Related papers: Obtaining Potential Field Solution with Spherical …
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…
The purpose of this research is to describe an efficient iterative method suitable for obtaining high accuracy solutions to high frequency time-harmonic scattering problems. The method allows for both refinement of local polynomial degree…
High-harmonic generation from solids can be utilized as probe of ultrafast dynamics, but thus far only over extended sample areas, since its spatial resolution is diffraction-limited. Here we propose spatial polarization gating, that is…
We investigate whether the method of wavelet-based Faraday rotation measure (RM) Synthesis can help us to identify structures of regular and turbulent magnetic fields in extended magnetized objects, such as galaxies and galaxy clusters.…
An accurate measurement of magnetic field is very important for understanding the formation and evolution of solar magnetic fields. Currently there are two types of solar magnetic field measurement instruments: the filter-based…
We present a numerical method for the solution of linear magnetostatic problems in domains with a symmetry direction, including axial and translational symmetry. The approach uses a Fourier series decomposition of the vector potential…
We employ the magnetic and velocity fields from turbulent dynamo simulations to synthesize the polarization of a typical photospheric line. The synthetic Stokes profiles have properties in common with those observed in the quiet Sun. The…
We construct three families of general magnetostatic axisymmetric exact solutions of Einstein-Maxwell equations in spherical coordinates, prolate, and oblates. The solutions obtained are then presented in the system of generalized…
The Sun's magnetic field is strongly structured over a broad range of scales. The magnetic spatial power spectral analysis provides a powerful tool to understand the various scales of magnetic fields and their interaction with plasma…
A common scientific inverse problem is the placement of magnets that produce a desired magnetic field inside a prescribed volume. This is a key component of stellarator design, and recently permanent magnets have been proposed as a…
The full ``classical" Dirac-Maxwell equations are considered under various simplifying assumptions. A reduction of the equations is performed in the case when the Dirac field is {\em static} and a further reduction is performed in the case…
The method of images to solve certain electrostatic boundary-value problems is taught worldwide in undergraduate-level physics courses. Though it is also possible to employ this technique for solving magnetostatic boundary value problems,…
We investigate numerical methods for wave equations in $n+2$ spacetime dimensions, written in spherical coordinates, decomposed in spherical harmonics on $S^n$, and finite-differenced in the remaining coordinates $r$ and $t$. Such an…
A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…
This paper presents compact, symmetric, and high-order finite difference methods (FDMs) for the variable Poisson equation on a $d$-dimensional hypercube. Our scheme produces a symmetric linear system: an important property that does not…
A rapid algorithm is derived for the Helmholtz--Hodge decomposition on the surface of the sphere in spherical coordinates. The algorithm uncouples modes of spherical harmonics with different absolute order, writes the conversion as…
We present an efficient and accurate algorithm for solving the Poisson equation in spherical polar coordinates with a logarithmic radial grid and open boundary conditions. The method employs a divide-and-conquer strategy, decomposing the…
In this paper a local approximation method on the sphere is presented. As interpolation scheme we consider a partition of unity method, such as the modified spherical Shepard's method, which uses zonal basis functions (ZBFs) plus spherical…
Homogeneous magnetic fields can be generated through the strategic arrangement of permanent magnets. The Halbach array serves as a prominent example of an effective design following this principle. However, it is a two-dimensional approach…
We present a target field approach to analytically design magnetic fields using permanent magnets. We assume that their magnetisation is bound to a two-dimensional surface and is composed of a complete basis of surface modes. By posing the…