Statistical Geometry and Lattices

Statistical geometry furnishes the tool that allows the transfer of results from a lattice with finite lattice parameter to the continuum. Since lattice simulations are simpler than continuum ones, this suggests that larger scale simulations for the continuum might be more effectively carried out on a lattice with finite lattice parameter followed by the indicated transfer. We also show that a statistical geometry, peculiar to hard particles on a lattice, can be developed. Among other things, this opens the possibility that a scaled particle theory on a lattice might be derived.     

Flow and geometry induced scattering of high frequency acoustic duct modes

Cut-on cut-off transition of acoustic modes in hard-walled ducts with irrotational mean flow is well understood for Helmholtz numbers of order unity. Previous finite-element simulations of this phenomenon, however, appear to indicate the possibility of energy scattering into neighbouring modes at moderately large Helmholtz numbers. In this paper, such scattering phenomena are explained and predicted in slowly varying aeroengine ducts using a multiple-scales approach. It is found that, for sufficiently high frequencies, two mechanisms exist whereby energy can be scattered into neighbouring modes by an incident propagating mode. One mechanism occurs only when there is a mean flow inside the duct and induces scattering at significantly lower frequencies than the other mechanism which remains present without mean flow. A coupled system of ordinary differential equations is derived and then solved numerically for a number of example cases to obtain the corresponding transmitted and reflected amplitudes of the scattered modes as well as the overall acoustic pressure field. The theory appears to demonstrate that some exchange of energy between the acoustic and mean flow fields occurs during scattering.     

On the nature of pulsars

The paper contains a relatively non-technical summary of some recent work by the author and Jeremy Butterfield. The goal is to find a way of assigning meaningful truth values to propositions in quantum theory: something that is not possible in the normal, instrumentalist interpretation. The key mathematical tool is presheaf theory where multi-valued, contextual truth values arise naturally. We show how this can be applied to quantum theory, with the ‘contexts’ chosen to be Boolean subalgebras of the set of all projection operators.     

Applications of Electron Microbeam Analysis in the Earth Sciences

 Naturally formed geological materials are not constrained in the number of elements which may be present and a wide range of concentrations can be expected. Oxides are a frequent component and water may be present. The particular problems posed for quantitative analysis in some representative applications are described and solutions suggested. Critical testing of the results for consistency with mineral formulae and for repeatability provides confidence in those results. Examples of applications of quantitative analysis of minerals are used to show the variety of problems encountered in electron microbeam analysis and how the analytical results can be used to determine the conditions (time, pressure, temperature) of the minerals or the rocks in which they occur.     

Discovery of new biocatalysts for the glycosylation of terpenoid scaffolds

The synthesis of terpenoid glycosides typically uses a chemical strategy since few biocatalysts have been identified that recognise these scaffolds. In this study, a platform of 107 recombinant glycosyltransferases (GTs), comprising the multigene family of small molecule GTs of Arabidopsis thaliana have been screened against a range of model terpenoid acceptors to identify those enzymes with high activity. Twenty-seven GTs are shown to glycosylate a diversity of mono-, sesqui- and diterpenes, such as geraniol, perillyl alcohol, artemisinic acid and retinoic acid. Certain enzymes showing substantial sequence similarity recognise terpenoids containing a primary alcohol, irrespective of the linear or cyclical structure of the scaffold; other GTs glycosylate scaffolds containing secondary and tertiary alcohols; the carboxyl group of other terpenoids also represents a feature that is recognized by GTs previously known to form glucose esters with many different compounds. These data underpin the rapid prediction of potential biocatalysts from GT sequence information. To explore the potential of GTs as biocatalysts, their use for the production of terpenoid glycosides was investigated by using a microbial-based whole-cell biotransformation system capable of regenerating the cofactor, UDP-glucose. A high cell density fermentation system was shown to produce several hundred milligrams of a model terpenoid, geranyl-glucoside. The activities of the GTs are discussed in relation to their substrate recognition and their utility in biotransformations as a complement or alternative to chemical synthesis.     

Dual‐Polarization Imaging of a Dual‐Fluorophore Ion Sensor: A Single‐Molecule Study

The fluorescence emission of the dual‐fluorophore Ca²⁺ ion sensor molecule, calcium‐green 2 (CG‐2), has been characterized using dual‐polarization imaging at the single‐molecule level. By comparing the fluorescence intensity of individual CG‐2 molecules in two mutually orthogonal polarization image channels, information about the relative orientation of the two constituent fluorophores in the molecule is obtained. Experimental results from polarization measurements are compared with those predicted from a geometric model based on coupled‐fluorophores that are randomly distributed in space. The results confirm previous optical spectroscopy‐based predictions of the orientation of CG‐2′s fluorophores, and the general applications of this dual‐polarization imaging approach for characterizing the optical properties of molecules containing multiple fluorophores is discussed.     

Investigation of new band parameters with temperature dependence for self-broadened methane gas in the range 9000 to 14,000 cm−1 (0.71 to 1.1 μm)

This paper describes new measurements and modelling of the absorption of methane gas, one of the most important gases observed in the atmospheres of the outer planets and Titan, between 9000 and 14,000 cm^?1 (0.7 to 1.1 μm) and compares them with current best available spectral models.A series of methane spectra were measured at the UK's Natural Environment Research Council (NERC) Molecular Spectroscopy Facility (based at the Rutherford Appleton Laboratory, Oxfordshire, UK) using a Brüker 125HR Fourier transform spectrometer. To approximate the conditions found in outer planet atmospheres, the spectra were measured over a wide range of pressures (5 bar to 38 mbar) and temperatures (290–100 K) with path lengths of 19.3, 17.6, 16.0 and 14.4 m. The spectra were recorded at a moderate resolution of 0.12 cm^?1 and then averaged to 10 cm^?1 resolution prior to fitting a series of increasingly complex band-models including temperature dependence. Using the most complex model, a Goody line distribution with a Voigt line shape and two lower energy state levels, the typical rms residual error in the fit is between 0.01 and 0.02 in the wings of the main absorption bands.The new spectral parameters were then compared with the measured spectra and spectra calculated using existing data and shown to be able to accurately reproduce the measured absorption. The improvement in the temperature dependence included in the model is demonstrated by comparison with existing cold methane spectral data for a typical Jovian path.