We consider a $${\mathcal {C}}^1$$ vector field X defined on an open subset U of the plane with compact closure. If has no singular points and if is simply connected, weak version Poincaré–Bendixson theorem says that limit sets in are empty but one can define non extended contained boundary U. give elementary proof this result, independent classical theorem. A trapping triangle {T}}$$ based at ...

We report microstructures of SU-8 photo-sensitive polymer with high-aspect-ratio, which is defined as the ratio of height to in-plane feature size. The highest aspect ratio achieved in this work exceeds 250. A multi-layer and single-photon lithography approach is used in this work to expose SU-8 photoresist of thickness up to 100 μm. Here, multi-layer and time-lapsed writing is the key concept ...

This report outlines the possibilities to be found using one or more diffraction-limited high-quality light beams to activate a weakly absorbing gas in a regime where the diffraction spread can be controlled by converging optical devices to within a ratio ofJ2 of the minimum at the beam waist (corresponding lengths between converging elements are within twice the Rayleigh range). Our desigr.s u...