Efficient discretization of pressure‐correction equations on non‐orthogonal grids

An alternative discretization of pressure‐correction equations within pressure‐correction schemes for the solution of the incompressible Navier–Stokes equations is introduced, which improves the convergence and robustness properties of such schemes for non‐orthogonal grids. As against standard approaches, where the non‐orthogonal terms usually are just neglected, the approach allows for a simplification of the pressure‐correction equation to correspond to 5‐point or 7‐point computational molecules in two or three dimensions, respectively, but still incorporates the effects of non‐orthogonality. As a result a wide range (including rather high values) of underrelaxation factors can be used, resulting in an increased overall performance of the underlying pressure‐correction schemes. Within this context, a second issue of the paper is the investigation of the accuracy to which the pressure‐correction equation should be solved in each pressure‐correction iteration. The scheme is investigated for standard test cases and, in order to show its applicability to practical flow problems, for a more complex configuration of a micro heat exchanger. Copyright © 2003 John Wiley & Sons, Ltd.     

A field-sensitivity analysis of the relativistic motion of a single electron submitted to a perpendicular magnetic field

Sensitivity of the velocity of a single electron, in the relativistic case, to a perpendicular magnetic field is evaluated by defining a parameter which becomes useful in a number of cases related to dynamical systems. In particular, the ultrarelativistic case is examined.     

The Cosmological Constant in the Framework of Gravito-Magnetodynamic Waves in Weak Gravitational Fields

Using the linearization of Einstein's equations for weak gravitational fields, a specific model of gravito-magnetofluid is elaborated. The study of wave formation and propagation in such a medium is necessarily connected to the existence of the cosmological constant.     

The fifth dimension: Theodor Kaluza's ground‐breaking idea

Theodor Kaluza (1885–1954) attracted the attention of the physical community since 1921 with his unified field theory of gravitation and electromagnetism in five dimensions. Despite Einstein's great interest in Kaluza's theory, 50 years elapsed before it contributed toward a paradigm shift in modern theoretical physics. The biography of this still unknown scientist is briefly presented along with an outline of his work in physics. A short history of the theories of unification and the dimensionality of space‐time is followed by a discussion of the significance of Kaluza's five‐dimensional unified theory in modern physics from the point of view of superstring and M‐theory.     

On the trajectory of a single electron under the action of a linearly polarized laser field

The dynamics of a single electron submitted to a linearly polarized laser field is examined in the non-relativistic case by calculating an upper bound of the position of the electron in the time domain.     

Finding Robust Solutions Using Local Search

This paper investigates how a local search metaheuristic for continuous optimisation can be adapted so that it finds broad peaks, corresponding to robust solutions. This is relevant in problems in which uncertain or noisy data is present. When using a genetic or evolutionary algorithm, it is standard practice to perturb solutions once before evaluating them, using noise from a given distribution. This approach however, is not valid when using population-less techniques like local search and other heuristics that use local search. For those algorithms to find robust solutions, each solution needs to be perturbed and evaluated several times, and these evaluations need to be combined into a measure of robustness. In this paper, we examine how many of these evaluations are needed to reliably find a robust solution. We also examine the effect of the parameters of the noise distribution. Using a simple tabu search procedure, the proposed approach is tested on several functions found in the literature. This revised version was published online in August 2006 with corrections to the Cover Date.     

Cosmological Particle Creation and Dynamical Casimir Effect

We compute particle creation for a real massive scalar field conformally coupled to a spatially closed Robertson–Walker space-time background, with time-dependent scale factor. This is a dynamical Casimir effect with moving boundaries.     

Monotone Mappings and Flows of Viscous Media

We establish solvability of the boundary-value problems describing stationary and periodic flows of viscoplastic media. In the case of stationary flows we study the question of convergence of the Galerkin method. For the problem of periodic flows we prove a version of the second Bogolyubov theorem.     

Transition energies, wavelengths, oscillator strengths and transition probabilities between 1s, 1sns and 1snp (2?n?9) states for He-like Silicon

Multiconfiguration Hartree-Fock calculations with Breit-Pauli relativistic corrections are reported for electric dipole transition (E1) energies, wavelengths, weighted oscillator strengths and transition probabilities between all of the 1s², 1sns and 1snp (2?n?9) states for He-like silicon. The results are found to compare very well with available other results except Δn=0 due to differences in the calculated excitation energies.     

Problem of the free oscillations of a capillary bridge

The free oscillations of a capillary bridge whose equilibrium shape is determined by the surface tension forces and the static gravity field are investigated. The values of 25 “lower” levels of the spectrum of natural oscillations of the capillary bridge are found for various control parameters in accordance with the experimental conditions.