated potential coupling matrix elements have been neglected. Our idea is to minimize the potential coupling by using the time dependent electronic density to generate molecular basis functions. We present the first results for 16 MeV S{^16+} on Ar.

Exact Solution of the Nonlinear Dynamics of Recurrent Neural Mechanisms for Direction Selectivity

Different theoretical models have tried to investigate the feasibility of recurrent neural mechanisms for achieving direction selectivity in the visual cortex. The mathematical analysis of such models has been restricted so far to the case of purely linear networks. We present an exact analytical solution of the nonlinear dynamics of a class of direction selective recurrent neural models with threshold nonlinearity. Our mathematical analysis shows that such networks have form-stable stimulus-locked traveling pulse solutions that are appropriate for modeling the responses of direction selective cortical neurons. Our analysis shows also that the stability of such solutions can break down giving raise to a different class of solutions ("lurching activity waves") that are characterized by a specific spatio-temporal periodicity. These solutions cannot arise in models for direction selectivity with purely linear spatio-temporal filtering.

A cell by cell anisotropic adaptive mesh ALE scheme for the numerical solution of the Euler equations

In this paper a cell by cell anisotropic adaptive mesh technique is added to an existing staggered mesh Lagrange plus remap finite element ALE code for the solution of the Euler equations. The quadrilateral finite elements may be subdivided isotropically or anisotropically and a hierarchical data structure is employed. An efficient computational method is proposed, which only solves on the finest level of resolution that exists for each part of the domain with disjoint or hanging nodes being used at resolution transitions. The Lagrangian, equipotential mesh relaxation and advection (solution remapping) steps are generalised so that they may be applied on the dynamic mesh. It is shown that for a radial Sod problem and a two-dimensional Riemann problem the anisotropic adaptive mesh method runs over eight times faster.

Voronoi, Delaunay, and Block-Structured Mesh Refinement for Solution of the Shallow-Water Equations on the Sphere

Alternative meshes of the sphere and adaptive mesh refinement could be immensely beneficial for weather and climate forecasts, but it is not clear how mesh refinement should be achieved. A finite-volume model that solves the shallow-water equations on any mesh of the surface of the sphere is presented. The accuracy and cost effectiveness of four quasi-uniform meshes of the sphere are compared: a cubed sphere, reduced latitude–longitude, hexagonal–icosahedral, and triangular–icosahedral. On some standard shallow-water tests, the hexagonal–icosahedral mesh performs best and the reduced latitude–longitude mesh performs well only when the flow is aligned with the mesh. The inclusion of a refined mesh over a disc-shaped region is achieved using either gradual Delaunay, gradual Voronoi, or abrupt 2:1 block-structured refinement. These refined regions can actually degrade global accuracy, presumably because of changes in wave dispersion where the mesh is highly nonuniform. However, using gradual refinement to resolve a mountain in an otherwise coarse mesh can improve accuracy for the same cost. The model prognostic variables are height and momentum collocated at cell centers, and (to remove grid-scale oscillations of the A grid) the mass flux between cells is advanced from the old momentum using the momentum equation. Quadratic and upwind biased cubic differencing methods are used as explicit corrections to a fast implicit solution that uses linear differencing.

Projected gradient approach to the numerical solution of the SCoTLASS

The SCoTLASS problem-principal component analysis modified so that the components satisfy the Least Absolute Shrinkage and Selection Operator (LASSO) constraint-is reformulated as a dynamical system on the unit sphere. The LASSO inequality constraint is tackled by exterior penalty function. A globally convergent algorithm is developed based on the projected gradient approach. The algorithm is illustrated numerically and discussed on a well-known data set. (c) 2004 Elsevier B.V. All rights reserved.