An invariant for unbounded operators

For a class of unbounded operators, a deformation of a Bott projection is used to construct an integer-valued invariant measuring deviation of the non-commutative deformations from the commutative originals, and its interpretation in terms of -theory of -algebras is given. Calculation of this invariant for specific important classes of unbounded operators is also presented.

     

Potassium Doped Single Wall Carbon Nanotubes: Resistance under Pressure

Abstract

We report in situ measurements of four-probe de resistance (R) of K-doped purified single wall carbon nanotube (SWNT) “buckypaper” as a function of quasi-hydrostatic pressure. Doped samples show completely different behavior compared to that of pristine nanotubes in the pressure range up to 90 kbar. The characteristic increase in the resistance of pristine buckypaper above 10 kbar, associated with the formation of kinks or/and twists of tubes, is not observed in K-doped samples. This may originate from 1) a substantial change in electronic band structure of donor intercalated nanotubes, 2) completely different transport properties of defect structures, or 3) higher stiffness of doped SWNT's which prevents formation of kinks and twists in this pressure range. On deintercalation, the pristine behavior of R(P) is restored, establishing the reversibility of potassium vapor-transport doping.     

A Riemann–Hilbert approach to Painlevé IV

The methods of [vdP-Sa, vdP1, vdP2] are applied to the fourth Painlevé equation. One obtains a Riemann–Hilbert correspondence between moduli spaces of rank two connections on ?¹ and moduli spaces for the monodromy data. The moduli spaces for these connections are identified with Okamoto–Painlevé varieties and the Painlevé property follows. For an explicit computation of the full group of Bäcklund transformations, rank three connections on ?¹ are introduced, inspired by the symmetric form for PIV, studied by M. Noumi and Y. Yamada.     

Solutions of the Classical Yang–Baxter Equation and Noncommutative Deformations

We show that given a finite-dimensional real Lie algebra acting on a smooth manifold P then, for any solution of the classical Yang–Baxter equation on , there is a canonical Poisson tensor on P and an associated canonical torsion-free and flat contravariant connection. Moreover, we prove that the metacurvature of this contravariant connection vanishes if the isotropy Lie subalgebras of the action are trivial. Those results permit to get a large class of smooth manifolds satisfying the necessary conditions, introduced by Eli Hawkins, to the existence of noncommutative deformations. Recherche menée dans le cadre du Programme Thématique d’Appui à la Recherche Scientifique PROTARS III.     

Adaptive remeshing for ductile fracture prediction in metal formingRemaillage adaptatif pour la prévision de la rupture ductile en mise en forme

The analysis of mechanical structures using the Finite Element Method in the framework of large elastoplastic strain, needs frequent remeshing of the deformed domain during computation. Indeed, the remeshing is due to the large geometrical distortion of finite elements and the adaptation to the physical behavior of the solution. This paper gives the necessary steps to remesh a mechanical structure during large elastoplastic deformations with damage. An important part of this process is constituted by geometrical and physical error estimates. The proposed method is integrated in a computational environment using the ABAQUS/Explicit solver and the BL2D-V2 adaptive mesher. To cite this article: H. Borouchaki et al., C. R. Mecanique 330 (2002) 709–716.     

Some Infinite-Dimensional Algebras Arising in Spin Systems and in Particle Physics and their Grand Algebra

We indicate similarities in the structure of two types of infinite-dimensional algebras, one introduced 28 years ago in connection with the mass problem of elementary particles and the other seven years ago in connection with spin systems (XY models). We show that these algebras can be considered as representations of a single Grand Algebra, the enveloping algebra of an affine Kac–Moody algebra built on the Poincaré Lie algebra. As an associative and coassociative bialgebra of operators, the latter representation of the grand algebra is a preferred nontrivial deformation of the Ising case bialgebra.     

On singular limits to Bodner–Partom model

This paper proves global in time existence of large solutions for a problem in non‐linear inelasticity with viscosity given by the term $cL\partial_tu$\nopagenumbers\end . In addition we study singular limits $c\mapsto0$\nopagenumbers\end . The proofs are based on energy methods. Copyright © 2001 John Wiley & Sons, Ltd.     

Detection of Photoemission of Electrons into Anthracene Crystals by Studying Recom ination Radiation

Evidence for photoemission of electrons from a calcium contact into anthracene crystals is presented. It is based on the observation of recombination radiation resulting from mutual annihilation of photoinjected electrons with holes which are supplied by an ohmic counter-electrode. The method avoids spurious effect's due to optical release of trapped electrons. The problem of photoemission of electrons from alkali-metals into anthracene crystals is discussed.     

Photolithographically Patterned Hydrogels with Programmed Deformations

Programmed deformations are widespread in nature, providing elegant paradigms to design self‐morphing materials with promising applications in biomedical devices, flexible electronics, soft robotics, etc. In this emerging field, hydrogels are an ideal material to investigate the deformation principle and the structure‐deformation relationship. One crucial step is to construct heterogeneous structures in a facile yet effective way. Herein, we provide a focus review on different deformation modes and corresponding structural features of hydrogels. Photolithography is a versatile approach to control the outer shape of the hydrogel and spatial distribution of the component in the hydrogel, endowing the patterned hydrogels with programmed internal stress and thus controllable deformations. Specifically, cooperative deformations take place in periodically patterned hydrogels with in‐plane gradients, and multiple morphing structures are formed in one patterned hydrogel using selective preswelling to direct the buckling of each unit. The structural control strategy and deformation principles should be applicable to other materials with broad applications in diverse areas.