Static Field Solutions Research Articles

Publisher’s Note: Biconformal symmetry and static Green functions in the higher-dimensional Reissner-Nordström spacetimes [Phys. Rev. D91, 064037 (2015)

We study a static scalar massless field created by a source located near an electrically charged higher dimensional spherically symmetric black hole. We demonstrated that there exist bi-conformal transformations relating static field solutions in the metric with different parameters of the mass M and charge Q. Using this symmetry we obtain the static scalar Green function in the higher dimensional Reissner-Nordstrom spacetimes.

Biconformal symmetry and static Green functions in the higher-dimensional Reissner-Nordström spacetimes

We study a static scalar massless field created by a source located near an electrically charged higher dimensional spherically symmetric black hole. We demonstrated that there exist bi-conformal transformations relating static field solutions in the metric with different parameters of the mass M and charge Q. Using this symmetry we obtain the static scalar Green function in the higher dimensional Reissner-Nordstrom spacetimes.

The treatment of geometrically small structures in FDTD by the modification of assigned material parameters

A number of different improvements to the analysis by finite-difference time-domain (FDTD) of small structures, such as wires, strips and slots have been proposed in the literature. One of these methods takes account of the fringing fields associated with metal edges and wires by empirically modifying the assigned material parameters in neighboring cells. In this contribution it is shown that, in many cases, it is possible to derive these modified assigned material parameters (MAMPs) analytically. In this form, the approach provides an alternative, and novel, way of incorporating Static Field Solutions into the FDTD method which has advantages of simplicity and robustness over existing techniques. Results are presented for a number of structures including wire transmission lines and a microstrip patch antenna.

FDTD analysis of bow-tie antenna by incorporating approximated static field solutions

In this letter, finite-difference time-domain analysis of the bow-tie antenna, including a feeding point, was studied by incorporating an approximated static field solution without additional computation time. By reformulating the static field solution in the rotated coordinate system, we can easily calculate the correction factors and obtain the result that shows a remarkable agreement with the method of moments result in spite of relatively coarse meshes.

Neutrino conversions in solar random magnetic fields

We consider the effect of a random magnetic field in the convective zone of the Sun super-imposed to a regular magnetic field on resonant neutrino spin-flavor oscillations. We argue for the existence of a field of strongly chaotic nature at the bottom of the convective zone. In contrast to previous attempts we employ a model motivated regular magnetic field profile: it is a static field solution to the solar equilibrium hydro-magnetic equations. These solutions have been known for a long time in the literature. We show for the first time that in addition they are twisting solutions. In this scenario electron antineutrinos are produced through cascades like ν eL → ν μL → V ̃ eR , The detection of V ̃ eR at Earth would be a long-awaited signature of the Majorana nature of the neutrino. The expected signals in the different experiments (SK, GALLEX-SAGE, Homestake) are obtained as a function of the level of noise, regular magnetic field and neutrino mixing parameters. Previous results obtained for small mixing and ad-hoc regular magnetic profiles are reobtained. We confirm the strong suppression for a large part of the parameter space of the V ̃ eR- flux for high energy boron neutrinos in agreement with present data of the SK experiment. We find that MSW (Mikheyev-Smirnov-Wolfenstein) regions ( Δm 2 ≅ ]0 −5 eV 2, both small and large mixing solutions) are stable up to very large levels of noise ( P = 0.7−0.8) but they are acceptable from the point of view of antineutrino production only for moderate levels of noise ( P ≅ 0.95). For strong noise and a reasonable regular magnetic field, any parameter region ( Δm 2, sin 2 2 θ) is excluded. As a consequence, we are allowed to reverse the problem and to put limits on the r.m.s. field strength and transition magnetic moments by demanding a particle physics solution to the SNP in this scenario.

A new technique for the stable incorporation of static field solutions in the FDTD method for the analysis of thin wires and narrow strips

The behavior of the fields around many common objects (e.g., wires, slots, and strips) converges to known static solutions. Incorporation of this a priori knowledge of the fields into the finite-difference time-domain (FDTD) algorithm provides one method for obtaining a more efficient characterization of these structures. Various methods of achieving this have been attempted; however, most have resulted in unstable algorithms. Recent investigations into the stability of FDTD have yielded criteria for stability, and this contribution for the first time links these criteria to a general finite-element formulation of the method. It is shown that the finite-element formulation provides a means by which FDTD may be generalized to include whatever a priori knowledge of the field is available, without compromising stability. Example results are presented for extremely narrow microstrip lines and wires.

Analysis of curved and angled surfaces on a Cartesian mesh using a novel finite-difference time-domain algorithm

The widely accepted finite-difference time-domain algorithm, based on a Cartesian mesh, is unable to rigorously model the curved surfaces which arise in many engineering applications, while more rigorous solution algorithms are inevitably considerably more computationally intensive. A nonintensive, but still rigorous, alternative to this approach has been to incorporate a priori knowledge of the behavior of the fields (their asymptotic static field solutions) into the FDTD algorithm. Unfortunately, until now, this method has often resulted in instability. In this contribution an algorithm (denoted 'SFDTD' for second-order finite difference time domain) is presented which uses the static field solution technique to accurately characterize curved and angled metallic boundaries. A hitherto unpublished stability theory for this algorithm, relying on principles of energy conservation, is described and it is found that for the first time a priori knowledge of the field distribution can be incorporated into the algorithm with no possibility of instability. The accuracy of the SFDTD algorithm is compared to that of the standard FDTD method by means of two test structures for which analytic results are available.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Use of static field solutions in the FDTD method for the efficient treatment of curved metal surfaces

The treatment of surfaces which are curved or which are not parallel to the co-ordinate axes using the finite difference time domain (FDTD) method is notoriously problematic. The Letter describes a technique which is general, comparatively simple and requires negligible computational overhead. Results are given for the example of a circular cylindrical cavity resonator which show good agreement with analytical formulas.

Modelling of narrow microstrip lines using finite difference time domain method

The finite difference time domain technique is a much used method for the analysis of microstrip circuits. If, however, the strip widths are small, a fine mesh usually has to be used to resolve the geometrical detail. In the Letter, static field solutions are used to reduce this constraint on the mesh and to allow a unit cell size which may be much greater than the strip width. It is shown that efficiency can be much improved while maintaining accuracy.

The incorporation of static field solutions into the finite-difference time domain algorithm MMIC structures modelling

The authors demonstrate how the accuracy, speed, and flexibility of finite-difference time-domain (FDTD) analysis can be improved for the modeling of MMIC structures. Correction factors, obtained from the known behavior of static fields close to discontinuities, can be incorporated into the algorithm for application in the regions of high field variation where errors would otherwise occur. Application is made to both enclosed and open microstrip structures.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An error‐based approach to complementary formulations of static field solutions

AbstractThe constitutive relationship between fields in electromagnetic media is cast in error form. For well‐posed static problems, the error splits systematically into complementary functionals. Error minimization provides a universal variational principle that generates complementary and dual solution formulations. The error, which is wholly attributed to the numerical constraints in approximate solutions, is always defined and computable locally and globally.