This work presents an algorithm for injectively parameterizing surfaces into spherical target domains called spherical orbifolds. Spherical orbifolds are cone surfaces that are generated from symmetry groups of the sphere. The surface is mapped the spherical orbifold via an extension of Tutte’s embedding. This embedding is proven to be bijective under mild additional assumptions, which hold in ...

We search for spherically symmetric solutions of f(R) theories of gravity via the Noether Symmetry Approach. A general formalism in the metric framework is developed considering a point-like f(R) Lagrangian where spherical symmetry is required. Examples of exact solutions are given. PACS numbers: 98.80.-k, 95.35.+x, 95.35.+d, 04.50.+h

We obtain various explicit solutions to the interior Einstein-Maxwell equations in spherical and plane symmetry when the pressure is proportional to the mass density.

We study the properties of certain affine invariant measures of symmetry associated to a compact convex body L in a Euclidean vector space. As functions of the interior of L, these measures of symmetry are proved or disproved to be concave in specific situations, notably for the reduced moduli of spherical minimal immersions. MSC 2000: 53C42

In the context of simple mechanical systems with symmetry, we give a method based on blowing up the amended potential for obtaining symmetry-breaking branches of relative equilibria bifurcating from a given set of symmetric relative equi-libria. The general method is illustrated with two concrete mechanical examples, the double spherical pendulum and the symmetric coupled rigid bodies.

In this paper, we propose a new numerical method to compute the ground state solution of trapped interacting Bose-Einstein condensation (BEC) at zero or very low temperature by directly minimizing the energy functional via finite element approximation. As preparatory steps we begin with the 3d Gross-Pitaevskii equation (GPE), scale it to get a three-parameter model and show how to reduce it to ...

In this paper, we propose a new numerical method to compute the ground-state solution of trapped interacting Bose–Einstein condensation at zero or very low temperature by directly minimizing the energy functional via finite element approximation. As preparatory steps we begin with the 3d Gross–Pitaevskii equation (GPE), scale it to get a three-parameter model and show how to reduce it to 2d and...

In this work, the non-isothermal Navier–Stokes equations are studied from the group theory point of view. The symmetry group of the equations is presented and discussed. Some standard turbulence models are analyzed with the symmetries of the equations. A class of turbulence models which preserve the physical properties contained in the symmetry group is built. The proposed turbulence models are...

Chemists have defined the point group of a molecule as the group of rigid symmetries of its molecular graph in R3. While this group is useful for analyzing the symmetries of rigid molecules, it does not include all of the symmetries of molecules which are flexible or can rotate around one or more bonds. To study the symmetries of such molecules, we define the topological symmetry group of a gra...

In this paper we study enumeration problems for polytopes arising from combinatorial optimization problems. While these polytopes turn out to be quickly intractable for enumeration algorithms designed for general polytopes, tailor-made algorithms using their rich combinatorial features can exhibit strong performances. The main engine of these combinatorial algorithms is the use of the large sym...