The principle of equivalence and projective structure in space-times

This paper discusses the extent to which one can determine the space-time metric from a knowledge of a certain subset of the (unparametrised) geodesics of its Levi-Civita connection, that is, from the experimental evidence of the equivalence principle. It is shown that, if the space-time concerned is known to be vacuum, then the Levi-Civita connection is uniquely determined and its associated metric is uniquely determined up to a choice of units of measurement, by the specification of these geodesics. It is further demonstrated that if two space-times share the same unparametrised geodesics and only one is assumed vacuum then their Levi-Civita connections are again equal (and so the other metric is also a vacuum metric) and the first result above is recovered.Comment: 23 pages, submitted to Classical and Quantum Gravit

On the Theory of Killing Orbits in Space-Time

This paper gives a theoretical discussion of the orbits and isotropies which arise in a space-time which admits a Lie algebra of Killing vector fields. The submanifold structure of the orbits is explored together with their induced Killing vector structure. A general decomposition of a space-time in terms of the nature and dimension of its orbits is given and the concept of stability and instability for orbits introduced. A general relation is shown linking the dimensions of the Killing algebra, the orbits and the isotropies. The well-behaved nature of "stable" orbits and the possible miss-behaviour of the "unstable" ones is pointed out and, in particular, the fact that independent Killing vector fields in space-time may not induce independent such vector fields on unstable orbits. Several examples are presented to exhibit these features. Finally, an appendix is given which revisits and attempts to clarify the well-known theorem of Fubini on the dimension of Killing orbits.Comment: Latex, 19 pages, no figur

Coulomb plus power-law potentials in quantum mechanics

We study the discrete spectrum of the Hamiltonian H = -Delta + V(r) for the Coulomb plus power-law potential V(r)=-1/r+ beta sgn(q)r^q, where beta > 0, q > -2 and q \ne 0. We show by envelope theory that the discrete eigenvalues E_{n\ell} of H may be approximated by the semiclassical expression E_{n\ell}(q) \approx min_{r>0}\{1/r^2-1/(mu r)+ sgn(q) beta(nu r)^q}. Values of mu and nu are prescribed which yield upper and lower bounds. Accurate upper bounds are also obtained by use of a trial function of the form, psi(r)= r^{\ell+1}e^{-(xr)^{q}}. We give detailed results for V(r) = -1/r + beta r^q, q = 0.5, 1, 2 for n=1, \ell=0,1,2, along with comparison eigenvalues found by direct numerical methods.Comment: 11 pages, 3 figure

Lipopolysaccharide-specific acyloxyacyl hydrolase

" An acyloxyacyl hydrolase from the human promyelocyte cell line HL-60 has been found to specifically hydrolyze fatty acids from their ester linkages to hydroxy groups of 3-hydroxyfatty acids, the latter being being bound in turn to lipopolysaccharide glycosaminyl residues. The hydrolyzed fatty acids may include dodecanoic acid, tetradecanoic acid and hexadecanoic acid. This enzyme showed a molecular weight by gel exclusion chromatography between about 50,000 Daltons and about 70,000 Daltons, and a molecular weight by polyacrylamide gel electrophoresis with sodium dodecylsulphate, using reduced molecular weight standards, of approximately 54,000 to 60,000 Daltons. Altered bacterial lipopolysaccharide substantially without fatty acids bound in ester linkage to hydroxy groups of 3-hydroxyfatty acids covalently linked to a glucosaminyl moiety of lipopolysaccharide lipid A are produced. Since the structure of the lipid A moiety is highly conserved, acyloxyacyl hydrolase may act on lipopolysaccharide of many different pathogenic bacteria (for example Salmonella, Escherichia, Hemophilus, and Neisseria). Such altered bacterial lipopolysaccharide, having toxicity reduced more than immunostimulatory activity, may be therapeutically useful: (1) as vaccines to prevent Gram-negative bacterial diseases by inducing antibodies to lipopolysaccharide O-polysaccharide or R-core antigens, (2) as antidotes to treat or prevent Gram-negative bacterial sepsis (""septic shock""), or (3) as adjuvants to enhance formation of antibodies to other antigens. the acyloxyacyl hydrolase itself may be prophylactically or therapeutically useful to detoxify endogenous lipopolysaccharide in patients with Gram-negative bacterial diseases. The enzyme may also be used to remove toxic lipopolysaccharide from therapeutic injectants. "Board of Regents, University of Texas Syste

Semiclassical energy formulas for power-law and log potentials in quantum mechanics

We study a single particle which obeys non-relativistic quantum mechanics in R^N and has Hamiltonian H = -Delta + V(r), where V(r) = sgn(q)r^q. If N \geq 2, then q > -2, and if N = 1, then q > -1. The discrete eigenvalues E_{n\ell} may be represented exactly by the semiclassical expression E_{n\ell}(q) = min_{r>0}\{P_{n\ell}(q)^2/r^2+ V(r)}. The case q = 0 corresponds to V(r) = ln(r). By writing one power as a smooth transformation of another, and using envelope theory, it has earlier been proved that the P_{n\ell}(q) functions are monotone increasing. Recent refinements to the comparison theorem of QM in which comparison potentials can cross over, allow us to prove for n = 1 that Q(q)=Z(q)P(q) is monotone increasing, even though the factor Z(q)=(1+q/N)^{1/q} is monotone decreasing. Thus P(q) cannot increase too slowly. This result yields some sharper estimates for power-potential eigenvlaues at the bottom of each angular-momentum subspace.Comment: 20 pages, 5 figure

FearNot! An Anti-Bullying Intervention: Evaluation of an Interactive Virtual Learning Environment

Original paper can be found at: http://www.aisb.org.uk/publications/proceedings.shtm

A novel model for one-dimensional morphoelasticity. Part I - Theoretical foundations

While classical continuum theories of elasticity and viscoelasticity have long been used to describe the mechanical behaviour of solid biological tissues, they are of limited use for the description of biological tissues that undergo continuous remodelling. The structural changes to a soft tissue associated with growth and remodelling require a mathematical theory of ‘morphoelasticity’ that is more akin to plasticity than elasticity. However, previously-derived mathematical models for plasticity are difficult to apply and interpret in the context of growth and remodelling: many important concepts from the theory of plasticity do not have simple analogues in biomechanics.\ud \ud In this work, we describe a novel mathematical model that combines the simplicity and interpretability of classical viscoelastic models with the versatility of plasticity theory. While our focus here is on one-dimensional problems, our model builds on earlier work based on the multiplicative decomposition of the deformation gradient and can be adapted to develop a three-dimensional theory. The foundation of this work is the concept of ‘effective strain’, a measure of the difference between the current state and a hypothetical state where the tissue is mechanically relaxed. We develop one-dimensional equations for the evolution of effective strain, and discuss a number of potential applications of this theory. One significant application is the description of a contracting fibroblast-populated collagen lattice, which we further investigate in Part II

A novel model for one-dimensional morphoelasticity. Part II - Application to the contraction of fibroblast-populated collagen lattices

Fibroblast-populated collagen lattices are commonly used in experiments to study the interplay between fibroblasts and their pliable environment. Depending on the method by which\ud they are set, these lattices can contract significantly, in some cases contracting to as little as 10% of their initial lateral (or vertical) extent. When the reorganisation of such lattices by fibroblasts is interrupted, it has been observed that the gels re-expand slightly but do not return to their original size. In order to describe these phenomena, we apply our theory of one-dimensional morphoelasticity derived in Part I to obtain a system of coupled ordinary differential equations, which we use to describe the behaviour of a fibroblast-populated collagen lattice that is tethered by a spring of known stiffness. We obtain approximate solutions that describe the behaviour of the system at short times as well as those that are valid for long times. We also obtain an exact description of the behaviour of the system in the case where the lattice reorganisation is interrupted. In addition, we perform a perturbation analysis in the limit of large spring stiffness to obtain inner and outer asymptotic expansions for the solution, and examine the relation between force and traction stress in this limit. Finally, we compare predicted numerical values for the initial stiffness and viscosity of the gel with corresponding values for previously obtained sets of experimental data and also compare the qualitative behaviour with that of our model in each case. We find that our model captures many features of the observed behaviour of fibroblast-populated collagen lattices

Photoelectric observations of Mars and Jupiter with a scanning polarimeter

Photoelectric observations of Mars and Jupiter with scanning polarimete

PC-based aviation training devices (PCATDs): research, development and certification

This paper examines the development of two PCATD’s (one helicopter, one fixed-wing) and their eventual certification by CAA. Certification has demonstrated the potential these devices have for aviation training in New Zealand. Traditionally FTD‘s and PCATD’s have been sourced from foreign companies, and they represent a considerable financial investment for large flying training organisations. The procurement of these simulator types is generally beyond the financial resources of most small to medium sized flying schools. Aviation training in NZ is facing significant financial constraints as well as an increasing demand to simulate complex glass cockpit systems that are now installed in most new General Aviation (GA) aircraft. The development, utilisation and certification of this type of PCATD technology could solve these difficult challenges