Spikes for the gierer-meinhardt system with many segments of different diffusivities

We rigorously prove results on spiky patterns for the Gierer-Meinhardt system with a large number of jump discontinuities in the diffusion coefficient of the inhibitor. Using numerical computations in combination with a Turing-type instability analysis, this system has been investigated by Benson, Maini and Sherratt

On the Leibniz rule and Laplace transform for fractional derivatives

Taylor series is a useful mathematical tool when describing and constructing a function. With the series representation, some properties of fractional calculus can be revealed clearly. This paper investigates two typical applications: Lebiniz rule and Laplace transform. It is analytically shown that the commonly used Leibniz rule cannot be applied for Caputo derivative. Similarly, the well-known Laplace transform of Riemann-Liouville derivative is doubtful for n-th continuously differentiable function. By the aid of this series representation, the exact formula of Caputo Leibniz rule and the explanation of Riemann-Liouville Laplace transform are presented. Finally, three illustrative examples are revisited to confirm the obtained results

Molecular Dynamics Computer Simulation of the Dynamics of Supercooled Silica

We present the results of a large scale computer simulation of supercooled silica. We find that at high temperatures the diffusion constants show a non-Arrhenius temperature dependence whereas at low temperature this dependence is also compatible with an Arrhenius law. We demonstrate that at low temperatures the intermediate scattering function shows a two-step relaxation behavior and that it obeys the time temperature superposition principle. We also discuss the wave-vector dependence of the nonergodicity parameter and the time and temperature dependence of the non-Gaussian parameter.Comment: 5 pages, Latex, 6 postscript figure

Glass-Like Heat Conduction in High-Mobility Crystalline Semiconductors

The thermal conductivity of polycrystalline semiconductors with type-I clathrate hydrate crystal structure is reported. Ge clathrates (doped with Sr and/or Eu) exhibit lattice thermal conductivities typical of amorphous materials. Remarkably, this behavior occurs in spite of the well-defined crystalline structure and relatively high electron mobility ($\sim 100 cm^2/Vs$). The dynamics of dopant ions and their interaction with the polyhedral cages of the structure are a likely source of the strong phonon scattering.Comment: 4 pages, 3 postscript figures, to be published, Phys. Rev. Let

Effects of increased cholesterol level on BK channels

published_or_final_versionThe 16th Medical Resarch Conference (MRC), The University of Hong Kong, Hong Kong, China, 22 January 2011. In Hong Kong Medical Journal, 2011, v. 17, suppl. 1, p. 61, abstract no. 10

The surface plasmon enhancement effect on adsorbed molecules at elevated temperatures

The surface plasmon enhancement effect on adsorbed molecules at elevated substrate temperatures is studied theoretically using surface enhanced Raman scattering (SERS) as an example. The surface structure is idealized to be a monodisperse spherical particle with its nonlocal dielectric response accounted for. The temperature effects are modeled using a temperature-dependent collision frequency in the Drude model. Numerical results show that only a small decrease in the SERS enhancement ratio occurs for temperatures up to the melting point of the substrate, even for scattering close to the surface plasmon resonance frequency of the metal. More definitive results are subjected to more realistic modeling as well as systematic experimental studies. The implication of this result to other surface photochemical processes is discussed

Electrophysiological mechanisms of long and short QT syndromes

The QT interval on the human electrocardiogram is normally in the order of 450 ms, and reflects the summated durations of action potential (AP) depolarization and repolarization of ventricular myocytes. Both prolongation and shortening in the QT interval have been associated with ventricular tachy-arrhythmias, which predispose affected individuals to sudden cardiac death. In this article, the molecular determinants of the AP duration and the causes of long and short QT syndromes (LQTS and SQTS) are explored. This is followed by a review of the recent advances on their arrhythmogenic mechanisms involving reentry and/or triggered activity based on experiments conducted in mouse models. Established and novel clinical risk markers based on the QT interval for the prediction of arrhythmic risk and cardiovascular mortality are presented here. It is concluded by a discussion on strategies for the future rational design of anti-arrhythmic agents.GT received a BBSRC Doctoral Training Award at the University of Cambridge and thanks the Croucher Foundation of Hong Kong for supporting his clinical assistant professorship. YC is supported by the ESRC for her PhD studies