Large-scale computation of pseudospectra using ARPACK and eigs

ARPACK and its MATLAB counterpart, eigs, are software packages that calculate some eigenvalues of a large non-symmetric matrix by Arnoldi iteration with implicit restarts. We show that at a small additional cost, which diminishes relatively as the matrix dimension increases, good estimates of pseudospectra in addition to eigenvalues can be obtained as a by-product. Thus in large-scale eigenvalue calculations it is feasible to obtain routinely not just eigenvalue approximations, but also information as to whether or not the eigenvalues are likely to be physically significant. Examples are presented for matrices with dimension up to 200,000

Do Childhood Vaccines Have Non-Specific Effects on Mortality

A recent article by Kristensen et al. suggested that measles vaccine and bacille Calmette–Guérin (BCG) vaccine might\ud reduce mortality beyond what is expected simply from protection against measles and tuberculosis. Previous reviews of the potential effects of childhood vaccines on mortality have not considered methodological features of reviewed studies. Methodological considerations play an especially important role in observational assessments, in which selection factors for vaccination may be difficult to ascertain. We reviewed 782 English language articles on vaccines and childhood mortality and found only a few whose design met the criteria for methodological rigor. The data reviewed suggest that measles vaccine delivers its promised reduction in mortality, but there is insufficient evidence to suggest a mortality benefit above that caused by its effect on measles disease and its sequelae. Our review of the available data in the literature reinforces how difficult answering these considerations has been and how important study design will be in determining the effect of specific vaccines on all-cause mortality.\u

Computing Lyapunov constants for random recurrences with smooth coefficients

In recent years, there has been much interest in the growth and decay rates (Lyapunov constants) of solutions to random recurrences such as the random Fibonacci sequence $x_{n+1} = \pm x_{n} \pm x_{n-1}$. Many of these problems involve non-smooth dynamics (nondifferentiable invariant measures), making computations hard. Here, however, we consider recurrences with smooth random coefficients and smooth invariant measures. By computing discretised invariant measures and applying Richardson extrapolation, we can compute Lyapunov constants to ten digits of accuracy. In particular, solutions to the recurrence $x_{n+1} = x_{n} + c_{n+1} x_{n-1}$, where the $\{c_{n}\}$ are independent standard normal variables, increase exponentially (almost surely) at the asymptotic rate $(1.0574735537...)^{n}$. Solutions to the related recurrences $x_{n+1} = c_{n+1}x_{n} + x_{n-1}$, and $x_{n+1} = c_{n+1}x_{n} + d_{n+1}x_{n-1}$ (where the $\{d_{n}\}$ are also independent standard normal variables) increase (decrease) at the rates $(1.1149200917...)^{n}$ and $(0.9949018837...)^(n)$ respectively

Eigenvalues and Pseudospectra of Rectangular Matrices

Pseudospectra of rectangular matrices vary continuously with the matrix entries, a feature that eigenvalues of rectangular matrices do not have. Some properties of eigenvalues and pseudospectra of rectangular matrices are explored, and an efficient algorithm for the computation of pseudospectra is given. Applications are given in (square) eigenvalue computation (Lanczos and Arnoldi iteration), square pseudospectra approximation, control theory (nearest uncontrollable system) and game theory

6500 BP Oldsquaw Duck (Clangula hyemalis) from Northern Ellesmere Island, Arctic Archipelago, Canada

A nearly complete skeleton, including partially preserved feathers, of an Oldsquaw duck (Clangula hyemalis L.) was recovered from Holocene marine deposits in Clements Markham Inlet, Ellesmere Island, N.W.T., Canada. The specimen was 2 m lower in the section than allochthonous terrestrial plants previously dated at 6400 ± BP (Sl-4314) and is estimated to be 6500 years old. These deposits represent a marine, prodeltaic sedimentary environment that emerged from the fiord as the result of postglacial isostatic uplift. Comparison of the specimen's present elevation and age with the inlet's emergence curve indicates the duck was buried in a paleowater depth of 38 m. Isostatic uplift is ubiquitous in the Canadian Arctic, exposing ocean bottoms and prodeltas. The deposits from these environments deserve closer scrutiny for fossils by Quaternary scientists, as they can contribute to a better understanding of the biologic development of the Canadian Arctic.

A Review of Materials for Gas Turbines Firing Syngas Fuels

Following the extensive development work carried out in the 1990's, gas turbine combined-cycle (GTCC) systems burning natural gas represent a reliable and efficient power generation technology widely used in many parts of the world. A critical factor was that, in order to operate at the high turbine entry temperatures required for high efficiency operation, aero-engine technology, i.e., single-crystal blades, thermal barrier coatings, and sophisticated cooling techniques had to be rapidly scaled up and introduced into these large gas turbines. The problems with reliability that resulted have been largely overcome, so that the high-efficiency GTCC power generation system is now a mature technology, capable of achieving high levels of availability. The high price of natural gas and concern about emission of greenhouse gases has focused attention on the desirability of replacing natural gas with gas derived from coal (syngas) in these gas turbine systems, since typical systems analyses indicate that IGCC plants have some potential to fulfil the requirement for a zero-emissions power generation system. In this review, the current status of materials for the critical hot gas path parts in large gas turbines is briefly considered in the context of the need to burn syngas. A critical factor is that the syngas is a low-Btu fuel, and the higher mass flow compared to natural gas will tend to increase the power output of the engine. However, modifications to the turbine and to the combustion system also will be necessary. It will be shown that many of the materials used in current engines will also be applicable to units burning syngas but, since the combustion environment will contain a greater level of impurities (especially sulfur, water vapor, and particulates), the durability of some components may be prejudiced. Consequently, some effort will be needed to develop improved coatings to resist attack by sulfur-containing compounds, and also erosion