Development of a novel metastable composite material

The development of a new family of mouldable metastable composite materials has been demonstrated. Their special quality is derived from the ability to maintain the matrix as a supercooled liquid or gel whose solidification can be triggered mechanically, as desired, by a user. This article describes some aspects of the development work. In particular, the following are explained: the choice of matrix material; the use of additives to enhance the properties of the matrix; and the selection of reinforcement fibre. As part of the work, some mechanical testing was performed on several variations of a matrix-fibre pair and, to demonstrate the potential of such materials, some comparisons were made with a possible competitor material, a glass-reinforced urethane. It was shown that the metastable material could be formulated to provide mechanical properties that would make it suitable for applications such as orthopaedic casting, splinting and body armour, and in items of sports equipment, these being areas where its mouldability could be particularly desirable

Two stochastic models useful in petroleum exploration

A model of the petroleum exploration process that tests empirically the hypothesis that at an early stage in the exploration of a basin, the process behaves like sampling without replacement is proposed along with a model of the spatial distribution of petroleum reserviors that conforms to observed facts. In developing the model of discovery, the following topics are discussed: probabilitistic proportionality, likelihood function, and maximum likelihood estimation. In addition, the spatial model is described, which is defined as a stochastic process generating values of a sequence or random variables in a way that simulates the frequency distribution of areal extent, the geographic location, and shape of oil deposit

Reward and uncertainty in exploration programs

A set of variables which are crucial to the economic outcome of petroleum exploration are discussed. These are treated as random variables; the values they assume indicate the number of successes that occur in a drilling program and determine, for a particular discovery, the unit production cost and net economic return if that reservoir is developed. In specifying the joint probability law for those variables, extreme and probably unrealistic assumptions are made. In particular, the different random variables are assumed to be independently distributed. Using postulated probability functions and specified parameters, values are generated for selected random variables, such as reservoir size. From this set of values the economic magnitudes of interest, net return and unit production cost are computed. This constitutes a single trial, and the procedure is repeated many times. The resulting histograms approximate the probability density functions of the variables which describe the economic outcomes of an exploratory drilling program

A slowly rotating perfect fluid body in an ambient vacuum

A global model of a slowly rotating perfect fluid ball in general relativity is presented. To second order in the rotation parameter, the junction surface is an ellipsoidal cylinder. The interior is given by a limiting case of the Wahlquist solution, and the vacuum region is not asymptotically flat. The impossibility of joining an asymptotically flat vacuum region has been shown in a preceding work.Comment: 7 pages, published versio

Dual cathode system for electron beam instruments

An electron beam source having a single electron optical axis is provided with two coplanar cathodes equally spaced on opposite sides from the electron optical axis. A switch permits selecting either cathode, and a deflection system comprised of electromagnets, each with separate pole pieces equally spaced from the plane of the cathodes and electron optical axis, first deflects the electron beam from a selected cathode toward the electron optical axis, and then in an opposite direction into convergence with the electron optical axis. The result is that the electron beam from one selected cathode undergoes a sigmoid deflection in two opposite directions, like the letter S, with the sigmoid deflection of each being a mirror image of the other

Spectral Densities of Response Functions for the O(3) Symmetric Anderson and Two Channel Kondo Models

The O(3) symmetric Anderson model is an example of a system which has a stable low energy marginal Fermi liquid fixed point for a certain choice of parameters. It is also exactly equivalent, in the large U limit, to a localized model which describes the spin degrees of freedom of the linear dispersion two channel Kondo model. We first use an argument based on conformal field theory to establish this precise equivalence with the two channel model. We then use the numerical renormalization group (NRG) approach to calculate both one-electron and two-electron response functions for a range of values of the interaction strength U. We compare the behaviours about the marginal Fermi liquid and Fermi liquid fixed points and interpret the results in terms of a renormalized Majorana fermion picture of the elementary excitations. In the marginal Fermi liquid case the spectral densities of all the Majorana fermion modes display a |omega| dependence on the lowest energy scale, and in addition the zero Majorana mode has a delta function contribution. The weight of this delta function is studied as a function of the interaction U and is found to decrease exponentially with U for large U. Using the equivalence with the two channel Kondo model in the large U limit, we deduce the dynamical spin susceptibility of the two channel Kondo model over the full frequency range. We use renormalized perturbation theory to interpret the results and to calculate the coefficient of the ln omega divergence found in the low frequency behaviour of the T=0 dynamic susceptibility.Comment: 26 pages, 18 figures, to be published in Eur. Phys. J.

Simple and accurate modelling of the gravitational potential produced by thick and thin exponential discs

We present accurate models of the gravitational potential produced by a radially exponential disc mass distribution. The models are produced by combining three separate Miyamoto–Nagai discs. Such models have been used previously to model the disc of the Milky Way, but here we extend this framework to allow its application to discs of any mass, scalelength, and a wide range of thickness from infinitely thin to near spherical (ellipticities from 0 to 0.9). The models have the advantage of simplicity of implementation, and we expect faster run speeds over a double exponential disc treatment. The potentials are fully analytical, and differentiable at all points. The mass distribution of our models deviates from the radial mass distribution of a pure exponential disc by <0.4 per cent out to 4 disc scalelengths, and <1.9 per cent out to 10 disc scalelengths. We tabulate fitting parameters which facilitate construction of exponential discs for any scalelength, and a wide range of disc thickness (a user-friendly, web-based interface is also available). Our recipe is well suited for numerical modelling of the tidal effects of a giant disc galaxy on star clusters or dwarf galaxies. We consider three worked examples; the Milky Way thin and thick disc, and a discy dwarf galaxy

Odd Parity and Line Nodes in Non-Symmorphic Superconductors

Group theory arguments have been invoked to argue that odd parity order parameters cannot have line nodes in the presence of spin-orbit coupling. In this paper we show that these arguments do not hold for certain non-symmorphic superconductors. Specifically, we demonstrate that when the underlying crystal has a twofold screw axis, half of the odd parity representations vanish on the Brillouin zone face perpendicular to this axis. Many unconventional superconductors have non-symmorphic space groups, and we discuss implications for several materials, including UPt3, UBe13, Li2Pt3B and Na4Ir3O8.Comment: 4 page

Axistationary perfect fluids -- a tetrad approach

Stationary axisymmetric perfect fluid space-times are investigated using the curvature description of geometries. Attention is focused on space-times with a vanishing electric part of the Weyl tensor. It is shown that the only incompressible axistationary magnetic perfect fluid is the interior Schwarzschild solution. The existence of a rigidly rotating perfect fluid, generalizing the interior Schwarzschild metric is proven. Theorems are stated on Petrov types and electric/magnetic Weyl tensors.Comment: 12 page