Green’s Function Method for Electromagnetic and Acoustic Fields in Arbitrarily Inhomogeneous Media

An analytical method based on the Green\'s function for describing the electromagnetic field, scalar-vector and phase characteristics of the acoustic field in a stationary isotropic and arbitrarily inhomogeneous medium is proposed. The method uses, in the case of an electromagnetic field, the wave equation proposed by the author for the electric vector of the electromagnetic field, which is valid for dielectric and magnetic inhomogeneous media with conductivity. In the case of an acoustic field, the author uses the wave equation proposed by the author for the particle velocity vector and the well-known equation for acoustic pressure in an inhomogeneous stationary medium. The approach used allows one to reduce the problem of solving differential wave equations in an arbitrarily inhomogeneous medium to the problem of taking an integral.

ALMA full polarization observations of PKS 1830−211 during its record-breaking flare of 2019

We report Atacama Large Millimeter Array (ALMA) Band 6 full-polarization observations of the lensed blazar PKS 1830−211 during its record-breaking radio and gamma-ray flare in the spring of 2019. The observations were taken close to the peak of the gamma activity and show a clear difference in polarization state between the two time-delayed images. The leading image has a fractional polarization about three times lower than the trailing image, implying that significant depolarization occurred during the flare. In addition, we observe clear intra-hour variability of the polarization properties between the two lensed images, with a quasi-linear increase in the differential electric-vector position angle at a rate of about two degrees per hour, associated with changes in the relative fractional polarization of ∼10%. This variability, combined with the lower polarization close to the peak of gamma activity, is in agreement with models of magnetic turbulence to explain polarization variability in blazar jets. Finally, the comparison of results from the full and differential polarization analysis confirms that the differential polarization technique (Martí-Vidal et al. 2016, A&A, 593, A61) can provide useful information on the polarization state of sources like gravitationally lensed radio-loud quasars.

Change in the direction of the polarization vector and redshift of an incoming light ray as observed from a rotating frame

In the present work, the change in the direction of the polarization vector of an incoming light ray is extensively calculated for a rotating observer. The change in the direction of the polarization vector calculated here is only due to the effect of the non-inertial rotating frame, considering that the light source is at a distance and it is emitting plane-polarized light. The metric tensors for a rotating observer have been collected from existing literature. Accordingly, the electric displacement and magnetic induction values as applicable for a rotating observer have been calculated. These values are used to calculate the change in the orientation of the electric vector of an incoming plane-polarized light ray. Earth has been taken as an example of a rotating frame and the calculated amount of change in the direction of the polarization vector has been found to be dependent on the azimuthal and polar coordinates of the rotating frame. The present work also discusses the redshift as observed by a rotating observer and the value of the redshift has been calculated for an observer sitting on a rotating earth.

180° rotations in the polarization angle for blazars

Rotations of the electric vector position angle (EVPA) in blazars are often close to an integral multiple of 180°. There are many examples of this in the literature, and we strengthen the evidence by showing that, in the RoboPol monitoring program, nπ rotations occur more frequently than otherwise expected by chance. We explain this using a model consisting of two polarized emission components: a “jet” that is constant in time and a “burst” that is variable. The EVPA of the combination is EVPAjet at both the beginning and the end of the burst, so the net rotation across the burst must be nπ. Several examples of this model are analyzed on the Stokes plane, where the winding number for the Stokes vector of the combination gives the value of n. The main conclusion is that the EVPA rotation can be much larger than the physical rotation of the emission region around the axis of the jet, but this requires the EVPAs of the jet and the burst to be nearly orthogonal. Shock-in-jet calculations can provide a physical model for our toy model and in addition they automatically give the required orthogonality. The model is illustrated with data from the literature on OJ 287. We suggest that the large rapid EVPA rotation seen in OJ 287 might be a phase effect and not representative of a physical rotation.

Application of Whitney elements for the reconstruction of electric arc current density in low-voltage circuit breakers

Purpose This paper aims to present the mathematical formulations of a magnetic inverse problem for the electric arc current density reconstruction in a simplified arc chamber of a low-voltage circuit breaker. Design/methodology/approach Considering that electric arc current density is a zero divergence vector field, the inverse problem can be solved in Whitney space W2 in terms of electric current density J with the zero divergence condition as a constraint or can be solved in Whitney space W1 in terms of electric vector potential T where the zero divergence condition naturally holds. Moreover, the tree gauging condition is applied to ensure a unique solution when solving for the vector potential in space W1. Tikhonov regularization is used to treat the ill-posedness of the inverse problem complemented with L-curve method for the selection of regularization parameters. A common mode approach is proposed, which solves for the reduced electric vector potential representing the internal current loops instead of solving for the total electric vector potential. The proposed inversion approaches are numerically tested starting from simulated magnetic field values. Findings With the common mode approach, the reconstruction of current density is significantly improved for both formulations using face elements in space W2 and using edge elements in space W1. When solving the inverse problem in space W1, the choice of the regularization operator has a key role to obtain a good reconstruction, where the discrete curl operator is a good option. The standard Tikhonov regularization obtains a good reconstruction with J-formulation, but fails in the case of T-formulation. The use of edge elements requires a tree-cotree gauging to ensure the uniqueness of T. Moreover, additional efforts have to be taken to find an optimal regularization operator and an optimal tree when using edge elements. In conclusion, the J-formulation is to be preferred. Originality/value The proposed approaches are able to reconstruct the three-dimensional electric arc current density from its magnetic field in a non-intrusive manner. The formulations enable us to incorporate a priori knowledge of the unknown current density into the solution of the inverse problem, including the zero divergence condition and the boundary conditions. A common mode approach is proposed, which can significantly improve the current density reconstruction.