Noether Gauge Symmetries for Petrov Type D-Levi-Civita Space-Time in Spherical and Cylindrical Coordinates

SPH in spherical and cylindrical coordinates

New kernel functions for spherically, planar and cylindrically symmetric problems are developed, based on the fundamental interpolation theory of SPH. The Lagrangian formalism is used to derive the corresponding set of modified SPH equations of motion. The results show good agreement both with analytical and numerical results, in the case of the Sod shock tube test, the Noh infinite shock probl...

Marching Cubes in Cylindrical and Spherical Coordinates

lsosurface extraction is a colrirnon analysis and visualization technique for tllrec-dirne~ls ior)al sc.a]ar data. Marc.]iing (hlt)cs k the Inost cow)rno~lly-used a]gorit]lm for fl]lding ~)o]ygona] reprcm)itatiolls of isosurfaces in such data. We extc]ld hflarching 011.)es to produce geometry f o r data scis that lie in spherical and cylirldric.al coordi]]atc syskns as well as show the ste]w fo...

Section 13.7 Cylindrical and Spherical Coordinates

Gauge Symmetries and Noether Currents in Optimal Control

Abstract. We extend the second Noether theorem to optimal control problems which are invariant under symmetries depending upon k arbitrary functions of the independent variable and their derivatives up to some order m. As far as we consider a semi-invariance notion, and the transformation group may also depend on the control variables, the result is new even in the classical context of the calc...

Transformations Generalizing the Levi - Civita ,

Preliminary results concerning non-quadratic (and non-bijective) transformations that exibit a degree of parentage with the well known Levi-Civita, Kustaanheimo-Stiefel, and Fock transformations are reported in this article. Some of the new transformations are applied to non-relativistic quantum dynamical systems in two dimensions.