Propagation speed of combustion and invasion waves in stochastic simulations with competitive mixing

We consider the propagation speeds of steady waves simulated by particles with stochastic motions, properties and mixing (Pope particles). Conventional conservative mixing is replaced by competitive mixing simulating invasion processes or conditions in turbulent premixed flames under the flamelet regime. The effects of finite correlation times for particle velocity are considered and wave propagation speeds are determined for different limiting regimes. The results are validated by stochastic simulations. If the correlation time is short, the model corresponds to the KPP–Fisher equation, which is conventionally used to simulate invasion processes. If the parameters of the simulations are properly selected, the model under consideration is shown to be consistent with existing experimental evidence for propagation speeds of turbulent premixed flames.     

Anglo-Danish conference on History of Mathematics in Education: Bath Spa,August 2016

We report on the Anglo-Danish History of Mathematics in Education conference, drawing on an article written for the Danish Association of Teachers of Mathematics (LFMK) by Jeanette Axelsen (Vordingborg Gymnasium), Kristian Danielsen (Center for Science Studies, University of Aarhus) and Henrik Kragh Sørensen (Department of Science Education, University of Copenhagen). Thirty attendees enjoyed an intense programme of talks and practical workshops over three days in Bath. Teachers from Denmark and England shared their pedagogical developments inspired by the history of mathematics.     

The invariant constrained equilibrium edge preimage curve method for the dimension reduction of chemical kinetics

This work addresses the construction and use of low-dimensional invariant manifolds to simplify complex chemical kinetics. Typically, chemical kinetic systems have a wide range of time scales. As a consequence, reaction trajectories rapidly approach a hierarchy of attracting manifolds of decreasing dimension in the full composition space. In previous research, several different methods have been proposed to identify these low-dimensional attracting manifolds. Here we propose a new method based on an invariant constrained equilibrium edge (ICE) manifold. This manifold (of dimension nr) is generated by the reaction trajectories emanating from its (nr-1)-dimensional edge, on which the composition is in a constrained equilibrium state. A reasonable choice of the nr represented variables (e.g., nr "major" species) ensures that there exists a unique point on the ICE manifold corresponding to each realizable value of the represented variables. The process of identifying this point is referred to as species reconstruction. A second contribution of this work is a local method of species reconstruction, called ICE-PIC, which is based on the ICE manifold and uses preimage curves (PICs). The ICE-PIC method is local in the sense that species reconstruction can be performed without generating the whole of the manifold (or a significant portion thereof). The ICE-PIC method is the first approach that locally determines points on a low-dimensional invariant manifold, and its application to high-dimensional chemical systems is straightforward. The "inputs" to the method are the detailed kinetic mechanism and the chosen reduced representation (e.g., some major species). The ICE-PIC method is illustrated and demonstrated using an idealized H2O system with six chemical species. It is then tested and compared to three other dimension-reduction methods for the test case of a one-dimensional premixed laminar flame of stoichiometric hydrogen/air, which is described by a detailed mechanism containing nine species and 21 reactions. It is shown that the error incurred by the ICE-PIC method with four represented species is small across the whole flame, even in the low temperature region.     

Extremal static AdS black hole/CFT correspondence in gauged supergravities

A recently proposed holographic duality allows the Bekenstein–Hawking entropy of extremal rotating black holes to be calculated microscopically, by applying the Cardy formula to the two-dimensional chiral CFTs associated with certain reparameterisations of azimuthal angular coordinates in the solutions. The central charges are proportional to the angular momenta of the black hole, and so the method degenerates in the case of static (non-rotating) black holes. We show that the method can be extended to encompass such charged static extremal AdS black holes by using consistent Kaluza–Klein sphere reduction ansatze to lift them to exact solutions in the low-energy limits of string theory or M-theory, where the electric charges become reinterpreted as angular momenta associated with internal rotations in the reduction sphere. We illustrate the procedure for the examples of extremal charged static AdS black holes in four, five, six and seven dimensions.     

On surface coils and depth pulses

A computer program has been developed which calculates the signal response to a generalised depth pulse both on and off resonance. Results are displayed on a grey scale for any plane which includes the axis of the circular surface coil used to apply the pulse. Use of separate (coaxial) transmitter and receiver coils can be accommodated, and both in-phase and out-of-phase signal components can be displayed. Some methods of improving spatial resolution are demonstrated and the off-resonance performance of several depth pulses is compared. Results of the computer simulations are compared with experimental results on phantoms using a simple surface coil.     

Crystal structures of S-benzylisothiouronium hexachloroplatinate (IV) and tetrachloroaurate (III)

The crystal structures of two S-benzylisothiouronium salts, [C₆H₅. CH₂. S. C (NH₂)₂ ]₂ PtCl₆ and C₆H₅. CH₂ S. C (NH₂)₂AuCl₄, have been determined from three-dimensional X-ray data obtained from integrated Weissenberg photographs. Both structures were refined by full-matrix least squares toR = 0.11. The packing in both structures occurs in alternating sheets representing polar and apolar regions. The ion pairs are held together by ionic forces and a large number of hydrogen bonds.     

Search for direct single-photon production at large pT in photon-proton collisions at √s = 62.4 GeV

As part of a study of large p_T phenomena in photon-proton collisions at the CERN ISR, a search for direct single photon production has been performed. A statistical division of the data sample into the fraction consistent with single photon and the fraction due to multiphoton decays of neutral hadrons is accomplished by measuring the average conversion probability for the sample in a one radiation length thick converter. The fraction of the sample attributable to direct single photon production is 〈γ/all〉 = 0.074 ± 0.012 for 6 GeV/c < p_T 10 GeV/c, and 〈γ/all〉 = 0.26 ± 0.04 for p_T > 10 GeV/c, with an additional systematic uncertainty of ±0.05 for both values.     

Comment on the reply by T. Ozawa

Journal of Thermal Analysis and Calorimetry -     

Temperature-induced reversible changes in long spacing in oriented polyethylene

The possible explanations for the temperature-induced reversible changes in long spacing in polymers are reviewed. The observation of particularly large changes in certain irradiated samples of oriented low-density polyethylene is reported. By combining these results with those obtained by DSC and other means it is concluded that the spacing changes are caused by partial melting of small lamellae within the lamellar stacks which alters the mean periodicity. The requirement of an irregular lattice explains why the effect is observed primarily in bulk samples and especially in materials which contain intrinsic irregularities.