In this paper, we implement finite volume Weighted Essentially Non-Oscillatory (WENO) schemes in both cylindrical and spherical coordinate systems for the Euler equations with cylindrical or spherical symmetry. We analyze three different spatial discretizations: one that is shown to be high-order accurate but not conservative, one conservative but not high-order accurate, and one both high-orde...

A new converter with spherical cap for energy scavenging is proposed. Based on the method of separated variables within the torrid coordinate system, a corresponding analytical model for spherical cap converter is further established so as to obtain the analytic expressions of the topology capacitance and the output voltage. The concept of energy increment factor is specifically defined to deno...

Aims. We extend our framework for 3D radiative transfer calculations with a non-local operator splitting methods along (full) characteristics to spherical and cylindrical coordinate systems. These coordinate systems are better suited to a number of physical problems than Cartesian coordinates. Methods. The scattering problem for line transfer is solved via means of an operator splitting (OS) te...

Let G be a simple algebraic group over an algebraically closed field k of characteristic zero and O be a spherical conjugacy class of G. We determine the decomposition of the coordinate ring k[O] of O into simple G-modules.

For many problems in astrophysics and space sciences, it is desirable to compute solutions in a way that preserves spherical symmetry, so that the dynamics of small perturbations about the spherically symmetric case are not overwhelmed by numerical error. Traditionally, such calculations have been done by discretizing the equations expressed in spherical coordinates. This approach has significa...

The subject of this paper is the application of the Gaussian beam method to the propagation of surface waves on a laterally heterogeneous, spherical earth taking fully into account the curvature of the Earth’s surface. This is achieved by constructing a ray centred coordinate system on general curved surfaces. The application of this method to a spherical shell leads to a ray centred coordinate...

The results of theoretical calculations or measurements on antennas are generally given in terms of the vector components of the radiated electric field as a function of direction or position. Both the vector components and the direction parameters must be defined with respect to a spherical coordinate system fixed to the antenna. Along the principal planes there is no ambiguity about the terms...

A spherical map of a cortical surface is often used for improved brain registration, for advanced morphometric analysis (eg, of brain shape), and for surface-based analysis of functional signals recorded from the cortex. Furthermore, for intersubject analysis, it is usually necessary to reparameterize the surface mesh into a common coordinate system. An isometric map conserves all angle and are...