The wave equation for vectors and symmetric tensors in spherical coordinates is studied under the divergence-free constraint. We describe a numerical method, based on the spectral decomposition of vector/tensor components onto spherical harmonics, that allows for the evolution of only those scalar fields which correspond to the divergence-free degrees of freedom of the vector/tensor. The full v...

In this work, we derive the well-established expression for the quantum amplitude associated with the resonance energy transfer (RET) process between a pair of molecules that are beyond wavefunction overlap. The novelty of this work is that the field of the mediating photon is described in terms of a spherical wave rather than a plane wave. The angular components of the field are constructed in...

The elastic wave equation in spherical coordinates is solved on a spherical section by a Chebyshev spectral method. In the presented algorithm the singularities in the governing equations are avoided by centering the physical domain around the equator. The highly accurate pseudo-spectral (PS) derivative operators reduce the required grid size compared to nite-diierence (FD) algorithms. The non-...

In practical engineering, the use of Pauli algebra can provide a computational advantage, transforming conventional vector to straightforward matrix manipulations. this work, matrices in cylindrical and spherical coordinates are reported for first time their representing three-dimensional is discussed. This method leads unified representation 3D multivectors with algebra. A significant advantag...

Partial differential equations (PDEs) play an important role in describing many physical, industrial, and biological processes. Their solutions could be considerably facilitated by using appropriate coordinate transformations. There are many coordinate systems besides the well-known Cartesian, polar, and spherical coordinates. In this article, we illustrate how to make such transformations usin...

Abstract Techniques for coordinate changes that depend on both dependent and independent variables are developed and applied to the Maxwell-Vlasov Hamiltonian theory. Particle coordinate changes with a new velocity variable dependent on the magnetic field, with spatial coordinates unchanged, are lifted to transform the noncanonical Poisson bracket and, thus, the field Hamiltonian structure of t...

The neurons of the human cerebral cortex are arranged in a highly folded sheet, with the majority of the cortical surface area buried in folds. Cortical maps are typically arranged with a topography oriented parallel to the cortical surface. Despite this unambiguous sheetlike geometry, the most commonly used coordinate systems for localizing cortical features are based on 3-D stereotaxic coordi...

We present image segmentation and highlight detection algorithms based on the dichromatic reflection model. For image segmentation, we use the model prediction that objects of a certain colour produce lines (the matte lines) radiating away from the origin of the RGB colour space. These lines therefore show up as peaks in a 2-dimensional histogram of the angular coordinates of a spherical polar ...

We study the residual gauge freedom within the null quasi-spherical (NQS) gauge for spacetimes admitting an expanding shear-free null foliation. By constructing the most general NQS coordinates subordinate to such a foliation, we obtain both a clear picture of the geometric nature of the residual coordinate freedom, and an explicit construction of nontrivial NQS metrics representing some well-k...