We show that the set of conical points of a rational function of the Riemann sphere supports at most one conformal measure. We then study the problem of existence of such measures and their ergodic properties by constructing Markov partitions on increasing subsets of sets of conical points and by applying ideas of the thermodynamic formalism. 1 Introduction. In this paper we recall from U2] the...

The study of conical refraction for media other than biaxial non-magnetic crystals has never been considered in the literature – as far as the authors are aware. Hence, in this paper, we investigate how conical refraction can arise for broader classes of biaxial metamaterials using a new classification scheme previously developed by the authors. Namely, conical refraction is shown to occur for ...

Topological defects in elastic media may be described by a geometric field akin to three-dimensional gravity. From this point of view, disclinations are line zero width corresponding singularity the curvature an otherwise flat background. On other hand, two dimensions, Frank free energy nematic liquid crystal interpreted as Abelian Higgs Lagrangian. In work, we construct model coupled ``gravity...

Bow-shock standoff distances over sphere and spherically-blunted cone geometries were examined through experiments in two facilities capable of high-stagnation enthalpy hypersonic flows simulating Mars planetary entry conditions. High-speed high-resolution schlieren images obtained the California Institute Technology T5 reflected shock tunnel Hypervelocity Expansion Tube to examine facility ind...

In this paper we calculate the magnetic and electric self-forces, induced by the conical structure of a cosmic string space-time, on a long straight wire which presents either a constant current or a linear charge density. We also show how these self-forces are related by a Lorentz tranformation and, in this way, explain what two different inertial observers detect in their respective frames. P...

From the point of view of the duality between points and horocycles in a symmetric space, the counterparts to the spherical functions on the symmetric space are the conical distributions on the manifold of horocycles. While the conical functions are closely related to certain finite-dimensional representations of semisimple Lie groups, in the present work the conical distributions are found to ...

This work was aimed at researching and developing a computer model, as well an optimization control algorithm for calculating pore shapes separating membranes in separation processes. Two types of flow fluid rates through with various pores configurations were considered. Here, the first type had form tortuous channel sharp narrowing endings, which, turn, could be assumed “zero” wall thickness ...

density functional theory (dft) calculations were performed to investigate the properties of planar, tubular and conical forms of silicon nanostructures. the evaluated parameters including averaged bond lengths, binding energies, gap energies and dipole moments were then evaluated for the optimized models of study. the results indicated that the bond lengths between silicon atoms are different ...