We have studied the large-scale beam breakup and filamentation of femtosecond pulses in a Kerr medium. We have experimentally monitored the formation of stable light filaments, conical emission, and interactions between filaments. Three major stages lead to the formation of stable light filaments: First the beam breaks up into a pattern of connected lines sconstellationd, then filaments form on...

A dilatation structure encodes the approximate self-similarity of a metric space. A metric space (X, d) which admits a strong dilatation structure (definition 2.2) has a metric tangent space at any point x ∈ X (theorem 4.1), and any such metric tangent space has an algebraic structure of a conical group (theorem 4.2). Particular examples of conical groups are Carnot groups: these are simply con...

Estimating the intrinsic dimension of a high-dimensional data set is a very challenging problem in manifold learning and several other application areas in data mining. In this paper we introduce a novel local intrinsic dimension estimator, conical dimension, for estimating the intrinsic dimension of a data set consisting of points lying in the proximity of a manifold. Under minimal sampling as...

Many mammals forage and burrow in dark constrained spaces. Touch through facial whiskers is important during these activities, but the close quarters makes whisker deployment challenging. The diverse shapes of facial whiskers reflect distinct ecological niches. Rodent whiskers are conical, often with a remarkably linear taper. Here we use theoretical and experimental methods to analyze interact...

Casimir energies for a massless scalar field for a conical wedge and a conical cavity are calculated. The group generated by the images is employed in deriving the Green function as well as the wave functions and the energy spectrum.

A number of commonly available density functionals have been tested for their ability to describe the energetics and the geometry at conical intersections in connection with the spin-restricted ensemble referenced Kohn-Sham (REKS) method. The minimum energy conical intersections have been optimized for several molecular systems, which are widely used as paradigmatic models of photochemical rear...

Two-particle azimuthal correlations in central Au+Au collisional at RHIC have revealed a broadened away-side structure, with respect to perpherial Au+Au, pp, and d+Au. This could be explained by different physics mechanisms such as: large angle gluon radiation, deflected jets, Ĉerenkov gluon radiation, and conical flow generated by hydrodynamic shock-waves. We can discriminate the scenarios wit...