Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives

We generalise the construction of fuzzy CP^N in a manner that allows us to access all noncommutative equivariant complex vector bundles over this space. We give a simplified construction of polarization tensors on S^2 that generalizes to complex projective space, identify Laplacians and natural noncommutative covariant derivative operators that map between the modules that describe noncommuative sections. In the process we find a natural generalization of the Schwinger-Jordan construction to su(n) and identify composite oscillators that obey a Heisenberg algebra on an appropriate Fock space.Comment: 34 pages, v2 contains minor corrections to the published versio

The cosmological constant and dark energy in braneworlds

We review recent attempts to address the cosmological constant problem and the late-time acceleration of the Universe based on braneworld models. In braneworld models, the way in which the vacuum energy gravitates in the 4D spacetime is radically different from conventional 4D physics. It is possible that the vacuum energy on a brane does not curve the 4D spacetime and only affects the geometry of the extra-dimensions, offering a solution to the cosmological constant problem. We review the idea of supersymmetric large extra dimensions that could achieve this and also provide a natural candidate for a quintessence field. We also review the attempts to explain the late-time accelerated expansion of the universe from the large-distance modification of gravity based on the braneworld. We use the Dvali-Gabadadze-Porrati model to demonstrate how one can distinguish this model from dark energy models in 4D general relativity. Theoretical difficulties in this approach are also addressed.Comment: Invited Review for a special Gen. Rel. Grav. issue on Dark Energy, 22 pages, 13 figures, references adde

Renormalization of composite operators

The blocked composite operators are defined in the one-component Euclidean scalar field theory, and shown to generate a linear transformation of the operators, the operator mixing. This transformation allows us to introduce the parallel transport of the operators along the RG trajectory. The connection on this one-dimensional manifold governs the scale evolution of the operator mixing. It is shown that the solution of the eigenvalue problem of the connection gives the various scaling regimes and the relevant operators there. The relation to perturbative renormalization is also discussed in the framework of the $\phi^3$ theory in dimension $d=6$.Comment: 24 pages, revtex (accepted by Phys. Rev. D), changes in introduction and summar

Two-Dimensional Diffusion in the Presence of Topological Disorder

How topological defects affect the dynamics of particles hopping between lattice sites of a distorted, two-dimensional crystal is addressed. Perturbation theory and numerical simulations show that weak, short-ranged topological disorder leads to a finite reduction of the diffusion coefficient. Renormalization group theory and numerical simulations suggest that longer-ranged disorder, such as that from randomly placed dislocations or random disclinations with no net disclinicity, leads to subdiffusion at long times.Comment: 10 pages, 6 figure

The Information Geometry of the Ising Model on Planar Random Graphs

It has been suggested that an information geometric view of statistical mechanics in which a metric is introduced onto the space of parameters provides an interesting alternative characterisation of the phase structure, particularly in the case where there are two such parameters -- such as the Ising model with inverse temperature $\beta$ and external field $h$. In various two parameter calculable models the scalar curvature ${\cal R}$ of the information metric has been found to diverge at the phase transition point $\beta_c$ and a plausible scaling relation postulated: ${\cal R} \sim |\beta- \beta_c|^{\alpha - 2}$. For spin models the necessity of calculating in non-zero field has limited analytic consideration to 1D, mean-field and Bethe lattice Ising models. In this letter we use the solution in field of the Ising model on an ensemble of planar random graphs (where $\alpha=-1, \beta=1/2, \gamma=2$) to evaluate the scaling behaviour of the scalar curvature, and find ${\cal R} \sim | \beta- \beta_c |^{-2}$. The apparent discrepancy is traced back to the effect of a negative $\alpha$.Comment: Version accepted for publication in PRE, revtex

Absorption Line Studies in the Halo

Significant progress has been made over the last few years to explore the gaseous halo of the Milky Way by way of absorption spectroscopy. I review recent results on absorption line studies in the halo using various instruments, such as the Far Ultraviolet Spectroscopic Explorer, the Space Telescope Imaging Spectrograph, and others. The new studies imply that the infall of low-metallicity gas, the interaction with the Magellanic Clouds, and the Galactic Fountain are responsible for the phenomenon of the intermediate- and high-velocity clouds in the halo. New measurements of highly-ionized gas in the vicinity of the Milky Way indicate that these clouds are embedded in a corona of hot gas that extends deep into the intergalactic space.Comment: 7 pages, 1 figure; Invited review at the conference "How does the Galaxy work ?", Granada/Spain, June 200

Preparation and some properties of cholesterol oxidase from Rhodococcus sp. R14-2

Rhodococcus sp. R14-2, isolated from Chinese Jin-hua ham, produces a novel extracellular cholesterol oxidase (COX). The enzyme was extracted from fermentation broth and purified 53.1-fold based on specific activity. The purified enzyme shows a single polypeptide band on SDS-PAGE with an estimated molecular weight of about 60 kDa, and has a pI of 8.5. The first 10 amino acid residues of the NH2-terminal sequence of the enzyme are A-P-P-V-A-S-C-R-Y-C, which differs from other known COXs. The enzyme is stable over a rather wide pH range of 4.0¿10.0. The optimum pH and temperature of the COX are pH 7.0 and 50°C, respectively. The COX rapidly oxidizes 3ß-hydroxysteroids such as cholesterol and phytosterols, but is inert toward 3¿-hydroxysteroids. Thus, the presence of a 3ß-hydroxyl group appears to be essential for substrate activity. The Michaelis constant (Km) for cholesterol is estimated at 55 ¿M; the COX activity was markedly inhibited by metal ions such as Hg2+ and Fe3+ and inhibitors such as p-chloromercuric benzoate, mercaptoethanol and fenpropimorph. Inhibition caused by p-chloromercuric benzoate, mercuric chloride, or silver nitrate was almost completely prevented by the addition of glutathione. These suggests that -SH groups may be involved in the catalytic activity of the present CO

Fuzzy Scalar Field Theory as a Multitrace Matrix Model

We develop an analytical approach to scalar field theory on the fuzzy sphere based on considering a perturbative expansion of the kinetic term. This expansion allows us to integrate out the angular degrees of freedom in the hermitian matrices encoding the scalar field. The remaining model depends only on the eigenvalues of the matrices and corresponds to a multitrace hermitian matrix model. Such a model can be solved by standard techniques as e.g. the saddle-point approximation. We evaluate the perturbative expansion up to second order and present the one-cut solution of the saddle-point approximation in the large N limit. We apply our approach to a model which has been proposed as an appropriate regularization of scalar field theory on the plane within the framework of fuzzy geometry.Comment: 1+25 pages, replaced with published version, minor improvement

Magnetoplasmon excitations in an array of periodically modulated quantum wires

Motivated by the recent experiment of Hochgraefe et al., we have investigated the magnetoplasmon excitations in a periodic array of quantum wires with a periodic modulation along the wire direction. The equilibrium and dynamic properties of the system are treated self-consistently within the Thomas-Fermi-Dirac-von Weizsaecker approximation. A calculation of the dynamical response of the system to a far-infrared radiation field reveals a resonant anticrossing between the Kohn mode and a finite-wavevector longitudinal excitation which is induced by the density modulation along the wires. Our theoretical calculations are found to be in excellent agreement with experiment.Comment: 9 pages, 8 figure

Engineering - young people want to be informed

Young people in developed nations recognise the contribution that science and technology make to society and acknowledge their importance now and in the future, yet few view their study as leading to interesting careers. Some countries are taking action to raise interest in science, technologies, engineering and mathematics and increase the number of students studying these subjects. One of the barriers to young people pursuing engineering is their limited or distorted perception of it - they associate it only with building and fixing things. Young people rarely encounter engineers, unlike other professionals, engineering has little or no advocacy in the media and there are few opportunities to experience engineering. Many of the pupils surveyed at the start of Engineering the Future, a three year EPSRC-funded project, wrote “don’t know what engineering is” and/or “would like more information”. This paper reports on work with researchers, policy makers and practitioners in Scotland to develop a sustainable model of activities and interactions that develops pupils’ understanding of the nature of engineering, embeds experiences of engineering within the school classroom and curriculum and promotes engineering as a career. After learning about engineering through the activities the pupils’ perceptions had improved. Almost all considered it important that young people know about engineering, because it is an essential part of everyday life and, in the words of one pupil - “If we know more about it, our minds wouldn’t stay closed to it. We would maybe take it up.