On piecewise trivial Hopf—Galois extensions

We discuss a noncommutative generalization of compact principal bundles that can be trivialized relative to the finite covering by closed sets. In this setting we present bundle reconstruction and reduction

Strong Connections on Quantum Principal Bundles

A gauge invariant notion of a strong connection is presented and characterized. It is then used to justify the way in which a global curvature form is defined. Strong connections are interpreted as those that are induced from the base space of a quantum bundle. Examples of both strong and non-strong connections are provided. In particular, such connections are constructed on a quantum deformation of the fibration $S^2 -> RP^2$. A certain class of strong $U_q(2)$-connections on a trivial quantum principal bundle is shown to be equivalent to the class of connections on a free module that are compatible with the q-dependent hermitian metric. A particular form of the Yang-Mills action on a trivial U\sb q(2)-bundle is investigated. It is proved to coincide with the Yang-Mills action constructed by A.Connes and M.Rieffel. Furthermore, it is shown that the moduli space of critical points of this action functional is independent of q.Comment: AMS-LaTeX, 40 pages, major revision including examples of connections over a quantum real projective spac

The Weyl bundle as a differentiable manifold

Construction of an infinite dimensional differentiable manifold ${\mathbb R}^{\infty}$ not modelled on any Banach space is proposed. Definition, metric and differential structures of a Weyl algebra and a Weyl algebra bundle are presented. Continuity of the $\circ$-product in the Tichonov topology is proved. Construction of the $*$-product of the Fedosov type in terms of theory of connection in a fibre bundle is explained.Comment: 31 pages; revised version - some typoes have been eliminated, notation has been simplifie

Structural Transitions and Global Minima of Sodium Chloride Clusters

In recent experiments on sodium chloride clusters structural transitions between nanocrystals with different cuboidal shapes were detected. Here we determine reaction pathways between the low energy isomers of one of these clusters, (NaCl)35Cl-. The key process in these structural transitions is a highly cooperative rearrangement in which two parts of the nanocrystal slip past one another on a {110} plane in a direction. In this way the nanocrystals can plastically deform, in contrast to the brittle behaviour of bulk sodium chloride crystals at the same temperatures; the nanocrystals have mechanical properties which are a unique feature of their finite size. We also report and compare the global potential energy minima for (NaCl)NCl- using two empirical potentials, and comment on the effect of polarization.Comment: extended version, 13 pages, 8 figures, revte

Effect of Impurities on Pentacene Thin Film Growth for Field-Effect Transistors

Pentacenequinone (PnQ) impurities have been introduced into a pentacene source material at number densities from 0.001 to 0.474 to quantify the relative effects of impurity content and grain boundary structure on transport in pentacene thin-film transistors. Atomic force microscopy (AFM) and electrical measurements of top-contact pentacene thin-film transistors have been employed to directly correlate initial structure and final film structures, with the device mobility as a function of added impurity content. The results reveal a factor four decrease in mobility without significant changes in film morphology for source PnQ number fractions below ~0.008. For these low concentrations, the impurity thus directly influences transport, either as homogeneously distributed defects or by concentration at the otherwise-unchanged grain boundaries. For larger impurity concentrations, the continuing strong decrease in mobility is correlated with decreasing grain size, indicating an impurity-induced increase in the nucleation of grains during early stages of film growth.Comment: 18 pages, 4 Figures, 1 Tabl