High-order accurate methods for Nyström discretization of integral equations on smooth curves in the plane

Boundary integral equations and Nyström discretization provide a powerful tool for the solution of Laplace and Helmholtz boundary value problems. However, often a weakly-singular kernel arises, in which case specialized quadratures that modify the matrix entries near the diagonal are needed to reach a high accuracy. We describe the construction of four different quadratures which handle logarithmically-singular kernels. Only smooth boundaries are considered, but some of the techniques extend straightforwardly to the case of corners. Three are modifications of the global periodic trapezoid rule, due to Kapur–Rokhlin, to Alpert, and to Kress. The fourth is a modification to a quadrature based on Gauss–Legendre panels due to Kolm–Rokhlin; this formulation allows adaptivity. We compare in numerical experiments the convergence of the four schemes in various settings, including low- and high-frequency planar Helmholtz problems, and 3D axisymmetric Laplace problems. We also find striking differences in performance in an iterative setting. We summarize the relative advantages of the schemes.     

2-D absolute OH concentration profiles in atmospheric flames using planar LIF in a bi-directional laser beam configuration

1 (6) rotational line in the A²Σ⁺(v^′=0)←X²Π(v^′′=0) band of OH at 309 nm. The requirements for obtaining a good signal-to-noise ratio for the technique are discussed and the possibilities of single-shot measurements are investigated. Received: 31 October 1996/Revised version: 3 December 1996     

Combined approach for high-throughput preparation and analysis of plasma samples from exposure studies

In drug discovery today, drug exposure is determined in preclinical efficacy and safety studies and drug effects are related to measured concentrations rather than to the administered dose. This leads to a strong increase in the number of bioanalytical samples, demanding the development of higher throughput methods to cope with the increased workload. Here, a combined approach is described for the high-throughput preparation and liquid chromatography/tandem mass spectrometry (LC/MS/MS) analysis of drug levels in plasma samples from the preclinical efficacy and safety studies, i.e. exposure studies. Appropriate pharmacokinetic (PK) compartmental models were fitted to data from PK screening studies in the rat, which were subsequently used to simulate the expected plasma concentrations of the respective exposure studies. Information on the estimated drug concentrations was used to dilute the samples to appropriate concentration levels. A Tecan Genesis RSP liquid handling system was utilized to perform automated plasma sample preparation including serial dilution of standard solutions, dilution of plasma samples, addition of internal standard solution and precipitation with acetonitrile. This robotic sample preparation process permitted two studies of 1-96 samples each to be run simultaneously. To ensure the performance of this method the accuracy and precision for diazepam were examined. Two novel drugs were used to illustrate the suggested approach. In conclusion, our method for sample preparation of exposure samples, based on the combined use of PK simulations, a liquid handling system and a fast LC/MS/MS method, increased the throughput more than three times and minimized the errors, while maintaining the required accuracy and precision.     

A randomized algorithm for the decomposition of matrices

Given an $m\times n$ matrix A and a positive integer k, we describe a randomized procedure for the approximation of A with a matrix Z of rank k. The procedure relies on applying $A^{\mathrm{T}}$ to a collection of l random vectors, where l is an integer equal to or slightly greater than k; the scheme is efficient whenever A and $A^{\mathrm{T}}$ can be applied rapidly to arbitrary vectors. The discrepancy between A and Z is of the same order as $\sqrt{lm}$ times the $(k+1)$st greatest singular value ${\sigma }_{k+1}$ of A, with negligible probability of even moderately large deviations. The actual estimates derived in the paper are fairly complicated, but are simpler when $l?k$ is a fixed small nonnegative integer. For example, according to one of our estimates for $l?k=20$, the probability that the spectral norm $6A?Z6$ is greater than $10\sqrt{(k+20)m}{\sigma }_{k+1}$ is less than ${10}^{?17}$. The paper contains a number of estimates for $6A?Z6$, including several that are stronger (but more detailed) than the preceding example; some of the estimates are effectively independent of m. Thus, given a matrix A of limited numerical rank, such that both A and $A^{\mathrm{T}}$ can be applied rapidly to arbitrary vectors, the scheme provides a simple, efficient means for constructing an accurate approximation to a singular value decomposition of A. Furthermore, the algorithm presented here operates reliably independently of the structure of the matrix A. The results are illustrated via several numerical examples.     

Initial oxidation of the Mg(0001) surface,an electron spectroscopy study

The initial oxidation of Mg(0001) has been studied using AES (Auger electron spectroscopy), LEED (low energy electron diffraction), and EELS (electron energy loss spectroscopy). The oxidation proceeds through different stages; first oxygen atoms are incorporated to chemisorption sites below the top layer magnesium. This chemisorption phase is followed by the formation of an oxide layer. The oxide layer covers the Mg surface after an oxygen exposure of ～ 10 L O₂. After this exposure the bulk-like MgO formation slowly increases the oxide thickness. The oxide layer formed for exposures up to ≤ 10 L O₂ gives rise to a diffuse LEED pattern of the same symmetry as the original “clean” LEED pattern; the possibility of an epitaxial oxide formation at this stage is discussed.     

Mechanics of Materials with Periodic Truss or Frame Micro-Structures

This paper describes the mechanics of materials with periodic skeletal micro-structures in infinite domains. The principal technical results consist of certain Korn-type inequalities that provide upper and lower bounds for the linear elastic strain energy in the material. Using these inequalities, existence and uniqueness results for the equations of linear elastic equilibrium are derived, and some asymptotic properties of the solutions are described. Particular attention is paid to the question of when a lattice structure can accurately be modeled as a pin-jointed truss, and when a rigid-node frame model must be employed. A practical technique for how to distinguish between the two types of material is given, and the distinct differences in their mechanical behavior are described.     

Communication modes in vector diffraction

The communication modes, which mathematically correspond to singular value decomposition, have proven a useful concept in optical scalar-field diffraction, with applications in resolution studies, image synthesis, and wave propagation. For optical near-field geometries the communication modes have to be extended to electromagnetic field accounting for the polarization properties. In this paper we present the vector-valued communication modes method based on the rigorous electric-field diffraction integral. As a special case the transverse-electric scalar field modes are obtained. The intensity and polarization properties of the leading electromagnetic communication modes in near-field arrangements with rectangular apertures are discussed in terms of the Stokes parameters. For small separations between the transmitting and receiving apertures the fundamental mode possesses a ring-shaped hollow structure. The polarization properties of the near-field modes show features on spatial scales smaller than the wavelength of light. The system symmetries lead to degenerate communication modes.