A mixed‐FEM formulation for nonlinear incompressible elasticity in the plane

This article deals with an expanded mixed finite element formulation, based on the Hu‐Washizu principle, for a nonlinear incompressible material in the plane. We follow our related previous works and introduce both the stress and the strain tensors as further unknowns, which yields a two‐fold saddle point operator equation as the corresponding variational formulation. A slight generalization of the classical Babu?ka‐Brezzi's theory is applied to prove unique solvability of the continuous and discrete formulations, and to derive the corresponding a priori error analysis. An extension of the well‐known PEERS space is used to define an stable associated Galerkin scheme. Finally, we provide an a posteriori error analysis based on the classical Bank‐Weiser approach. © 2002 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 18: 105–128, 2002     

Cathodoluminescence study of extended defects in hydrothermal ZnO crystals

Understanding the luminescence of ZnO is very important for some applications. In spite of the many studies carried out, there are still some points concerning the origin of some of the luminescence emissions in ZnO crystals that require additional study; in particular, the role of extended defects remains to be a matter of controversy. We present here a cathodoluminescence analysis of the defects generated by Vickers indentation in hydrothermal HTT crystals. Special emphasis was paid to the luminescence band peaking around 3.3 eV. The origin of this band is a matter of controversy, since it has been related to different causes, extended defects being one of the candidates for this emission. The CL images were acquired around crystal defects. It is observed that the 3.3 eV emission is enhanced around the crystal defects; though it is also observed, but weaker, out of the defect regions, which suggests that there exist two luminescence emissions peaking very close to 3.3 eV. The two emissions, one related to structural defects and the other to the LO phonon replica of the free excitonic band, appear very close each other and their relative intensity should determine the shape of the spectrum.     

Rotational Motion of a Solute Molecule in a Highly Viscous Liquid Studied byC NMR: 1,3-Dibromoadamantane in Polymeric Chlorotrifluoroethene

The viscosity-dependent retarding effect of a polymeric solvent on the rotation of small solute molecules is investigated by¹³C NMR relaxation measurements. It is found that the relaxation data of 1,3-dibromoadamantane in highly viscous polymeric chlorotrifluoroethene can be explained neither by isotropic nor by realistic anisotropic tumbling in a single environment. The experimental data are rationalized in terms of fast exchange between at least two environments with correlation times differing by up to two orders of magnitude. The study shows that a uniform retardation of molecular tumbling by a polymeric solvent, desirable for shifting the NMR observation window in studies of intramolecular mobility, is not always feasible.     

Proof of the Mixing Theorem for Statistical Systems in Classical Physics

In a general measure-theoretic context, it is proved that the action of a stochastic map on a pair of probability distributions can be characterized by the criterion of decreasing mixing distance.     

Reihenentwicklungen im Weylschen Grenzkreisfall über einem halbunendlichen Intervall

Zusammenfassung Im Anschlu an eine frühere Arbeit beweisen wir im Grenzkreisfall für das Intervall s< einen Entwicklungssatz für reelle Funktionen bei vorgeschriebenen reellen Randbedingungen in s=0 und s=. Die Hilfsmittel sind: 1) der reelle Ansatz; 2) der explizite Ausdruck für die Greensche Funktion von Weyl und 3) die allgemeine Parsevalsche Gleichung.     

Accurate determination of wavenumbers for iodine molecular lines in the red spectral region

The hyperfine structure of various absorption lines of molecular iodine with wavenumbers between 12980 and 13890 cm^–1 has been resolved using Doppler-free polarization spectroscopy. The wavenumbers of theo-component of 17 rovibrational lines of I₂ due to the transitionB ³ _ou ⁺ –X¹ _g ⁺ with even rotational quantum numbers have been determined with an accuracy of 0.001 cm^–1. A comparison of the centers of gravity of these 17 lines with the values of the iodine atlas of Gerstenkorn et al. yields a difference of thus corroborating the data of the iodine atlas in the red region within limits of error.     

Chiral Derivatives of Achiral Molecules: Standard Classes and the Problem of a Right-Left Classification

Chemistry judging by its applications, physics according to its methods, and heavily reliant upon the tools of mathematics—that is what makes theoretical chemistry. And yet that is where its strength lies—in the variety of these sciences. It is quite natural that, in answer to specific problems, results and methods can sometimes be developed whose scope extends far beyond the original application. Rather it is a mark of quality if consequences can be found in chemistry and physics and the pathway leads via new mathematical procedures and concepts. Regrettably, any publication aiming to present such aspects will usually encounter little resonance since the linguistic confusion in science, its disciplines, and subdisciplines, lies like a veil over our understanding. The author nevertheless wishes to attempt to present, in a series of articles, results of research into chemical themes in a manner designed to appeal to the interest of chemists, without neglecting interdisciplinary aspects. All that is required to understand the argumentation is a lively interest. The first two articles are concerned with the chirality of molecules, and in particular with questions relating to the chirality phenomenon of molecules in the framework of molecular classes. In view of the algebraic nature of the mathematical methods adopted, it is not surprising that precise statements result. It appears of primary interest to establish the degree to which such statements can be considered valid for molecular models or molecules themselves.