Bulk and boundary g2g_2 factorized S-matrices

We investigate the $g_2$-invariant bulk (1+1D, factorized) $S$-matrix constructed by Ogievetsky, using the bootstrap on the three-point coupling of the vector multiplet to constrain its CDD ambiguity. We then construct the corresponding boundary $S$-matrix, demonstrating it to be consistent with $Y(g_2,a_1\times a_1)$ symmetry.Comment: 7 page

Diffraction-limited CCD imaging with faint reference stars

By selecting short exposure images taken using a CCD with negligible readout noise we obtained essentially diffraction-limited 810 nm images of faint objects using nearby reference stars brighter than I=16 at a 2.56 m telescope. The FWHM of the isoplanatic patch for the technique is found to be 50 arcseconds, providing ~20% sky coverage around suitable reference stars.Comment: 4 page letter accepted for publication in Astronomy and Astrophysic

Consistent expressions for the free-surface Green function in finite water depth

This is the final version. Available on open access from Elsevier via the DOI in this recordFast and accurate computation of the free-surface Green function is of key importance for the numerical solution of linear and second-order wave-structure interaction problems in three dimensions. Integral and series expressions for the Green function are derived for which the limiting values for zero and infinite frequency are consistent with the zero and infinite frequency Green function defined in terms of infinite series of Rankine image sources. The integral expressions presented here have the advantage that they are slowly varying with the non-dimensional wave frequency, making them more efficient to approximate compared with previous expressions.Engineering and Physical Sciences Research Council (EPSRC

Towards gravitationally assisted negative refraction of light by vacuum

Propagation of electromagnetic plane waves in some directions in gravitationally affected vacuum over limited ranges of spacetime can be such that the phase velocity vector casts a negative projection on the time-averaged Poynting vector. This conclusion suggests, inter alia, gravitationally assisted negative refraction by vacuum.Comment: 6 page

Error correcting code using tree-like multilayer perceptron

An error correcting code using a tree-like multilayer perceptron is proposed. An original message \mbi{s}^0 is encoded into a codeword \boldmath{y}_0 using a tree-like committee machine (committee tree) or a tree-like parity machine (parity tree). Based on these architectures, several schemes featuring monotonic or non-monotonic units are introduced. The codeword \mbi{y}_0 is then transmitted via a Binary Asymmetric Channel (BAC) where it is corrupted by noise. The analytical performance of these schemes is investigated using the replica method of statistical mechanics. Under some specific conditions, some of the proposed schemes are shown to saturate the Shannon bound at the infinite codeword length limit. The influence of the monotonicity of the units on the performance is also discussed.Comment: 23 pages, 3 figures, Content has been extended and revise

Confined compression of collagen hydrogels

Reconstituted collagen hydrogels are often used for in vitro studies of cell-matrix interaction and as scaffolds for tissue engineering. Understanding the mechanical and transport behaviours of collagen hydrogels is therefore extremely important, albeit difficult due to their very high water content (typically > 99.5%). In the present study the mechanical behaviour of collagen hydrogels in confined compression was investigated using biphasic theory (J. Biomech. Eng. 102 (1980) 73), to ascertain whether the technique is sufficiently sensitive to determine differences in the characteristics of hydrogels of between 0.2% and 0.4% collagen. Peak stress, equilibrium stress, aggregate modulus and hydraulic permeability of the hydrogels exhibited sensitivity to collagen content, demonstrating that the technique is clearly able to discriminate between hydrogels with small differences in collagen content and may also be sensitive to factors that affect matrix remodelling. The results also offer additional insight into the deformation-dependent permeability of collagen hydrogels. This study suggests that confined compression, together with biphasic theory, is a suitable technique for assessing the mechanical properties of collagen hydrogels

Hybrid Lattice Boltzmann - Molecular Dynamics Simulations With Both Simple and Complex Fluids

The behaviour and properties of colloidal suspensions strongly depend on the interactions arising between the immersed colloidal particles and the solvent. However, modelling such interactions is not at all straightforward; the larger time and length scales experienced by the colloidal particles compared to the solvent molecules makes all-atom molecular dynamics (MD) simulations of such systems completely impractical. Therefore a coarse-grained representation of the fluid is required, along with a method to couple this fluid to the colloidal particles. In the first part of this thesis, we propose a new method for coupling both point and composite MD particles to an isotropic lattice-Boltzmann fluid. This coupling is implemented through the use of conservative forces, calculated by assuming elastic collisions between the particles and the fluid. With the implementation of a thermal lattice-Boltzmann method, the fluid acts as a heat bath for the MD particles without requiring external Langevin noise. This method has been implemented into the open source molecular dynamics package, LAMMPS, providing an efficient technique for explicitly including hydrodynamic interactions in MD simulations. If a liquid crystal (LC) is used as a solvent instead of an isotropic fluid, anisotropic forces develop among the immersed colloidal particles even in the absence of flow. These forces arise due to a preferred orientation of the LC molecules on the colloidal surface, leading to the formation of topological defects in the bulk LC. A thorough understanding of the resulting forces is important, as their anisotropic nature could potentially be used to manufacture non-close packed photonic colloidal crystals. In the second part of this thesis, we use a lattice-Boltzmann LC algorithm to investigate the interactions arising among colloidal particles in a LC. Using a cholesteric LC, we present results for a defect bonded particle chain, and a diamond colloidal crystal. In addition, as the defects and distortions generated in the LC result in a non-uniform pressure exerted on the particle surface, we also investigate the behaviour of 2D deformable particles in a nematic, as any potential shape change could have a significant impact on the resulting interactions

Narrative tradition in early Greek oral poetry and vase-painting

Archaic Athenian vase-painting of the sixth century BC exhibits visual narrative phenomena that are very similar to the verbal narrative patterns of traditional, orally composed poetry: in the poetry these are the familiar formulaic phrases and themes analyzed by Milman Parry and the ensuing train of oral theorists; in the art they take the form of repetitious iconography and recurrent compositional structures.1 In the vase-paintings as in the poems the same question arises: do the repetitions have an aesthetic or significatory function in the narrative context, or are they rather incidental and even impedimental to the process of reception? In his recent work on oral traditions, John Miles Foley (1991) has recognized the need to develop a new theory of reception for oral and oral-derived poetry, one that takes into specific account the peculiar characteristics of oral composition. It will be argued that this theory can usefully be applied also to the vase-paintings

VISIONS OF TRAGEDY TRAGIC STRUCTURING IN ATTIC BLACK-FIGURE REPRESENTATIONS OF THE STORY OF TROILOS

The quest for the origins of tragedy has a long history, and its emphasis has tended to be on form rather than concept, with good reason since for the ancient writers the stem .,pa-y- conveyed a primary denotation of dramatic performance. Yet Aristotle in the Poetics is far more concerned with the concept than the form. In discussing the nature of tragedy, he is at pains to describe the best kind of tragic figure and the best kind of plot-structure in general terms

CLASSICS IN SOUTH AFRICA-A WAY FORWARD

Sometimes there is a certain rightness in the timing of things. When it was agreed two years ago that "Change and Continuity in the Ancient World" would be the theme for this conference, it was perceived as appropriate to the millennium; we did not then foresee that it would, with a slight rewording, become something of a rallying cry: "Change, and Continuity of the Ancient World." Then, two years ago also, we accepted the offer of the University of the Western Cape as a hosting venue. It seemed wryly appropriate at the time, as a campus that had long been vigorously associated with the desire for change rather than continuity of the older order. I wonder how many of you have now observed the University's motto: respice - prospice: Look back, look forward. This is highly appropriate to our chosen theme, and appropriate too to the situation in which we find ourselves. It is perhaps most appropriate of all to the timing of this conference and of our crisis, at the end of a millennium when indeed everyone feels a need to look back in assessment of what has passed, to look forward and to try to plan for the future