A Monte Carlo simulation has been performed to track light rays in cylindrical fibres by ray optics. The trapping efficiencies for skew and meridional rays in active fibres and distributions of characteristic quantities for all trapped light rays have been calculated. The simulation provides new results for curved fibres, where the analytical expressions are too complex to be solved. The light ...

Spaces with radially symmetric curvature at base point p are shown to be diffeomorphic to space forms. Furthermore, they are either isometric to Rn or Sn under a radially symmetric metric, to RPn with Riemannian universal covering of Sn equipped with a radially symmetric metric, or else have constant curvature outside a metric ball of radius equal to the injectivity

We report analytical results for the development of the viscous fingering instability in a cylindrical Hele-Shaw cell of radius a and thickness b. We derive a generalized version of Darcy's law in such cylindrical background, and find it recovers the usual Darcy's law for flow in flat, rectangular cells, with corrections of higher order in b/a. We focus our interest on the influence of the cell...

Gromov conjectured that the fundamental group of a manifold with almost nonnegative Ricci curvature is almost nilpotent. This conjecture is proved under the additional assumption on the conjugate radius. We show that there exists a nilpotent subgroup of finite index depending on a lower bound of the conjugate radius.

Three-dimensional transient deformations of clamped flat and doubly curved polycarbonate (PC) panels impacted by a rigid smooth hemispherical-nosed circular cylinder have been numerically studied by the finite-element (FE) method to delineate effects of the panel radius of curvature to its thickness ratio on their penetration resistance. The PC is modeled as thermoelastoviscoplastic with the ef...

We examine the quark mass dependence of the pion vector form factor, particularly the curvature (mean quartic radius). We focus our study on the consequences of assuming that the coupling constant of the ρ to pions, gρππ, is largely independent of the quark mass while the quark mass dependence of the ρ–mass is given by recent lattice data. By employing the Omnès representation we can provide a ...

We present a novel algorithm to compute multi-scale curvature fields on triangle meshes. Our algorithm is based on finding robust mean curvatures using the ball neighborhood, where the radius of a ball corresponds to the scale of the features. The essential problem is to find a good radius for each ball to obtain a reliable curvature estimation. We propose an algorithm that finds suitable radii...

By applying the spectral decomposition of a submanifold of a Euclidean space, we derive several sharp geometric inequalities which provide us some best possible relations between volume, center of mass, circumscribed radius, inscribed radius, order, and mean curvature of the submanifold. Several of our results sharpen some well-known geometric inequalities.