Locally Collapsed 3-Manifolds

We prove that a 3-dimensional compact Riemannian manifold which is locally collapsed, with respect to a lower curvature bound, is a graph manifold. This theorem was stated by Perelman and was used in his proof of the geometrization conjecture.Comment: Final versio

Identifying collapsed buildings

THE WORK TO RECOVER AND REBUILD FOLLOWING an earthquake requires reliable information on the condition of structures in the affected areas. In developed areas, efforts to gather this information can be time-consuming and prone to errors, often resulting in incomplete or inaccurate information. A new, software-based methodology to recognize collapsed buildings utilizes classification of satellite images combined with height variation information. The methodology was demonstrated in a full-scale, real-life scenario by a team led by Prof. Valerio Baiocchi of the University of Rome. According to Baiocchi, the team’s work was intended to demonstrate the methodology on actual data available for the entire city of L’Aquila in the Abruzzo region of central Italy, in an actual and complete simulation of quick damage assessment in a real emergency. The team utilized satellite imagery of the city of L’Aquila, which experienced a magnitude 6.3 earthquake on April 6, 2009. The work demonstrated a robust classification of collapsed structures that was completed quickly and with good confidence

Theory of electrostatically induced shape transitions in carbon nanotubes

A mechanically bistable single-walled carbon nanotube can act as a variable-shaped capacitor with a voltage-controlled transition between collapsed and inflated states. This external control parameter provides a means to tune the system so that collapsed and inflated states are degenerate, at which point the tube's susceptibility to diverse external stimuli-- temperature, voltage, trapped atoms -- diverges following a universal curve, yielding an exceptionally sensitive sensor or actuator that is characterized by a vanishing energy scale. For example, the boundary between collapsed and inflated states can shift hundreds of Angstroms in response to the presence or absence of a single gas atom in the core of the tube. Several potential nano-electromechanical devices can be based on this electrically tuned crossover between near-degenerate collapsed and inflated configurations