The internal structures, stability, and elastic properties of free-standing filament bundles of bent-core smectic liquid crystals are studied using polarizing microscopy, scanning electron microscopy, and a customized cantilever containing, temperature controlled heat stage for force measurements. We find that in bundles, the individual filaments fuse together to form semiseparable filaments wi...

Using extensive Molecular Dynamics simulations we study the behavior of polyelectrolytes with hydrophobic side chains, which are known to form cylindrical micelles in aqueous solution. We investigate the stability of such bundles with respect to hydrophobicity, the strength of the electrostatic interaction, and the bundle size. We show that for the parameter range relevant for sulfonated poly-p...

We study projectivizations of a special class of toric vector bundles that includes cotangent bundles, whose associated Klyachko filtrations are particularly simple. For these projectivized bundles, we give generators for the cone of effective divisors and a presentation of the Cox ring as a polynomial algebra over the Cox ring of a blowup of a projective space along a sequence of linear subspa...

Discrete vector bundles are important in Physics and recently found remarkable applications in Computer Graphics. This article approaches discrete bundles from the viewpoint of Discrete Differential Geometry, including a complete classification of discrete vector bundles over finite simplicial complexes. In particular, we obtain a discrete analogue of a theorem of André Weil on the classificati...

We review some recent results in the theory of affine manifolds and bundles on them. Donaldson–Uhlenbeck–Yau type correspondences for flat vector bundles and principal bundles are shown. We also consider flat Higgs bundles and flat pairs on affine manifolds. A bijective correspondence between polystable flat Higgs bundles and solutions of the Yang–Mills–Higgs equation in the context of affine m...

The actin bundles in Drosophila bristles run the length of the bristle cell and are accordingly 65 microns (microchaetes) or 400 microns (macrochaetes) in length, depending on the bristle type. Shortly after completion of bristle elongation in pupae, the actin bundles break down as the bristle surface becomes chitinized. The bundles break down in a bizarre way; it is as if each bundle is sawed ...

After a quick review of the Picard variety and Brill–Noether theory, we generalize them to holomorphic rank-two vector bundles of canonical determinant over a compact Riemann surface. We propose several problems of Brill–Noether type for such bundles and announce some of our results concerning the Brill–Noether loci and Fano threefolds. For example, the locus of rank-two bundles of canonical de...