The Boolean Prime Ideal Theorem Plus Countable Choice Do Not Imply Dependent Choice

Two Fraenkel-Mostowski models are constructed in which the Boolean Prime Ideal Theorem is true. In both models, AC for countable sets is true, but AC for sets of cardinality 2 and the 2m = m principle are both false. The Principle of Dependent Choices is true in the first model, but false in the second. Mathematics Subject Classification: 03E25, 03E35, 04A25.     

Domain decomposition methods for the study of the particular behavior of a very thin long structure

The homogenization process of the Poisson equations in a thin structure leads to partial differential equation systems on different subdomains. As a result, it produces artificial interfaces and particular transmission conditions. © 1996 John Wiley & Sons, Inc.     

On the Distribution of Free Path Lengths¶for the Periodic Lorentz Gas

Consider the domain

Dynamic behavior of photoablation products of corneal tissue in the mid-IR: a study with FELIX

2 . Dynamic parameters such as the extension of the ablation cloud, the initial velocity and momentum of the ablated particles as well as the ablation threshold, the ablated mass, and the particle size were investigated. The ablation plume was made visible with a stroboscopic technique. For a fluence of 3.1 J/cm² the average initial velocity of the ejected particles was deduced from the extension of the plume to range from 120–400 m/s. Measurements of the recoil momentum using a sensitive pendulum led to values between 0.5 and 2.0 mm g/s. All measured properties were related to the spectroscopically determined absorption coefficient of cornea α_cornea. Where absorption due to proteins is high (at λ=6.2 and 6.5 μm), ablated mass, velocity and recoil momentum behave according to α_cornea. For the first time, variations of the ablation plume from pulse to pulse were observed. Those, as well as the particle size, not only depend on the absorption coefficient, but also on the predominant absorber. Received: 4 November 1997/Revised version: 7 September 1998     

High resolution electron backscatter diffraction (EBSD) data from calcite biominerals in recent gastropod shells

Electron backscatter diffraction (EBSD) is a microscopy technique that reveals in situ crystallographic information. Currently, it is widely used for the characterization of geological materials and in studies of biomineralization. Here, we analyze high resolution EBSD data from biogenic calcite in two mollusk taxa, Concholepas and Haliotis, previously used in the understanding of complex biomineralization and paleoenvironmental studies. Results indicate that Concholepas has less ordered prisms than in Haliotis, and that in Concholepas the level of order is not homogenous in different areas of the shell. Overall, the usefulness of data integration obtained from diffraction intensity and crystallographic orientation maps, and corresponding pole figures, is discussed as well as its application to similar studies.     

Probing the fluctuation-dissipation theorem in a Perrin-like experiment

In this Letter, we present a new experimental approach to investigate the effective temperature concept as a generalization of the fluctuation-dissipation theorem (FDT) for nonequilibrium systems. Simultaneous measurements of diffusion coefficient and sedimentation velocity of heavy colloids, embedded in a Laponite clay suspension, are performed with a fluorescence-recovery-based setup. This nonperturbative dual measurement, performed at a single time in a single sample, allows for a direct application of the FDT to the tracer velocity observable. It thus provides a well-defined derivation of the effective temperature in this ageing colloidal gel. For a wide range of concentrations and ageing times, we report no violation of the FDT, with effective temperature agreeing with bath temperature. This result is consistent with recent theoretical predictions on the coupling between the velocity observable and nonequilibrium gels dynamics.     

Short-range order and F ion diffusion inside the Pb1 − xAlxF2 + x solid solution Part II: Al NMR investigation and proposal of clustering process

A ²⁷Al nuclear magnetic resonance (NMR) investigation at room temperature of the Pb_{1 − x}Al_xF_{2 + x} (0 ≤ x ≤ 0.12) solid solution and of the ordered Pb₉Al₂F₂₄ phase is carried out. Two different types of aluminium ions are identified and their ratio is determined as a function of x. A clustering process based on the formation of column clusters, more and more extended when x increases, is proposed on the basis of results issued from the ¹⁹F (Part I) and ²⁷Al NMR investigations.