The Central Correlations of Hypercharge, Isospin, Colour and Chirality in the Standard Model

The correlation of the fractionally represented hypercharge group with the isospin and colour group in the standard model determines as faithfully represented internal group the quotient group {\U(1)\x\SU(2)\x\SU(3)\over\Z_2\x\Z_3}. The discrete cyclic central abelian-nonabelian internal correlation involved is considered with respect to its consequences for the representations by the standard model fields, the electroweak mixing angle and the symmetry breakdown. There exists a further discrete $\Z_2$-correlation between chirality and Lorentz properties and also a continuous \U(1)-external-internal one between hyperisospin and chirality.Comment: 18 pages, latex, macros include

Study for the Revision of the plaice box - Draft Final Report

This project has attempted to evaluate the effectiveness of the fisheries management measure known as the “Plaice Box” (PB) for the conservation of plaice and other species of marine organisms in the south-eastern North Sea. The study provides an inventory of existing information and collects new material on the effects of the PB on the conservation of plaice and the impact of the PB on various components of the commercial fishing fleets. Based on an analysis of key processes that affect the impact of the PB, modifications will be explored to improve the positive effect on the conservation of plaice and other species of marine organisms, including catches and bycatches of other marketable fish. An economic assessment of the consequences of those modifications, in terms of their cost-effectiveness, and implications for profitability of the activity is presented. Finally, the data requirements for future evaluations of the effects of the PB on conservation is discussed

Biodiversity and species-environment relationships of the demersal fish assemblage at the Great Meteor Seamount (subtropical NE Atlantic), sampled by different trawls

Quantitative data collected with different bottom trawls at the Great Meteor Seamount (subtropical NE Atlantic, 30°N; 28.5°W) in 1967, 1970 and 1998 are compared. Bootstrap estimates of total catch per unit effort increased from 6.96 and 10.8 ind. m–1 h–1 in 1967 and 1970, respectively, to 583.98 ind. m–1 h–1 in 1998. Gear effects and an effect of gear over time accounted for 47.1% and 20% of species variability. Further significant factors were time of day and habitat, while season was not significant. A total of 43 species was collected. Including supplementary species information, a grand total of 46 species was found associated with the Great Meteor Seamount. Diversity was higher in 1967 and 1970 (Shannon's diversity: H′=2.5 and 1.6) than in 1998 (H′=0.9). Species–environment relationships are discussed in terms of a sound-scattering layer–interception hypothesis, i.e. utilisation of prey from a diurnally moving sound-scattering layer for the bentho-pelagic community. This is probably augmented by concentration effects in a circular current around the seamount (Taylor-column). Long-term changes are discussed with respect to a decrease in biodiversity due to considerable increases in Macroramphosus scolopax and Capros aper. In 1998, the increase of abundance of Trachurus picturatus and the respective decreases for genuine benthic species were likely to have been caused by a change of gear

Modelling gravity on a hyper-cubic lattice

We present an elegant and simple dynamical model of symmetric, non-degenerate (n x n) matrices of fixed signature defined on a n-dimensional hyper-cubic lattice with nearest-neighbor interactions. We show how this model is related to General Relativity, and discuss multiple ways in which it can be useful for studying gravity, both classical and quantum. In particular, we show that the dynamics of the model when all matrices are close to the identity corresponds exactly to a finite-difference discretization of weak-field gravity in harmonic gauge. We also show that the action which defines the full dynamics of the model corresponds to the Einstein-Hilbert action to leading order in the lattice spacing, and use this observation to define a lattice analogue of the Ricci scalar and Einstein tensor. Finally, we perform a mean-field analysis of the statistical mechanics of this model.Comment: 5 page

Finite difference schemes for second order systems describing black holes

In the harmonic description of general relativity, the principle part of Einstein's equations reduces to 10 curved space wave equations for the componenets of the space-time metric. We present theorems regarding the stability of several evolution-boundary algorithms for such equations when treated in second order differential form. The theorems apply to a model black hole space-time consisting of a spacelike inner boundary excising the singularity, a timelike outer boundary and a horizon in between. These algorithms are implemented as stable, convergent numerical codes and their performance is compared in a 2-dimensional excision problem.Comment: 19 pages, 9 figure

Pseudospectral Calculation of the Wavefunction of Helium and the Negative Hydrogen Ion

We study the numerical solution of the non-relativistic Schr\"{o}dinger equation for two-electron atoms in ground and excited S-states using pseudospectral (PS) methods of calculation. The calculation achieves convergence rates for the energy, Cauchy error in the wavefunction, and variance in local energy that are exponentially fast for all practical purposes. The method requires three separate subdomains to handle the wavefunction's cusp-like behavior near the two-particle coalescences. The use of three subdomains is essential to maintaining exponential convergence. A comparison of several different treatments of the cusps and the semi-infinite domain suggest that the simplest prescription is sufficient. For many purposes it proves unnecessary to handle the logarithmic behavior near the three-particle coalescence in a special way. The PS method has many virtues: no explicit assumptions need be made about the asymptotic behavior of the wavefunction near cusps or at large distances, the local energy is exactly equal to the calculated global energy at all collocation points, local errors go down everywhere with increasing resolution, the effective basis using Chebyshev polynomials is complete and simple, and the method is easily extensible to other bound states. This study serves as a proof-of-principle of the method for more general two- and possibly three-electron applications.Comment: 23 pages, 20 figures, 2 tables, Final refereed version - Some references added, some stylistic changes, added paragraph to matrix methods section, added last sentence to abstract

First-order symmetrizable hyperbolic formulations of Einstein's equations including lapse and shift as dynamical fields

First-order hyperbolic systems are promising as a basis for numerical integration of Einstein's equations. In previous work, the lapse and shift have typically not been considered part of the hyperbolic system and have been prescribed independently. This can be expensive computationally, especially if the prescription involves solving elliptic equations. Therefore, including the lapse and shift in the hyperbolic system could be advantageous for numerical work. In this paper, two first-order symmetrizable hyperbolic systems are presented that include the lapse and shift as dynamical fields and have only physical characteristic speeds.Comment: 11 page

On 2D2D quantum gravity coupled to a \s-model

This contribution is a review of the method of isomonodromic quantization of dimensionally reduced gravity. Our approach is based on the complete separation of variables in the isomonodromic sector of the model and the related ``two-time" Hamiltonian structure. This allows an exact quantization in the spirit of the scheme developed in the framework of integrable systems. Possible ways to identify a quantum state corresponding to the Kerr black hole are discussed. In addition, we briefly describe the relation of this model with Chern Simons theory.Comment: 9 pages, LaTeX style espcrc2, to appear in Proceedings of 29th International Symposium Ahrenshoop, Buckow, 199

Exact Solution of Photon Equation in Stationary G\"{o}del-type and G\"{o}del Space-Times

In this work the photon equation (massless Duffin-Kemmer-Petiau equation) is written expilicitly for general type of stationary G\"{o}del space-times and is solved exactly for G\"{o}del-type and G\"{o}del space-times. Harmonic oscillator behaviour of the solutions is discussed and energy spectrum of photon is obtained.Comment: 9 pages,RevTeX, no figure, revised for publicatio