Boundary value problems on the eccentric annulus are quite complex and cannot directly be solved analytically using cartesian or polar coordinates. Many mathematical techniques have been used to solve such a problem by using conformal mapping and bipolar coordinate. In the literature, Carrier and Pearson [Partial differential equation-theory and technique. New York, Academic Press, 1976, pp 68 ...

A generalization of fractional vector calculus (FVC) as a self-consistent mathematical theory is proposed to take into account general form non-locality in kernels differential and integral operators. Self-consistency involves proving generalizations all fundamental theorems for generalized In the FVC from power-law nonlocality space, we use (GFC) Luchko approach, which was published 2021. This...

The two–body problem is a milestone in numerical relativity that has not yet been attained. Even the relatively simple case of the head–on collision of two equal mass, non-rotating black holes remains uncertain for black holes that are initially separated by large distances. By exploiting the 2–dimensional nature of the problem, the obvious first choice of coordinates in which to solve the Eins...

With this note, we would like present a method to compute the incompatibility operator in any system of curvilinear coordinates/components. The procedure is independent of the metric in the sense that the expression can be expressed by means of the basis vectors only, which are first defined as normal and tangent to the domain boundary and then extended to the whole domain. It is in some sense ...

We present a novel scheme to interactively visualize time-varying scalar fields defined on a curvilinear grid. We create a 3D warp texture that maps points in R into the grid coordinate system. At rendering time, the warping function is reconstructed at each fragment using tri-linear interpolation, and provides the 3D texture coordinates required to look up a scalar field value stored in a sepa...

In molecular replacement, a model, described as a list of orthogonal coordinates, is to be moved into a new position and orientation. The orthogonal coordinate system also has to be related to the crystallographic system, which may not be orthogonal, and crystallographic symmetry must be considered, which applies to coordinates expressed as fractions of the unit cell. Elementary properties of r...