Exponential averaging for traveling wave solutions in rapidly varying periodic media

Reaction diffusion systems on cylindrical domains with terms that vary rapidly and periodically in the unbounded direction can be analyzed by averaging techniques. Here, using iterated normal form transformations and Gevrey regularity of bounded solutions, we prove a result on exponential averaging for such systems, i.e., we show that traveling wave solutions can be described by a spatially homogenous equation and exponentially small remainders. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

THE PECULIAR α-AMIDOALKYLATION OF VINYLTRIMETHYLSILANE

Abstract

α-Amidoalkylation of allyttrimethylsilane with methyl-2-chloro-2-(p-chlorobenzoylamino)-ethanoate 1 gave in the presence of Lewis acid racemic methyl-2- (p-chlorobenzoylamino)-4-penteno ate 2. Under the same conditions, vinlytrimethylsilane afforded (±)-trans-2-(p-chlorophenyl)-5,6-dihydro-4-methoxycarbonyl-6-trimethylsilyl-4H-1, 3-oxazine 4 as the major, by n.m.r. data and x-ray crystallography established product.     

Partitioned solution to fluid–structure interaction problem in application to free-surface flows

In this work we discuss a way to compute the impact of free-surface flow on nonlinear structures. The approach chosen relies on a partitioned strategy that allows us to solve the strongly coupled fluid–structure interaction problem. It is then possible to re-use the existing and validated strategy for each sub-problem. The structure is formulated in a Lagrangian way and solved by the finite element method. The free-surface flow approach considers a Volume-Of-Fluid (VOF) strategy formulated in an Arbitrary Lagrangian–Eulerian (ALE) framework, and the finite volume is used to discrete and solve this problem. The software coupling is ensured in an efficient way using the Communication Template Library (CTL). Numerical examples presented herein concern the 2D validation case but also 3D problems with a large number of equations to be solved.     

Economy of effort in different speaking conditions. I. A preliminary study of intersubject differences and modeling issues

This study explores the hypothesis that clear speech is produced with greater "articulatory effort" than normal speech. Kinematic and acoustic data were gathered from seven subjects as they pronounced multiple repetitions of utterances in different speaking conditions, including normal, fast, clear, and slow. Data were analyzed within a framework based on a dynamical model of single-axis frictionless movements, in which peak movement speed is used as a relative measure of articulatory effort (Nelson, 1983). There were differences in peak movement speed, distance and duration among the conditions and among the speakers. Three speakers produced the "clear" condition utterances with movements that had larger distances and durations than those for "normal" utterances. Analyses of the data within a peak speed, distance, duration "performance space" indicated increased effort (reflected in greater peak speed) in the clear condition for the three speakers, in support of the hypothesis. The remaining four speakers used other combinations of parameters to produce the clear condition. The validity of the simple dynamical model for analyzing these complex movements was considered by examining several additional parameters. Some movement characteristics differed from those required for the model-based analysis, presumably because the articulators are complicated structurally and interact with one another mechanically. More refined tests of control strategies for different speaking styles will depend on future analyses of more complicated movements with more realistic models.     

Analysis of relative isotopologue abundances for quantitative profiling of complex protein mixtures labelled with the acrylamide/D3-acrylamide alkylation tag system

The new method of analysis of relative isotopologue abundances (ARIA) applied here is based on the evaluation of total isotope patterns of tryptic protein fragments measured by matrix-assisted laser desorption/ionisation time-of-flight mass spectrometry (MALDI-TOFMS) to calculate the mixing ratios of composites consisting of stable isotope labelled and isotopically natural (unlabelled) proteins, as described in an accompanying paper in this issue. Recently, Sechi (Rapid Commun. Mass Spectrom. 2002; 16: 1416-1424) and Gehanne et al. (Rapid Commun. Mass Spectrom. 2002; 16: 1692-1698) introduced the use of differential quantitative mass analysis by MALDI-TOFMS using mixtures of standard proteins alkylated prior to two-dimensional polyacrylamide gel electrophoresis (2D-PAGE) with either acrylamide (AA) or deuterium-labelled [2,3,3'-D(3)]-acrylamide (D3AA). In the present study we validate the AA/D3AA system, firstly by measuring the yield of proteins alkylated with AA, and secondly by using differential radioactive labels ((125)I and (131)I) to quantitatively establish that non-comigration in 2D-PAGE is negligible. ARIA is then applied to quantitatively estimate the relative proportions of peptides labelled with AA or D3AA in the validated system, using typical silver-stained 2D-PAGE protein spots from 2D gels loaded with 150 microg of total liver protein. The precision and limitations of ARIA quantification of peptides differentially alkylated with isotopomeric reagents are discussed.     

A Deterministic Filter for non-Gaussian State Estimation

The usual mathematical method to represent uncertain quantities, for example the state of a dynamical system with uncertain initial conditions, are random variables (RVs). In many problems the space of elementary events Ω, on which the RVs are defined as functions of these events, is not concretely accessible, so that the usual idea of a function (e.g. given as a formula) loses much of its meaning. The representation of RVs is therefore often strikingly different from what is used for “normal” functions. With the help of RVs one can formulate Bayesian estimators for the uncertain quantity when additional information (usually noisy, incomplete measurements) becomes available. A common way to derive such an estimator is to use an instance of the projection theorem for Hilbert spaces. In this work we present a linear Bayesian estimation method which results from using a recently popular representation of an RV, the polynomial chaos expansion (PCE), also known as “white noise analysis”. The resulting method is completely deterministic, as well as computationally efficient. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stochastic upscaling of random microstructures

In this work we present an upscaling technique for multi-scale computations based on random microstructures modelled as realisations of lognormally distributed random fields, or described by randomly distributed inclusions in a homogeneous matrix. Their corresponding coarse-scale model parameters are considered as uncertain, and are approximated by random variables, the distributions of which are obtained via polynomial chaos based Bayesian procedures in which the fine-scale energy is used as an observation. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Calculation of the energy-level scheme of Pr3+ in crystalline PrF3 from optical and inelastic neutron scattering data

By using a semi-empirical fitting approach and appropriate results of optical spectroscopy and inelastic neutron scattering experiments the energy-level scheme of the crystal field-splitted ³H₄-multiplet of Pr³⁺ in PrF₃ is determined. The results are shown to be in good agreement with the experiments.     

Uncertainty Quantification and Non-Linear Bayesian Update of PCE Coefficients

The Bayesian Update is quite vital for uncertainty quantification. With BU we can take into account the given measurements of our physical model and update the a priori probability density function (which is very often far away from the truth) of the uncertain parameter. The standard full BU is based on sampling and sampling is not always acceptable or possible. In addition, it can require a very large number of samples and is expensive. This led to the development of sampling-free Bayesian updates. We derive it from the variational problem associated with conditional expectation. Whereas the linear BU is a linear function of the prediction mismatch, here we used higher order polynomials. As an example we took the chaotic Lorenz 84 model. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)