Related papers: A Note on the Dipole Coordinates
Many authors have studied the numerical computation of conformal mappings (numerical conformal mapping), and there are nowadays several efficient numerical schemes. Among them, Amano's method offers a straightforward numerical procedure for…
A transverse multipole expansion is derived, including the longitudinal components necessarily present in regions of varying magnetic field profile. It can be used for exact numerical orbit following through the fringe field regions of…
The proton radiography diagnostic is widely used in laser-plasma experiments to make magnetic field measurements. Recent developments in analysis have enabled quantitative reconstruction of path-integrated magnetic field values, but making…
The Earth's magnetic field can be decomposed into spherical harmonics, and the exact coefficients of the decomposition can be determined through a few measurements of its value at different locations. Using measurements from a magnetometer…
Optical spectropolarimeters can be used to produce maps of the surface magnetic fields of stars and hence to determine how stellar magnetic fields vary with stellar mass, rotation rate, and evolutionary stage. In particular, we now can map…
A method of solving Maxwell equations in a vicinity of a multipole particle (moving along an arbitrary trajectory) is proposed. The method is based on a geometric construction of a trajectory-adapted coordinate system, which simplifies…
In this paper, a function on any pair of graphs is defined whose properties are similar to the properties of dot product in vector space. This function enables us to define graph orthogonality and, also, a new metric on isomorphism classes…
Recent progress in studying the physics of amorphous solids has revealed that mechanical strains can be strongly screened by the formation of plastic events that are typically quadrupolar in nature. The theory stipulated that gradients in…
The identification of the interfacial molecules in fluid-fluid equilibrium is a long-standing problem in the area of simulation. We here propose a new point of view, making use of concepts taken from the field of computational geometry,…
Many students meet quite early this dipole-dipole potential energy when they are taught electrostatics or magnetostatics, and it is also a very popular formula, featured in the encyclopedias. We show that by a simple rewriting of the…
We construct natural local coordinate systems on the phase space of two-field cosmological models with orientable target space, which allow for a description of cosmological flows through quantities of direct physical interest. Such…
We propose a geometrical approach to the investigation of Hamiltonian systems on (Pseudo) Riemannian manifolds. A new geometrical criterion of instability and chaos is proposed. This approach is more generic than well known reduction to the…
In this paper, we present a mathematical model for the angular projection of a rectangular arrangement of points in a grid. This simple, yet interesting problem, has both a scholarly value and applications for data extraction techniques to…
A typical geometry extracted from the path integral of a quantum theory of gravity might be quite complicated in the UV region. Even if such a configuration is not physical, it may be of interest to understand the details of its nature,…
This paper presents a complete Pascal interpolation scheme for use in the plane geometry mapping applied in association with numerical methods. The geometry of a domain element is approximated by a complete Pascal polynomial. The…
In high-temperature plasma physics, a strong magnetic field is usually used to confine charged particles. Therefore, for studying the classical mathematical models of the physical problems it needs to consider the effect of external…
A combination of observation, theory, modeling, and laboratory plasma experiments provides a multifaceted approach to develop a much greater understanding of how magnetic fields arise in galactic settings and how these magnetic fields…
Dimensional metrology and positioning operations are used in many fields of particle accelerator projects. This lecture gives the basic tools to designers in the field of measure by analysing the spatial layout of measurement systems since…
The analogue of polar coordinates in the Euclidean space, a polar decomposition in a metric space, if well-defined, can be very useful in dealing with integrals with respect to a sufficiently regular measure. In this note we handle the…
Space plasma studies frequently use in situ magnetic field measurements taken from many spacecraft simultaneously. A useful data product of these measurements is the reconstructed magnetic field in a volume near the spacecraft observatory.…