New Possibilities for Constructing Heuristic Solutions to Problems of Electromagnetic Diffraction

The paper formulates the foundations of a recently developed approach, named the method of fundamental components, intended for constructing heuristic solutions in problems of electromagnetic diffraction, for the first time. The difference between the new method and the known heuristic approaches lies in the application of an adjustment procedure that increases the accuracy. The possibility of the mentioned method for obtaining new results is illustrated with the help of the author’s previously published works. The advantages of the new method in constructing high-speed solvers and in the physical interpretation of numerical solutions are shown.

On the Counter-Rotation of Closed Time-like Curves

While it is tempting to think of closed time-like curves (CTCs) around rotating bodies, such as a black hole, as being “caused” by the rotation of the source, Andréka et al. pointed out that the underlying physics are not as straightforward as this, since such CTCs are “counter-rotating”, i.e., the time orientation (the opening of the local light cones) of the CTCs is opposite to the direction in which the singularity or the ergosphere rotates. It was also suggested that this is a generic phenomenon that calls for a deeper intuitive physical understanding. In this short note, we point out—with Kerr–Taub–NUT as an example—that CTCs are counter-rotating with respect to the local angular velocity of the spacetime, not the global angular momentum, nor the angular velocity of the black hole horizon, which makes the physical interpretation of CTCs being “caused” by a rotating source even more problematic.

The Microscopic Mechanisms Involved in Superexchange

In earlier work, we previously established a formalism that allows to express the exchange energy J vs. fundamental molecular integrals without crystal field, for a fragment A–X–B, where A and B are 3d1 ions and X is a closed-shell diamagnetic ligand. In this article, we recall this formalism and give a physical interpretation: we may rigorously predict the ferromagnetic (J < 0) or antiferromagnetic (J > 0) character of the isotropic (Heisenberg) spin-spin exchange coupling. We generalize our results to ndm ions (3 £ n £ 5, 1 £ m £ 10). By introducing a crystal field we show that, starting from an isotropic (Heisenberg) exchange coupling when there is no crystal field, the appearance of a crystal field induces an anisotropy of exchange coupling, thus leading to a z-z (Ising-like) coupling or a x-y one. Finally, we discuss the effects of a weak crystal field magnitude (3d ions) compared to a stronger (4d ions) and even stronger one (5d ions). In the last step, we are then able to write the corresponding Hamiltonian exchange as a spin-spin one.

Explainable Deep Learning for the Analysis of MHD Spectrograms in Nuclear Fusion

In the nuclear fusion community, there are many specialized techniques to analyze the data coming from a variety of diagnostics. One of such techniques is the use of spectrograms to analyze the magnetohydrodynamic (MHD) behavior of fusion plasmas. Physicists look at the spectrogram to identify the oscillation modes of the plasma, and to study instabilities that may lead to plasma disruptions. One of the major causes of disruptions occurs when an oscillation mode interacts with the wall, stops rotating, and becomes a locked mode. In this work, we use deep learning to predict the occurrence of locked modes from MHD spectrograms. In particular, we use a Convolutional Neural Network (CNN) with Class Activation Mapping (CAM) to pinpoint the exact behavior that the model thinks is responsible for the locked mode. Surprisingly, we find that, in general, the model explanation agrees quite well with the physical interpretation of the behavior observed in the spectrogram.

Handling Cellwise Outliers by Sparse Regression and Robust Covariance

We propose a data-analytic method for detecting cellwise outliers. Given a robust covariance matrix, outlying cells (entries) in a row are found by the cellFlagger technique which combines lasso regression with a stepwise application of constructed cutoff values. The penalty term of the lasso has a physical interpretation as the total distance that suspicious cells need to move in order to bring their row into the fold. For estimating a cellwise robust covariance matrix we construct a detection-imputation method which alternates between flagging outlying cells and updating the covariance matrix as in the EM algorithm. The proposed methods are illustrated by simulations and on real data about volatile organic compounds in children.