Analysis and convergence of the MAC scheme. Part 1: The linear problem

The MAC discretization of fluid flow is analyzed for the stationary Stokes equations. It is proved that the discrete approximations do in fact converge to the exact solutions of the flow equations. Estimates using mesh dependent norms analogous to the standard H(sup 1) and L(sup 2) norms are given for the velocity and pressure, respectively

Construction of higher order accurate vortex and particle methods

The standard point vortex method has recently been shown to be of high order of accuracy for problems on the whole plane, when using a uniform initial subdivision for assigning the vorticity to the points. If obstacles are present in the flow, this high order deteriorates to first or second order. New vortex methods are introduced which are of arbitrary accuracy (under regularity assumptions) regardless of the presence of bodies and the uniformity of the initial subdivision

Iterative methods for elliptic finite element equations on general meshes

Iterative methods for arbitrary mesh discretizations of elliptic partial differential equations are surveyed. The methods discussed are preconditioned conjugate gradients, algebraic multigrid, deflated conjugate gradients, an element-by-element techniques, and domain decomposition. Computational results are included

Theory and computation of electromagnetic transition matrix elements in the continuous spectrum of atoms

The present study examines the mathematical properties of the free-free ( f-f) matrix elements of the full electric field operator, of the multipolar Hamiltonian. Special methods are developed and applied for their computation, for the general case where the scattering wavefunctions are calculated numerically in the potential of the term-dependent (N-1) electron core, and are energy-normalized. It is found that, on the energy axis, the f-f matrix elements of the full operator have singularities of first order in the case of equal photoelectron energies. The numerical applications are for f-f transitions in Hydrogen and Neon, obeying electric dipole and quadrupole selection rules. In the limit of zero photon wave-number, the full operator reduces to the length form of the electric dipole approximation (EDA). It is found that the results for the EDA agree with those of the full operator, with the exception of a photon wave-number region about the singularity.Comment: 39 pages, 11 figure

On substructuring algorithms and solution techniques for the numerical approximation of partial differential equations

Substructuring methods are in common use in mechanics problems where typically the associated linear systems of algebraic equations are positive definite. Here these methods are extended to problems which lead to nonpositive definite, nonsymmetric matrices. The extension is based on an algorithm which carries out the block Gauss elimination procedure without the need for interchanges even when a pivot matrix is singular. Examples are provided wherein the method is used in connection with finite element solutions of the stationary Stokes equations and the Helmholtz equation, and dual methods for second-order elliptic equations

New discretization and solution techniques for incompressible viscous flow problems

Several topics arising in the finite element solution of the incompressible Navier-Stokes equations are considered. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. The role of artificial viscosity in viscous flow calculations is studied, emphasizing work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some modifications are mentioned

Cost of regulation and impact of EU membership on policy enforcement

Recent public debate on the costs and benefits of EU membership has focused more on the costs and less on the benefits. This paper explores the benefits from improved regulatory or policy implementation and enforcement. If actual regulatory enforcement differs from the socially optimal level, membership of a regional bloc that strengthens accountability mechanisms can improve the quality of implemented regulation. However, if the regional bloc tends to over-regulate, the overall increase in the regulatory burden, together with strengthened accountability, will move a country farther away from its socially optimal state. Membership of the EU is beneficial for countries with weak enforcement institutions, but it may worsen the welfare of countries with strong regulatory institutions. Infringement statistics indicate that no member state of the EU has a perfect record in implementation and enforcement

Synoptic and dynamic characteristics of selected deep depressions over Cyprus

International audienceIn this study, the spatial and temporal distributions of dynamic and synoptic characteristics of a selection of 32 deep baroclinic depressions have been investigated. The study covers the cold period months of November till March, in the period from 1 November 1986 to 31 March 2003. For the needs of the study, several synoptic characteristics of these depressions have been extracted. Also, several dynamic characteristics during the evolution of the depressions were studied: relative vorticity, divergence, vertical motion and a static stability parameter. The results are presented in the form of isobaric distributions over, three tropospheric isobaric levels, namely the lower 850 hPa, the middle 500 hPa and the upper 300 hPa

Transoral laser surgery for laryngeal carcinoma: has Steiner achieved a genuine paradigm shift in oncological surgery?

Transoral laser microsurgery applies to the piecemeal removal of malignant tumours of the upper aerodigestive tract using the CO2 laser under the operating microscope. This method of surgery is being increasingly popularised as a single modality treatment of choice in early laryngeal cancers (T1 and T2) and occasionally in the more advanced forms of the disease (T3 and T4), predomi- nantly within the supraglottis. Thomas Kuhn, the American physicist turned philosopher and historian of science, coined the phrase ‘paradigm shift’ in his groundbreaking book The Structure of Scientific Revolutions. He argued that the arrival of the new and often incompatible idea forms the core of a new paradigm, the birth of an entirely new way of thinking. This article discusses whether Steiner and col- leagues truly brought about a paradigm shift in oncological surgery. By rejecting the principle of en block resection and by replacing it with the belief that not only is it oncologically safe to cut through the substance of the tumour but in doing so one can actually achieve better results, Steiner was able to truly revolutionise the man- agement of laryngeal cancer. Even though within this article the repercussions of his insight are limited to the upper aerodigestive tract oncological surgery, his willingness to question other peoples’ dogma makes his contribution truly a genuine paradigm shift