Theoretical framework and experimental procedure for modelling mesoscopic volume fraction stochastic fluctuations in fiber reinforced composites

Many engineering materials exhibit fluctuations and uncertainties on their macroscopic mechanical properties. This randomness results from random fluctuations observed at a lower scale, especially at the meso-scale where microstructural uncertainties generally occur. In the present paper, we first propose a complete theoretical stochastic framework (that is, a relevant probabilistic model as well as a non-intrusive stochastic solver) in which the volume fraction at the microscale is modelled as a random field whose statistical reduction is performed using a Karhunen–Loeve expansion. Then, an experimental procedure dedicated to the identification of the parameters involved in the probabilistic model is presented and relies on a non-destructive ultrasonic method. The combination of the experimental results with a micromechanical analysis provides realizations of the volume fraction random field. In particular, it is shown that the volume fraction can be modelled by a homogeneous random field whose spatial correlation lengths are determined and may provide conditions on the size of the meso-volumes to be considered.     

Enhanced Binding in Non-Relativistic QED

 We consider a spinless particle coupled to a photon field and prove that even if the Schr?dinger operator p ² +V does not have eigenvalues the system can have a ground state. We describe the coupling by means of the Pauli-Fierz Hamiltonian and our result holds in the case where the coupling constant α is small. Received: 7 January 2002 / Accepted: 8 November 2002 Published online: 13 January 2003     

Crystallographic report: Crystal structure of 1‐bromo‐1′‐[(2S)‐N‐(1‐hydroxy‐3‐methylbutane‐2‐yl)]‐ferroceneamide

For the unsymmetrical title compound, 1‐bromo‐1′‐[(2S)‐N‐(1‐hydroxy‐3‐methylbutane‐2‐yl)]‐ferroceneamide, two independent molecules were found in the asymmetric unit. Copyright © 2003 John Wiley & Sons, Ltd.     

Analysis and interpretation of new low-energy \pi\pi scattering data

The recently published E865 data on charged decays and phases are reanalyzed to extract values of the two S-wave scattering lengths, of the subthreshold parameters and , of the low-energy constants and as well as of the main two-flavour order parameters: and in the limit taken at the physical value of the strange quark mass. Our analysis is exclusively based on direct experimental information on phases below 800 MeV and on the new solutions of the Roy equations by Ananthanarayan et al. The result is compared with the theoretical prediction relating 2a ₀ ⁰-5a ₀ ² and the scalar radius of the pion, which was obtained in two-loop Chiral Perturbation Theory. A discrepancy at the 1- level is found and commented upon. Received: 11 December 2001 / Revised version: 28 March 2002 / Published online: 7 June 2002