Contractibility results for certain spaces of Riemannian metrics on the disc

We provide a general contractibility criterion for subsets of Riemannian metrics on the disc. For instance, this result applies to the space of metrics that have positive Gauss curvature and make the boundary circle convex (or geodesic). The same conclusion is not known in any dimension $n\geq 3$, and (by analogy with the closed case) is actually expected to be false for many values of $n\geq 4$.Comment: Final pre-print version; to appear in Mathematical Research Letter

Multifunctional Conductive Paths Obtained by Laser Processing of Non-Conductive Carbon Nanotube/Polypropylene Composites

Functional materials are promising candidates for application in structural health monitoring/self-healing composites, wearable systems (smart textiles), robotics, and next-generation electronics. Any improvement in these topics would be of great relevance to industry, environment, and global needs for energy sustainability. Taking into consideration all these aspects, low-cost fabrication of electrical functionalities on the outer surface of carbon-nanotube/polypropylene composites is presented in this paper. Electrical-responsive regions and conductive tracks, made of an accumulation layer of carbon nanotubes without the use of metals, have been obtained by the laser irradiation process, leading to confined polymer melting/vaporization with consequent local increase of the nanotube concentration over the electrical percolation threshold. Interestingly, by combining different investigation methods, including thermogravimetric analyses (TGA), X-ray diffraction (XRD) measurements, scanning electron and atomic force microscopies (SEM, AFM), and Raman spectroscopy, the electrical properties of multi-walled carbon nanotube/polypropylene (MWCNT/PP) composites have been elucidated to unfold their potentials under static and dynamic conditions. More interestingly, prototypes made of simple components and electronic circuits (resistor, touch-sensitive devices), where conventional components have been substituted by the carbon nanotube networks, are shown. The results contribute to enabling the direct integration of carbon conductive paths in conventional electronics and next-generation platforms for low-power electronics, sensors, and devices