A metric property of umbilic points

In the space $\mathbb U^4$ of cubic forms of surfaces, regarded as a $G$-space and endowed with a natural invariant metric, the ratio of the volumes of those representing umbilic points with negative to those with positive indexes is evaluated in terms of the asymmetry of the metric, defined here. A connection of this ratio with that reported by Berry and Hannay (1977) in the domain of Statistical Physics, is discussed.Comment: 8 pages, 1 figur

Stabilizing Entangled States with Quasi-Local Quantum Dynamical Semigroups

We provide a solution to the problem of determining whether a target pure state can be asymptotically prepared using dissipative Markovian dynamics under fixed locality constraints. Beside recovering existing results for a large class of physically relevant entangled states, our approach has the advantage of providing an explicit stabilization test solely based on the input state and constraints of the problem. Connections with the formalism of frustration-free parent Hamiltonians are discussed, as well as control implementations in terms of a switching output-feedback law.Comment: 11 pages, no figure

Burst statistics in Alcator C-Mod SOL turbulence

Bursty fluctuations in the scrape-off layer (SOL) of Alcator C-Mod have been analyzed using gas puff imaging data. This reveals many of the same fluctuation properties as Langmuir probe measurements, including normal distributed fluctuations in the near SOL region while the far SOL plasma is dominated by large amplitude bursts due to radial motion of blob-like structures. Conditional averaging reveals burst wave forms with a fast rise and slow decay and exponentially distributed waiting times. Based on this, a stochastic model of burst dynamics is constructed. The model predicts that fluctuation amplitudes should follow a Gamma distribution. This is shown to be a good description of the gas puff imaging data, validating this aspect of the model.Comment: 8 pages, 6 figure