Engineering Nanomotor Components from Multi-Walled Carbon Nanotubes via Reactive Ion Etching

Abstract. It has been shown that a multi-walled carbon nanotube (MWCNT) can be used as the rotation enabling element for nanoelectromechanical systems. Modification of the MWCNT to create a rotational bearing in previous devices has concentrated on smaller diameter tubes and mechanical methods to create the bearing. We here investigate reactive ion etching of a MWCNT as a means to engineer nanomotor components, including the rotational bearing

The Pure Virtual Braid Group Is Quadratic

If an augmented algebra K over Q is filtered by powers of its augmentation ideal I, the associated graded algebra grK need not in general be quadratic: although it is generated in degree 1, its relations may not be generated by homogeneous relations of degree 2. In this paper we give a sufficient criterion (called the PVH Criterion) for grK to be quadratic. When K is the group algebra of a group G, quadraticity is known to be equivalent to the existence of a (not necessarily homomorphic) universal finite type invariant for G. Thus the PVH Criterion also implies the existence of such a universal finite type invariant for the group G. We apply the PVH Criterion to the group algebra of the pure virtual braid group (also known as the quasi-triangular group), and show that the corresponding associated graded algebra is quadratic, and hence that these groups have a (not necessarily homomorphic) universal finite type invariant.Comment: 53 pages, 15 figures. Some clarifications added and inaccuracies corrected, reflecting suggestions made by the referee of the published version of the pape

Around the tangent cone theorem

A cornerstone of the theory of cohomology jump loci is the Tangent Cone theorem, which relates the behavior around the origin of the characteristic and resonance varieties of a space. We revisit this theorem, in both the algebraic setting provided by cdga models, and in the topological setting provided by fundamental groups and cohomology rings. The general theory is illustrated with several classes of examples from geometry and topology: smooth quasi-projective varieties, complex hyperplane arrangements and their Milnor fibers, configuration spaces, and elliptic arrangements.Comment: 39 pages; to appear in the proceedings of the Configurations Spaces Conference (Cortona 2014), Springer INdAM serie

Length control and sharpening of atomic force microscope carbon nanotube tips assisted by an electron beam

Abstract We report on the precise positioning of a carbon nanotube on an atomic force microscope (AFM) tip. By using a nanomanipulator inside a scanning electron microscope, an individual nanotube was retrieved from a metal foil by the AFM tip. The electron beam allows us to control the nanotube length and to sharpen its end. The performance of these tips for AFM imaging is demonstrated by improved lateral resolution of DNA molecules