Vibrational modes of circular free plates under tension

The vibrational frequencies of a plate under tension are given by the eigenvalues $\omega$ of the equation $\Delta^2u-\tau\Delta u=\omega u$. This paper determines the eigenfunctions and eigenvalues of this bi-Laplace problem on the ball under natural (free) boundary conditions. In particular, the fundamental modes --- the eigenfunctions of the lowest nonzero eigenvalue --- are identified and found to have simple angular dependence.Comment: 17 pages. To be submitted for publication shortly

Feasibility of self-structured current accessed bubble devices in spacecraft recording systems

The self-structured, current aperture approach to magnetic bubble memory is described. Key results include: (1) demonstration that self-structured bubbles (a lattice of strongly interacting bubbles) will slip by one another in a storage loop at spacings of 2.5 bubble diameters, (2) the ability of self-structured bubbles to move past international fabrication defects (missing apertures) in the propagation conductors (defeat tolerance), and (3) moving bubbles at mobility limited speeds. Milled barriers in the epitaxial garnet are discussed for containment of the bubble lattice. Experimental work on input/output tracks, storage loops, gates, generators, and magneto-resistive detectors for a prototype device are discussed. Potential final device architectures are described with modeling of power consumption, data rates, and access times. Appendices compare the self-structured bubble memory from the device and system perspectives with other non-volatile memory technologies

A second eigenvalue bound for the Dirichlet Schroedinger operator

Let $\lambda_i(\Omega,V)$ be the $i$th eigenvalue of the Schr\"odinger operator with Dirichlet boundary conditions on a bounded domain $\Omega \subset \R^n$ and with the positive potential $V$. Following the spirit of the Payne-P\'olya-Weinberger conjecture and under some convexity assumptions on the spherically rearranged potential $V_\star$, we prove that $\lambda_2(\Omega,V) \le \lambda_2(S_1,V_\star)$. Here $S_1$ denotes the ball, centered at the origin, that satisfies the condition $\lambda_1(\Omega,V) = \lambda_1(S_1,V_\star)$. Further we prove under the same convexity assumptions on a spherically symmetric potential $V$, that $\lambda_2(B_R, V) / \lambda_1(B_R, V)$ decreases when the radius $R$ of the ball $B_R$ increases. We conclude with several results about the first two eigenvalues of the Laplace operator with respect to a measure of Gaussian or inverted Gaussian density

Extending DerSimonian and Laird's methodology to perform network meta-analyses with random inconsistency effects.

Network meta-analysis is becoming more popular as a way to compare multiple treatments simultaneously. Here, we develop a new estimation method for fitting models for network meta-analysis with random inconsistency effects. This method is an extension of the procedure originally proposed by DerSimonian and Laird. Our methodology allows for inconsistency within the network. The proposed procedure is semi-parametric, non-iterative, fast and highly accessible to applied researchers. The methodology is found to perform satisfactorily in a simulation study provided that the sample size is large enough and the extent of the inconsistency is not very severe. We apply our approach to two real examples.DJ, RT and IRW are employed by the UK Medical Research Council (code U105260558). JB is supported by the UK MRC grant numbers G0902100 and MR/K014811/1.This is the final version of the article. It first appeared from Wiley via http://dx.doi.org/10.1002/sim.675

Concentrations of Polychlorinated Biphenyls (PCB’s), Chlorinated Pesticides, and Heavy Metals and Other Elements in Tissues of Belugas, Delphinapterus leucas, from Cook Inlet

Tissues from Cook Inlet beluga whales, Delphinapterus leucas, that were collected as part of the Alaska Marine Mammal Tissue Archival Project were analyzed for polychlorinated biphenyls (PCB’s), chlorinated pesticides, and heavy metals and other elements. Concentrations of total PCB’s (ΣPCB’s), total DDT (ΣDDT), chlordane compounds, hexachlorobenzene (HCB), dieldrin, mirex, toxaphene, and hexachlorocyclohexane (HCH) measured in Cook Inlet beluga blubber were compared with those reported for belugas from two Arctic Alaska locations (Point Hope and Point Lay), Greenland, Arctic Canada, and the highly contaminated stock from the St. Lawrence estuary in eastern Canada. The Arctic and Cook Inlet belugas had much lower concentrations (ΣPCB’s and ΣDDT were an order of magnitude lower) than those found in animals from the St. Lawrence estuary. The Cook Inlet belugas had the lowest concentrations of all (ΣPCB’s aver-aged 1.49 ± 0.70 and 0.79 ± 0.56 mg/kg wet mass, and ΣDDT averaged 1.35 ± 0.73 and 0.59 ± 0.45 mg/kg in males and females, respectively). Concentrations in the blubber of the Cook Inlet males were significantly lower than those found in the males of the Arctic Alaska belugas (ΣPCB’s and ΣDDT were about half). The lower levels in the Cook Inlet animals might be due to differences in contaminant sources, food web differences, or different age distributions among the animals sampled. Cook Inlet males had higher mean and median concentrations than did females, a result attributable to the transfer of these compounds from mother to calf during pregnancy and during lactation. Liver concentrations of cadmium and mercury were lower in the Cook Inlet belugas (most cadmium values were <1 mg/kg and mercury values were 0.704–11.42 mg/kg wet mass), but copper levels were significantly higher in the Cook Inlet animals (3.97–123.8 mg/kg wet mass) than in Arctic Alaska animals and similar to those reported for belugas from Hudson Bay. Although total mercury levels were the lowest in the Cook Inlet population, methylmercury concentrations were similar among all three groups of the Alaska animals examined (0.34–2.11 mg/kg wet mass). As has been reported for the Point Hope and Point Lay belugas, hepatic concentrations of silver were r

Avoided intersections of nodal lines

We consider real eigen-functions of the Schr\"odinger operator in 2-d. The nodal lines of separable systems form a regular grid, and the number of nodal crossings equals the number of nodal domains. In contrast, for wave functions of non integrable systems nodal intersections are rare, and for random waves, the expected number of intersections in any finite area vanishes. However, nodal lines display characteristic avoided crossings which we study in the present work. We define a measure for the avoidance range and compute its distribution for the random waves ensemble. We show that the avoidance range distribution of wave functions of chaotic systems follow the expected random wave distributions, whereas for wave functions of classically integrable but quantum non-separable wave functions, the distribution is quite different. Thus, the study of the avoidance distribution provides more support to the conjecture that nodal structures of chaotic systems are reproduced by the predictions of the random waves ensemble.Comment: 12 pages, 4 figure

On the boundary of the attainable set of the Dirichlet spectrum

Denoting by $\mathcal{E}\subseteq \R^2$ the set of the pairs $(\lambda_1(\Omega),\lambda_2(\Omega))$ for all the open sets $\Omega\subseteq\R^N$ with unit measure, and by $\Theta\subseteq\R^N$ the union of two disjoint balls of half measure, we give an elementary proof of the fact that \partial\E has horizontal tangent at its lowest point $(\lambda_1(\Theta),\lambda_2(\Theta))$.Comment: 7 pages, 3 figure