Related papers: A Note on the Dipole Coordinates
This paper introduces the conformal model (an extension of the homogeneous coordinate system) for molecular geometry, where 3D space is represented within R^5 with an inner product different from the usual one. This model enables efficient…
This paper describes in detail the construction of a local right-handed, orthogonal curvilinear coordinate system whose axes are along the local tangent, the local azimuth and the local normal of an analytically defined 3D surface of…
An alternative model to describe the electronic and thermal properties of quantum dot based on triangle geometry is proposed. The model predicts characteristics and limitations of the system by controlling the magnetic field and…
The proper handling of 3D orientations is a central element in many optimization problems in engineering. Unfortunately many researchers and engineers struggle with the formulation of such problems and often fall back to suboptimal…
We investigate the phase diagrams of two-dimensional lattice dipole systems with variable geometry. For bipartite square and triangular lattices with tunable vertical sublattice separation, we find rich phase diagrams featuring a sequence…
We study a new spacetime which is shown to be the general geometrical background for Thermal Field Theories at equilibrium. The different formalisms of Thermal Field Theory are unified in a simple way in this spacetime. The set of…
Vector displacements expressed in spherical coordinates are proposed. They correspond to electromagnetic fields in vacuum that globally rotate about an axis and display many circular patterns on the surface of a sphere. The fields basically…
Orthogonal polynomials on quadratic curves in the plane are studied. These include orthogonal polynomials on ellipses, parabolas, hyperbolas, and two lines. For an integral with respect to an appropriate weight function defined on any…
We present a new technique for the numerical simulation of axisymmetric systems. This technique avoids the coordinate singularities which often arise when cylindrical or polar-spherical coordinate finite difference grids are used,…
This paper proposes an algorithm for image processing, obtained by adapting to image maps the definitions of two well-known physical quantities. These quantities are the dipole and quadrupole moments of a charge distribution. We will see…
This report describes a new magnetohydrodynamic numerical model based on a hexagonal spherical geodesic grid. The model is designed to simulate astrophysical flows of partially ionized plasmas around a central compact object, such as a star…
A charged particle in a suitably strong magnetic field spirals along the field lines while slowly drifting transversely. This note provides a brief derivation of an effective Lagrangian formulation for the guiding-centre approximation that…
A numerical scheme is described for accurately accommodating oblique, non-aligned, boundaries, on a three-dimensional cartesian grid. The scheme gives second-order accuracy in the solution for potential of Poisson's equation using compact…
Current "Earth-like" numerical dynamo simulations are able to reproduce many characteristics of the observed geomagnetic field. One notable exception is the geomagnetic octupolar component. Here we investigate whether a stably stratified…
Straight-field-line coordinates are very useful for representing magnetic fields in toroidally confined plasmas, but fundamental problems arise regarding their definition in 3-D geometries because of the formation of islands and chaotic…
In this work, we provide an overview of various control strategies aimed at steering plasma toward desired configurations using an external magnetic field. From a modeling perspective, we focus on the Vlasov equation in a two-dimensional…
This work introduces a theoretical extension of the characteristic mode formulation for analysing the vertical electric dipole lying above a lossy dielectric half-space. As the conventional characteristic formulation fails to maintain the…
We explore the role of complex multipolar magnetic fields in determining physical processes near the surface of rotation powered pulsars. We model the actual magnetic field as the sum of global dipolar and star-centered multipolar fields.…
Contact Geometry is an odd dimensional analogue of Symplectic Geometry. This vague idea can actually be formalized in a rather precise way by means of a Symplectic-to-Contact Dictionary. The aim of this review paper is discussing the basic…
It is known that epipolar geometry can be computed from three epipolar line correspondences but this computation is rarely used in practice since there are no simple methods to find corresponding lines. Instead, methods for finding…