Retarded boundary integral equations on the sphere: exact and numerical solution

In this paper we consider the three-dimensional wave equation in unbounded domains with Dirichlet boundary conditions. We start from a retarded single-layer potential ansatz for the solution of these equations which leads to the retarded potential integral equation on the bounded surface of the scatterer. We formulate an algorithm for the space-time Galerkin discretization with smooth and compactly supported temporal basis functions, which were introduced in Sauter & Veit (2013, Numer. Math., 145-176). For the debugging of an implementation and for systematic parameter tests it is essential to have at hand some explicit representations and some analytic properties of the exact solutions for some special cases. We will derive such explicit representations for the case where the scatterer is the unit ball. The obtained formulas are easy to implement and we will present some numerical experiments for these cases to illustrate the convergence behaviour of the proposed metho

A Galerkin method for retarded boundary integral equations with smooth and compactly supported temporal basis functions

We consider retarded boundary integral formulations of the three-dimensional wave equation in unbounded domains. Our goal is to apply a Galerkin method in space and time in order to solve these problems numerically. In this approach the computation of the system matrix entries is the major bottleneck. We will propose new types of finite-dimensional spaces for the time discretization. They allow variable time-stepping, variable order of approximation and simplify the quadrature problem arising in the generation of the system matrix substantially. The reason is that the basis functions of these spaces are globally smooth and compactly supported. In order to perform numerical tests concerning our new basis functions we consider the special case that the boundary of the scattering problem is the unit sphere. In this case explicit solutions of the problem are available which will serve as reference solutions for the numerical experiment

Fast quadrature techniques for retarded potentials based on TT/QTT tensor approximation

We consider the Galerkin approach for the numerical solution of retarded boundary integral formulations of the three dimensional wave equation in unbounded domains. Recently smooth and compactly supported basis functions in time were introduced which allow the use of standard quadrature rules in order to compute the entries of the boundary element matrix. In this paper we use TT and QTT tensor approximations to increase the effciency of these quadrature rules. Various numerical experiments show the substantial reduction of the computational cost that is needed to obtain accurate approximations for the arising integrals

Introduction of Potentially Allergenic Foods in the Infant's Diet during the First Year of Life in Five European Countries

Background: Little information is available on infants' age at first introduction of potentially allergenic foods as part of complementary feeding. We aimed to analyze age at the introduction of potentially allergenic foods in healthy term infants relative to recommendations in 5 European countries. Method: Recruitment was conducted from October 2002 to June 2004. A total of 1,678 infants {[}588 breastfed (BF) and 1,090 formula-fed (FF) infants] were studied. In 1,368 infants, at least one 3-day weighed food diary at the age of 1-9 and 12 completed months was available. Results: Six percent of BF infants and 13% of FF infants consumed some potentially allergenic food already prior to the recommended minimum age of 4 months, and 4% of BF infants and 11% of FF infants had already received gluten. There were significant differences in the timing of the introduction of potentially allergenic foods between the countries at the age of 4-6 months (p < 0.001). Conclusion: The time of first introduction of potentially allergenic foods in infants differed significantly between countries, and they were introduced much earlier than recommended in some countries. FF infants received potentially allergenic foods earlier than BF infants. Better information and counseling of parents is desirable. Copyright (C) 2011 S. Karger AG, Base

MuSK induces in vivo acetylcholine receptor clusters in a ligand-independent manner

Muscle-specific receptor tyrosine kinase (MuSK) is required for the formation of the neuromuscular junction. Using direct gene transfer into single fibers, MuSK was expressed extrasynaptically in innervated rat muscle in vivo to identify its contribution to synapse formation. Spontaneous MuSK kinase activity leads, in the absence of its putative ligand neural agrin, to the appearance of ε-subunit–specific transcripts, the formation of acetylcholine receptor clusters, and acetylcholinesterase aggregates. Expression of kinase-inactive MuSK did not result in the formation of acetylcholine receptor (AChR) clusters, whereas a mutant MuSK lacking the ectodomain did induce AChR clusters. The contribution of endogenous MuSK was excluded by using genetically altered mice, where the kinase domain of the MuSK gene was flanked by loxP sequences and could be deleted upon expression of Cre recombinase. This allowed the conditional inactivation of endogenous MuSK in single muscle fibers and prevented the induction of ectopic AChR clusters. Thus, the kinase activity of MuSK initiates signals that are sufficient to induce the formation of AChR clusters. This process does not require additional determinants located in the ectodomain

Numerical solution of exterior Maxwell problems by Galerkin BEM and Runge-Kutta convolution quadrature

In this paper we consider time-dependent electromagnetic scattering problems from conducting objects. We discretize the time-domain electric field integral equation using Runge-Kutta convolution quadrature in time and a Galerkin method in space. We analyze the involved operators in the Laplace domain and obtain convergence results for the fully discrete scheme. Numerical experiments indicate the sharpness of the theoretical estimate

Ocean warming and long-term change in pelagic bird abundance within the California current system

As a result of repeated sampling of pelagic bird abundance over 3 x 105 km2 of open ocean 4 times a year for 8 yr, we report that seabird abundance within the California Current system has declined by 40% over the period 1987 to 1994. This decline has accompanied a concurrent, long-term increase in sea surface temperature. The decline in overall bird abundance is largely, but not entirely, a consequence of the 90% decline of sooty shearwaters Puffinus griseus, the numerically dominant species of the California Current. Seabirds of the offshore waters we sampled showed a different pattern from seabirds of the shelf and slope waters. Leach's storm-petrels Oceanodroma leucorhoa, the commonest species offshore, significantly increased during 1987 to 1994, while sooty shearwaters and other inshore species declined. Thus the clearest pattern that emerges from our data is one of gradual but persistent changes in abundance that transpire at time scales longer than 1 yr. Nevertheless, we did find evidence of change at shorter time scales (weeks and months) that may relate to the El Niño episode of 1992 to 1993: Pronounced positive anomalies of abundance of brown pelicans Pelecanus occidentalis and Heerman's gulls Larus heermani in fall 1991, and black Oceanodroma melania andleast O. microsoma storm-petrels in late summer 1992, likely reflect northward dispersal following reproductive failure in the Gulf of California