Sharp-interface limit of the Allen-Cahn action functional in one space dimension

We analyze the sharp-interface limit of the action minimization problem for the stochastically perturbed Allen-Cahn equation in one space dimension. The action is a deterministic functional which is linked to the behavior of the stochastic process in the small noise limit. Previously, heuristic arguments and numerical results have suggested that the limiting action should “count” two competing costs: the cost to nucleate interfaces and the cost to propagate them. In addition, constructions have been used to derive an upper bound for the minimal action which was proved optimal on the level of scaling. In this paper, we prove that for d = 1, the upper bound achieved by the constructions is in fact sharp. Furthermore, we derive a lower bound for the functional itself, which is in agreement with the heuristic picture. To do so, we characterize the sharp-interface limit of the space-time energy measures. The proof relies on an extension of earlier results for the related elliptic problem. Mathematics Subject Classification (2000) 49J45, 35R60, 60F10     

Diffraction reflection of a focused X-ray wave by a multilayer crystal

The Bragg diffraction of a narrow X-ray beam in a multilayer crystal is studied in the reflection geometry. It is shown by computer simulation of the experiment that strong integrated kinematic reflection occurs at any boundary of a multilayer crystal at the point of intersection of a narrow beam with the boundary. In contrast to the dynamic diffraction of a plane wave, attenuation of a narrow incident beam due to the reflection is small in comparison with the conventional absorption. As an example of a multilayer crystal, a Fabry-Perot interferometer is considered, which consists of two 70-μm-thick crystal Si layers separated by a 100-μm-thick air layer. The 12 4 0 reflection is studied at a photon energy of 15 keV. Three methods of formation of a narrow beam are considered: wavefront limitation by a slit, focusing with a parabolic lens, and focusing with a zone plate. It is shown that, for a local analysis of the thickness of layers and scattering parameters, the method of parabolic lens focusing has some advantages in comparison with the other methods.     

Determining conductivity by boundary measurements II. Interior results

In a recent paper [6] we showed that an unknown real-analytic conductivity γ may be determined from static boundary measurements. Here we extend this analysis by demonstrating that a similar result holds for piecewise real-analytic conductivities. In addition, for the special case of a layered structure we show that a three times continuously differentiable conductivity is identifiable by boundary measurements.     

Semiclassical description of inelastic atom scattering by surfaces

Inelastic scattering of atoms of moderate energies (say<5 eV) by solid surfaces is almost entirely due to energy exchange with lattice vibrations. It can give valuable information about the atom-surface interaction potential and the vibrational dynamics at surfaces. Theoretically this process represents a challenging many-body problem, calling for suitable approximation methods. Work in progress (K. Burke, L. D. Chang, and W. Kohn) is described. (1) We have solved a simple model problem in which the normal modes of the lattice are schematized by a single one-dimensional harmonic oscillator, initially in its ground state (T=0). The classical solution gives a unique energy loss. We have calculated the leading quantum correction and find a Gaussian final energy distribution whose width is proportional toh ^1/2. Our exact results are in general different from the so-called trajectory approximation. (2) We are about to propose a new type of atom-surface scattering experiment, which will provide a direct measure of the quantum corrections to classical scattering.     

An X-ray photoelectron spectroscopic study of novel SiON glasses

Novel SiON glasses obtained by melting mixtures of crystalline α-SiO₂ and α-Si₃N₄ were investigated by means of X-ray photoelectron spectroscopy (XPS). The incorporation of nitrogen into the SiO₂ network was recently proved by ²⁹Si-MAS-NMR (magic-angle spinning nuclear magnetic resonance) and Si K-XANES (X-ray absorption near edge structure). The Si 2p XPS and the Si KLL XAES (X-ray excited Auger electron spectroscopy) studies of the SiON glasses confirm the formation of mixed structural units (SiO_xN_4-x) by the presence of an additional spectral component energetically located between SiO₂- and Si₃N₄-like signals. The N 1s and O 1s XPS spectra support the conclusion about the incorporation of nitrogen into the SiO₂ network.     

Quantification of deoxynivalenol in wheat using an immunoaffinity column and liquid chromatography

A simple and accurate method to quantify the mycotoxin deoxynivalenol (DON) in wheat is described. The method uses immunoaffinity chromatography for DON isolation and liquid chromatography (LC) for toxin detection and quantification. Wheat samples are extracted in water, filtered twice and applied to an immunoaffinity column. Following a water wash, DON is eluted from the column with methanol and injected onto an LC system with a UV detector for quantification. Test performance was evaluated in terms of antibody specificity, limit of detection, percentage recovery, precision, column capacity, assay linearity and comparison with the GC-electron-capture detection (ECD) method of Tacke and Casper. Specificity of the immunoaffinity column cleanup procedure was confirmed with only DON (>80%) and its 15-C derivatives (40-50%) being recognized by the antibody while 3-C DON derivatives, nivalenol, T-2 and fusarenon-X did not bind. The limit of detection is at least 0.10 microg/g. Percentage recovery for the entire assay range averages 90% with an average relative standard deviation of 8.3%. Naturally contaminated samples showed comparable precision. Column capacity was determined to be 3.3 microg. The assay showed a high degree of linearity (r2=0.999) and an optimum assay range of 0.10 to 10.0 microg/g. Comparative analysis of 28 naturally or artificially contaminated wheat samples using DONtest-HPLC and the GC-ECD method of Tacke and Casper showed that DONtest-HPLC is a statistically significant predictor of the GC-ECD method (r2=0.982).     

Copolymerization of studies. Copolymerization of methyl α-cyanocrotonate with styrene,acrylonitrile, and vinyl acetate

Copolymers of methyl α-cyanocrotonate with styrene, acrylonitrile, and vinyl acetate were prepared in bulk by free radical initiation. The copolymerization parameters were determined for each pair by several methods. The basic properties, that is, intrinsic viscosity, solubility, melting range, and glass transition temperature of the obtained copolymers, were determined.     

Einwirkung der natriumzitrate auf das berlinerblau

1. Prussian blue is soluble in the sodium citrates to form sodium ferrocyanide and sodium ferric citrate. It is much less soluble in disodium citrate than in trisodium citrate, and nearly insoluble in monosodium citrate. 2. Colloidal solutions are formed when the sodium citrates are added to Prussian blue in much smaller quantities than is required to produce a complete solution. 3. The peptizing action of the sodium citrates is explained by the formation of water soluble colloidal sodium ferric ferrocyanide NaFe[Fe(CN)₆]. 4. The peptizing action of the potassium oxalates and of the neutral alkali tartrates is also explained by the formation of KFe[Fe(CN)₆].