Segmented multigrid domain decomposition procedure for incompressible viscous flows

The application of grid stretching or grid adaptation is generally required in order to optimize the distribution of nodal points for fluid-dynamic simulation. This is necessitated by the presence of disjoint high gradient zones, that represent boundary or free shear layers, reversed flow or vortical flow regions, triple deck structures, etc. A domain decomposition method can be used in conjunction with an adaptive multigrid algorithm to provide an effective methodology for the development of optimal grids. In the present study, the Navier-Stokes (NS) equations are approximated with a reduced Navier-Stokes (RNS) system, that represents the lowest-order terms in an asymptotic Re expansion. This system allows for simplified boundary conditions, more generality in the location of the outflow boundary, and ensures mass conservation in all subdomain grid interfaces, as well as at the outflow boundary. The higher-order (NS) diffusion terms are included through a deferred corrector, in selected subdomains, when necessary. Adaptivity in the direction of refinement is achieved by grid splitting or domain decomposition in each level of the multigrid procedure. Normalized truncation error estimates of key derivatives are used to determine the boundaries of these subdomains. The refinement is optimized in two co-ordinate directions independently. Multidirectional adaptivity eliminates the need for grid stretching so that uniform grids are specified in each subdomain. The overall grid consists of multiple domains with different meshes and is, therefore, heavily graded. Results and computational efficiency are discussed for the laminar flow over a finite length plate and for the laminar internal flow in a backward-facing step channel.     

Upwind schemes and boundary conditions with applications to Euler equations in general geometries

A unified treatment of several upwind shock capturing algorithms is presented. Each algorithm has a Riemann initial value problem as its basis. The treatment of boundaries involves solving the associated Riemann initial-boundary value problem. The first author's algorithm, applied to multidimensional Euler equations in general geometries, is then presented. Its worth is verified by various calculations, which include Mach 8 supersonic flow past a circular cylinder.     

A dynamic nuclear magnetic resonance study of 1,3-intramolecular shifts in pentacarbonyl-chromium(O) and -tungsten(O) complexes of β-2,4,6-trimethyl-1,3,5-trithian, 1,3,5-trithian, 1,3-dithian and 2-methyl-1,3-dithian: the x-ray crystal structure of [W(CO)5{SCH(Me)SCH(Me)SCH(Me)}]

Variable temperature ¹H NMR spectroscopy has been used in the study of 1,3-intramolecular shifts of the M(CO)₅ moiety in complexes of the general formula [M(CO)₅L], (M = Cr or w), L = $\text{SCH}{}_2\text{SCH}{}_2\text{SC}$H₂, $\text{SCH}{}_2\text{SCH}{}_2\text{CH}{}_2\text{C}$H₂ and $\text{SCH(Me)SCH}{}_2\text{CH}{}_2\text{C}$H₂. For the 1,3,5-trithian complexes precise energy barriers for the process have been obtained by detailed computer simulation of the static and dynamic spectra. Our results suggest that the magnitude of ΔG^≠ (298.15 K) for the 1,3-shift is largely dependent upon the skeletal flexibility of the ligand system. In this context we have investigated the X-ray crystal structure of the highly substituted trithian complex [W(CO)₅{β-$\text{SCH(Me)SCH(Me)SC}$H(Me)}].     

The early iron age of the Mössbauer era

The demonstration that the 14.4 keV level of⁵⁷Fe was an ideal Mössbauer example produced a veritable explosion in the discoveries of new physical phenomena. Among the important features of⁵⁷Fe are its ready availability and ease of preparation, its magnetic properties in many environments, the high intensity of its Mössbauer spectrum even at elevated temperatures, the relative sharpness of the Mössbauer lines, and the possibility of obtaining the resolution provided by this sharpness by relatively simple techniques. This paper hopes to capture some of the excitement and enthusiasm generated by the discoveries and demonstrations of the nuclear Zeeman effect, together with its polarization properties, the nuclear isomer shift, the quadrupole splitting, the temperature effect, temporal effects, nuclear hyperfine fields, transferred magnetism, the gravitational red shift, and many other new or newly elucidated phenomena.     

General boundary conditions for the wave equation around non-homogenous scatterers

To solve the wave equation inside a region that contains an inhomogenous dielectric material of arbitrary shape under the influence of an incoming wave, we establish a generalized boundary condition. The solutions inside a finite region resulting form a given incoming wave from the outside, are determined by a linear relation between the normal gradient and the function values on the boundary. This boundary condition is non-local and we show how it can be used in conjunction with the variational principle applied to an open system.     

Light-cone superspace and the ultraviolet finiteness of the N=4 model

Superspace in the light-cone frame takes a simple form. No auxiliary fields are necessary, and application to extended supersymmetries is straightforward. It is shown that the N=4 model, in a certain form of the light-cone gauge, is completely free of ultraviolet divergences in any order of perturbation theory. It follows that the β-function vanishes in any gauge, to all orders of perturbation theory. Our method differs from the conventional method in that we use only half the number of θ's as there are supersymmetry operators. All fields are unconstrained and independent of the $\text{θ}\text{'}\text{s}$.     

New formulation of quantum mechanics

A reformulation of the mathematical foundations of quantum mechanics is presented. This new framework is based on the concepts of measurement, generalized action, and a unique universal influence function. The main axiom is that the probability of a measurement outcome is the sum (or integral) of the influences between pairs of alternatives that result in the outcome when the measurement is executed. The framework provides answers to various puzzling questions of traditional quantum mechanics. Moreover, it gives a realistic model that extends the usual quantum mechanical formalism.