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

Temperature and orientation dependence of kinetic roughening during homoepitaxy: A quantitative x-ray-scattering study of Ag

URL:http://link.aps.org/doi/10.1103/PhysRevB.54.17938 DOI:10.1103/PhysRevB.54.17938Kinetic roughening during homoepitaxial growth was studied for Ag(111) and Ag(001). For Ag(111), from 150 to 500 K, the rms roughness exhibits a power law, σ∝tβ over nearly three decades in thickness. β≈1/2 at low temperatures, and there is an abrupt transition to smaller values above 300 K. In contrast, Ag(001) exhibits layer-by-layer growth with a significantly smaller β. These results are the first to establish the evolution of surface roughness quantitatively for a broad thickness and temperature range, as well as for the case where growth kinetics are dominated by a step-ledge diffusion barrier.Support is acknowledged from the University of Missouri Research Board, the NSF under Contract Nos. DMR-9202528 and DMR-9623827, and the Midwest Superconductivity Consortium ~MISCON! under DOE Grant No. DE-FG02-90ER45427. The SUNY X3 beamline is supported by the DOE under Contract No. DE-FG02-86ER45231, and the NSLS is supported by the DOE, Div. of Materials Sciences and Div. of Chemical Sciences. One of us ~W.C.E.! acknowledges support from the GAANN program of the U.S. Department of Education. We thank Ian Robinson for the Ag~111! crystal

Shrinking Point Bifurcations of Resonance Tongues for Piecewise-Smooth, Continuous Maps

Resonance tongues are mode-locking regions of parameter space in which stable periodic solutions occur; they commonly occur, for example, near Neimark-Sacker bifurcations. For piecewise-smooth, continuous maps these tongues typically have a distinctive lens-chain (or sausage) shape in two-parameter bifurcation diagrams. We give a symbolic description of a class of "rotational" periodic solutions that display lens-chain structures for a general $N$-dimensional map. We then unfold the codimension-two, shrinking point bifurcation, where the tongues have zero width. A number of codimension-one bifurcation curves emanate from shrinking points and we determine those that form tongue boundaries.Comment: 27 pages, 6 figure

Reversibility of both sinus node dysfunction and reduced HCN4 mRNA expression level in an atrial tachycardia pacing model of tachycardia-bradycardia syndrome in rabbit hearts

published_or_final_versio

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