Temperature dependence of the cristobalite α-β inversion

The cristobalite - inversion has been studied using DSC on cristobalites produced by firing high purity quartz with and without addition of a mineraliser. If no mineraliser was used, the inversion temperatures and hysteresis on heating and cooling increased with firing temperature. Firing time had little or no effect on inversion temperature. When a mineraliser was used, the same general trend was observed with increases in firing time at low temperatures leading to splitting of the inversion peak. The amount of mineraliser added had little effect. Tridymite inversions were also observed. The results are explained in terms of the degree of order of the cristobalite structure.We are grateful for the award of an S.E.R.C. CASE award in conjunction with Specialist Refractory Services to SJS. Helpful discussions have been held with Mr. D. W. Bailey and Dr. P. Watkins.     

Hermite–Birkhoff–Obrechkoff four-stage four-step ODE solver of order 14 with quantized step size

A four-stage Hermite–Birkhoff–Obrechkoff method of order 14 with four quantized variable steps, denoted by HBOQ(14)4, is constructed for solving non-stiff systems of first-order differential equations of the form y^′=f(t,y)$y^{\prime }=f(t,y)$ with initial conditions y(_t0)=_y0$y\left(t_0\right)=y_0$. Its formula uses y^′$y^{\prime }$, y^″$y^{″}$ and y^?$y^{?}$ as in Obrechkoff methods. Forcing a Taylor expansion of the numerical solution to agree with an expansion of the true solution leads to multistep- and Runge–Kutta-type order conditions which are reorganized into linear Vandermonde-type systems. To reduce overhead, simple formulae are derived only once to obtain the values of Hermite–Birkhoff interpolation polynomials in terms of Lagrange basis functions for 16 quantized step size ratios. The step size is controlled by a local error estimator. When programmed in C ++, HBOQ(14)4 is superior to the Dormand–Prince Runge–Kutta pair DP(8,7)13M of order 8 in solving several problems often used to test higher order ODE solvers at stringent tolerances. When programmed in Matlab, it is superior to ode113 in solving costly problems, on the basis of the number of steps, CPU time, and maximum global error. The code is available on the URL www.site.uottawa.ca/~remi.     

Compactness of the Space of Minimal Hypersurfaces with Bounded Volume and <Emphasis Type="Italic">p</Emphasis>-th Jacobi Eigenvalue

Given a closed Riemannian manifold of dimension less than eight, we prove a compactness result for the space of closed, embedded minimal hypersurfaces satisfying a volume bound and a uniform lower bound on the first eigenvalue of the stability operator. When the latter assumption is replaced by a uniform lower bound on the p-th Jacobi eigenvalue for \(p\ge 2\) one gains strong convergence to a smooth limit submanifold away from at most \(p-1\) points.     

Bryozoan metabolites: an ecological perspective

This Highlight covers the chemical ecology of bryozoans, primarily the ecological functions of bryozoan natural products. The Highlight is arranged taxonomically, according to the bryozoan Treatise classification (P. Bock, Bryozoa Homepage, 2006, http://bryozoa.net).     

Graded annihilators of modules over the Frobenius skew polynomial ring, and tight closure

This paper is concerned with the tight closure of an ideal in a commutative Noetherian local ring of prime characteristic . Several authors, including R. Fedder, K-i. Watanabe, K. E. Smith, N. Hara and F. Enescu, have used the natural Frobenius action on the top local cohomology module of such an to good effect in the study of tight closure, and this paper uses that device. The main part of the paper develops a theory of what are here called `special annihilator submodules' of a left module over the Frobenius skew polynomial ring associated to ; this theory is then applied in the later sections of the paper to the top local cohomology module of and used to show that, if is Cohen-Macaulay, then it must have a weak parameter test element, even if it is not excellent.

     

Finite difference Poisson-Boltzmann electrostatic calculations: Increased accuracy achieved by harmonic dielectric smoothing and charge antialiasing

A common problem in the calculation of electrostatic potentials with the Poisson-Boltzmann equation using finite difference methods is the effect of molecular position relative to the grid. Previously a uniform charging method was shown to reduce the grid dependence substantially over the point charge model used in commercially available codes. In this article we demonstrate that smoothing the charge and dielectric values on the grid can improve the grid independence, as measured by the spread of calculated values, by another order of magnitude. Calculations of Born ion solvation energies, small molecule solvation energies, the electrostatic field of superoxide dismutase, and protein-protein binding energies are used to demonstrate that this method yields the same results as the point charge model while reducing the positional errors by several orders of magnitude. © 1997 by John Wiley & Sons, Inc.     

Femtosecond laser ablation characteristics of nickel-based superalloy C263

Femtosecond laser (180 fs, 775 nm, 1 kHz) ablation characteristics of the nickel-based superalloy C263 are investigated. The single pulse ablation threshold is measured to be 0.26±0.03 J/cm² and the incubation parameter ξ=0.72±0.03 by also measuring the dependence of ablation threshold on the number of laser pulses. The ablation rate exhibits two logarithmic dependencies on fluence corresponding to ablation determined by the optical penetration depth at fluences below ∼5 J/cm² (for single pulse) and by the electron thermal diffusion length above that fluence. The central surface morphology of ablated craters (dimples) with laser fluence and number of laser pulses shows the development of several kinds of periodic structures (ripples) with different periodicities as well as the formation of resolidified material and holes at the centre of the ablated crater at high fluences. The debris produced during ablation consists of crystalline C263 oxidized nanoparticles with diameters of ∼2–20 nm (for F=9.6 J/cm²). The mechanisms involved in femtosecond laser microprocessing of the superalloy C263 as well as in the synthesis of C263 nanoparticles are elucidated and discussed in terms of the properties of the material.     

Large Deviations,Fluctuations and Shrinking Intervals

This paper concerns the statistical properties of hyperbolic diffeomorphisms. We obtain a large deviation result with respect to slowly shrinking intervals for a large class of Hölder continuous functions. In case of time reversal symmetry, we obtain a corresponding version of the Fluctuation Theorem.