In this paper, we introduce a hierarchical indexing for adjacency queries specially for applying subdivision schemes on some simple spherical and toroidal polyhedrons as the base model for the content creation process. The indexing method is created from integer coordinates of regular 2D domains (connectivity maps) resulting from unfolding polyhedrons. All connectivities are found using algebra...

We revisit the fundamental topic of light scattering by single homogenous nanoparticles from the new perspective of excitation and manipulation of toroidal dipoles. It is revealed that besides within all-dielectric particles, toroidal dipoles can also be efficiently excited within homogenous metallic nanoparticles. Moreover, we show that those toroidal dipoles excited can be spectrally tuned th...

Electric forces play a key role in the conductance of ions in biological channels. Therefore, their correct treatment is very important in making physical models of ion channels. Here, we present FORTRAN 90 codes for solution of Poisson’s equation satisfying the Dirichlet boundary conditions in realistic channel geometries that can be used in studies of ion channels. For a general channel shape...

Neoclassical simulations of alpha particle density profiles in high fusion power plasmas on the Tokamak Fusion Test Reactor [Phys. Plas. 5, 1577 (1998)] are found to be in good agreement with measurements of the alpha distribution function made with a sensitive active neutral particle diagnostic. The calculations are carried out in Hamiltonian magnetic coordinates with a fast, particle-followin...

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...

ABSTRACT: This study was conducted to establish the pattern and spatial associations of Amazon commercial tree groups. In a region extending across 2,000 ha in Tapajós National Forest (FNT), Pará, forest census conducted. The included trees perimeter at breast height (PBH), equal or greater than 158 cm Cartesian coordinates their bearings. Using Ripley’s K function, discerned, with 5 m radius b...

We study the toroidality testing and toroidal embedding problems in the context of bounded space algorithms. Specifically, we show that the problem of embedding a toroidal graph on a surface of genus 1 can be solved by an algorithm that runs in deterministic logarithmic space. The algorithm rejects whenever the graph is not toroidal. This algorithm is optimal as we also show a matching hardness...

A criterion given by Castejon-Amenedo and MacCallum (1990) for the existence of (locally) hypersurface-orthogonal generators of an orthogonally-transitive two-parameter Abelian group of motions (a G2I) in spacetime is re-expressed as a test for linear dependence with constant coefficients between the three components of the metric in the orbits in canonical coordinates. In general, it is shown ...

Disruptive high b tokamak plasmas can be stabilized by the addition of a sheared toroidal flow. Nonlinear simulations demonstrate that confinement in flow-free high b tokamaks is rapidly destroyed by growing fingers of hot plasma that jet out from the center of the discharge to the wall. The added toroidal flow eliminates the growing fingers, maintaining confinement. As b increases further, the...

We derive a self-consistent equation for the turbulent transport of toroidal angular momentum in tokamaks in the low flow ordering that only requires solving gyrokinetic Fokker-Planck and quasineutrality equations correct to second order in an expansion on the gyroradius over scale length. We also show that according to our orderings the long wavelength toroidal rotation and the long wavelength...